fclBLIOTHECA I REGIA

ATHANASII KIRCHERI

FVLDENSIS

SOO IESV PRESBYTERI.

MVSVRGIA

VNIVERSALIS

A R S M A G N A

CONSONI ET DISSONL

Tomus I I,

j" In Lib. VIII. Muficam Mirificam . Quicontinet . < In Lib. IX Magiam Confoni & Diflbni . In Lib. X. Harmoniam Mundi .

Mille T>elut PhiUmela f»nes Epi^lottide promit , Stc Ars Alagna fuo hoc dat mille V olumine uoces .

Prtfaga Z/ati Auis efl Apollini ,

Qui Mufica almus fertur & metri parens . Tcrcnc .

ROMl> Typis Ludouici Grignani . Anno Iubilati MDCL. S V P E R I 0 R V M P E R M I S S V.

Digitize

TRISTYCHON IN TOMVM II-

OR GANVM agir MundusdenisvocalcRegiftris, Rcrumineoquotfunt Euia,tot Mctra funt. Eft DEVS Harmoftes, in Cj\io Sapicntia Patris ,

Qu*bcncdifpofuir,SpiritusvnitAmor. Hic amor harmonia eft, hoc Mundus amot e ligatur; 0"*>UH>»hiinc mundum Numinis cfle negas ?

fifcEM *WfVM-

TRISMEGISTVS IN ASCLEPIO. Muficamkilahud cft,quam ommum ordincmfcirc-» .

A R T I S

MAGNAE

C O N S O N I.

•-•> .^^■^■^.aii.Miii.yiyiijiS.S. D I S S O N I

LIBER OCTAVVS

MVSVRGIA MIRIFICA

hoc eft

AKS NOVA MVSARITHMICA RECENTER INVENTA,

qua quiuis eriam quantumuis Muficse imperitus,ad perfe&am componendi notitiam breuitemporepertingerepoteft.

P R AE P A x i o.

T A in omnibus arttbus @r fcientijs Praxis Theoria ceniun* Elionem ambiuntf <vt una fi alteram defiituat , merito <vtraaui cadat ; neque enim praxis fuam Jine Theoria obtinet exifttmatio» nem;neque fine praxi fola fuamTheoria, qufvtitn altjs,itapo- ttfimumin Muftca facultate locum habent; Etf% enim Theoris M ufice folo ixritatis amore contenta finem aUquo modo confecu- ta dici pofsity fiilicet propriam delefiationem: fieritamen nulla ra- tionepoterit , *vt ft omnimoda praxi deslitutus fit Muftcus, quicquam tkcd diBamfa* cultatemdi^num prefkt\Hincab tncuntcctatetgo wriquc exfquo incumbendum du-

A xi ;

z Artis Magtut Conjbni , & Difsoni

xi; Ut cui ad intima Muficf arcana profundiits rimanda animus efiet , in txtcutionis tnttnttonr necTheoriam praxt>,ncc praxtm 7 htortadtftttutrtf.slimulum dd propofitu txtautndum addidtt , Symphonttarum mtre praEltcorum arrogans obiurgatto , *vt dum putant,fierinonpoffeyut Thcoricus Melodtam eo arttfcio elegantia {jjf gratia com- ponat , qua iure mertto Mufica moderna requtrtt; immo contrarium afftrtntes rifit cac- chinnifque exapiant ; *vt hanc eorum obturgdtionem falfam iniuftamque ofienderem . Serio iam d multis annis huic negotio incubut , nthil non intentatum reltnquendo , quo Artemaliquam repcrirem, qua quiuis etiam quantumuis Muficf imperitus , td exiguo temporis fpacto (fr fine laboreconfequipoffet, quod pratlict Compofitores *vix multorum annorum jpacio conftquuntur .

Cum ttaftie fequenti Muficf experientid doclus , magnam *vim combtnationum fub Mufuis intetualUs tonorumque dtuerfttatt abditam noturem;principia totiusMu- furgice combinationis artis analytica fubftdio aggreffus, prtftanttorts ^Mufurgifq; ma- gis nectfiarias harmonicarum relationum mttaihefes in tabulas magnofane labore re- degied arcani artificij dtfpofitione; <vt quocunque fttu MelotaBica columna ordinaren- tur, noua ftmper emergent harmonia . Qu* miranda fane Melotacltta cobinatio, cum in fimplicitantum Contrapuntlo , *vtpotein primisadhuc incunabults njagtens, fuos foriiretur fuccefus haud pcenitendos; connnuo mtntis edu ahepius tjs non cotentus ant- mum ad <vniuerfa\em Mufurgte Mtlothttic* methodum eruendam adttciy quo quidem id precfiitiffe t idtor,^vt omnem harmonices Tenufiatc,^ gratia und cu drtificijs ucr- iis compcttnttlus, exhtbuenm; Qua res cum Muficts prtmo (g^ (dnc prodt£i*-

fa *vidercntur; expertmento tamen d dtuerfis tllufirtbus VirisfaRotonuttlt, ei Arttfi- demdtdtcerunthabere, cutus prtncipia nefctrent. Confifiit autem hacnoua nofira Mu- furgia maxtme tn TabtUarum melotatlicarum artifictofa combmmtone; qud quomvdo- libet faBa,noua ftmperntceftkrtotmergathmmoma]itun*t tum hutufmodt compoftio- nes prope ftnt infintu, infiniia quoque harmontct concenius dwerfita* nafcatur . Sgutcu- que tgttur Tabella> nofiras MtlotaQtcaSyiuxta reguUs a nobts paulo poft prafcrtbendas adaptare, numerofij;harmomcos tn fcalam mtiotatltcam rtte trantferre nouertf.is etiam tjuocunquetono @f quibufuts nverborum texttbus datts, quafiunquf autfictofas canttlt- nasfimpbcesj compofitas.flortdas, dimtnutasjpcopatas, amfictofs Ugaturts intextas, fugarumque tn modumfefe infetlantes eddem facilitate fe nouerit compoftturum. Nam qutmadf.A»*» im. ^Jg^— I m&Attgnl* tcnorem feSlando, paradoxarum qutfltonu tluctdationes perficitted facilxtate, njtoptrans ipfequod fecerit nefciat , adtoque tnexpc- Batus efftElus Logtfld <vix cogttante prodeat; ua hic regularum pfjtfcriptarum tenorem fcttanttbus Melothetts defiderata harmonia,fiue d Mufica peritts,fiue ah etufde ignau ris,pucris ettam, $r M uUeribus ptraBta pxodtbiu Certe ad arcanum hoc pubUcandum multumpotuere , Patrum nofirorum inremottffimas terrarum Indias commigrantmm evota.ffi efficax deprecatio; Cum tnim bdrharorum hominum.attr acito in mufict exer- city laudumque dtuinarum frequentationeconftflat, neque Jxmper Uhri xmprefst.aut co- pnfuores adfint, tnaximc hanc JMufurgiamijS 'vfui futuramcredebant , cum hac non defideratas tantum cantiUnas ,tn latina lingna,fed & qudcunquc propofitd Ungua, etiam Indici, & quantumuis barbari %dtomatts,<vt poslea fuse dtcetur,fint efetlnrt ,

Hts

Lib.VUl. De MufurgiaMirtjica. j

His igitur mdutlus Mujurgiamhanc mirificam publict tuhs facere njolui , nequicqud quod ad cultum honoremque diutnum propagandum in hoc negotio faceret, omtftjfe t*. derer . V rrmax ne dtutius autdum Ltftorts antmum fufpendamus, negotiu feltctbus au- sjnijs aggrediamur . 7%e wero in arte noua @r inaudtta afu^iJha progrederemur , ev ordine @r mtthodo procedemus, quam Aiufurgia hac mirifra iure fuo n/endicat .

MVS VRGIAE MIRIFICAE

PARS PRIMA» MVSVRGIA COMBIN ATORIA

LEMMAl. M VSV RGIC V M.

QVandocunque ratio v. g. A ad B. dicitur compofira, vcluti cx rationibus AEI.di- cocandcm coraponicx ijfdcm quocunqueordine pofitis , hoceft interduos . terminos AB licitum cfle continuarcdiclasrationcstotics,quoticspoflunpin- tcr lcmutarclocumi V.g.fumanrurtot numcri in fcrie naturaIi5quor resfunt propofi- ' ue: muJtipIicatjenim mujccm producuntfummam mutationum , ita vtproduabusrc- Dusdui,pro tnbusrcbusfex,proquatuor a4.pro qumquc lao. mutationcsproucniat.

Paradigma.

i OZnt dua: v. g. i es propofita? A & B, dico cas bis mutari poiTe non pluries, natru. O «IiiAuisfemcltaturapriroumoccupabitlocumjVtin maroinepatet , hienirn & numeriinterknaultiplicatiproducuntduo.

a At trcsrcsfcxmodisvarjaripo(runt.Namhi numcri r.2.3. infe ordinedu&ipro- oucunt fcx,fifciI.dicam fcmcl 2,racit a.&bis 3,facit6. &c.ratiohuius eft,quiavna- <jua:que r es pnmum tencbit locu m fcmcl , & reliqux dux bis poiTunt mutan inter fc , vt wcxcmplolequentipatct. r

Exemplum .

ORA | OARJ

AB 1

BAi

Cl

IROAI j	( 1 AOR
1 RAO 1 (	; 1 ARO

3 Sintquatuorrcsintcrlcmutandjrjduc iui|uc i.iuatcrnanum m eum quiexpro- ximamultipIicationcproducluscft,VideIicetin 6. Sl produccntur 24 mutationcs, quia hi numeri 1, 2, 3,4,interfeordincmultipiicatiproducuht 24. Nam vnaqusrquc rcsfe- mel tantum primumtenebit Iocum,&rcliqu«trcsfexicsintcrfcvariari poflunt. Vcrfi excmplum praefens infpicc-* .

ExempJum .

1

2

3 4 5 6

A 1.

AMEN

AMNE

AEMN

AENM

ANEM

ANME

-V8AT

10 11

12

M 2.

7 MAEN

8 MANE

9 MEMN MENM MNAE MNEA

Et.

13 EAMN

14 EANM

15 EMAN

16 EMNA

17 ENAM 1$ ENMA

N4-

19 NAME

20 NAEM ai NMAE

22 NMEA

23 NEMA

24 NEAM

4 Si

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4 Artis Magtue Confini Difsoni

a Sivero 5.resmutarevelis,ponc numeros ordinc naturali,vdeqmtur i. 2.3.4.5. deinde omnes ordinc inter fe multiplica 5 & producentur r ao , & toties res dico intcr ic commutari poffe,vtin fequentiexemplo patet , vbiquinque vocalts cetum & viginti vicibus mntari poffe oftendimus. Nam vnaquxq;htcra cx 5 .vigcfies quatcr ponipotclr, & reliqu* intcrfe mutari , vt in fequenti exempJo patct .

Exemplura commutationis quinque rerum .

7

8

9 10

11 12

»3

"4

*5 16

17 18

19

20 21 22

»3 »4

a	a e
1	aeiou	»5	eaiou	49
2	aeiuo	26	cai u 0	5°
3	aeoiu	*7	ea 0 i u	51
4	ae oui	28	ca oui	5*
5	ae u io	29	eau io	53
6	aeuoi	3°	ca uoi	54

a leou ai e u o aioeu a io uc aiu oe aiu eo

31 3l 33 34 35 3«

eiaou eiauo eioau eioua e iuao ciu oa

55 5<5 57 58

59

60

3		A		5
i		O		U
iaeou	73	0 a e i u 1	97	u a c 1 0
ia e u 0	74	oacu i	98	u ae oi
ia 0 c u	75	oai eu	99	u ai e 0
iaou e	76	oaiuc	100	u a i 0 c
iau c 0	77	oauei	IOI	u a 0 c i
i a u oc	78	oa uic	102	ua oie
ieaou	79	0 e a i u	103	u c aio
ieauo	80	0 ea u i	104	ueaoi
ieoau	81	oc ia u	105	1 u cia 0
ieoua	82	oci u a	106	ucioa
ieuao	«3	0 e u ai	107	u e oai
1 euoa	84	oeu i a	108	ueoia

a ociu aoeu i ao icu aoiu c a ou ci aouie

37 38

39 40

41

4*

c o a 1 u eoa ui coi au eoiua e ouai eouia

61

6i

63 64 6$ 66

au cio

auc o i au ieo aui oe a uoc i auoie

43 44 45 46

47 48

euaio cua oi euiao eu ioa e uoai cuoia

67 69 69 70 71 7*

o ac u oau c ocau oc u a ou ac ouea

85 86

87 88

89 90

01 acu o iauc oiea u oieua oiuac oiuea

109 110 iii iia

"3 114

u taeo u i a o e u i e a o ui e o a ui o a e u io ea

uaeo uao e ueao ueoa u oac u oea

91 9* 93 94 95 96

ouaei ouaie oue ai oueia ou iae o uie a

"5 116

117 118 «19 120

uoa ei uoaic uoeai uo eia u o i ac uoiea

Haudfccu* HMd f-u -«Ll-Ufrrfc naturaii difpofiti, & in fcmultiplicati , da- bummutat,0ncsquotcunqucrerumpropofitanim,Vcrum ad hoc mtcll.gendum nil aliud rcouiri videtur, nifi ttbulafcqucns, cx qua qu*cunquc hucufque diOa funt,foic dariuseluccfcunt.

HfrAH-Qt M4MA3 |t K3AM - H

TABV-

Digitized by Goo

Lib.VUL DtMufi*p*Mmfie*: $

TABVLA L Combinatoria.

i

iao 5040

362880

£ 628800 79916800 479001600 62x7010800 14 / 8778291200

XJ / '^0767436800 16 I 20922789888000 '7 /J55687428096000 /8 /64023737057*8000 , 'P /'21645100408812000

-0 /2432902008176640000 2' /5 '090942 17 1709440000 22 / x 1 24000727777607680000 5852016738884976640000 24 '62 044840 1733 239439360000

Mutationes, & fic in infinicum .

Vidcs Htur quomodo numcris quibufuisordinc naturali pofitis , exmultiplicatione numerorQ ordinc intcr eos fatfa producatur numcrus mutationfirebuscoueniens.ita ioresintcrfccombinaripoflunt, 2628800. vicibus aorcs »43i9o*o°?»70944°°o©. vicibus . Qu* tix credi potfunt, nifl dcmonftratio noftrum conuinccrct intellcCtum .

L E M M A II.

QVandocunquc veroresfimilcs occurrunt ,vcl quod idcm eftreseatdeminrebus ' combinandis fxpius ponuntur , Combinatio totius per numcrum combinatio- nis rcrum fimilium in prxccdenti tabula propofitarum diuifk, dabit numerurru.

combinationisquxfitum . ' , t _ , .

Sit propofitum nomcn MARIA; quod ciim duas litcras fimiies habeat,fiue quod ide Mon|i0flW eft, vnamlitcram A,vidclicet}bisporitaraiquxriturquoacsidcombmaripomt;Curn_. non inispen.

itaque noraen fit pentagrammatoo fiuc qumquelitcrarum ,& proinde , fiomne! '^«x

diucrfxfoient,combinationeiiabcrent i2oin prxcedenti tabulapropolitam. diuida- ,Itcr? fimile$

tur luc numeruspcr numcrumcombinationis binarijfiue pcr 2. vt tabulamonitrat,da-

bitquc quotiens 60. & totics combinari poterit quodiibet nomcn 5 . hterarum quod ta-

mcn duasliterashabucritfimilcsfiueeaidem,vt inprxfenti nominc duoAA.

Iteriim dctur nomen trigrammaton fiue trium literai um,in quodux literx bis ponu- Nominij ^

tur,vtinnomineALA&quilpiam fcircdefideret,quoticsid combinanpomt, net is ptmmm.

voti compos; fi combinationcm totius, fcilicct combinationcm trmm rerum qux ctt 6, pcrnumcrumcombinationisbinan,,quicft2.diuilcrit,piodibitenimtcxaacombniatio

propofiti r.ouums quxfita_«. Vidcs

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6'

Ariis tifafn* Cdrtfent\ & Difso?n

Vidcsigitur in hoc cxcmplo,hoc nomcn nonadmitterc mfi rrcsmutatio- A A L ficspropter Abispdfitum; Si enim duo AA inprincipiofcrrtcrpofireris i de- j\L A inde vnum in principio & in finc altcrum . 3. duo in finc , cxhaufta erit tota_. j A A combinatio . lterura 11 tctragrammatiduarum firailium literarum combina- tioncm fcirc vclis,diuides 24 pcr a. prodibitquc 1 z, combmatio dicli norainis quacfita.

f c \ V-

Exemplum Tetragrammati nominis in quo duae literae fimiliter bis ponuntur .

	7	mrr	1
vnrt	8 9	in.T	•1 1 3
mrt	9	nnv
irvrt	1 0	nmi	4
nvn	1 1	n^m	5
vnn	11	vim	6

Vidcs in cxcmplo, hoc nomen non eflc combinabilc nifiduodecies, vt exemplum_ docet , vbi videsrtfcxies inprincipio pofitum 1 tcr&uerquxfimuliunftaconftituunt 12 quxfitum numerura combinationishuius norninis tctragrammati; idcm dicendum dc quouisalio nomine tctragraramato . Si verd trcs litcras quodpiam tetragrammaton. haberet fimiles, idcft,caldcm , 24per6diuifa dabunt quxlitam combinatioms muta- tionera , vt in fecundoexcmplo patct. Vbi vides impolfibilc cfle, vt id admittat prxter- quara 4mutationcs.

Exempl. Tetragrammati in quo tres literaefimiles funt quater tantum mutari poffunt, vt in AAAL.

ITerumfitpcntagrammatonfiuequinque]itcrarumvox,quactreslitcras A A A L

firailes habcat,vt AMARA.eius habebiscombinationem ; Sicombina- ^ L A

tionem quinquererum,fcilicet 120, diuifcris per corabinationem numeri ajaa

ternarij, quem in tabula fexta inucnics. Quotus enim dabit 2 o combinatio- j

nem nominis quxfitam , vt in cxcmplo patet , in quo vides hoc nomen aha L A A A combinationcm admittcrenonpoflL-» .

fJO

1 AMAKA x AMAAR

3 AMRAA

4 ARMAA $ ARAAM

6 ARAMA

7 AARAM

8 AAMRA

9 AAMAR 10 AARMA

1 1 1 1

14

16

>7

18

»9 zo

A A ARM AA AMR MA ARA M A A AR M ARA A MRAA A RA AAM RA AM A RAMAA RMAA A

Volui hxc pauculacxeplahicponerc vtin paruis cxemplisvcritas innorcfceret. VcrQ vt quacunq;aliarnm reru combinationcm in promptu habcat curiofus LcAor, hic tabu- lam adiungercvoluimus, inquadiclo citiusvidcbisomma,qua;hucufquediclafunt .

TABV-

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VkVllL MufurgiaMmfica. f

TABVLA II. Combinatoria oftendens numerum mutaticnum, rerum, in quibus non prsecifa diuerfi- tas , fed quardam funt limiles .

ietici reri Combiruti* diucj fnu . teia omniii

	diucifcxuin .	Combinitio	4 CttiMti*		H	R 1
* I	O	rcrumia rjua I uniiici.				1
				5 CAiaiuo
II	2	0	tcru ta quft | fioulei .
III	O	5	O	reii inqui «uiruiei.	6
			C6bimtM»
IV		12	4		ictu in qu» ] urullcr .	7
						CAbiniti* leru lo qui • fimiici .	8
V	IXO	60	20	s
		O		Cobinitio reri in qtu 7£nuie» •
							9
VI	720	360	120	*$	6	O
VII		2530	840	2 IC				rciu in qui ( laiici .
504O	4*	7	O
VIII	40320	20160	6720	I663		5«	8	0	rerfi inqu» 9 fimiiec.
IX	361880	181440	60480				7»	8
	JC24	504	O
	3628800		604800			5040	720
X	1804400	M953°	30240	00	IO
				IV			VII	VIII	IX
	I	II	III	V	VI

Tlbul* C*. bma toria-i.

V S V S T A B V L AE.

HAbet hxctabuU loculumnas ,ordinc proportionalitcr deciefccntcsinprinu-. continentur 10 numcri iignjrkantes res combinabilesfiue fcriem rcrum com- binabilium . Sccunda colum na contjnet combinationci rci um, quaru Gngulx intcr fc d.fferut.ita rcslV mutaripoflunt 1 2o.viul»us,Vll vero rcs so^o.TcrtiacoJunacotjncc combinationes rcrum , quarum dux exdcm funt . Quarta tolumna continet combina- tioncs rcrura,quarumtrescxdemlunt,&. ficde ccetcrisordinecoluninisvfqueaddc- cimam columnam in qua combinationcs rcrum , quarum nouem exdcm funt ,conti-

ncntar* I- o

Vfus igitur huius tabulx hic eft fi quis fcire cupiat^uories noraen aliquot a. v,

o.litcrarum mutaripoffit,quodtamen4literashabeatcaldem,vtihocfiAura nomert lje*' * u* MARABANA oftendit,in quo cum 4iitcrxilnt exdcm , quxnturquoticsid combi- nari polllt . Quxrc igitur in prima columna VI II. ( tot cnim literarum nomcn propofi- tum cft) deinde columnam combinationisrcrum, quarum quatuorcxdem lunt,&an- guluscommunis dabit i663.&totiespropofitum nomen81iterarum quaium^cxdem funt, combinari poterit. Ita nomen fcx literarum quarum tres e$dcm fiint, ri» vicibuscommurabile cft.quem rtumerum habcbis inanguloc6muni,fianuraeroVl. in primacolumna traniuerfim, 3c in tertia columnafuriumafcenderis.

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£ Artis Magn* Confini , & Dijfoni

Ita vides fex res omncs differctes 720 vicibus mutari poflc; Si verd illaru du$ fucrint, e*dcm,36Q4,3,cxdem i 20. fi4,eardcm zy, f\ 5,cxdcmfcxie2, fi6,rcsca:dem o.Haud lccus proccdcs dc aiijs rcbus quotlibet inti a dcnanum contentis . Compofuimus autc hanc tabulam ex regulis pajlo ante traditis . vt proinde difficile non fit eam ad qucm- cunquc numerum extenderc . Vcrum hanc tabulam fuiimmc declaramus in Artc no- ftra Combinatoria,vbi cam ad quarumcur.que artium & fcicntiarumprincipiaapplica- mus, ad quam fuo tcmporc Lcftor curiofus 1 ecurrcre potcrit .

iT

.4

C A P V T I. De Notarum Combinationibus .

— _-

P

EraliquotProblemata hic docebimus modum acratione qua dctcrminarc liccac quomodo & quotics Notc. quotcunquc vanan ac intcr fc combinari valeant.

Problema I. Combinatorium.

Datd uoce quotcunque notarum , quottes illa intra certum interuaUutn

mutari fofsit , mnenire .

S

q . QtU i J*3 . > 1 I " • - ■ 1 • ■ - - - ■ . '■ * ' — ~ — ~- .

It prim6 vox trium notarum qu? pcr tertiam afcedat ex C per D inE. qucntur quo-

\ tics illa intra hoc interuallum ita mutari polfit, vt nulla bis ponatur in codem gra- du,fcd Gngulaj intra idem intcruallum dirTercntcs fint ? Refuondco fexies id fieri pofTe nonphirfes,cumenim iuxtal. Lc-matresdiuerfc res, fcxiesmutaripoflint, hic autc fint trcsnotac intribusdiucrfisgradibuspofitc, fcquitur neceflartdillasfexiesquoquc in- tra 1 ntcrua 1! 11 m v n iu s tertije rnutari pofle . Verum ad huius vltcrtorcm dcnaonftration& nihil 3hud requiri videtur niH ociilaris dcmonftratio, qua: fequitur .

'J 4

Videsigitur in cxemplo , quomodo voxpropofita fcxies ita muterur , vt nulla bis in aliqnn gradu ponatur.ied fingul* differcntes finr intra idcm intemallum i fecimus igjh turquod eratpropofitum_* .

Haud fecus vox quatuornotarum gradatim cxC in F pervnam quartam afcenden- dentiu, 24 vicibusiuxtaLemma I. mutari potcnt. Cum cnim 4 loca in intcruallo quar- t£,om nia diuerfa fint; Vox fexies mu tari potcrit, incipiedo i chorda C. & fexies a chor- daD, &fexiesincipiendoachordaE. & fcxiesdcniqueincipiendovoccs mutationis a chorda F.quatuor autem in 6 dufta dant numcrum totius combinationis propofitum. Vt in fequcaticxemplo patct i

6 incipiuntaG.

* $

I

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6 muta-

Djgitized by Goo

Lib. yill: ^Mufurgia Mirifica . 6 mutationesincipiunt a D.

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Vides igitur nullam in hac combinatione nota bis in codcra gradu inucniri,fcd 24 mutarioncsprorfusdifFerentes cfl"e_-> ,

Problemall. Combinatorium .

Data 'ooce quotctmqHe notarum , quarum quotltbet notajufer eandem chordam cxijlant, combinationemfrofo/ttavoas muenire.

HOc problcma foluitur fine vlla difficultate ex prcccdenmabulall.Combinatoria. Sit iguur primo vox quarpiam fcx notaruni ,quarumdua?fint eatdem fiuefupcr candem cijordam F cxiftant.ciujcritur vocis combi-

natio? diuidc combinationem lcnarij, vfcdclkec 720 tl3PS!3SSS22SE3S^l:|^ pcr combinationcm binanj numeri & quoticns 3 60 j \ • fr- — «: — ^EuC dabit quaefitam combinationemitoticsenhn pro^o- ' ' '<3rv ^ -^.|.|«. p

jfita vox mutaripotenr.vel pcrtabulam prcccdentc:

Quxrc inprimaColumnaVI. &colun>na: iccun da? anguluscomunis dabit36».quc,- fitam combinationera vt prius .

Sit itcrum vox quatuor notarum> quarum duc. cardcm funtiinquiritur combinatro; diuide igitur combinationcm quatcrnarij videlicet 2 4per combinationem binarij 2.& (quoticnsdabit 12. combmationcrn quarfitam vt in cxcmplopatct.

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Videsin hoc exemploomnesvocesrautari ,raanentibusfempcrfupereande chor- dam, duabus nous i rcliquis initium mutantibus , & in primis quidcm 6 mutationibus mancntibusduabus notis fupcr cbordam F vt,in qua& initiuro fit:in 6 aiijs mutatiom- bus trcs aotx fcmpcr incipiunt inGi&j in A, rehqws binis notis fcmpcr manentibus

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fca vox oclo notarum pcr octauam gradatim difpofitarum > mutationcm vocum con- tinct 403 1». Si verd dux cx 0A0 notis quomodocunquc difpofitis candem chordara tetigerint, admittat illa vox iuxta tabulam 1L Combinatonam 20160 murationes . Si tres candcm chordam tetigerint , admittet 67 20. Si 4 candcm chordam tctigcr rnt , 1662. Si j.eandem chordamtctigerintn6.Si6. 56. Si7 denique eandem chordam tctigerint 8 mutationcs admittct vti tabulapulchre deroonftrat .

Problema III. Combinatoriura .

Datd voce quotcunquc notarum, & intcr cas quothbet binarijs , ternar ri/s, quatcrnanjfue notarum Jufcr eandem, aut diucrfas ckor- das exijientibus, mutationes Docis inuenire .

Sltprimdpropofita vox 5 notarum quarum duat notas in hla,mi*c> fint &totidem-. in B fa,la, mi, vt in cxcmplo patct. Quamrur quotics illa mutari pofiit cum Uic lint duo binarij ? eos primo in fc ducesfiue quadrabis, habebifquc diuiforemj>er quem co- bmatioquinquc rcrum vidchcet 1 jodiuilareliquit 30 combinationcm imc ™M*U0T ncm vocis propofitr qucfitam. Verum ad huiusproblematis notitum mnil aliua rcqui- ritur, nifi ocularis cxempli fcqucntis infpeftio,& cxaminatio .

Combinatio wcis s notarum in qud du* not* cadcm bis

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Vides igitur propofitam voccm non nifi trigcfies mutari pofle, idque ob duos biiuu r ios no tarum in ijfdcm vcl diucrfis chordis cxiftentes .

Alterum exemplura.Si porrd vox quxdam fit noucm notarum quat in duabus diucr- fis chordistrcsnotas habcat cxiftcntesquomo- _ docunque difpofitas vt in fequcnti cxcmpio:quc- g"=:~~T^:^!^^j5i:v^ ritur mutatio > ita progrcdicris, ciim rres notc fint \ -^-V-V-V — — in duabus diucrfis chordis cardem combinatione" ! —^.-~JL-.. -.-.>■ ■ g, cui in primatabulainucnicscorrefponderc 6> t infccrgo 6duccs,vthabeas36diuifor€;pcrhunccnimc6binatio9.ideft36i88odiui-

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Problema IV. Combinatorium .

Datd voce quotcunque notarum 3quarwn du<e ead:m in vna chord&—> fint, tresnjeroeadcm in alia chordai combinationem, ideflnu- tncrum mutationis uccumrepcrirc .

»It vox qu^piam noucm notarura,quarum duc c^dcm in chorda A. tres vero ee.dcm > in chorda C. & duc, alic. itcrum in chorda A* vt in prcfcnti exemplo patet ; queri- tur mutatio vocis propofitc; ? itaprogredere.duc combinariori/era tcrnanj.huc cl\6 pcr quadratum_. combinationisduarum retum ,hoc cft pcr 4. habc- bifqucdiuiiorcra 24. pcr hunc diuidc combinatio- ncnoucnaritvidclicet 362880. &prodibut 15 120, queluntin vocedata mutationes qucfitc. quadntnm Si iterum occurrat vox 22 notarum,quarum due. repetuntur bis; & 1 quq repetatur cobinario- ter,&due aK$ querepetantur quater,qucritur quotiesvox mutari polfit ? itaprocedi- b-*[tjJ; tur , quadrabis combinationem *.&habebis4. hunc ducesin 6 combinationcm ter- narij vthabeas i4>uncdeinde iterum ducesin quadratum combinationis 4. hoccfr ln 5 76. & produftum 1 38a4dabit diuiforem , per hunc numerus combinatioms a ». id clt H24ooo7277776o768oooo,diuifusdabit 8130792301632000. numcrum mutatio- niscantusquefiti.

Excmplavaria. ln voce mucm notarum^.

QVandocunquc omncs norc lunt difTe- . rcmxsfitujhabcbitvox 362880 mu- tationes vt . Quandocunquc due note ex 9 eundem_» fitum habuerint , habebit vox mutationcs 181440. "'

Quandocunque tres ex nouem fupra ean- dcra chordaru nierint , vox mutationcs habe- bit 60480.

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tationes, quxfurama tanta eft, vt fi quifpiam fingulis diebus mutationum carundem.. tantummillefcriberet,is in dcfcribcndo laboraturus fit 21260896143 annis. Res oranino ijs qui vim numerorum&combinationis naturam nefciunt incredibilis , qux facilc tamen ex prxcedentibus demonftrantur . Vndc ctiam patct quiminconceptibi- lismutationum multitudo cxMoteclaquapiamfubindc 50. 100.200 notis conftante emanarepolfit. Certc fitotamundanamachinachartarepleretur , ilia non fufficercc adomrrcs mutationescontinendasvclin 3onotarumcombinationc.

Problema V. Vniuerfale . Datis in loce quafiam quothbet notis fiue dtfferentibus » fiue non diffe- rentibus, quoties quilibet alius ex ajjumpto $) determinato hocnumero, notarum numerus mutari fofsit y

HAbet hqc propofit io mirificum quiddam , vndc aitius ordiri vifum cft i & vt me n- tcm noftram faciliuscxpliccraus,ab ipfo exeploinitium facicmus propofitionis. Proponat igitur quifpiam c Mufurgis hoc Aenigma_, combinatorium propofitis ordine notis 2 2 primo om- nibusdiffcrcntibus pertrifdiapafonafcendenribustoc nimirum , quot voces funt in icala muficah Giudoms , vtinhocpr^fcntifchcmateapparct.

Quxritur prim6,quotics illx fimpliciter mutaripof- fint?atquc huic quxftioni ftatim fatisfaciemus pcr Le- mal. & Probl. L ciim cnim omncs differcntes fint.ad- mittcnt confuetam 22 numeri combinationem ,vt L Tabula oftcdit vidclicct 1 1 24000042 171709440000.

Quxritur igiturfccundo , quotiesdux notx intra_. fpacium trifdfapafon mutari poffint , quotics icerum_. , 4 r.6. 7.8.9.&ftcvfque ad 22 exclufiue numeru, quotiesinquam inrra determinatum trildiapalon in- teruallum aiTumptaex 22. notisquotlibct notarum- vox mutabilis fn \ Hoc itaque vt fuatur, lta agc . Cum 22 notxa(Tumpt„fmt.Ducesprim6 2 2 in 21 ,fcilicct in prpxima vnitarc mmorem numcrum , & producen- tur 462 . & totics du_ notxintra trifdiapafon interual- lumdifponi poftunt , fcmpcr diffcrcntes. Ratio huius reicft,cum cnim 2 2 dux notx omnesdifferenccs fint & cradatim aiccndentcs, fietconfequcncer , vtordincm vipefiesfcmel rautare poflit. Nam prima rautatio per _i%radusfiti Secunda mutatio fietcum noraeita di- fponentin , vcl pcr tcrtiam afccndant . Tcrtia mutario notariim fict pcr quartam. Quarta per qumtam.Quin- tamutatioperfextam,& fic dcccetcris vfque ad 21

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intia trescnftauashoceft »» notascum interuallis mutari poteft 1*893126400. Pari Mirjcombi parte v»dc6 interuallum 5 . ixue 5 numerosmutari pofle 4683336365740320000 vici- bus . Et fit dc coeteris . Vcriim cura hxc Arithmetices imperito mcrcdibilia videantur > Combinatioantcni hxcctiamfi ioooannislaboraretur,a 10000 krtptoribus exhau- rir i tamcn non poflit , ideo hic excmpla in minoribus nuincris , apponcrc vifum cft , vt per combinationis mutationes expanfas veriusrcicognofcatur jtdemenimin paiuts ac BMW numcris procedendi modus eft .

Exempla in minoribus numeris .

CVpiat itaquc quifpiamfcircquotiescx quinquc notis propofitis dux tantum no- tx mutari poflint vt femper diflercntes fint ; Cantulquc lemper faciat intcr ualla dirferenria.ira procedito,ponantur numeriordine naturali , vt in cxemplopatet in_* quoprimus numcrus monftratnotasquinqucfiuc intcgrum . Secunda columna numeris latinis fignitkat partes tntcgri , quotics vidclicet par- * tes quinque notarum intraquinariumintcruaJlum mutari poflint.Tcrtia * ^ columna fienificat mutationcs ipfas, ita vidcsvnicam notam quinquies 4 " *

tantum mutaripofle,duas notas vigcfies,trcs fcxagcfiesi quatuor ccn- 3 III 60 ties vigefies ; Quinque tandcm notas totics quoties ordinaria primx ta- x IV 1 1 o bulscombinatio prxfcribit. Fit autemhxctabula facillimc hoc paclo f y |iQ duc 4 in 5. & productum 20 dabit duarum notarum mutationem . iterQ 3 in 2o&habcbis3 notarum mutationes videlicct 60. Itcrum 2 in 60 &prod but 120 quatuor notarum mutariones,& 1 in 1 ao dabunt ordinariam combinationcm rci vt di- ctum cft, fcd rem cxemplis oftcndamus ,

Mutationes duarum notarum ex quinque >ide(l , intra interuallum *vnius quinta, tta vtnunquam bisjupra eandem cbordam refcriatur.

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Problema VI. Combinatorium vniuerfaliflimum .

Datis quotlibet notis , quot mutationes fierifofsint de quolibet notarum numero exiis afiumftofiue c<c nou dtfferentes fint,fiueeadcm , aHtfimiles,fiuefimiles & dtfferentcs .

IN prxccdentimodum oftendimus , quomododatis quotlibet notismutationesdif- ferentesexquolibetnotarum numeroaiTumptoeJjcerc pofif mus . Nuncoftcndc- dum quoquc cft, quumodo ex quohbet numerojntraccrtum intci uallum aifiimptum, jnutauones notarum ficr. pofftnt , fiuc UJC fuerjnt diiTercntes , fiue fimilcs , fiuc partira Jimilcs&partira differentcs. B

lta igitur age . Sit Syfterna maximum fcal* mufic*, j , notis conftans Pro cxemplo,- delidcrct autcm quiipiam fcirc,quotics fingula interuaUa mufica intra id aiTumpta prcl cifasrnutarionesadmittant . V. g.defidero vidercquot 2 notxintrafcajam muficaiem vanc difpofitx , mutationes fufcjpianr . Ita age,duc 22 notas in fc i cVprtnicnient 484 atquehxiuntmutationcs,quas2 notxintratotumfyftcma varic difpofitx fubire pof- funt. porro hunc numcrum 484 itcrum duc in 2 2 . & habcbis 10648 mutationes trium notarum intra diftatn, fcalam quxfitas. .

' Hocpaclo 22 jn 100V8 ducluproducent 224: numcrum niutationum quatuor notarum 1 ,trafcalam varie difpoiirarum.Sic»» in 2 142 5 6 proximeinuentum numeru duita dabunt mutationcs notarum intradatumSyftcma varie pofitarum, & ficfem- pcrvUii^umproduclummuitipIicandoper noras toriusfcalxfiucpcria ,producetur numcrusommurn umratjonum notarumeius numeri , qui inordincnaturaliproxime iucccditi Si verovclisfcircnumerura notanjmpartimfimilium panirji difrcrcntium-i Numeros prxccdcntis tabulx a aumcris huius tabulx fubtrahe, & rcliquum dabit que,-

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fnum . Excmpli gratia . Si numcrus 9 2 40 mutationum om- nino difierentium in tnbus notis clucefccntium prxcedcntis tabulx fubtraharura numcrocobinationis j.hiccorrcfpon- dentcvjddiccta io648.rclinquct 1408. mutationestnura notarura intra trifdiapafon partim fimilium , parrim diflimi- liumquxfitas. Ita*. notarumcombinatioinpriori tabula-, vidclicct i75 5ao.lubtradaabhuius tabellx quatuor nota- rum c6binationc vidclicet a »341 5 6,relinquet 6 2 696. mu- tationcs 4notarum partim fimilium partim HHfirnUiUin Verum,vtartificiumfingulorum meliuscapias,hic tripliccm tabcllam tibi ob oculos poncmus vnam odauam tantum_. comprchcndcntcm,quarum prima oftcndit mutationcs dif- fercntes i Sccunda partira firailcs partim differcntes , conti- netquc dirfcrcntias numcrorum 1 & 3 tabdlxafc inuiccm fubtraftorum , Tertia mu- tationcs nourum partim dirTercncium, partim carundcm fimilium, partim fimiliuin «C difierentium : Vt fcquitur .

12

484 10648

11 3379904 *4943J78*& J4«7j873J3<

Et ficininfinitum.

Tabclla prima» continens notarum mucacioncs dirTcrcnces .

Tabella /^«iwk.mutatio- num partim carudcm, panim difTcrcntiu^cftqi difTerentia inccr vcraqi I&III columnam*.

t a 3 4 5 6

7 8

21

46« 9240

1755* 3 19008

537x1360

85941760

12893 126400

Tahcllatertia, mutationum partim difTcrentium p.ir- tim carudcm partim difc fcrcntium & fimilium-ii

1

2

3 4

5 6

7 8

1408

61696

837614

60669544 I408416H8

41881746936

I

2

3 4 5 6

7 8

21

484 I0648 IJ4I56 51536JI

«13379904 H94357888

54875873536"

Iun«m bicaliudcombinationis gcnus,quod nimirum mutationcs fieri poflint , ex 21 notis quarum 1 1 fupra chordam candcm & vna fupra d.ucrfam pon itur Secu ndo qJot mutationcs fienpoflint cx 11 notis, quarum »0 fupra ^^^^^^ Scnt & 1 fupradiuer(am,at candem,&fic de coetcris vfquead J-f b nc enim decrcfcff- tes quo muudonura nuracrocrcucrant,eo decrcfcent , fcd ad cxphcationcm n.h.l a- liud rcquirividetur. quim Paradigmata fingulorunu .

Hae 22. notae nullam mutationcm admittunt."

1 I zk-*-^

• "* • * ' - ' •' ;

11

rrics

ZZ— 11- Mutationes .

35 t

Z Notxii & i.mutantur 22.

Vidcs

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J9

j ^-r hocf__*muunrura*i.

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19

zttiz

— hoc fitu murantur 1 540.

I

18

— hocfitu mutantur 7315.

1"

6 ■

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5

mutantur 16334.

_l6

— mutantur 74613.

15

z±±i**±tz

7

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s

10

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- mutantur 170544.

- mutantur 319770.

'i5:^:', -^n *

- muuncur 4974*0.

10

- muuntur 64664*.

h- <:Z*i Y.Z «

11

11

Z ruutantur 70^43 x.

Vides dirpofitionera nourum, iamvnicuml-Jtcm-^pIumdcmasftcund^ftrici « Lc &or curioiui vidcat, quomodo mW tationcs fieridcbcanr.

V.

20

Artis Magtue Cohfont\^ Diffoni

Excmflummutationumfic*nd<efirieifr<eccdentisfchematis qua 21 notafontur Jemftr fuper / chordam, & 1 nota fufra alteram cbordam.

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Lib.VlU. Mufurgia Minfca. jj

Vidcs igitur in hoc vnicoexcmplo fecundx ferici quomodo mutationes fempcr fiat diucrfc;quoadvnam notam vfquc ad n.atquc hanc diucrfiratemclarcdemonftrant notjcnigr^.Inferiever61ecunda,vbiducnota:inutant filura fiunt mut.ttiones 231. quia hx dux notx femper manentcs in cadem chorda in /ingulis 22 norisdccics muta- n pofiunt in fingulis zz notarum fcriebus& pauld amplius quxconficiunt 23 1. muta- tioncs. Non fccus ratiocinaberisde rcliquislericbus , quarura mutationes adfcripcx func .

c a P v T 11.

Dc combinatione valoris notarum .

Dlximus in prxcedcnribus Problematis , de combinationibus mutationibufque-* notarum,fiuequociesdaCx not$ mutarcintcr fefitum poflint , diucrfafque vo- ces conftituere, nunc oftendcmus quoque qui ratione fcirepoifimus, quotics notxdi- tierfi valoris etiam in vna chorda di Jpoiicc mutari pofllnt . Sic itaquc .

Problema I.

DataDoce quotcunque notarum qu<e omnes dtff.rentis valoris /int , quoties tlLe nou dtffercntis valoris tnter Je mutaripofsintjnuenire.

ffffl *"*"*• ' 'T _ -3 0 1 °L__?- cl • I

NOn dcmonftrarnushic quoties notc propofitj locqm mutarc poffint, fcd tancum quticsdiucrfivalorisnotx etiani lnvna&eademchoidadifpofitXs intcrfey mu:ari& varie difponipoflint. Vt igitur a paruisexemplis ordiamur. Sinttrcs note, dif* fcrentis valoris propoiit?, velifquc fcire quoties illx inter fe mutari pofliiic .

Cubicabisternariumtcrpoiitumvtelatcrepatec,duccndoj inavtn.lt 9 333 dcindc,duces 3 in 9 ,&nabebis 27.atquctotiestres not$ dirferentis valoris mucari inter fe poftunt, vt in fubiuh&o excmplo patct . - ' • < r ' - 1 -il III

9

*7

m

Mutatio 3 notarum cuuerfi valoris.

i	zfc	ii.

1 * 3 4 5 * .7 f 9 10 11 12 ij 14 15 1.6 '7 J8

H I

20

21

22

13

24 25 26 27

. J1lr ::- • .

Atquc ex hoc exCmpIo modusprocedendifatisclare patec, vbivides femibrcucmJ nouiesponi in prima ferie ; in fecunda fetic nouicsponi minimam ; Si nouics in tertia_,

ferie

22 Artis Magfue Cwfont , & Difioni

feric femiminiraam, rcliquas confcqucntcr diucrfas inutationes iortiri .

Si vcro 4. dcntui nota: cmncs diticicntcs.ponatur numerusnotarum x 4 ordinc naturali , vt vides in bic > dcindc 1 ducin^ ,prouenicnt 4 c 2 j6 rcgione 1 poncnda,hunc iterum duc in 4 proucnicnt 1 6 e regionc 1 po- 3 64 ncnda, dcinde 4 ducantur iterum in i6,& prodibunr 64 crc^ionc 5 po- 4 256

ncnda , c^dcnique^iterum ducanturin 64 & prodibunt 256. numcius — .

mutationum 4 notarum dirTcrenrium . Non iecus in quibuslibct alijs nu- I$;i tw diffcrentisvalorisaiTumptisproccdes. Vcrum vt mcntcm noftram_. meliuscapiashic pinaccm iubiun«crc vifum cft, quadido citius , quot nutationes, quotlibct notis diuerfi vaioris propolitis, Heri poflint , quam confulc— » ■

^Tabula 'vniuerfatis qua mutationcs notarum intra fpacium dtapajbn fartim fitutparttmi>alorc>partim Dtroquc-mo- do dtffcrcntium oficnduntur .

ffitn.

COLVM.I. M utatiou. no- tarum fitu ta- tum diftcrcnt.

Ordo Totutn

•a

o,

o

c

M

ti

Q —

II

III

! 5

IV

*.F7

o

-a

2

3

- VI

Cdbina. vocu fi- '11 ditfcr.

COLVMNAII. Mutatioms notarum taotom valorc ■ diftcrcntium .

Ordo

'o

120

II

710

VII

- — f!

VII

T

VlT

5020

III

IV

VI

Cobinatiooo- tarum vaiorc ; imum dirTcr.

*7

tj6

COLVMNA III.

Mutationisnotarum' C0LvNJN A IV. fitu* valorc uit- fcrcntiurn .

Combinatio notirum t; 1 1: .V valorc dif- w fercnfHim .

PataJigmatica.

Exemyla.

162

6144

!»*5

46616

VII

8tjjo6i

16777216

37 jooo

33570720

676i55359,l°

.,.;.;

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LikVUL MufurgiaMirifica. 23 V S V S T A B V L AE.

SVnt in hactabuIa4columnx,primaoftcndir vocuoi quotlibct mutationcs vfquc~s ad 8, quoad fitum tantum;iecunda oftendit mutationcs notarura quotlibct vfq; adSquoad valorcm tantum,Tcrtiaoftendit mutationes quotlibetnotarura intra o- ciauam tum fitu,tum valore dirTcrcntium . Quarta oftenditrotum ncgotiumin exe- plis . Si quis igitur fcire cupiat, quoties quinque notx,qux iemper intra icalam diuersu iitum habent, mutationcsadmittar.isquxratin columnaI.ordinis,V.voccs,&eregio- ncincolumnacombinationis repcriet 120. routationes quinque notarum qucTuas. Si vcrd veiis fcire , quoties quinque notc, valorc tantum dirferentes ( cuiufmodi in col. IV . nora* 5 differcntes c rcgione V. oftendunt ) inuenics incol. II. e regionc V«3 125.

3uinquc notarum diucrfi valoris , fiuc intra idem interuallum , fiuc fecundum gradus ifpofirarum mutationcs . Si vcro fcire velis quotics dictx quinquc note, tum fitu tum valorc differenrcs mutaripoflint ; id tibi oftcdet III columna e regione V. vidcliccc nu- merus 375000. Notx 5. igiturin quintoexemplo oranesdifferentes,primdfine omni mutatione fitus^ 125 mutari pofTunt , varia tantum notarum diuerfi valoris tranfpo- fitionc intra eandem quintam vcl ctiam fupra eandem chordam facxa: fi vero accedat mutatio fitus, quem intra interuallum diapcnteiuxtal. col. 120 mutare poteft , fTcnt Ihutationcs 375 000, vti diCrura cft & III. Columna oftendit .

Problema 1 1 .

Datd voce quotlibct notarum cum fitu tum valore differcntium quoties ix)x data sub hac duflict varietatemutarifojfit, inucnire .

IN prxcedenti problemate oftendimus,quoticsvox quotlibet notarum differentis valoris routari poflit nulio refpectu habico mutationis loci . Hoc pr blematc vero demonftrareintcdimus,quones vox quotlibct notarum,tum fitutum valore differe- tium mutari tranfponiquepoflit .

Sit itaqucregula vmucrfaiis . Quotiefcunque nore. in voce aliqua tum fitu tum valo- rc differunt . prirad ducenda eft combinatio notarum fitu diffcr en tiu rn,in combinatio- nem valore ditTcrentium & produftum dabit quxfitum . Vcrum rem in minimis nume- ris oftendamus. Siitaquequifpiamvclitfcirequotics vnvdnamm nnnnim fitu&va- lore diffcrentium mutari poifn s ducet combinatio- nem notarum fitu tantum dinercntiurn fcilicet2,vt prima columna oftendit ,in combinationem notarfi valoredifferentiumfcilicctin 2. numcrG, vtfccun- dacolumnamonftrat,&productum dabit qucfitfi, I 2 34

videlicet 4-vt patet. Si vero 3 notarQ tu fitu tu valorc diffcrentiu mutationesfcire defi- dcres,ducescombinationem ternarijvidclicct6in priraa columnaincombinationem ternarij infccundacolumna vidclicct 27, & producentur i62mutationcsquxfitx.

Haud fecusin reliquis omnibusordine proccdcs ■, fcmper combinationero notarum fitu diffcrentium, quam prima columna tibi oftendit,ducendo in combinationem no- tarumvalorcdiffcrentium ,quamx tabuiaoftendit: &habebis mutationis notarurrui quotlibctaflumptarum turafitu tum vaiore diffcrentium,numerum quxfitum . Vcrum preccde ns tabula orania exa<fte docet. Si vero in tribus notis vna differat dua- bis reliquis Iimilibus,cubusex ternario bis in fedu&o,vt elatercapparetpro- 333 ductus^videlicetz^, dabit intribus notisinquibusvna diffcrt,rcliauisfimi- 9 libus, murationisnumcrum qu^fuum ,vtfubiuiKtumexemplumdocet. 17

Vides

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Vides igitur in hoc excmplo voccs trium notarum idem eiTe vnam notam diffcrre , & z diffcrre . Supponitur cmm hic in hoc tcrnario fempcr duas notas /imiics & vnanu diflimiieaui.

L E M M A.

SI numcnisquilibctalTumptus bis,ter,quatcr, quinquics&c. vfqueininfiVtum-. , ordinercpctitus fucrit,produccntnumeri ordine rcpetitorum in fcordined.cii , numerum cofficumeiusordinis,quemchara(fter numeri ordine naturali conrinuati,fi- ue qucra numcri exponcntes dcmonftrant. Sit tcrnarius numcrus aliquotics re- « m petitusiVtinhoccxemplopatct.Deindc R. v adaigebu ducatur 33 inlchabcbirque QJi 3 Q^ 2 afHnitas. in fc ordine ducatur, habebitus biqua- C. 3 dratus, & fic dc coeteris vt tabella oftc- QQ^ 4 ditinqua vidcs3 bispofitaatquein fe SS. * 5 ducta producuntquadratum, quc cha- QC. 6 racler cofficus Q^antc binarium pofitus indicat , dicuntur autem numeri naturaliferic continuari exponentes , co quod expo- nant, quoties poni dcbeat numerus aflumptus quorieiq; in fc muitipiicari , vt procrec turdcfidcratadignitas algebraka pcr chaiaftercm cxponentibusprcrixum.indicara. Ita exponcns4oftendittna quatcrponi debcte, deindc in femuiriplicari, vt produca- tur8i biquadtarusternarijnumcri per charactcremQpjndicatus. 6 vero cxponcns oftendit3 iexiesponi debcrc «Scordine in fc raulriplican vtgcnerctur 719 quadrato- cubustcrnarij numcri ,quem characlcr QCindicat. HocitaqueprxmiilumLcmma_» ad icqucntia problcmata apphcabimus .

Problema III.

In Polyphoniis,fiue multarum vocum mclodiis, quotuis notarum,qu<t tamen fitu #) valorc aqualcs fint, mutattones vocum co ordtne crescunt,quo in numcris foteslates algebratc* .

1 -•' . :r». .ri .iHJnio. .^*i.b «^s j-.rtitoruvf2u:'

Slt v. g.propofitumtetraphonium , fiue 4vocumclaufuIa 3 notarum fitu & valorc aqualiura, vtfcquitur cupiatque quifpiam fcirc, quot mutationcs cx duabus,3.4 : vocibus

3

33

m mi 33333 333333

3 Radix .

9 Quadr.

17 Cubus.

81 Biquadratus .

243 Surlohdus.

719 Quadratocubus,

Digitized by Gc

Lib.VUL MufurgutMirtfca. ij

vocibus cnoergant^ra procedc; ponarur pro radice pro»rcffioni$ Coflice ipfa combi- nario nuvncri norarumqnem quqfibec voxhabet ,c]uicum inhocexemplo fit ^.eiuiq; combinatio iuxta i. tabulamcombinatoriam fit 6. erithic fenarius numerus radixto- tiusprogrcflionisCoflic^harmonic^. Hic iraqucfcnarius bis pofirus, arquc in fc_-» du&us procrcabit 36 Quadrarum, qui# oflcndit mutationes 2 vocum.quai um vna- qu^quc 3 notas habct, valore ^quales^.mutaripofle. Cumcnimprima vox 6muta- ripuQfn cantantcpnmo vnam cxlexipotcrit jntcnm iccundus 6 omncscantare eodem tempore & cantante primofecundam voccm cxluis 6, fccundusinterim alias6 canta- bifi &fic vfqucdum primus cantans, fcx mutationesabfoJuit,aIius j6abfoluerit ,atq; bcx eft ratio, curdue; voccs 36. mutaripoflint. Hinc candem obcauiam tres voccsmu- tari poflunt 216. quiaquemadmodum 6 tcr pofita&in ie ordine dycla producuntcu- tum ,ka tres vocesquaxum vnaqucquc k xics murcbiliscft , in lc inuiccm ducl^ pro- <ducunt quaficubum harmonicum videlicct 1 16. ruutationestnutn vocum quefitas. Hac rationc 6 quater ordinc pofita & in fe ducta producunt biquadratum harrnonicu fcilicet 1296 mutationcs4 vocum.& fic decceteris ;vt rabuia icquens oftendit ,itafi ficrcnt 8 voccs,quarum vnaque,quc 3 notas haberct c.quiualentes,producerctur cx 8 icnarijsordinc pofitis & in feductis quadrato-quadrati quadratus harraonicus, fcilicct 167961 6 mutationcsSvocumquarfit^.

Gene/is mutattonis polyfhonuxrum-> . , n t ,

Exponcntes Radix

Vox I Voccs 2 Voccs 3 Voccs 4 Voces 5 Voccs 6 Voces 7 Voces 8

6

66 666 6666 66666 666666 6666666

66666666 Quadrato^quadrati quadr.harmonicus 1679616.

Radix harmonica	6.
Qiiadr. harmon.	tSk
Cubus harmon.	216.
Biquadrarus harmon.	1196.
Surdefolidus harmon.	7776.
Quadraucubus	46656.
Bifrurdefolidus	179936.

Vides in hoc vnico cxemplo, quomodo in reliquis proccdcndum fir; vr fi v.g. voces ComplurcselTcntquarum vnaqu^que^ norisvalore^quiualenribus conftaret,habebis mutationes vocum duarurn 3. 4. & quotJiber; deniquc fi combinationcm quaternarij, id cit^^proradiccpoteftatisdjgnitatiftjue Coflico-harmonicc, ftatuas , eo prorfusor- «line cum replicando, vt in pra*cedenti exemplofadrum eft. lta 24. 24. radix bis pofita & in le ducu dabit quadrarum harmomcum idcft?76 mutarionesdiiarum vocum_o «juarum vnaquxque qua uornonsxquiualenrtbusconftar. Siterpoiiram 24. »4-24. infe duxerisprodibit cubus harmonicus,id efttriumvocum murariones, &iic decce. teris. Vcriimad racjiorem rcrum inrelligcnriam hicradicesharmonicasoftonumero- rum poncmus. Radiccs harmonica? .

M i } ,6

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Harum radicum fingulz bis, ter, quater, quinque &c. pofitx arque in fe daSix ,pro- ducentpotcftatcscoflico-harmonicasmutationum,qux heri poiTuntinduabus,rribu5,

D quatuor,

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26 Artis tfliagnA Conjbni, & Difloni

quatuor, quinquc &c. vocibus.itaradix 403x0, otficsj-cpctica & in fcducla dabicQO^ Quadratum harmonicum, mutationcsS vocum,quarum vnaquc,que8 notis^quiuiiiC- tibus conftat>continentcm_i.

Datts

quotlibct

Problema IV.

Voeum notisptu imequalibus, valore aquakbus combinationes earundcm repcrirc .

Slnt v. g. voccs 4. fcx notarum, quarum ramcn in finguiis duo binarij reperiant ur ii- miless ita proccdcs, diuidcs 7x0 combinationis 6 notarum numcrum pcr quadra- tura combinationis binarij , hoctlt per 4 , proucnicnt 180 numcrus mntationis que;(i« tus, critqucradix harmonica ad duarum,trium > quatuor&c. vocumpoteftatesCofli-. co-harmonicas , fiuc quod idcm eft, rautationes inucftigandas quefita. Excmplura noa addo, cum ex dictis omniafacilc innoccfccrcpoflinc .

.iw:m:.iw::v -n-i

Problema V.

Datis 4 Vocibusquarumfrima^ notis confiatftcunda tribus }tertia 4, fedi flimiltbus, quartasnotis conflet,valorcdifferentibusy mutattones omnium vocum reperire .

Slt hoc preTcns tctraphonium, & quifpiam vclit fdre_ t, quotiesvocesmutaripo(fint,is ica procedec. Cum prima vox 4VOceshabeatomnesequiualentcs ,&intra_» interuallum quarte. fint conftitutc. erit iuxta predi&a I. Probl. eiuscombinatio »4. Cum vcro fecunda voxtres tantum notas habcate,quiualentes , intra diateflaron in- teruallum conftitutas, eiufque combinatio fic 6. iuxca ta- bulamI.Combinacoriam,duccstfin 24, &habebis 144. mucationesprim;&fecundf vocis qucjitas .fiporro triu j vocum corabinationcs defidcrCs,.Tertia vero vox qua- tuor quide notashabctquaruduc, fupra idc fpaciu.iuxra pr^cedens,combinatione quaternarijper » dmides;pro- dibuntq; i2,que,in I44ductadabunt i7i8.triura vocura routationesqucfitas. Sidcniquc 4 Vocu mutarjoncsde- iideres, quarta verovox 5 notas habcat.diflimiks.ciufq, combraatipocdinariafit tao.hcx in 3 vocum mutationcs videlicct in I7i8.duc}a4a- bunt4 vocum inutationcsqucfitas,vidclicct 207360.

x r e— t

iiiiili

Problema V I. Datis fpccicbus confonantiarumdiatefldron, diafente $J diapa/bn ,

carum mutattoncs rcpertrc .

I Vid fint fpcciesdiatcflaron, diapente & diapafon fusc didtum eftin lib. III. Cum itaque lvnt 3 fpccies> diatcflaron . < diapctc,&7 diapafon ,vt, citato loco pro- "~ 'batum cft > nihil aliudad hoc problcma folucndura requiritur , nifi vt ad mu-

tatio-

Digitized by

Lib. FIll. sMufurgiaMirifica. 27

tationes trium fpecicrum diatcflaron inuenicndas,trip erurcombinarioquaternarij fi- uc diatcflaronvidcJicet j4.hicenimnumcrustnplatusproducit 72 mutarionestnura. di£arum fpecierum qusfitassadmutationcsquinquefpccierum verddiapente,quin- tuplanda cft combinatio diapcnte fiue quinari), quem in tabula I. inuenies 1 20. & pro- dibunt 600 mutationcs quinquc fpccierum diapentcad mutationes verd feptcm fpc- cierum dhpafoninucniendas > feptuplandaeftcombinatH>oclonariifcilicct403ao.«& prodibunt 3 22 560. mutariones fcpremfpccierum quadirc .

De mutationibus ex 12 diutrfis modis Jiuc *T onis rcsultantibus .

C

>Vm fcptem diapafon fpecies conftituant 1 2 diuerfos modos, vnufquifqi verd mo- 1 dus intra /i*'t*H* tnldiapalbn mutan poifir mxta l.Probl. 40$ 10 vicibus,hi mul- tiplicati per 1 2 dabunr 48 3 840 1 2 tonorum mutationes , fi fingula: oftauc. fc orfim con- fiderentur.fi vero miftjrfumanrur,quadratus huiusnumcri 48348040611 quxfituro-*> icilicet 234083727360 mutationcs.

6s

MVSVRGIAE MIRIFICAE

P A R S II

MVSVRGIA RHYTHMICA SIVE POETICA.

C A P V T I. DeRhythmicffartis vi& efficacia .

^•«Efcio fanc , que^cculra&hueufquc impcnetratavisnaturae motui in-- Jr C fit, quoid in aIiopoffevldcmus,quod ipfcfacit;qi

poffe vldcmus, quod lpfe focit; quod non in extrinfe- co tantura corporismotu^fcd&potiflimumco in ftK>ru,qui lingu^of- ^5 fi*-''0^ ln verba & canrusprorumpcntis. Vidcmuscnim vclvnumcan- 9 tantcm » ac* ldcrn a'i°s faciendum occulta quadam vi , ( llue id mctu ,

m&5^s**vTm vt Jn panico timorc pcrcu 1 fis, fiue inftinftu lxtiti*,vt in faltannbus co- tingit) cxcitarei qucdcumin ahjsmoubus fiar, certemaximc locunvbabetin vocibu* humanis.Voxenrm humana cumjiihilaliudfu, quimartificiofusquidam motus lia- Voih(l gujc iuxtaintentioneruhominisadaliqoid fignihcandum iuru.utus ,prorlus id in alijs naadimui xacere videmus quod ipfe pr.rftat, Expericntia enim docuir, vnum canrillantc vel plan- d^m prouo» gentcm, vcl fibilanrtmautetiam ofcitancem ad idtm faciendumalios excitare .quod ' cum vcrum fit in fonis voc ibufque etiam r udibus impolitifque , certe multo magis , in_» concinno verborum vocumquecontextu venricabitur. Notarunthancabditam natu- ratvimaprincipioprimiujcfapientij» Magiftri;hrhc laildc^sDeorumimmortalium non quolibct for tuitoue verborum contcjftu.»icd vinculis vduti inieclis orationes fuas har- monica quadam menfura ita conftringeDanti vt ipfa vcrborum mcnfura inrcrnisanimi arTeelibusprxcisd congruerer,vrvel hincprima qu$damfacrxpoefeosrudimetaa<»ncfc. fcasjquar vtitunc, ita nullo non tempore nefcio quid diuinum apud pofteros obtipuit in animis horr.inumj Nam hac non tantum Gcnios, Deofque fympathica quadam •Ite- ratione fibi vicinosfittcrc; Scd & hominumanimosMn quodcunquemutare fepoiTe_#> crcdebant j Quar omma tam prcclaTe miv/iJhxiei ille docct Horatius; vt ad eiusverbr nihil aliud adiungi poflc videatur . -

D a Aut

cai .

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iS Ariis Magtue Conjont , Dijfom

Aut prodcffe volunt aut deleclare Poets

Aut /imul& iucunda & idonea diccre vits

Silueflrcs homintt facer interprefque Deorum

Cadibus & viSlu fcedo decerntturOrpbeus

Diclus ab boc lenire Tjgros rapidufque Leonet

DicTus & Amphton Thebana condttor arcis Quo kntn Saxa mouere fono teiludinis , & prece blanda

feril eTf»! Ducere quo vcllet , fuit bac fpientia quondam

xa aaxerint. Pubbca priuatis fecemere , facra profanis

Concubituprobibere vago ; dare htraMaritis

Oppida moliri , leges incidere bgno

Sic bonor df nomen diuinis vatibus , atqui

Carminibus i'enit,pofl hos infignis Homerus

TyrUufque Mares animas m trifha beUa

Verfibus exacuit, diclapercarmina fortes - Et uiM monfhata via efi, & gratia Regum

perifs fcntata modis, ludufyui repertus .

Certe hanc diuinam & impcnctrabilc vim,vt cQ PJatonc loquar,origincm fuam non habcrcnifiamotuharmonico,a!ibifufiusdcclarauimusi prcfercim fi is ipternis ani- miarTcclibiiscommcniuratusrefpondcat,commenfuiatusaut5correfrx)ndcbit; fi per breuitatem aut longitudincrn lyllabarum in aptas harmoniofafquc pcriodos dcducTa_. ftringaturoracio.fiue quod idcmcftceleresanimi motus,cclcr &ve!oxfequacur men- furaitardos tarda:& quamuishcc ficutiin Metricafeu Rhythmicaarrc vira mirificarn_. polfidet, certe multo maioiem in Mufica poefi fiuc Rhythmica cncrgiam habcre, com- pcrtumeftsillacnimhuicconiuncTa,veluci omnibus numeris completa ,prodigiol'os prorfuscffecTusinanimis homitium obtinere,inrimTaprope Hiftoricorum monumcnta tcftantur i Eft cnim vc pauld antc quoqjdixi ,nefcioquidintcranimum noftrum mo- tufqucharmonicos& Rhythmicos fympathicum,vt fimul ac aunbus mctnca hannonia fiftitur mcns varijsagitataarTccTibus , nunc gaudij modo amoris, nunc mceroris , com- paifionis, iue, gemitusaliaquc pathcraatum indicia prxbeat, quc tantum fubinde in- crcmcntum habet, vt mensintcrrjisanimiclauftris contincri nclcia , cxterna quoquc membraad acTuspathcmatirefpOndentescxcitet i Vcriim cumhxcfuse in Artenoftra Magnctic4ub.IILdeMagncnfmoMufic^iScTarantifmo oftendcruuus , eoLecTorcnu. remittimus.

Vt igitur ctlam imperiti Muficx Rhythmos barmonicis numcris aptc &fine vllo erro- reconiungcre fcircnt hocloco Rhythmicam muficam fiuePoetkam harmoniam prc- mittere vilumeft ,vt iuxra illam directnntento aftccTu potirentur. Comprehendimus tutcmfubhacmetricanoftraartc nonpoefintantum , fed& Khetoiicam, id eftfolu- txoiariohisconcianas pcriodoseirlccicatqueapta fyllabarumprolatione muficis mo» dulis applicare . Quc.curu itafint.aprimis incunabulisrem ordiamur. «_at . :i' cni 6lluoi 5i i>j , >j,i!ii.!.j.-m. i mctft (•.'•■' /✓inoi niin mrnav ii.u>

C A P V T I I.

De Accentibus .

A Cccntus nihil aliud cft quam ratio cleuande, aut deprimenda», quoad tonum, f) I- /\ labae : Eftquc apud Gijecos tnplex . Acutus, Grauis, & Circuraflexus . Latini a- cutotantum & circumflcxo gaudcnc, neglcfto graui vtdicTum cft. Eftauccmaccen- Quid Acci- tus acutus quo fyllabaactollitur, cuius cnccTus cft ofcn« id cftclcuacio igrauis ,quo fyl- msacutus. j^jj-j deprimitur, arnac i Vocantur autcm ab accmendo, coquod cantum luie ic-

cita-

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Lib.yill. MufurgiaMinfoa. 29

citationcm numcrofam modercnrur , Vndc 3cpaflim toni quoque, renores>voculatio- ncs & fuftigia vocum dicuntur. dc quibus vide Ciccr. lib. 3 . dc orat. dcindc 1. 2. Quin- tilianum l.i.c.y. Gcllium 1. 1 3. c.6.MartinumCapellam»q^uiaccentum vocatanimani focum & mufuc; ieminarium ; Sicut porro acccntus impolitusfyllabis,non oftcnditca fyllabam fupra quam ponirur elTe breucm aut longam , ita tcmpora harmonica , fiue-/ notc, quoquc non indicantlongitudincmautbrcuitatem illius fyllaba:,ad quamappii- cantur, fcd pr$cisc tantum clcuatio aut exprcfllo vocis pcr tcmpus vclox aut tardum_o indicata attcnditur . Vndc triplcx quantitas in lyllab^pronunciationc confiderari po- tcft,primacft temporis, quo fyllabc conceptu immoramur antcquamabciusprolatio- T[£'" n c ceftemus, & hec cft illa, que ab author ibus intelligirur , cum lyllabanu* b* pron

brcucm elfe aut longam dicunt . ad breuem cnim profcrcndara vno tem- ~* - cuuone

porcad lonoam duobus temporibus vtebantur,vt innotismuficisinhic — -jrjp pofitispatet .hinc antiqui,vtQuintilianusl.i.c.7.docct, fyllabas longas ZuZ.—Z gcmina vocalipronunciabant, vtMaaterpro Mater,aeemitpto demit>ptjpit pro pipit>poonit pro ponit>puunit pro punit. Secunda quantitas cft intcniiua tenoris , qu;t intenfiuselcuatur aut remiiTus dcponitur tonus vocis ,& hcc cerni-

nirin fcalc; muticc. gradibus , quarceadfmfyllabafiuelongafiuew» — — ; —

breuis, fi acuta fit vno aradu,& laltem fcmitonio altiorcm notam re- — — ir —

quirit, quam fi grauis iit; vtin A patet;fi vero circumflcxa fir , duas ~sSS$- "i^— notasrcquirit , quarumvnafitingradufupcriori ,altera veroinuv A B feriorii vt in B vidctur . Tcrtiaquantitas orta ex accentu,cft mora, • qua non tam fyllaba cadem , quam eius imago pcr acrcm propagata perdurat in aere , & fpacio quod cum acre occurlat . Nam fyllaba acuta aut circumflcxa longiusinterual- N lum penctrat&plures fuifimileslyllabaspropagat inaere, ideoque&diutius viuiteius Udooii imago aud.bilis,& a diftatibus melius pcrcipitur,& maiori intcruallo rcpetitur ab Echo, cjuam fyllaba grauis , autfyllabico accentu rcmifse prolata. Non iecusacrit inchorda intenfius ductt , quam in ea quae rcmiflius , & hinc nimirum cft , vt fyllaba ac uta videa- tur femper longior, quam grauis; lpccTata fcilicct mora, non quia dum eft in ore profc- rentis ipfi infillitur,lcd qua cius fpccicsinaere viuit .

Vidcs igitur quomodoex naturaacccntuspaulatim Muficacxcrcuerit.Nam hcc to- tumhumanxfermocjnationis negotium dingit , ita vt tanto fit cloquium clegantius quantd fueritacccntibus fuisdiftinclius jHrnc om hcs £enres,& nationcsfuos proprios acccntus habent nationis proprios, cV quo a ccetcris genribus diftinouantur . Veriim-» cum hxc omnia alijs rractatibus rcfcruauerimus, hic Tongiorcs efle holumus . Sicut igi- tur accentus partunt iyllabicam pron unciat ionem, ita mu fiCus acccntus , harmonica . & ficuticx fyllabicapronuncianone Rhythmus nunc vdoci nunc tardo pedum motu incedcns, nafcitur, ita & Rhythmusharnaonicus. Visaigitur natura accentus,iam quid Rhythmus fit inquircndum rcftat .

CAPVT III. De Rhythmo ciufque accentu.

' muiT".T; r;i . «JUtJiLicj suhcqi.UJM K cjtnrtaD j jinQflijipiiioivuiuri i.t 4.

RHythmus igitur prout tcmpus&motum fpeclat, tam Poetit,^? Oratorlbus,quam Muficiscommuraseft,cum.tam^iquam illi voccs vocumqBCperiodoscertistc- ponbus diftinguant . Diftei unt tamen in hcc quod apud Poetas omnes fyllabx breues finteiuldcmbrcuitatis ,&omneslongx ciufdcmiongitudinis &produvtionis;contrx apud Muficos non ura prxcise iuxta naturam iumirur fyllabarum correptio & produ- ctio; Scd media tantiim longa veibrcuis intrilyllabisi in tctrafyllabis vero ,penultima longa velbrcuis attcnditur,quam breuitatem &longitudincm vario notarum valOrc^ racniuram, vt pauld poft oftendctur . Variorum ttaque tcmporum & racofurarum or-

do

«

3 o Artis Magna Confoni, Dtflom

doRhythmus dicitur, quemPlatos deJegibus umn^ lagfrid cft motiis ; Arifto^ xcnus verdTtfv X&*ot* ro'£i»id eft temporumordinem definit.adedvt minimumaliquod tempus idemefle potTit in Rhythmo, quod lbnusin Mufica,in Geometricapunduni,2c vnitasin Arithmetica; Rhythmus enim fitcx certo motuum veltemporum tardorurru. vel velocium ordinc, qui 111 tonis, choris, chordis puifuquc arteriarum deprehenditur . Abhocautem Rhythmo quitarditaccm &celeritatcm temporis & motiis in ipfa har- monicarum vocum longitudinc breuitatequc elucefcentem conftituit, Mufica Rhyth-, mica nuncupatur;Harmoniaenim motu vocis abacutoin grauem,velutielocoad lo- cum tendens, id foliim fpcctat, vt foni per debitas mteruallorum dimc nfiones, fuis iru« locis & fcdibus aptc difponantur, qux tamen nifi Rhychmus eius veluti anima accedat > ntanca meritd Sc imperfe&a confebitur .

Quantum vcro Khythmusafonorum grauitate &acuminediifcrat,conftat,cxvcr- fuum fimplici pronunciationc, qux ncque crigitur , ncquc "depnmitur ;fed cundem te- norem a principioad finem vique feruar , patet id ctiam m tympani ftrepitu, cuius fono dum pullandovariapro vanjs belli circumftantijsindicant^Khythmumquidemferuat» fed nullam poiTunt lonotum grauitatem , nullum acumen cxinbent ; Cum quacunque intv nfione ccrium fcrias,femper idem percipiarur fonus; & tamen infignem in conata- dismilitum animisvim obtinct, pre^cirimfiRhythmus prxcisc oblcruetur, idque ob analogiam quandam , quam primus jAus habet cum icquentibus , aut quam omncsfi- mul collccticmciunt. Stacim enimprimus iftusduorum fcquentium longitudincm a> quat , ftatimquc vltimus duobus anttcedentibus refpondet , & fic dc costeris quos vcl in dupla, vel ln hcmiola vel cpitriti ratjone tfficiuot a Vt proindcRhythmus latc fum- Rbrthmi. ptus nihil aliud fit,quam fonus qu dam proportionatusex tardis & velocibus motibus, Definicio iJUc quod idcm eftex varijs acummis & grauitatis s;radibuscompofitus. Stncniis verd fumptus nihdaliud eft,quam conformatio quxdam ct veluti cbaravter qualitatis votis, quo vox hoc vcl illo modoconformata Rhythmum perrkit , Ariftoteics quoquc irw Khythmis motionem in fonorum grauium & acutorum ordine imitationcm habcre— >» omncfque Khythmoscantico&ty mphonijsgaudcre aflcrit; adco vt omnes motusor- dinati & certa legc aftricu Rhythmj di£i,ppiltnc . .

Siitaque Mulurgijs Rhythme poecico,harmouicosRhychmos,id cftnura,crosadiun- xCi itj is certe; Audltpres non ppte/ir tjpn in admn at lonem raperc . Quid enim non po- tcft DUmcrofa u t Jodia > & quo Khythmus deganrior aptiorque fuerit, eo faciliiis audi- tores mouebit, pcr quorum amroos arij & tbclb vcJuri pedibus decurret, motibulque—» concinnis.errabit.-itapcdibus Jongjs fpondcis, moiollis , cpitrkisatfeclus graucs ;brc- uibus vero vt p^rrichijs, chorev, tryhra chis, p*onibusa hilarcs exprimcntur . Ycrum_» dc hispaulbfuiius tiactandumcit.

bltip Oixi<;V:n^3"Ji c*.:j:..;I .ijii^riiiiV -:noroi£d ?:;r: ir:f2noh«.-,i

C A P V T IV. De pedibusRJiythmorum fiue Metrorum.

PEs Metricus itaqw nibil airud cft, quam Verfus, Metri, fcu Rhythmi pars ccrto fyl- labarum numero arque ordinc dcfinita & ficutipaflus pedibus , ita metrum vo- Sdjfffi cibuslongis&brcuibusveJucipedibusmenfuratur.

w. e' MagnatamenintcrpcdesMufurgis& Poetis vfitatos diffcrcntia cft. Poetae cnirru* quaoutatcm lyllabarum in pcdibus mctro alicuidebitisexacliiis fcruant . Mulurgi vc- rovti&paul6autequoqucdnJtumcft,ad oranium fyllabarura corrcptioncm produ- clioncmque non rcfpiciuntded mediarum tanium fiuepcnultimarumiyllabarum qua- titaccmcum primisleruant;reliquas vcrbfyllabarumquantitates noncurant ,fiue cat longa: fint, fiue breucs. ita biflyllabarum pedcspronnicueprofponda»o,chorxo,Iam- bo, pytricAioaccipiuntMufurgijCumaudjtui in biiTyliabis h<-euicasauttarditas motiis

fit

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Lib.yill. MHfurgiaMmfca. si

(itjmperceptibilis? quis cnimauditu duos hofcc pcdts (Ponit&cpobtj quorum vnus cuoreus alter p\ rrkhius;difccraat Hum utcrque in Mufica atquali tcmpoi c pccjferatur. .

IntriiTyllabisvcropciiultima (yllabaiiue media tantum attendicurdMuiurgis >ita_i MololTus, Bachius, Anti^achius> Amphibrachyspro eodempede,cumspcnultimalon- gafit , attenditur . HaucTIcCus dactylus,'Trybrachysv,Anaperftus» Amphimacer, pro vno pcdc fumuntur , cuius penultima fiuc media breuis fit . Cuiufmodi lunt

pTctora, legtrcparwnt, tteidutfit. — _ . -t _ _

Pariiarioneintetrafyllabis nonnifi pcnuItimeTylltb? quantitas attenditura Mu- furgis,itadifpondc,usdichorcus, An«ipeftus,Ionicus<A minorc,pxon-tcrtius, & Epi-

rritusI.II.III.IV. veluti Or7torc7, comparare, eekbr7re, &Q.?afltm pio vno pcdc tecra-^ lyJIabo harmonico,(ruius penulrimalonga fit, uamuntur.ProcelcuImaclcus vcrojpcd- primus>pa?onfccundus, choriambus&fimilesquorum penultima fyllaba corripitur ,

vtiin hifccpatct regerercconcipircmiferu^parturiuntScc. pariterpro vno&eodempe- dcfumuntur . Qmsenimin hifce duobus pedibus Ora^rej & bonorati prima? iyila- ba; dirfercnrem quantitatemauditupcrcipiac?Vnde mirorcos, quiquanticatcmpcdu mctricorum pluszquofupcrftitiose" inmuficis adanimos concitandosadhibcndam_». cflc exiftimant^crtcquihapcpcniciusexpcndcritjviclcjbic in harrnonicupedibus nil nifipcnultimam fyllabarum obfcroandam . Reliqua vcrftomnla fuperflua elTc; fiue_j enim vt;mc cxcmplo dcclarem ,in fapphicis v. g. choraeum fiuciambum fiue pyrrichiu, fiuc fpondJEumponamjidemfcmperin muficislbnabit^ Vtin hoc inpphjet> p4tcr .

Ifte Confeffbr Domini facratus

P e Ccrfe/for deprecare Deum

Sancliu Confejfor Orateres audit . In hifcc folus primus vcrlus qui dcbitis fuis pcdibus conftat , pocticus eft i reJiqui vc- to duo Muficifunt nonferuantcspedum quantitatem,fcd Rhythmitantiim faltus fctv yant verfibus accomodatos. SeparacafylJabarura quantitatcpra;ter penultimam,qua: fcmper in hoc metroacccntumacutumpoftulat.

■ Hxc autem omnia dicla fint de vcr bis fiue polyfyllabis nullis metrorum Ic°ibus ad- ftriclisi vti fit, dum fupra aJiqucm cx Sacra Scriptura , vclfupra qucmcuque alium vcr- borum tcxtum foluta orationc modulos concinnamus i Nam vt pauloantc dixi foluta &numerofaorationonminus ad Rhythmicam pertincc, quamligaca, vt fit in mecris poeticis .

Si quis vcroharmoniam verfibus & metris iuxta profodix leges compofitis applicct . que madmodum nos in fequcntibus ex profeffo docemus, tanto opumcict abfolutius quanto carmcn fiue metrum fucrit artificiofius, & in faltibus cxaclius..

Vcr&m vtvideas, quomodo mctricos pedcsad harmonicos reducerc poffis,tibifin- gulospedcspoeticos, in notis harmonicis cxhibebimus, vbipnus ad mcjiorcm rcru dedarationcm quc^dam prxmiferimus.

Notandum igitur,quod ficutiapud Poctas vna tantum breuitatis & longitudinis fyl- labarum fpecics connderatur,ita apud Muficosplures pro varietate valoris 8c dimi- nutionis notarum : Exempligratia (pamar) fponda?us cft & apud Poctas fpecie vnus eft. apud Muficosveromultiplcxcflcppccft , cum omneshc. notxfequ.cutcsfponde.um cxprimerepoifint.

Yt Droindc vcl cx hoc vnico excmplo pateat, Muficam multd Poetica Jatius patcre, r maio-

— morcs

3* drtis Magn* Confini, & Difsoni

maioremquc habcre varictatem,& confequentcr maiorem in concitandis hominum_i affeftibus, cncrgam obtinerc . Vcrum paradigmata fingulorum dcmus .

Pedes foctici corrcj^ondemcs fcdibus barmonicis %

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.Atq; hi fiint pedes harmonici qui correfpondent pedibus metricis,in quibus hec cum primis obferuanda funt.

PRimd,Non omncs huiufmodi pcdcsaptoseffe pcdibus mctricis, nequc omncs cx- hiberipofle omnibus . Nara ii qms hunc pyrnchium ( Cyclus) pedibus harmon i- cis m quarta vel quinta colum na contcntis adhiberct , difficilem prorfus & iniucunda nonfinccxafpcrationcauriumproiationem caufaret; quod ordinarie occurritin bilTyl- Iabis in quibus frcquentesfuntconfonantcs . vcl in hiice bifTyllabis , conilans ,plenus> prorex ,portant ; & limilia quar vtitarditatem inpronunciandoamanr,itapedibusquo- quelongionbusrefponderc dcbent , cuiufmodiprima columnacontinet, contrain_» bifyllabis quar vocalibus abundanc, vti illar celcntatem amant, ita produclioribus quo- quc pcdibusharmonicis conftarc debent, vtiin hifce,%- , fuge , mala , & huiusgencris inhnita^.. °

Sccundo, Notandum hcc bifyllaba notis harmoniciscxprcfla vti tardiora,magis fpo- daicum grciTum iita celcnora magis pyrrichium amare . Chorseus vcro melius faciliuf- que duabus notispunaocollifis,expnmetur. vcletiamfyncopcprfrnifsi pausa, vtin_* fcquenticxemplo patct.

Surfum corda Licicuc

Aue Maris

lllicitus

Auc Maris Ljciioi

Iambusautem, vix in anabafifiue afcenfu tolerari poteft obaccentum grauem, quc inafccnfu, vltim? fyllaba? affingit, quo nihilinfulfius audiri poteft. Quis cnim non ridc- ret, fi quis hos duos iambos Auc maris bai yiona faccret. in quo tamf facpc noftrosMu- ficos impingcic rcpeno, pciTirnus in mufica accentus , cV fupra quam dici potcft abiur- dus. alis

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Lik.Flll. e^duJurgiaMirifca. jj

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Dc fcdibus harmonicis trisyllabis .

PRimd ,Triplex in trifyllabis pedibusharmonicisprogreflus confiderari poteft «W- /Het-ros lai&vm 8c v?»/S«to{. ProgrelTus anobatus cft, quando pcs mouctur furfum fiue id Hat pcr gradus , fiue per faltus. Ifobatos progreffus eft quando pcsxquo lupra_# cundcm gradum palTu mccdit. Katophatos cft, quando pes deorfum rel pcr gradus vel faltus mouetur, quae tripjex progrerfuum ratio tanti in metnca mufica momcnti eft , vt finc ijs nihil rccte in Mufurgiaconftituatur.vt in fequentibus vidcbitur. - Secundd, Arfeos&thefeosmaxima in trifyllabishabendaratioeft,quienimMolof- fum <p^S*v 3tnHncjpcrct> ridiculam prolationcfaceret;fccus fieretfi ^ra-ow eum proferret .

TertidjQuwfJaiu tnfyllabos pcdc» aptiores effe tcmpori pcrfc<fro,aIij temporiimper- fc«fto; qualcs vero hi fint pauld poft vidcbitur .

Quartd, Notaspuncto clifas multum facercin correptione voCum; Verum rem pro- pkis infpiciamus . Vt igitur folidius in noftra Mufurgia progrediamur ; pedes metricos pedibus harmonicis varijs modis accommodabimus, quibus vifis examinatifque,dein- de quis mcliormuficifque modulis aptiorfit decernemus.

Primo itaque confideranda cft in trifvllabis cumprimis raedia fyllaba , qua? vel brc- uis cft vel longa,intcr eos vero pcdes,quar mediam breucm habent cft.Daifylus,Tribra- (hys,AnapxJlus, Crct.cus quos & idcd roelobrachos vocat. Qua? vero media longa habct, h» lunt ; Aiolojfus, Bachius, Anttbachius, Amphibrachys; quos mefomacros ided vocamus; hos primo modoquidain itapedibusharmonjcisaccommodant , vt hifce figms quan- jtitaus n- <•» notjepcrfcftc refpondcant; vtkquitur.

TrisyUabifedcs quifecundam corrifiunt fiuc Mefobrachycs . Tribrachis Daclylus Anapajftus Crcticus

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Trisyllabi fedcs qui fecundam froducunt ftuc J^fejomacri . Moloflus Bachius Antibachius Amphibrachys

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8

Ecce hic eft modus quorundam,qui putant pedes metricos, ita modulis harmonicis adaptandoseffcvt fyllabarbrcues refpondeantnotisminoristeraporisjongc., maioris. Qyod cgo nulla ratione probo ; ingentcfquc in fyllabica harmonia crrores & ridiculas omnjno pronunciationes caulare poteft ; prefertim fi afcenfus defcenfufque notarum_

E nulia

Jj Artis Magmt Confom , & Difsoni

nullaratiohabeatur. F.t hocprimumoftendainpedibus, qui fecundam corripiunt ; Si enim quis hunc dactylum eurrere m.xta notasin $ & 4 columna. canundas cantando pronunciarct jisneceifario iccundam lyllabanu* natura brcuem longiufculam emceret , vt in exf- plo e latere apparet. qux rcs dici vix poteft>quan- tum afperitatisauribusadferat . Idcmdicendum eftde tribracho & Anapxfto> qui in omnibus.pa- fj Currere ricumdadrylopaflu proccdunt. Vnde vehemen- - « « ter miror, cur Meriennus pro daftyliciCantus paradigmate has notas propofuerit in_» harmon. Vniucrf.f0l.4Q 5»

Gaudia poftens gaudia poiteris j* r-

partant

Quis enim non vidctin hac daclylicapronunciationc mediam fempcrferc proferri longam cum maximo aurium cruciatu > quorum afpcritas tanto plus crcfcit> auanto notxfuerint tcmpons maioris>aut maionsfaltus . Eadem inconuenientiaacciditin-» Anapxfticicantuscxcmplo; Inquo fi quisanapc.ftos plurcs ordine iuxta notas ibidcm pofitas conferuaret, is fyllabicam cantus pronfi- ciationem faceret prorfus ridiculam » e tfi enim— fccundam breuiufculam pronunciarct, vltimam camen plusxquo acueret ,fingulifque Anapx- ftis in nne grauem acccntum affingeret > non fi- ne rifu auicultantium. vt in cxcmploapparet, vbi primusccfecundus pro^relTuSjgraui acccntu effcrtur, latinx pronunciationi inutilis. in tertio verd cxcmplo, ctii vitima non barytona fit > media tamen ob faltum producirur.

Ex quibusnifallor clariffimepatet, muficos modulos hacrationc mcthcis pedibus correfpondercnullarationc poflc,cumfic fumptiinflnitos folcecifmos in pronuncia- tionepariant. Quivcrof^liciter in hoc negotioprogredi volunt > fequenti mcthodofi- nem fuum confequentur.

Modus certus & aftifiimtis, quo metrici fedes harmonici , exaclef^ naturaliter fme fericulo fyllabica fronunciationis foloe- cifmoaccommodari fo/funt .

PRimoigitur notandum eft,nullam nosin triiyllabis primx Sc vltimc. iyllabx>fcd rae- dix tantum» fiuc ea corripiatur fiuc producatur , rationem haberc > ciim muficus progrcflus in trifyllabis medix tantum iyllabx quantitatcm ipcdtct. Provnoiojtur cVeodem pcdc fumi poflunt quatuor illi primi pedes , mefobracni, fiue quod idem eft, mediam breuem habentesj Tres enim hx notxindiffcrentesfunt,adquatuordi&ospedcs,fiue enimillisac- cSmode hxc vcrba facere,parcere&\xc h$c pariunt,comperunt. sepcr pro-

nunciatio quadrabit. Idem diccndumeft de quatuor pcdibus Mefo- macris> fiue media longa habetibus. Siue cnim hifce trious notis accd- mode bcc verba mefomacra comendans,laborans fiuc hcQjparataJLegin*

fcmper idem acccntus harmonicus pcrcipietur.

Notan-

Digitized by Googl

Ukrill. MufKpAMitificA. m

Uotzndumfecundo, Vt naturaJis fingulorum pcdum accentusferuetur,magnam ha- bcndam cflc rationcm aicenfus&defcenfusnotarfl.Sienim intrifyllabispedummefo- bracuorura fucritanobatusfiue afccnfiuusquacuraqi rationc fiue pcr gradusfiue per faltus, pronunciatio,non carcbitfollcecifmo;mcdiaenjm breuis hoc progreflu ncfcio, quam violentamproduftioncm caufabjt,quaetanto eritabfurdior,quanto fajtusfueric maior, vt in pratcedcnti cxcmplo patuit ? Contra progreiTuscatobatos fiue defcenGuus quacunquerationc corundempedumacccntum naturalem parict.

Tedum Mefohrac. progrefus illicittif. Pedum Mefokrachorum progreffuslicim,

liiliflipiiliiiiiigl

faccrc

fl faccre

Vbi vides Ifobaton arqualiter inccdcnte progreiTum tcncrc mcdium quafiarquali- wtis, a quo quantorcmorius reccdes, tanto pronunciationemfaciasimpcrfeftioreoi-.. itavt omnjumoptimus progreiTusfitifobatus.deindcillequiper gradus procedit,dc- indc quanto intcruallis conftitcrit maioribus,tant6 maiorcm vim auribus inferet .

In tniyllabis vero pedibus Mcfomacrisfiue mediam longam habentibus.progrciTus co ntrario modo fe babct . Nam Anobatus progrciTus naturalem acccntum quomodo-

4 Pedum Mefomacrorum progrefus illicitm .

ui cxemplo	Mtent.
•	Eorundem licitus 2

Defunclum phngebat Arater Arator

Oratar

Notandum Tertiu QuodficutiMefobrachorum pcdum quantitasbreuibus&femi- brcuibus notis non coftgruit, ita Mefomacrorumpedum quantitasnon bcne femimi- jnimis>pcjTimcfufisScfcinifufispropter naturalcm quandam atuT&avconucmt. Vcrum his itapramotatis iam rcgulas nonnullastrademus,quibusperfectum accentuta har- monicis modulis dare polfimus.

Regulal. Mefobrachi pedcs funt catobati vel ifobati ; Mcfomacri vcropedesfunt cotraanobati vcl ifobati. Mefobrachi pedcs commodc odttiibus poft minimas mi- roris valoris notisapplicantur,ob fimilirudine celeritatisinfitx . Mcfomacrivcrdom- nibus fcmiminimas prarccdetibusmaioris valoris notis 3pplican poflunt tam anobato , quam catobato progrciTu, ob rtaturale tarditatem , qux tam notis quara fyllabis incft .

Regub II. Pedcs mcfobrachi perfeclum & naturalcro accentum acquirunt , 11 media clidaturpunclo,qupd pundhim tantum potcft,vtin anobatoprogreiuicorreptioncnu-i mediar lyllabxialuct . Idem euenict , rlprima nota Mefobrachoru prarraifsa pausa fyn- copetur. Effectum tamen mcliorem habebit in catabafi, quam anabafi. Mefomacri tcro pedes perfeclum accentura acquircnti Siprimam notam prascciTcrit paufa fcmi- minima. Vcrum excmpla fingulorum dcmus.

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?6 Artis <&lagn* Confoni, & Bifjoni

'ProgrcJJus fedum Mcjobracborum fermisfi .

Parere facere condtunt partunt -^.

Oftirrue & ferficlis/sm* fronuncittionis funtbi, quorum media

eltdunturfunfio.

lEi!IiliiSiij|ilSai

facere parere condiunt pariunt

Quicunquc hr/tctrifyllabis Mcfobrachys vfus fuerit, is nullum -rnquam fcfolorcifrau commiflurum fibi pcrfuadcat .

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Pcdum Mejomaerorum frogreffusfcrmiffui 2

Progrcflus bonus Oftimus frogrcffus f$ fronunciationis ferfctlisfimat;

Sequetur Venator Capellam Saltante t> .-*- ii- *»■

In hoccxcmplo patet,quam medix concinnam pronunciationS acquirantpcr pau- fas & pcr fyncopcn_t . . .

Si veronotas prardiftasrcdcgcris in tempus perfcaura, prodibunt ni pcdcs alio mo-

donumens fuia conftante* .

Pcdcs Mejobracbi sccundum tcmfus ferfcclum . Boni Meliofei Optimi

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facere parium

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TriQyUdifedts Me/omacrt fecundum umfus fcrfittum .

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Scquetur Vcnator Capcllam Saltant?

Ia hoc cxcmplo vides huius gcncm tempusomne fere viciutn in fyllabarum pronu- ciatione tcgcrc . Vides igitur quinam potjflimum pedcs barmonici ad periectam enun- ciationcm aiTumi dcbcanr. quibus ita oftcnfis, iam ad tcti afyllabos progrcdiamur .

.11.

De fcdibus tetrasyUabiitfiuc quatmr syllabis conflantibus.

Pedes tcrraf) Uabi Pedesrerrafyllabi PeDuItima longa

Penultiraa breuii

Difpondarus Dichorarus Anripc.ftus Iunicus h minore Pxon tcrtius Epitritus primus u — Epitritustccundus — w Epitritusquartus jrrf

— — ~ — Oratoru

	U — U	dimicare
VJ	— « *■ w	amauere
U	U — « — -	iiauefaeli
u	J — u	celebrare

— reluclantes -• contulertmt v fortunata

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Diiambus Coriambus lonicus maior Paon primus Paoniecundus Paron quartus Epitntustcttius

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redimrre

rcfulferant

rtobilitas

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cfpiciw

doccbitur

calam tas

chmaueras

Eccc hi funt pedes quibus in mctris componcndis omnes Poctje vtuntur,quos qui- dam plus arquo fupcrftitiosd valori notarum applicant , Nam noris minimis pe- des longos,fcmiminimis brcuespcdcsapplicant quidam, fed qui in harmonicapronu- ciationc rifura vcnus > quam arTe&um concitarc potTcnt . Vndc iterum miror , cur Mcr- fennusccctcrumpcrfpicax.in fuatamen harmoma vniuerfali, hanc notarumcum rae- tricis pedibuscomparationcm eximium quid putat efie . Quisenim non ridcat ^huiul1- niodi harmonicam pronunciationcm , dum lonico maiori nasnotas Wtappiicaride- bere putat . ^

Miracula patrabitis S

Patet igitur in harmonicapronunciatione nullam I6gitudinis aut breuitatisfyllaba- rum,prxtcr foliuspenultima? fy!laba?,rationcm hab€dam cfle.Itavtomnesoftopau- 16 ante recenfiti pedcs pcnultimam producentes,pro vno & eodem harmonicopede-* fumipoffint. Itcrura oftopedcspenultimam corripientcs,proaliopcdcharmonicoac- cipi potTiint,adeoquc duo tantumfinttetrafyllabipcdcsharmonicij Vnus quipcnulti- mamcorripiat , alter qui producateandem . Quomodo verohipcdcsnotisapplicandi fint,rcftat inquircndum .

Pedespenultima longa tam anabato, quamcatabato aut ifobato progreiTu > harmo- nicam pronunciati oncm fuftincntivt in fequcnti cxemplo patct . ~

SS Artis Magtt* Cohsom , Diftoni

Pedes harmonict fenultimam longam habentes boni sunt (ffermisfi.

Oratores

Si verd nota? paufa pra?miiTa fyncopcntur, aut punclo elidantur, acquiren t pcrfecbra pronUnciationcm, vt in fcquenti cxcmplo patet .

. uifi» vV.>i£OiqtGo 'v^ti/- tti fr: « irtnttfio • in: .!»•.. ..i.-. «..-aoiriki

ffiV tetrasyllaborum fcnultimam longam habentium frocejpM, ofttmu* eft .

Oratons QiUbfari Wehclantts

*T etrasyllaborumfenultimalonga ficundum temftu ferficlum .

Oratoret

5?:

Vidcsigkur inhispaucisexcmplis,quararioncpcdesmctricipenuirima longa no- tis harmonicis adaptari debeant , vt perfeclam enunciationcrn obtiocant , ounc ad pc« desharmonicospcnultimamcorripkntesprogrediaraur .

Pedes tetrasjrllabi fenultima breuesnonfermittuntur, fifroccdant, ut sequitur . Processu* illtciti .

^Varturiunt '! :*-'. ' . !*»"•" . 1 V "> ^1^1^ ^

Si vero punSo elidantur , vclprasfixa paufa fyncopcntur , optimam perfeflamqu* cnunciationcmacquirunt, vt infequcntibuscxcmplrspatct.

Oftimifrogrcssus .

Parturiunt

Exem-

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L&.VIU. MlusurgU Mirifcd. Excmplumsecundumtempusperfcclum ,

Parrurionc >* t» " t- '""u.

Vidcs igitur ex hifcc exemplis, qua ratione harmonia pedibus mctricis adaptari dc- betjvc verba nairaonixaciommodatavenuftepronuncicntur.

C A P V T V. De var ictatc Me troru m .

MEt ru fiue verfus eft oratio cerro genere,numero 8c ordiae pedu no fine conccru alligata. Na verfus finc coccru nodiftinguererur afoJuta oratione,cu ea efle no poflicfinc aJicuo tandc numero,& ordinepedu.Et quemadmodu lincaex pu&ifluxu, & fupcrricies e lir.cc motu,&corpuscxfupcrficiciprodu&oncexurgit,ita &pescx lyl- laba & metrum cx pc d.bus conftituirur . Qui pedcs cum infinitam Iatitudinem habeae» infinitam qucque metrorum varieratera conftitucre poflunt . Quorum alij fumunt dc- nominationcmanumeropcdum. Quidam abexccflu&defcclu (yllabarura , nonnulli a pedibus, aJn a numero ftropharura, & membrorum, de quibus fingulisordinc . Vcr- fusa numcropedum inftiruti funtpIerumqueIambici&Trochaici,quorumpriraum_» cft dipodium fiueduorumpedum;NuJJum cnim metriminus haberc porcft duobuspe- dibus,aliasenim non metrum iedpesforet. Vnum igitur metrum dipodiumcft,Duo verd metra 4pedibus conftant, cuiufmodi funt verfus auos dimetros vocant,coftantq; quatuorpedibus. Sivcrdfcxpedibusconftctvcrfusaiiquistrimctcr,fiodotetramc- Qui pedet ter a Poetisdicitur. Quoniam nonnulh vcrfusperfyllabasquoquedenominant ,vt ab j^JSaf1 1 1 fyllabis,hcndecaiyIiabos vcrfus . Vcrum cum merra certo numero pedum nonita praecise menfurentur, vt in finc fubir.de ijsnon defit fyllaba, aut eadero abundet, hinc Poe tx verfus quibus in finc deeft fyllaba , vocant caraJcctos . quibus nihil deeft Acata- leclos vocant jquibus vero in rincabundat iyllaba , verfus hypercaraleclos appdlant ; Si vcro defueric ijs in finc pcs integer bibracbi catale&i dicuntur . atque haec eft prima vcrfuumatquc fimplcxdimcnfio. Secundaconfiderarmultitudinem metrorum,quas Qu;<jdjftro. odasvocant. quaeficarcatftrophis, dicetur Monoftropha ,id eftcuius ftropha vnico phos dko. verfu abfoluitur; Sivero ftropru duobus vcrfibusabfoIuarur> diftrophos;cuius rribus, lot* triftropbos , cuius quatuor , tenaftrcphosappellatur . Vel ratione diuerfitatis merrorfi ditiifio metrorumconfideraripoteft , fi emmftropha duobus vcrfuum geocribus ab- foluaturj^wXovid cft, duobus metris heterogeneis, fi tribus, cricttlon» u 4 cecracodon dicetur, Potcft igitur efle vt tetraftrophon fit dicolon,vt fit in fapphicis, qux tribus vcr- fibus conftant fimilibus, & vnovidelicct Adoniodilfimili.

Atquc ex hifcc luculcnter paict, innumcra verfuum gcnera eflc , qu^ omnia hoc Io^ co oftcndcrem, nifi hanc Pocticam Arfi noftr? combinatoria; referuaflem, ibi cnim fii- «e dc hifcc agctur. Quarc ad inftitnti noftri propria rcuertamur .

De Metris immutabdtfcdum quantitdte contlantihtui

SVnt prxterea aliqna mctra, qux variospedes admittut, id eft, qui non habcntcer- tam&fixam pedumftationcm,vtifunt Hexametra, Penrametra,Anap?ftica,H5- dccafyllaba,Alcaica, Choriambica. & alia huius farinar, dc quibus profodiographosco- fulc , Alia vero e contra funt qux ccrtam & immutabilcm pcdum ftationem feruant . Suntquefcqucntia. lAdo-

4* Attii Mdgn* Confitii 3 & Difsoni

1 Adonium-, quod fempcr in principio daftyjo & Tpond.ro conftat,

2 Glyconicum, pf imo loco fcmpw fpondaro & choraro, dcinde duobus daclylis con-

. 3 Alcaicum dactylicum quod conftat fpondao, Umbo & caefura longi, deinde duo- busdaclylrs. f Vldfs vt alta ffct niut candidum . SZ'..ZZ~.-.S~

4 AfclcptacLtum choriambicuni conftans fpondco , daftylo, carfura longa & duobus da<clylis . [MtceH.isAtauiscdittrtgibus.j1 ' 5 /^m5/c»OTF«r^i<«mcfttnbusiambisconitans,potcft tamcntcrtiolococtianu* admitrere ipondaeum & pyrrichium vt f Aut niaris Sttlla . ]

6 Anacrtomticum eft tribus iambis & lyllaba conftans ^ vt [ Roris vt fat bibifii dulci ci~ cadacantucampos rcpltsamanos.] «. V I £\. d

7 Ven\quc lambtcum Arcbibcbicum ,tiiit\c2ialc&iim quam hypcrcataJeclum [Dtut pottattr aflra t't prifca gcns mortakum . ]

Hifccacccdunt Phalcucium, hcndccaiyllabunij&fapphicura. Atque hxc mctra oniniuaptifnmafuntmodulisharmonicis,cumnumeri intjsmi*- fatithmis contcnti , ilji pcrpctud &finc crrorc applicari polfint . Vt pofteavidcbimus."

. uxufti:'. .V. canil f< j m ,".r> :J.f»b xiovi>»r> £;aryptJ0 }.> t«l«i/prtv»i!& rTVvjj

C A P V T VI.

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De Applicationc poetica metrica?,feu Rhythmica ad poefin harmonicam .

. ttx *] j/|i j( » j j ; iJtOfJO * OllJafw^oT lCf ' j)n '1*1 I 1 m tl *1 14' 'J4l 5 II I ' l'rt ' llft t IffT I) L> - I )i O il ' • f ils

IN prcecdenribusfusc declaratum eft in poetica harmonia , non precise Ipeftari fyl- labarum quantitatem,fcdaccentustanrumrationemhaberi> qui potiifimum m_» media aut pcnultima vocum fyllaba cluccfcit. Vcrum vtMufica? etiamquantumuisim- perituspantcr tamen omnis gcncrismctrain harmonicos concentusanimarc poflit» hic pnmo dcclaranda funtmctrahuic negotiopotitfimum apta& idonca. Namvtfu- praquoque diftumeft, non omnia carminaaptafunt harmonicis modulis,fcd catan- tiim quc, certam & immutabilem pedum ftationcru obtincnr, Qucmadmodura funt A- donia,Glyconica,quxdam Iambica, Phaleucjum , Sapphicum,& alia huius gcnerisi Hcxamctra enim c\'pentamctra, Anaparftica cum variam pcdum miftioncm fortiantur, &fi dairylum cum ipondjto in h*ne hcxamerrieximas,in rcliquis locis nullibi fixuai-» pcdem habeant; hinc fit , vt modulis quoquc harmon icis , non ira facilc accommodari polfint, nifi quiipiam eundcm perpetuo pcdum tenorem ieruarer, quod tamen dirrici- le negotium foret. Hcxamctra itaque & pentamctra fimiliaque inftabiiium pedum mc- tra non profodia? harmonic^ fed Rhetonca: fiuc folutx orationis numeris adfcnbenda cenfcmus,qua; quomodo muficis modulisaccommodandallnt, paulopoft apparcbit.

De Carmine Adonio fentasyllabo .

QVamuis in rigore Ioquendo, ex duobus Iambis, Chorcjs, Pyrrichijs>& Spondcis compofitavox mctrura dicipoffit, vtpote plunbusquam vno ,pedibuscon- ftans, quia tamen numerustetraiyllabus ob temporis breuitatcraaurcs clu- densfacileeuancfcit, neque vfque adeo motusproportionem exhibct . idcoa Poctis tanquam metrice, ineptusrojcitur . Nullum igitur tctraiyllabum propiie mctrumdici dcbct . Metrorum igitur primum mcrito pentalyllabum clti hoc cnim pcnt3iyllabum_i > prima & hefcio quam gratam motus proportionc auribusexhibet.cuiufmodi funt pcn- tafyllaba,Adonianuncupata,c6ftantq,duobuspcdibusdac1ty'lo&fpond$o,vt fcquitur.

l

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i tit VI 1 L M ufurgiaMirtfica * . ^

i Nubibus atris Mentis acumtn MctrometrjAdonijCatrainis

Vf Conditanullum . Ingeniique Terapusimpcrfeclum .

Fundert pojfunt Impcdit atrox ° t V ° °

Sydtra{umcn Soljicituao YtT?f

Oftendimus iammctri Adomjqualitatcmcondirio-; ,. fttff

ncmquc, modd Adonij raetrometri rationem cxplica- /? °f ° °

re nobisincumbit} fic cnim impofterum non pcdes ta- u-°fT0,° riimmctricos, fed &omnis gcneris metra,queisMu- ^fttff furgica metra apoericis diftinguarnus, appellabimus . T t t T t

Dum igitur dicimus Adonium Mufurgicum [Metro- Tcmpusperrcclura. mctrum] Glyconicum Mufurgicum,Iambicum Mufur- , J ° ° ° a ° gicum, & flc de coeteris , notas intclligimus mctromc- t°°oae* tras , accentibus mctrorum pocticorura rcfpondcntcs ,i°?y01" fiu e quc, carmcn ipfum mctiantur . H* cmm not* ap- 1 0,0 ° 6 *•

plicatorvcrbisalicuiusmetriilludperfcvK' tum quoad

xcmfuisjtum quoad acccntum menlurabunt: cuiulmodi hic pofu.imus. 1 1 Adonia Mu- furgica notis mctromctris cxprefTa , qux omnibus &fTngulis Adonijs pro materia ver- ^omraqueconditionc pulchrc appIicaripotcrunt.vtvcJhinc CuriofeLcftoradmiran- dam in lurraonicis varietatcm diicas . Si enim vnum tx his 5;4iotarum Adonijs fccu- dum diuerfumvaloremvariccombinesDrodibuntx56.mutationes, qua-prjecise fieri poffiint, ctiamfi ftarum & &umn^M^nnHltcs, ^^c* iupr^ inMufurgiacprabi-

natoria deraonftratummit,aded vt vnum adonium metricum 2y6 diucrfis adonijs Mu- furgicisexprimipoffit. Nos tamenhicex 256. duodecim tantum magisidonca fejegi- muii qui' abundctfymphoniurgofufficicnt , ad adonia mctrica qualiacunque exprirnc- da . Pofuimus auttm 8. adonia MufurgJcd tcmporis irnperfedti , Se 4 temporis pcrfcclt, vt ad beneplaciturn ijs vtipofTrtMufurgus . Verumdc cxplicationchorum fuse in fe- quent.bus. * latu^m

Ad Adonia Prirho reuocari pofliint Iambica Anftophanica, qua; ct(i duobus iambis conftent , & vn.i in/ine adiecla fyllaba, quiatamen primxtrcsfyllabar dadylum har- monicum exprimuot, pro adonijsMufurgicis vfurparipoflunt. vtfequentes verfus.

Tluit/slenti \ j Paratanobis j

V-iUcsper imas ^ v^r^rnenf^s^^ ^ Q GrMaMetaurus ^^/>^A^%^vO Nec»onfufm^ , , Mmajinbi., , ,Vl [ «J^, . v m^nru* . Caducatcmms.

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e ziriqo-ift 2ilu*>n

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X cura kx iylJMutumrAer/uuta^itur dactylic^ujq giya ton- >UUa? »Tol '« --ftardiiobus daclylalrE^que a^^M^irwraA^Wyi^hiWjn^Jiruiu^y • ^

norbcupinno inuenctk. Si enimin Adonio fpodaqm mutcs m ^t(T T T.'T ?."

dac^t) lumjhabcbis daclylicum. in Muf^rj^j^go j^^nt^^ ttt&X&Wi£y>ii

notamdupliccs, habebisMufurgicadaciylicaSvtnicappaictin 1 ^fltfT

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Sccundoloco (<<^uicur larabicumEuripcdcutru. Mctromctri Iambici Euripidxi pari rationc hetfafyllabon ,ied aprxcedenti ditiert > quod dactylicum duobus conftet dadjylis,hoctnbus iainbis,cuiufm©di eft vulgauffimus ilic EtcJcfiaiti. cus hyranus «

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Febxcaebporta. Eftquehoc mctri genus vt plurimum tetraftropho monocolonvt m exemplopatet.

HifcecorrcfpondenuaMufurgica Iambica appofui- mus, qux mctns diitisapplicata, caperfectc mcnfurat: tum quoadtcmpustumquoadacccntum .Suntautcm vt in praccdcntibus i a. cjuorum vnumquodque fingu- lis fttcphisaccommodanpoteft . V. g. vtbarmoniaxqualiorfitfingulis 4 ftrophisvnu e^hilcciiheftafyllabis mufurgicis lambicisapplicabis, vtin fcquentibusfufiusoftcn-

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Exhifce duodecim Anacreonticrsbarmonicisquodlibct,fIngulis ftrophis accom- modaripoteft; Cum vcropofteriusanapjftumin principio ftropharum habeat; habe- bisMuiurgicaAnacreonticaanap^ftic3,fipriorcstiot3s in fingulis pcntafyllabis in_* duaspriOrixqualesdiuidas.vttncxcmpIoappofitopatet,vbividcsnotas fingulasprio- resinduascquiualcntes diuilas,vtahacreonticum anap;fticumhabeas& quamuis a~ napc&cum O&ofyllabura fit, idem tamcncum Anactconticoheptafyllaboeft fiut-» accentum fpcftes, fiuc temporisprolauoncm-* .

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Lib.PlIl. Mu/urpaMiri/Tcs: 4$

NotaMetroractrar

§T V Iambici Archiiochii

De Iambico Archilocbio mctro oftosyllabo. ? 0 ? 0 ? rf ?

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POft hcptafyllabum mctrum fcquitur oclofyllabon , cantatifli- f YTtTT T* mumquccarminisgenuseft,itavtvix hymnusin Brcuiario fttt*f ?'f? Romano occurrat ,qui non hocgenerecarminisconftet,eftenim_* ©j j ©©o.©©. ftquod aliud Mufius modulis cumprimis congruum,Huiusgenc- ~ffy?©o©© ris funt hymni . Vexitta regis prodeunt . ^TTTTtft0

Vtni Creatcr Spiritus . Et iilud 1 o o © B o a 00. ,

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Muficenotx hisaccommodandrthicapponunrur ; & cum hu- iufinodimctrum vtplurimum tctxaftrophon llc vnumcxhifccia mctrometrisMufur- gicis finguJjsapplicaripotcrit.

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Iambici Archilochij

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IArabicum Archilochium diractrum hyper cataledhim eft Ennea- T 1 1 1 Tf*t?° fvUabum,cuiufmodi cx tctraftrophis Horatianis tcrtiura q uod- °'f f f f f f ° ° */ <»••<« °*t 1 090000

que metrum cft, vidchcct . • « « J

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lambicumdimctrum Alcaicum cft. vt i «000000«.«.

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Vtriufquemctrurn notismctromctrisMufurgicis ijfdem menfu- l ratur, vt patet in appofito Paradigmatc .

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JD<r metro decafyllabo .

Ambicum Alcmanium trimetrum . cataleCtum dccafyiubum cft,cuiufinodi eftle-

qucnsverfus: . .

Spernts decoros Vtrgints tboros . Vcriim cumiftiufmodicarmen variara mifturamfortiatur, &pedem plus a-quorao- bilem habcat,idcoilludccu minus pocfiharmonicaeaptum rcijcimus. Si quistamen ijs vti vcllet,ismcnfaramvcrfushicpaul6antcpofitipcrpetu6»iimmu- tabili paifti fcruarc dcberet . Quod fi ficret , tunc lilius mctri gcncris °??????ff° fyllabis nulloncgotiopraeccdentcs notas mctroractras applicarcj oc,?c,fTTtr poterit , fi penultimam notamin duas diuif^ zquiualentcs notas I tt 1 1 1 tt f t diuiferit .

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Artis oflddgn* Conjdni, & DiJJbni

- _ NotxMctrometrx

§. VII. Phakucij.

Z> metro hcndecafyllabo, Phaleucio,Safphico, Alcaico l U^V^ tV? ~ daclyltco vulgo H oratiano . ? T T ? ? T T T T ? ?

T TEndccafyllabum menum varium cft, nos ex multistriafek- JJJj^JiJJ?^ XI gimus harmonix magis apta. quorum prius Phaleucium eft . ?T T T T TT T T ? - Eftautcrn hocobfrequentcs chorc,os, harmonix maxime a^turn-.. ?T'tT*t T't '" ^ Imd Itali vix alio magis frcqucnti in poefi fua carminis gencrc vtun- °?*T ?*T ?*T ? ? ^ turjvt cuinullum magis harroonicis modulisaptumfit. cuiad per- £TTT T* T T ?T _s fedlam harmoniam conftituendamadiungcrc, vtplurimum folerjt , ^«««•■* Anacreonticum heptafyllabum. vt in fcquentibus videbirur . Jioecflooo <*> B B.

Quicunque igitur hoc gencre metri muficam poefin adaptare de- i |ao»oce:o n.o n a. fiderat, isprimd quantum ftcri poteft, curct , vt phalcucia fint pura, &frequentibus chore> conftent, reieais da<ftylis , anapxftis & tnbrachis , habebitque facileintcntura. Notx Metrometrxe regioncappofitx vidcntur , quatum vnamqua- que ex « vnicuiqueexphaleucijsapplicare potcris ,

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ncum metrum ,

Ltcrum Hcndccafyllabum Sapphkum eft , vulgatiflimum carroen , vt plurimurn_, triftrophon dicolon, id eft tnbus conftansftrophis, quibus in fineadneCtitur a- donium . aiquc adcoaduabusdiuerfisfpecicbusmetriidconftirucntibusdicolon d> flura. hoc prxcedcnti minime ccdit aptitudinc ad preftantuTimas harmcnias eflormanr das . Habct Cfiim abditam quandam in fe hoc metri genus harmoniam ita efhcaccm , vt vix aliter id ac per cantumfcanderc foleant Tyrones poefios ; marofeftum iignum_, maximx ciufdem cum MuficacognationisamnitatifquCidiffert a priorihendccafyllabophalcucio» quod illud chorcjs puris prcter MetvcmctraSap- chorxos Iambofque, hoc dactylis& anapxftis quoquc conftct . E^^^STi Huiufmodifuntin Breuiario Komano Hymnus : '"'^ ^ oo

IJeConfeJforDominicolentes,Scc. °??00??f? HymnusquoqueinfeftoS.IoannisBaptiftcrecirarifolitus. ??T ??J TTT ??

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FamofuTimum fanc mctrum, cuius occafionc Guido Arctinus jtli T?TYfTT?i Muficam figuratam inuenit, vtifuse" in prxcedentibus libris often- £ \ \ \ J \l la CBYtt. fumfuit. Notxmetrometrxhicapponuntur. i,BOoooo.Yoc««.

Nota hoc loco notas mctroractras prxcedentis Phaleucij Sap- i joc 0B 0 0 1 c oa B. phicisjvti & Saphica phaleucijs accommodari finc fcrupulo pofTc^. * 1 Adonij verotriftrophoannecledi notas mctroraetras dcfumcsex S.l."h*uius.

Ad explicaca hendecafyllabaiurc acccdere poteft Iambicum Hypponaftcum cuiuf- modi cft iliud .

Ternos vetufti Congios falerni Haufitpotentum Romuli nepotum Regnator audaX arbiterque Regu/n, &c.

Ter-

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*

Li&.Vlll. MuJurgiaMirifica: 4?

Tcrtium Hcndccafyllabum Alcaicum daclylicum eft vul- Mctrometra hendeca-

go Horatianum , co quod Horatius nulJo carmjnis genc- Jyllabi Horanani.-

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§. VIII.

De metro dodecasyllabo ,

Odecafyllabum mctrum Afclapiadxum Choriambicum ficqucntibus incedit clioriambis,cuiufmodi eft fequens illud Horatij :

Meeotnas Atauis cdtte regibus ° t V ?'T ° ?"t t T* t ?

Quodfimc Ljncis vatibus inferit VT TTT? °* TT T*t °

ibmiferiam xerticc/idera . C'T*T??° ? TTTT?

Huius notx metrornctrx eardcra funt cum prxcedencis hen- ?'t t T T ?~ ° ? T °* ? ° deca!yll3bi mctrometris, v ttamcn dodccafyllabon fiat,quarta_» • ?°???0£?tt?*t° nota in omnibusprxcedentibusmetromctris diuidenda cftin_# ^ttt TT ?T*t?I*t° duasdiuif5a?quales,& habebisnotasmctromctrasproAfclepia- ?ttttTTT?T*t? dcochoriamb.co quxfitas, vt in excmpJo paret . T T ? ? *? 1 1 T* t °

Porroquicquidvltra nfyllabas cxcurrit metrorum, id totQ 000000 °.©o©. 0© expraEcedentibus velcompofitumeft, veltantarapcdum varic- °????B 000 00°* tatc m obtmet v t Muficx pocfi difttcultcr feruirc pofllit vti Hexa- °* 0 0 ? ? " °* ? 0 °* ? 0 metia,pcntamctra,&muJta alia Lyricigcneris, qux confultd omittimus j Si quis tamen ea componerc defideraret , cum vti diftum eft , vnum fem- pcr pcdum tcnorcm lcruare oporterct ,• Vcrum visa natura verfuum muficx idoneo- rum,nihil rcftat nifi, vtaliquam hic quoquc compofitionis eorundcm combinarjoncm inftituamus.

SiitaqucSpondxumprefixcrisAdonio, habcbiscarmenpherecratium. Si fpond^um iterumprarixcris Adonio daclylico,habcbisGlyconicummetrum. Si huiccidcrafpond^oprarfixcrisjnafcctur Iambicum Anacreonticum . S 1 duo Adonia fimul lunxcris nafcctur Anaparfticum . Si duo AdoniadaftvIicafimuliunxeris,habebis Alclepiad^um choriambicum . Si Ad onio adiunxcris adonium daclylicum,habcbis Alcmanictim dadylicum fiuc-j Horatianunru/.

^ Sivero Anacronticoprxfigasfpondxum, habcbistertium metrumid eft Horatianu, fiue lambicum Archilochium .

Spondxus prxfixus Anacrontico generat Iambicum AIcmanicum_».

Idem pr^fixus lambico Archilochiogcncrat phaicuciumhendecafyllabum.

Vides itaquc quod vti pcs pedi, ita carmcn carmini addirum , aliud fempcr generet, quod negotium cum infinitx propc combinationis fit, vltcrius non producendum, fed curiofiLcctonsconfidcrationireJinqucndumduxi. Quxcunque autem hic diximus de notis cantiim mctromctris intclligenda funt. Veriim dehifcc fufiiis in ipfa praclica corapofitionc-/.

MVSVR-

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Jrtis Magn* Confoni, & Difsoni

MVSVRGIAE MIRIFICAE

P A R S 1 1 1

MVSARITHMORVM M ELOTH ETICORVM PRAXIN EXHIBENS.

C A P V T I.

De fcopo& inftituto Authoris .

; Vm in prxcedentibus mcthodum nos fnditurospromiferimus ,qua vnuf- quifquc ctiam Muficat impcritus ,ad p< rfcdtam componcndi notitiam^ pcruc nircpoflit,hoc loco promiffa foluerc voluimus vbi prius,in quo in- uentumnoftrumconfiftar,expJicaucrimus.

Cum frequcnti cxpcrimcnto doclior > vnum in omnibus & omnia in_* vnum a dinira bili quadam rationc contincri obferuaremi id eft in omni- busfcientijs & facultatibus vnum aliquod principium> ad quod fccundum anaJogianu* quandam rcliquaomnia rcuocarcntur,fagaciusperfpexiffem ;illa verdfine perfcctaco- binarionumfcicntjapertraftari nonpoffentj Artcm combinatoriam condidi inqui In omnibuJ mentis mcar fcnfa cxhibcns , omnium fcicntiarum principia , ita pcr varia orchemata_,> fcientijsda- oa,hsrepra;fentaui > vtnihilfacdiusvideripoffet > quameorum opebrcui tempore ad Upiie" exa&am rcrum omnium notitiam pcruenirc : Cum vcro tam mirabUcm combinarionis damcntum. rerum vim vtiin alijsomnibusiitapotiffimuminMuficarepcrcrim; Nihilaliud defidc- rari vidcbatur,nifi vt principia Muficx in prcccdentibus ftifius cxplicata,hic in metho- dicas tabulas, quas Mufarirhmos,fiuc harmonicos numcros intitulamus, redigereraus, quod vtianimoconceptum>ita protinuscxecutioni mandatumfuit.

Nc vero quicquam in Mufica cffct,quod ctiam J/*w»v ideft Muficc. imperitum later tt; Triatabulatum jyntagmatacondidimusin quibusper complurcsPinaccsmclotheticos quicquid in vniuerfa Mufica mel«h,etka , fiue compofitoria rarum & cgrcgium effct > c6drdine,&mcthodoiquaefequitur,digeflimus. Ordo Tabu. frimum Syntagfhs, continetdeccmpinaccs fiue tabulas quibus vniucrfam Mufurgia" larum con" poetkam fiue mctricam cxhibcmus, ita vt dato quouis verlus gcnerc fupcr eoquacu- flruclarum-, pctitaratione melodiam componerc poflis.

Tumcopoffl Pi«4Ar/.cxhibetnobisMufarithmospedumpolyfyllaborum, a byfyllabis vfque ad «one . heptafyllabos pcdes;comprchcndimus autcm in hoc Pipace tantum polyfyllabos,quo- rum pcnultimalongaeft, vt ipfa tabulx frons dcnionftrat ; in calce vcrd columnarum_« pofitq funt notoe metrometre, pcdcs datos mcnfurantcs.

pindH ff. cvmbct nobisMularithmospcdum pol)fylIaborum vna cum notis mc- tromctris vnicuique correfpondentibus, quorum penultima brcuis eft.

PinaxIII. exhibct nobisMufarithmos promctris Adonijs,dacrylicis > & quorunu» for me fu nt t Gaadia mundi, Toliite lumina .

Pinax IV. Mufarithmospro IambicisEuripcdc.is & dadrylicis exhibet,cuiusforma cft decantatiflimus ille hymnus Aue maris Jlella , pro tali ergo vcrfu nullo negotio . ope_^ huius tabuljB defidcratam mclodiam perficies i rcliqua minutiora tabulae iuis locis cx- plfcabuntur.

"^Ptifiwrff.exhibetMufarithmospro mctris Anacreonticis quorum forma eft, Oter qnaterguefelix, vnacumnorismetromctris vnicuiquc corrcfpondcntibus , in calce co- lumnarum adie&is.

Pm^r/.cxhibetMufarithmos prolambicis Archilochicis o&ofyllabis; quorum-.

quorum

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i

Lib.FllI. MufurpaMirifca. 4t

quorum fbrma t^VtniCrtatorStiritus ,pofuimusautem eos in quituor eolumnis vni cum tetraftrophisid eft pcr toticfem ftropbas vnacum notismcrroraetriscorrclpondc- tibus vnicuiquc.

PinaxVII. continctMufarithmospro IambicisArchilochicis cnneafyllabis,quora fbrma eft > Amant •vtntnaparricid* > ordinauimus autem cos in quatuor columnis tcra- ftrophis iuxta quatucr ftrophas, vna cum notis mctromctris corrcipondcntibus vnicni- que vti tabulf monftrant.

PmaxVIII. continctMufarithmospro metrisdecafyllabis, quorumforma eft ver- fus llle Prudcntij : Magnt Crtator rtrum cm»///miiuxtacolumnas tetraftrophas,& notas metromctras in calcc adicclas, difpofitos .

P inaxIX. continet Mufarithmospro metrisHendccafyllabis fiue Phaleucijs , quoru forma eft, 0 Virgo gloriof* Mattr Dti: iuxta columnas tctraftrophas vna cum notis mc- trometris in calceadicltis difpofiros .

Pinax X. continet Mufarithmospro roetris fapphicis , iuxta columnas tetraftrophas vni cum notismctromctris ordinc difpofiros.

Pinax XI conrinct Mufarithmos pro metris Afclepiadcis Choriambids dodecafyUa- bis , q uorum forma cft . Mecanas atauis editt regibus, mxta columnas tetraftrophas ordi- nevna cum notis metromctris, dtfpofitos .

Syntagmafecundumy continet VI.Pinaccs,quibus Mufurgiampocticam fiuc metrica syou„ u. Mularithrais floridis & artjficiofis exhibcmus.

Pinax I . continet Mufarithmos pro metris Adonijs & da&ylicis, florido & artificiofo vocum progrcflu , vna cum notis mctromctris vnicuiquc Mufarithmo anncxis , difpo- fitos.

PinaxII. continctMufarithmosprometris IambicisEuripedaMs,HcaafyIlabis,flo- rido &a.tificiofovocumprogreflu ,vnacumnotis metromctris finguhs Mufarithmis annexis, di.pofitos.

Pinax II I.contiact Mufarithmospro metris AnacreonticisHeptafyllabis,florido& Irtificiofo vocum progrcflu pcr notas metrometrasvnicuiquc annexas, difpofitos.

Phtax IV. continetMufarithmospro metris Iarabicis Archilochicis ocWyllabis, flo- rido & artificiofo vocum incquali progreflu pcr notas vnicuique annexas, dilpofitos.

^MAvP.continctMufari thmospro mctns Enneafyllabis &decafyUabisflorido&ar- tificiofo vocum progr JIu diipofitos .

PinaX VI. continctMufanthmosprometrisSapphicis & Phalcucijs hendecafyllabis, florido & artiflciofo ftylo per notas mctromctras vnicuique annexas difpofitos .

Syntagmattrtiumyconunct[cx Pinaccs,quod tamen hoc in opere omittcndum duxi- musobrationespofteafuolocoapcriendasi non tanrum Mufurgixpoetic$fcd&Rhe- SfnMg.DI- torica?accommodatos,quibuspcr fyncopationemfiucligaturarumjanificiofumque,-* figurarum progrcflum, oranem Muuca» gratiam exprimimus .

Pinax I. continct Mufarithmos pcdum polyfyllaborura , quibus fingulis fcrc notas mctrometras annexuimus.

Pinax II. continetprardictorumpcdumMufarithmos. / "< rr:cur>.m<::> « ^f

Pinax III. continct Mufarithmos fyncopationum,& Iigaturaru variarum magifque principaJium, atque ad affectus concirandos aptioru m .

?/»4^//V.continetMufarithmosfugarumaitificiofarum quibusinitiumahcuius ca- tilenx infiitui artificiosc poteft .

?j»4xr.continetMufarithmosPolyphonorum,idcftproMeIothcfTapJuribus,quim quatuorvocibusinftitucnda.

Pinax P/.continetMufarithmos melotheticostamftylorecitatiuoquam comico , theatraiique accommodatos,prctcrca chromatico, enarmonicoque ftylo muficarcom» ponendarrationcmcontinentes. «

Atquehifcctribusfyntagmatisquicquid in vniuerfaMufica rarum ,elcgans,pulchru &affcftuofum mcrito comprchendimusjvt in progrcffu opcris Lector cum admiratione vidcbit. * Confi-

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Artts Magn* ConJum \ $ Dijfont

Coniuliraurcm bcc noua noftra Mufurgia poti&mum in ai titiaofa eaJumnai u*n m c In qflo con- 1'otaclicarum compofitionccxquaquomodolibetfjcta n,ccc|fand Jcmpcr noua rciuitft hsl"co^npo'- bitharmonia, ita vtcumcompofirioneshutufmodi fint infinitc , infinita, quoquc h-ir-- nondiraco . rnonicarum vaiiationum diueifitas nafcatur v.g.pnmipinatiscombinationes tantc spt> vttotos mundusatcrra vfquc ad firmamentum facilius arena replcri poflit > quauuli- uerfitas harmoniarum indc relultantium cxhaurui. imd fi omncs Scriptorcs totius mu- diaborbc codito ferhper huiufmodiharmonicaru corabinationum defcriptioni incu- buiffcnt, nccduracastaxi^cncxhaufiircntiVerura harc folus numeiorum n.yltciiji ucr butisciim notafint,amplius illa profcqui nolo,pr*fertim aimhc.c in prima huiuslibri partc fuse demonftrauerimusi qu$ ctiara hic addcre volui,vt quorundam Muficoi um_» praclicorummalcdicentiamcompcfcam»quiftatira hifce vifisobijciunt Muficam fc^m- pcrcandem prodirc. Verumhorum ignorantiam nonmoramur , vcritatcm ipia do- ccbit cxpcricntia. Quicumquc igitur columnas hafce in mobiles tcficllas artiriciosc: iuxta regulas in quarta partc buius prc,lcribcndas adaptare , & numeros harmo» nicos in fcalam mclotaclicam rite transferrc noucrit, is quoquc tonoquocunvquc da- to & quibufcumque vcibis datis quofcumquc artificiofos modulos fc nonerit compo- fiturum,ita vt qucmadmodum in Algebra logifta reguJa: tcnprcm feclando pa,ra doxa- rum queftionum elucidationes pcrficit, ca faciJitatc , vt opcransiple, quid fcccrit , nc- fciat,adeoquc inexfpeclatus efle&us logifta vix cogitantc producuur , ua hic rc ■gubru cenorem fectantibus Melothetis ctiam a>b'«ic , deiidcrata tamcn Jiai monia prodibit . Verum nc dintiiis auidura Leclorcm fufpcndamus, iam ad artificij noftnMufurgia . r- canapropius acccdamus .

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CVm omnis fcicntia mathcmaticapotiusindemonflrationc ad vcriratcminucoic». dam,quam invago multifquc opinionum obicuritatibus obnoxiodijputiut <>c- ncrc coniiftat > addemonftiationes meliiispercipicndasfcnfibiJibus eas figttjsrepi^sc- tarc neceflarium tuiti Hinc punfta,fuperficies,corpora, numcros auoiquc chara6tcr« infinitos rcpercxantprim^uc fapienti^Magiftri ,quibusin charraxlipiciis ,fef\ia mettis rerumq*, conccptarum fignihcationcm prodcrcnt . Haud ablimili rationc Mufurgi , ad rcdacendasinatSum fpeculationes demonftrationefque fcnfibus oggcrcndas, figra_* quc; dam inucncru nt, quibus foni coeteroquin imperccptibiles vifibilium fignarum po- iiaoneinootcfcerent. Hos noslccutud Ipeculationes noftrasin praxin dcduccndas _ primoordinamusPalimpfeftumphonouclicum. Eftautem Palimplcftus niJiil aiiud ^fluj . m' quim coriacea illa cx afinina pcllc confeda membrana, qua pugillarcs fiuc fcriptonj li- belli paflimcoficiuntur,&qua moderni Mufici vt piuriraum prae cceteris omnibushuic ncgotioaptiflimavtifolcnt i In haccnim vtfaciie fcribitur, itaiicriptaiaciic delcntur .

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Phonotaclicum veroappellamusquod vocesfingulac in eaper fuapentagrammaf1 itaJ cnim vocamus penrades illas lineares,quibus nota* muficae ad interualla harmonica_, indicanda inferuntur) per fcaJas,claucfquc vnicuiquevoci conuenicntesadaptantur ,

Cantus duru« fiue naturalis . Cantus moJlis flue fiftus .

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fcala* mufi- entagrammo

Bafisponiturvelinmcdialincavelin quarta vel' iu quinta. Intranfponendiscantio«' nibus vt plurimumponirur in media , & tunc bafisaltius intonat . Si ponatur in<juar- ta linea tunc mediocrem vocibufque maxime naturalem femiditono inferiorem mto- nationcm indicat > in quinta denique lineapofita, quod rard rTt,profundiflimam & fe- miditono a praeccdente inferiorcm;denqtatintonauoucm . Scquuntur huius bafis co- ftitutionemrcliquarum vocumfignationcs, vtpauldantc patet . Atque hxceftprima fignatio, quam duramfeu naturalcmvocant . Altera eftmollis quam&fidara vocant &in nulloapracccdente dirTert,nifi quodfingulis vocibusin fpacioconuenientiappo- natur b.vtinfccundo ordinepatet .

Notahocloco quod vbicunquehocfignum $ii in bafis pentagrammo pofitum rc- peries,ibiFclaucmclTc noucris, Abhacenim furfum veldeorfum , numerando noti- tiam fedisclauiumfiiiecharacleriim 7.principa!ium ABCDEFG. quibus veluticlaui- busporta ad omncm modulationem apcritur,dcuenimus.

InTcnorevbicumquCreperiturhocfignum \ ibiC. clauemeiTenoueris, aquaJ

dcinde furfum vcl deorfum numerando dcucnics in notitiam alterius cuiufcumcjue_j clauis quaifit? i Qux in Alto fiue Contra-Tcnore Sc Cantu quoque obferuanda liint . In Cantu vero fiue vocc fuperiorl a Iinea cui clauem G impofitara videris, reliquarum clauiumfedes aufpicaberis, fed h$c Muficc praclicc ignarisdidla fint,in quorum gratia totum fyftema palimpfcftiphonotafticihic adiungendum cenfuimus .

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Artis Magn* Confoni, $ Difioni

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Atque hi funt modi fignandi 4 voces paffim a Muficis vfurpati fupra quos& nos ta- «juam iupra bafin&fundamentum Mufurgiam noftramrundabimus, &quamuisaliar fignationesadhuc poni poffint,quia tamcnaltioremautprofundiorcmintonationem, ^Sil0 humana vox ad C3m pfttingerepoflGr, dcnotant,idedpaflim rcijciuntur . Ex- plicitb igitur fyftcmatcphono.taaico iam ad aJterom Requifitum acccdamus .

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Slcuri prxcedens lyftcma phonoraclicum materialc quoddameft modulationum or- dinandarumprincipium,itahoc non immerito formale earundem principium ap- pe41arcr^frumus,.^nihUaJmdeft, quam iiTonorumiuxta 7. diapaion fpccics in». columnisvnicuiquetonoproprijs,fccundum numerosfuos harmonjcosrepraefentatio. Verum locofufiorum vcrborum hic totum lyftema tibiob oculosponimus: ncquar iri pra?cedentibuslibrisdetonis corumquc natura& condiuoncfusc traftauimus,hic rc- pctctecogamur.

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Hanc tabulam Tonographicam arcanoquodam artifi<uwucon«xuirou';, vr infini- tasprorfus harmonicarummodulationum combinationcs paucilTimis columnis com- N0r_nij_( prchcndcrimus , aded vt hcx mcnfa Tonographic^ non immerito bafis & fundamcntG ca Tabuia totius noftrae Mufuroia? mirifice- dici poflit , Atquc Toncs quidcm pailim in Ecclefia_* _a0^™p ^fitatosquos&idcoEcc]cfiafticp*<itCiniubduudec»m^ofuirnus,ne quicquam curio- im~" fo mclothetje ad imrr.cnfam raodulationum vanetatem deciTet . Etfiin rigore non ni- fi rcxfintToniperfectasfnutationcsfubeuntes; Coctcrienim Tonivelineademintcr- uallamciduntjvelaliaratione muta"sTonis duri irTmolIem, qiamtranfpofitioncm vo- cancMuTici,djflcrcntuimfuam fuinuntjvtpoflca dicctutjotdinem 1 tonoium naturalem in menfanonferuauimn3>vtordo^inncroruniricu^4»^»wei)t«interuallorum meliiu» paterct: &vtconucnicntinominc vnumqucmqucdcnominarc piofljts; VererumAp- pcllationcs vnicuique apppfuimus , vna cum natura vniufcuiulqOc , vt pro rationethe- matis quod hawnonia anfmare defideras,inipfistonis repetias«l!e<ftu«corr«fponden- tesiappofuimus tono vnicuique (durusvcl mollis) vtfiquifpiam tonus fucrit durus; Cnaracterifmo vterens canrui duro oponuno; fi moilisjnolli , vt>q^oq>©5ucn^tino- minc qucmlibcrrouoiudenominare poUcs.vnicuiquevctcjujn appellationesadiunxi- rrtis, vnacum nattir»eutufuis,vt viddicctpro rationc tbcmatjs^quodhaniionicji mt^ . dnlis animarc dcfidcras, affec~tus icpcrires correipondcntcs, lcibc^t gaudij,ainprjis,cc)- p3aionis,doioris>mftus^diflblutionis-, reUgicmH,vanrtata5,feroti«»indi2nationis,fi- niiliomquc adanimoshonunum cuLitandosoportunos. Navtimodulawiuxw primu ionMin.inftityta,ncfcioquidcfliacia:obtinetadnpinajiefc

tnoremquediuinum incitandum ita e contra miJitarisafcc^ionis&ferociaema;gna- nimitauiquc fcintillascxcitareproprium fcxtitonicft. Inprimaverocolumnaordine clauc<; \ cr u pttm literas A BCDEF G.indicatas^vciutiquandamtotiusopificijno- ftrijMulur«»icianimam duccmquepofuimus ,hxe enimcolumna tonorum columnas tranfucrfim percurrens,fingulorum'in quouis tbno interuallorum cum dauibuscorrc- ^ondcntiam mdnifeftat; vti poftea in praxi vidcbitur .

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j* Arus oMagtue Cottfini, & Difioni

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Rcquifitum I I I.

De vaiore notarum , £5» mcn/ura iemforie .

JEMnficximpcrinisinhocMijfurgiconoftroncfjotio rcmoram aliquam reperi- ret, notuhru m quoquc muficaJiu m 'qaas nos rn Mufarithmoru m tabulis notas metroroetras appeJlaaius ) valorcm bicapponcndum duxiraus.

Cum rtaqucmaxima fitmotuum harmonicorum (qui omnes in vna modulationc plurium vocum conucniunt) varictas, ita vt quidanj vcioci , noonulli tardo,alm ui mo- deraeo paflu proeedant,vii~um fuit Mufurgis ad conrufionem vicandam ccrtum lignum, iuxta quod Cantores vocem fuam dirtgcrent , ordinare , quod quidcm fignum cum-. veluti regula qu(dam fit , harmonicoru mquc motuum amulfis, illud immobile cflc noa conucnicbar,ad motum igitur manusaut altenus cuiuicumquc rci manu dcrcnti elc- uationeaut deprcfrionequam^wS: W^rvocabant, mobile pofuerunt; Itali vocant Aduencada £» battutth boexuxspiaufum, alij taffum St menjuram, nos Chronometren intitulamus . C5- ctfciTiOl. ftat autcm h^c mcnfura duabuspartibusvnapofitionc , quam fli'm»,ajrera cJcuatione manus, quarn a^<nt Vcteresdixere, rclpondentque motui languinisincorporc, quem Galenus Ji*+xh & mtr&nr appcllat. Sicutiigitur ex diaftole & fyAolc vnus pulfus venarum.ita exarfi&thefi vnum tempusfiuc menfura intcgra complctur; Chrono- mctri vcrocharaftercsfunt notat ille, muficc, vulgd vfirat^ ,quarum valorem hic vnico iotuitu tibi 00 oculos ponimus.

Tabula I. FttlorieNotarum.

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Brcuis Seaibreuis Manima Scminima Fufa Scmifufa

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Prior notula duas dcnotat mcnfuras ; fccundavnam ; tcrtiamediam menfuram_, quarta tnam quartam mcnfurz parte m, quinta vnam ocuuam & vJtima v nam decjma fcxtam partcm mcnfurc; dcnotat, fingulisabimmediareprarcedente notain dupJa pro- porttone dccrefcentibus. ita femibrcuis bisfumpta,conftituit brcucm ; Minima bissu- ptaconftituit femtbreuem ; Scmimimma bisfumpta minimara , Fula bis fumpta fc- tninimam ; Scmifufa dcniquc bis fumpta fufam ; Iterum femifufc. fedecim > iufx S > femiminim? 4.mmim^ du^,vnifcmpcrlcmibrcuia?quiuaJcnt. Vcrumhc,c intypo fe- qucntipatcnt.

Semi tt tt tt tt u 11 u II 11 U U U 11 U II U Futttt tttt ttttttltfe Scmi r t T T TTTT rainimc.

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UkFUL Mu/urgiaMmfie Ver um vt hxc taelius pcreipia n t ur de tempore hic pr i- md a Jiquid indjcandum . Eft jgitur cempus Muiicum ni- bil ahud quam certa & dcterminaraquantica* icu notu- larum fiue hgurarum minot um in vna brcoi vci femibre- uiconcenrsrum vc in prxccdcniiichematcpaccc. Eftque duplex pctfeclum & impericclum i Tempus perrcc~tum nv ucnicurin moduiationisprincipiofignacohoc charatfcre O quoindicatur breutm modulatjonem jn ommbusetTe pcrfectam, id eft f quiualerc tnbuslcmibrcuibus, vt bic e lacere ■, ac cum in pnncipio cantilen x ponitur medius cir-

culusfic <£ vt ehcereappareciindicacurhocchandercbrcucmciTeimpcrfcftain-,,

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id cil xquiuaJere duabus fcmibreuibus . Verum cum dc hifce in prxccdcncibus fuso djftum fit, hifcc tancum dictain mcmoriam rcuocare voiuimus .

De Paufis .

DEniquecum no femperomncs vcccsinmotufint,contingjt vcfubjndeqiuefcat. Hinc excogitatae func notx» quibus phonafcis indicatur, quanru cempons quie- fccrc de beant, vocancque has notas grxci muntt, larini muraro nomine paufas . Veru ad harum i ntclligcntiam aihil aliud rcquiri videtur nifi fynopfis paufarura , quam tibi hiccxhibco.

Tabula II.

*Tyfua Paufarum .

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Liacxpentogrammo infmx fanificant in hocfcheraatepaufas>numerifuprapoi> ti denotant valorcm paufarum ,ideaquottaaibus<juicfccrcd«b€anrphonafcii V^, prima paufarum fignatio oftcnditoftotaduu quietem,iecQda feptcm, tertiafex, quar- ta cuinque cum dimidio, & fic vfque ad vicimum , Nam vlcima oftcndic quicte | tcra- poris, pcnultima £ temporis, antepenuldma i cempoha fiue fcmitacoa durare dcbcrt-* Scd hcc vci facillima func & primisTyronibus noca , ica quoque vltcrius cxplicancuu» non duxi, folum capofui, vc Muficxprorfus ignaris aliquam prxbcrcm introduclione,

Requifitum I V. Mu/arithmorum notitia.

MVfarithmum hocloco nihilaliuddicimus , quam harmonicenim numeroru cer- tis pcdibus mecricis correfpondcncium acque inpinacesfeu cabulas mcthodi- cas redactorum aggregatum \ Quo quidem nouocicuio maxime appofico,3rcem no- uam cohoneftarc vifum eft . Eftenim Mufarichmusidcmac^w»w«ieit/i(j>«id eft nu- mcrorum fonororu congeries harmonicis periodis cxprimendis apciifimavt poftca vi-

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debitur, ouorum diuifioncm gooi ioprimacapite iatisddaipleuoiUfthkrijsTaeniVh- dislongiorcsefTcBOtairmiSjfcd ad eorundcm praximvfuracjiie 4emonftrandum> ncjt auidura Lc<fwre«diu«ius iulp«ndercinus, protinus nosaccmgerc vohimius.

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De Contrapunftofimplici&.quorno4o is primiSyntag-; matis Mufarithmis a cjuouis etiam Mufiq; imperito confici polTit .

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SYntagma I. prartcr i o continct duos pinaccs polyfyllaboru Mufarithmorfi, primus pinaxcontinetpolyryllabapenultimalonga ; Sctundus poJyJyllaba penultima_»- brcui, quorum ope oruncm conrrapun&um fimphccm racile cxpcdiac quiuis- ctiam_»- «M«Mspraxi paulo poft cxplicanda,pr$mifimus autem hocfyntagma Mu/arithmorurrL* tanquam reliquis fimplicius,vtfica faqljpribus fiarolicioribufqueinitium facicntcs mi- norem in rcJiquisfecuturisdifficultatc!ehtircfnts>& nein ncgotio didaclico */u*toJbg procederemus, mathematicorum ftylum fccuti,totiusMufurgia?noftra;artificiunipcr propofitiones practicas fcu problsmata quxdam dcmonftxarCvilum cft. Rem ig'tl# OHlibonoDeoaufpiccrnur. ip.xir -4 v!X

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Problema I. .osdii»»^

Dato quolibet wrborum themate 3 quouutono , cantilenam fetitam Jimflici contraftinft.0 comfonerc ex frimo finace .

SI ig»itur quifpiamartis noftrar experi.mentum in cont^apunfto fimplki furuere defi- derctiisantcomnia PaJrmpfcftumphonotaclicumiuxtacapitisfccundiHuiuspar- ^oniixmo. tesrequifitum pnmcVpra.paraturn babcat. Secundo meniam Tonographicam . Tcr- A»s • tk/Thcma vcrboiumlcorfim defcr iptum tcncat> iuxta quorum vcrborum cncrgjaoi-.». tonum fibi digat appropriatum , Sit igitur ad dioini Numinis grariam implorandam_f primo thema vcrborum : Vtni Creator Spiritus. Qua» verba ciim fpcm & fiduciam in_» diuma mifcricordia denotant>hifce raaxime lcxtus. quadrabit tonus fiue hypolydius . quicum moliisfit qucmadmodum dicli toniin tonographica mcnfatitulusdcmofttat, penfQgramma vocura in palimpicftophonotaclico molJis cantus fignabis charaeTcrifc roejdcindeiregioneadcolumnam clauium in menfa Tonographica feorfim exccp- tara Sexritonicoiumnam applicabis.ftabuquclchcma vt Jequitur .

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Ve ni crea tor Spiri tus

Pra?parato itaque palimpfefto phonoradtico &fcala dauium tono 6.feIefto correfpo- dente, pentagramma quatuor vocum in tot fpacia diftribuimus, quot in afiumpto the- mate fyllaba?funt, vt fchema docet. deindc mclothcfiam ordiri poteris duplici raodo. Vd pcr diuifa thematis verba,vel perconiunda feu quod idem cftper plures coluranas diuerfisthemaris vocibuscorrefpondcntcs,vel pcr vnam columnamintcgrx ahcui pe- riodi aiTumpti thematis correfpondcnti . ExcmpJigratia cum thema alfumptum iit tc- trailrophonicqucns,veluti quatuorconftans periodis .

VeniCreatorSpiritus m

Mentes tuorum •vifites

Imple fupernagratia

£j)uf tu creailt peclora . Et vnaquxque flropha feu periodusfit oclofyllabarum , excolumna oclofyllaba pi- nacis octoiy llabi excerpesquatuor mufarithmos quatuor ftrophis correfpondentcs,fi- uc ij in coliinaredtofiuc interruptoordinefcfcquantur,pcrindc cft, nos nic acccpimuf Mufarithmos i. z. 3. 4. vt hicfcquitur .

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Nota primo quatuor in vnoquoquc Mufarithmo nuraerorum fcricseiTc , auc qua-

tuor voubus,Cantui,AJto,Tcnori, & Bafi lcmpei corrcfpondcnt & Bafin quidem vJti-

ma fcries icmper & immutabiJitcr tanquam fundamcntum reliquoiumreprcfentat.re-

hquc, tres voces prolibitu compofitorismutaripoiTunt. Siue cnimprimam feriempro

Cantu , pro Tenore , aut Alto , fiue fecundam aut tcruam numeroru m feriem dcputcs ,

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pcrindeeft,(namin ccrtistonis vtnaturaliusvocumproceffusferuetur^fubindc muta- rraxis com^ rjdcbent,vt alibifuse dcclarabitur)nosUic confuijcinis cuitandar graria vocesordinc ^ibetoimiie naturaliiuxtaliteras c rcgioneappblitasdcfcripiimus":per Ccnira fuprcraa vox fiuc-j nam in Con- QanttU) pcr A /l//w-,per J. Ttrurr-> per B. dcniquc Bafis indicarur . ^ pfic"f °fim -Hisoblcruatispopa&antc tcpaiimpfdtumdi-ta pauio untc ratione praparatunt-. , vaaxum fcalaclauinni fexti tonicolumna: applicata, vt in priccdcnu pmadigmate__> p^ci^C^oraftomctpthdiam itaaufpicaberisd CantninkiH 'ZZCZlzi facicndo . Ciim igitur in prima primi Muiarithmi fcric 5 . o- Melorhefia primx vocis ctjcs replicctur , Yide cui in columaaclauiura Jitewerefpo- fiuc Cantus . q*

dcat 5. iiucquinarius ntfmerus; &rcperies eidcm rcfpon- dcrcC.inpcntagrammoitaqucCj»/;//in(paciocuiCiitc- 555555-55 ram inlcriptam vides,iuxta 8.fyllabas octo puncta iraprimes, cc c cc ccc _ 1

babciifque caooun .cJfigiatum.1 _ l |— , — ^_iJ

Sccwuddproyoccvl//i vidccuiig columna clauiuw litcrjr rcfpondeant hi numeri _,yj-87yg.& t<p««-S 7rcfpondereiiter_rE. In parallcloj»rammokaquc Alri in fpa- cio KulinealTtcnfEiTgnata, 4 puhfta imprimcs.prartcrca ciim 4 Icp- tenariosSJcquatiJri Videcui litcra: in coluxnnj: j:Iauitim4rcfpon_-. • Mclothcfia Alti. drar?. &TTiuenis--F. in- ipacio itaqjjc fcu li rrea pentagrarnraiyl/irf ii- teraF. fignatairap-iraes pun-lunii aim vcrd poft ©ctonarium nu- 77778778 rocruminferfehuntoorurh dtiQ»poflca77 bccurrant.yauTemrefpo- ' EEEEF EEF dcat literxE.duo aliapunctainlpacioF.imprimcs, & ciim vltimus numcriisroufarithmi/./fJiito-lonarius,huicautem in columnaclauium Frefpondcat> iroprimesin fpacio F. deputato vltimumpun-tum,habebifquc Alri vocem perfc&a.

Tertid ciiro Tenorts Mufanthmusfit - lajjiij, vidc cui litcrce in columna clauium binarius numc-usrcfpondeat&inucnitsiliumrefponderc «» G. lnfyacio itaque Pentagrammi Tt/toris fpacio litcrar G dcputa- MeIothefiaTcnori>\ totriapunfta luxtatriplicem binariuin MufarithmoTenorisoc- currentemiropriiacs idcmde vidc cuilitcracin columnar clauium 11135 jij rc/pondeat^. &inuenics AiTernanus autc tu bisponatur,impri- GGGAAGGA mcs in pentagrammi Tenoris fpacio litcra A fignati in ccllul is or- dinefcquentibus duo punffca , & iterum duo alia puntta in G. ob duos binarios feque- tcs, & litcram G. iignificantcsi cum dcniquc vltiraus numerus tcrnarius fit, & A. liter^ in coluranaclauiura refpondeat,imprimcs vltimum punclum in fpaciolitcra A fignatu, habekufquc conre&am Tenoris voccm .

Quarto cadcm prorfus rationc ciim Mufarirhmus Bafis hos numeros contincat 55538558. 1 555 autcmincoiumnaclauiumli-erarC. refpondcat; imprimesin pcnta- «rammi Bafis fpacio huius liter^ deputato tria pu ncta ; deinde cum 3. occurrat infcrieMufarithmi;triaautem incolumnaclauium rcfpo- Melothefia Baflt dcat A. imprimes in pcntagrammi BafisfpacioiitcrarA.deputato v- num puntfumidcindeob octonarium imraediat. in Mufarithraofc- 55538558 quentemaliud puniluminfpacio peatagrammi F liter^ dcfignato CCCAFCCF (8enimliter$WF.incolumnaclauiura refpondct.) poiteaaliaduo punctaobduplicem quinariumimmediatc lequentem duoalia puncia infpacio pcnta- grammi liter* C. dcputato ( j enimC . liter? refpondct) & deraura ob 8. Iiterar F . rc- fpondentcm in pentagrammo in fpacio F. vltimum punclum iraprimcs ; habebifqucj Bafis voccmconfeflairi , arqucadcoomnium quatuor vocum iaterualla harmonica_> fuis punflis detcrminata funt . Nihil igitur reftat nifi, vt puntfa fingula notis fuis metro- mettis veftias . Quod hac praxi perficics .

Ciim contrapunctusfimplcx fit,&confequentcr loix&vot id eftarqualis tcraporis,fi- uc quodidcmcftin quofyllabafyllaba? & nota notjc exaclc refpondcat ,atquc aded fingulx notae in quaruor vocibus ad eandem fyllabam pcrtincntes eiufdem valorisfint; «ccipicsincalcccolumnaeoctofyllaborum, quamcunquc notaiumfcricm,qux nificr-

ratum

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ratum fit , neccflario tot habcbit notas quot puncta fpacijs pcntagrammorum imprciTa junt.hafque notasfuprapunfta 5^/ordineimponcs;dcindchafce eafdem notas pfi- ftis T encrih & cafdem punctis Alti* & eafdcm dcniqi punclis Cantus infcribcs, habcbifq; primam thcmatis tui pcnodum fiue ftropham, omnibus numeris abfolutam_*. Diligentcr tamcn obferuabis,vt notae fuis lpacijs perpunctaindicatis prcxist* imponan- tur. Veruminfpice paradigmainpraccedentcexhibitum,quodtcmembratim omnia_f exactc docebit . Eaaem prorfus ratione & methodo reliquas ftrophas fiue pcriodos pcr Mufarithmosfuosinharmooiamanimabis. In omnibus enim reliquis eadcm prorfus praxisferuabitur. dato i«itur vcrborum thcmate,& certo tono ,contrapunttum fimpli- cemexpediuimus,quoderatfaciendum. Mclothcfiafcquitur.

VeniCratorSpiritu metes tuorfi vifita implefupcrnagratic quitu crcafti peftora

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Verum obijcient hoc Ioco Mufici pra&ici , hac ratione femper eandcm hai moniam_, prodituram, &confcquentcrnoneamharmoniarum,qaam Author prxtcndit , varic- Nouah« tatcm refultaturam . Hifcc facilc osclaudemus vbi admirandam diucrfitatem vcl in_» "cThPoXscll hoc vnicoexemplodemonftraucrimus. Falfaigitur cftobiectio. Nam hoc thcma inh> capaxinfini- nita» variationis capax efic tunc patebir, vbi quatdam primo praemifciimus . ms.*10"'0"

Dico itaque quadruplicitcr variari pofle hoc pr$diclum thcma. Primo quidem ratio- nc tranipoficionisMufarithmorum ; Secunddrationc tonorura . Tcrtio ratione notaru apponendarum.Quarto denique rationecoIumnarum,quaeperdiucrfos pcdcs ,quos vcl vna flropha habet, infinitas cobinationesadmittitiatnngulafcorfim exaraincraus.

Primociiva tetraftrophon hoc thcma quatuor Mufanthmis polyphonis conficiatur; ccrtura eft ratione quaternarij nuraeri vti in prima partehuiusMufurgiaiProbl.i.fuse* variatio ra- demonftratum eft , efle vigefies quatcr variabile id cft admirtere 24Combinationes ita none traTpo vtlempcr nouaharmonia&aprioridiuerfaemanet. Nam qua?Ubet cxdiclisqaatuor f'£™muf* .Mufanthmisprimura Iocumfcxicsoccuparepotcft,re]iquisfemper variabilibus , quae omniacumcirato lccodcmonftrata fint, eo Lecrorcmrcraittimus . Potcft igitur hoc thema tetraftrophonprimdvigcfiesquater iramutarivt nunquimeadcm fitbarmonia.

S*r»»<&rationeTonorum duodeciesiterum mutabilecft. Namclauiura fcaUmo- bilisad fingulas Tonorum columnas adraoca, fcmper diuerfas cflcntialker harmonias pro varia tonorum rationc producet . Si itaq, 24 ducas in 1 z. habebimus iam 288 mu- tationes,quibus hoc raeraoratum thema tetraftrophon rariabile eft.

TVrfwmutaripotcrit rationediueriarum notarum&iuxta 12 fcricsnotariimracalcc coiumnacpofitarum primo quidcm iuxta fimpliccm pofitionem, 3456.iuxtacombina- tioncs vcro notaruin inter fc quomodohbet faftas(nafcentur 1 65 54298 1 60800 muta- tiones )atquctotmodispoflibilibushocvnicumtctraftraphonin rigorc variabik cft.

H Qux

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Quf omnia citm in primo Iibro demonftrata fint» bic amphus dcducere fuperuacancuui cfle ratus fum, cum ua harc omnia in citato locodcmonftrauertmus , vtquifpiamigna- rus de his dubitaxe impoftcrum minimc poflit, ac debeat .

Quarta mutatiofTeripoteftin infinirum quafivariabilis,fi videlicetper diftinctospc- riodi metricacpcdescolumnae ordinctur . Kem excmplo dcclarandam duxi,fit igitur -

Problcma II.

ALIVS MODVS. Per di&in&a membra , syUabafue ajfumftum thema in modulos

animandi .

ALtcr modus cft perdiftincla pcriodi mCbra, fiuc iuxwcolunarupedibusmetricis adaptatarum colJeclionem.Praeparato itaquc palimpfcfto.phonotaclico, fpacijf-

Suc iux ta thcmatis aflumpti iyllabas dtrcmptis, columnas ordinarc incipics hoc pafto, itra aflumptu thema,fit: Veni Creator Spiritus,Sc prima thematis vox Venifit biflyllaba, columnam biflyllaborum poncs > fecunda vero vox Creator cum fit triflylla pcnuitima^ longa,accipiescolumnam tnfyllaborum penultimalongorum inpinaceprimo. appo- nefqucad columnam biflyllaborum .Citm vcrdvltima vox Sphritus fittrifyllabapenul» tima breuis, accipies in pinace fccundo columnam tnfyllaborum pcnultima breuium , & cam ordinabis ad columnamprxcedctcm ,habebijque tres colunas iuxtatresftro- phz pedes or dinatos .

Nota ramen hoc loco n6 efle neceltc femper accipere integras voces pro fingulispe- dibus, fcd poife voci vni acccdcre fyllabam vna veJ duas aut quotquot voluens ex vo- ce immediate fequcnte, vel ctiam voces duas in vnum coniunclas , vnum aliquod po- lyfyllabum vocabulum referrepofle. Qux,resiterumin infinitum quafi variabiliseft. Veruro vt haccmclius mtclligantur ,hicvnum cxemplumapponere vifumeft ,vt exeo mcutem noftram in rehquis lntelligeres .

/ | Veni Creator Sfiritus \ 2 FemCreator\Sfiritu4 J Veni

4 Veni Creator

5 VemCre\ator

Creator Sfiritus Sfiritus Sfiritus

6 Veni Crea \ torSfiritus \

7 Veni \C reator Sfi \ritus.

tcccfchema variationis thematis quo ad pcdcs ; Primum Cnim habetfe per modum octolyllabt vti in praccdentc exemplo ofteniiim fuit ; Secundum per modum rriutru, pediun .Tercium per modum duorum pedum, quorum phmus eft bifiyJJabus , fciiicet Vtni aJrer bectafylJabus, vtdelicct Creaur Spmtus^cx modum vnius vocabuh . Quartu haber in prtncipio pedem pentafyllabum,& in finc triiylJabum penultima breui. Quin- tu» ruptis fedtifquevocabulis, in principio habet pedem meti iam trifyllabum, vidcli- cct VeniCre I dcindebiflyJlabum jfor;tertio trifyllabum Spintus . Scxtum ex abftradis defcquentt vocabuJo duabus iyllabis , quas ctun primoadiungitconficit pedcm tetra- fyllabum ,remanentcaJtero tetraiylJabo torSpiritus. Septimum verovtmedium fit te- truiyJJabum abvltimo vocabuio fyJJabam mutuat.

Vides igitur quomodo ratione diucrfttatis pcdum ,qu$ in ailumpto themate conit- deran poffunt, m u tattoncs con tingan t . Vifis ttaque mutationibus, lam ad propofitum fMtrariigma reuertamur .

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Sit igitur thema propQfitura vt fupri J*e/ti Creator Spiritusy coniungas fingulorum pc- dum coluranas, vtidKtumeft. Hoc peraclo quomodocumquc hafcecolu unas difpo- iueris , dummodd MufarithmiMufarithmis icmper rcfpondeant, femper nouam har- moniam prodire neccfle eft . V. g. in paulo ante pofitis tribus columnis; pro mclothefia propofita trespinaccsprimos incolumnis Mufarithmoruaccipiamus,quibusfequcns fchemacorreipondet ,

vnacum columna clauium coiumnx toni lexti,vt prius ap- plicata,& videnumeros 13678x23 ad C<wi/«OTpertinentes quibus litcrisin columnaclauium rcfpodent,^ z, Gi 3, A, 6,D; 7,E; f »C;4,B; & ijG; 3, A . refponderc muenies , im- preffis itaquc pundisin pcntagrammoC4*/«/ ; Vide numc- rus hofcc 78876778.quibusincoIumna clauiu literisrefpo- deat, & inuenics 7 refpondcre tj/ E, 8 tot F, 7 n» E; 6 iq> D.

& deniquc 7 7&rE;impreffis iraqucinpentagrammoyl/tt infpacijs ditfis literisdeputa- tis punclis,habebis locanotarum. Non fecusin Tenaris ScBaJis Mufarithmis in Pcn- tagramrna propriatransfcrendisprocedes, quibus pcra&is ,iingulis pcdibusnotasin calcc coJumnarum corrcfpondcntcs, ex 1 2 quamlibet fingulis vocibus apponcs,habe- bifquc harmoniam perfeftam . Veriim exemplu temcliusdocebit ,quam Ego vel mul- tis vcrbis dcclarare valeam.

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Atque hac eadcm rationcrcliquasordincftrophasexpedies.Quicunq;igiturex5pla hucufq;data bcne intcllexcrit js nulli prorfus in reliquis fecuturis difficultate rcpcrict.

Vidcs ioirur quanta facilitatc qujeuis melothcfia: hac praxi expediantur . Et nc igna- rus artis noftra? Muficus nobis obi jccrc poiTct, femper eandem cantilenam prodire_* , facileilluconuincentca,quc de pnccdentis paradigmatisinfinitis fere mutationibus demonftrauimus . Nara ccrtuin cft, in harum trium columnarum tranfpofitione variaq; applicationc multo maiorem combinationum varietatem , quam in prccedentc occur- rcre. Mutationcs harum tante. funt vthuraanoingeniocomprehendiminime valeant. Sii<mure triura columnarum variaappUcationc tara inconccptibilis mutationum va- rietas nafcatur, quantam cx 10. ao.aut 3o.ctiam columnarum tranfpofitione varieta- tem emanaturam credimus ? Vcriim ciim ca vulgo paradoxa fint ideo filentio potius inuoluenda,quan\ fufiiis dcdaranda duximus. Solum hoc loco fpecimcn quoddam da- Li.nus,quarationc ha-ccadcmftropharationc diucrforuTonorum mutatione fubeat cflV ntialcm & primo quidcra in omnibus 1 2 tonis excepto IV,qui ob intercurrcntcr*-» fajfam quintain,hanc daufulam non fnftiner; nifiper g corrigatur .

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Mutatio compofiti thematis exfexto in frimum tonum clauium-

Sligiturquifpiam dcfidcrarct hoc fubicftum mutare inprimum tonum ,is columna applicct ad columnam primi Toni, atquc in paiimplcfto phonodiatico primo mu- RaiiomutS- tct charatftcrifmum molliscantus In durum > quod ablatione bfict,deindediligcnter «Jvnorono obferuet quibus literisin columnadauiumrelpondcantijdem nunien quatuor Mufa- m aiium To. rithmorum cx tribus columnis cxccrptorum . Nam eofdera fempcr Mularithmos ma- uunu.. nerevolumus ,vt horum maior varietaspaterTat. Sienim inpentagrammis vocu fpa- cijs literarum pcr numeros indicatarum pumfta imprcfTeris , notafquc iuxta pr^cedens paradigma metrometras,vt diftum eft,fingulis appofueris, habcbis harraoniam in tono prirao compofitam, a fexto tono effcntialitcr diiferentem , VT in primo exemplo fcquf- tis fchematis vniucrfalis apparet .

Vbi nota primd in columnatoni primi nf $ id cft fcnarjo numcro femper appofitum efle b. quinumeruscu v»D. in colunaclauiumrefpondeat,femperloco clauis b. vbi- cumque & in cuiufcumque vocis pentagrammo id repertum fucrit , fcias notq illo in_j loco occurrentiprxponendumbmollc, vtin 5 nota bafisfchematis fequcntis incolii- na prima primi toni apparct & in quinta nota Alti. & in tertia nota Tenons. qux omnia diligentiffimc notanda funt . Nam quxcunque hoc loco dicimus , impoftcrum irrcuo- cabilitcr feruanda funt .

Nota fccundo in columna pr^difta primi toni, numerum 7 cffc fignatum & figno fe- mitonij,acdenotare, quod vbicumque& incuiufcumquevocispentagrammo C litc- rainuentafuerit,quam7ni)meruscoIumna: Toni primiin columna clauium indicat> illoin loconotxoccurrentiferaperprxfigendumelfefignumX. Sitaraen notaimmc- diate fequens afcendcritaut finalisraerit;autpaufaimmediatcfecutafucrit}omittendii vcrofidefccnderit nifirarisincafibus , dc quibusalibi .Quodctiam dealiorum tono- rum columnis, in quibus 7 aut alius quiuis numcrus hoc figno notatus repertus fuerit, intelligcndum eife fcias.excmplum habesin voce Alti, vbi primara &fextam notam_. hoc fignoS notatam reperics,fequente nota iramcdiare afcendente . In vocc Cantus verdvltimam notam quodfinalisfitxhoc figno notatamrcperies.

Schema fecundum . Mutationis compofiti thematU ex fexto tono in fecundum mollem .

SI quis vero hoc compofituna theroa , iucundo & fubblando adulatorioquc ftylo co- poncrc defiderer, is fibi cligat fecundum tonum, quod fict , fi columnafm clauiu applicucritadcolumnamtoni 11 hypodonj, Si enim in pentagrammis quatuor vocu literasper quatuor Mufarithmos in columna clauium indicatas,punctis notifque vt di- £tum eftmctrometris, fignaucrit,prodibit nouum harmonix genusiucundo quodam , fubblando, & adulatono ftylo, quale fccundus tonus continet, compofitum,vt fccun- da columna fcquentisfyftematis vniuerfalis oftcndit: diligenter interim obferuando, vt vbicumqueinpcntagrammisquatuor vocum in E claui nota occurrerit , b mol- le,per numerum 6in columna fccunditoni,cui badiunctum rcpcries,indicatum iuxta monitumprimum prxcedentis, ci prxfigas ,Et vbicumq; Htcra per X 7 indicata occur- rcrit, huic notx firaili rationc fempcr prxfigas i Si tamen vt dixi nota fequcns afcc- dcrit aut finahs fuerit . Exemplum B. mollis habes in quinta nota Baffi , & in tcrtia nota Tenorisi fcmitonij verd exemplum habcs m prima & fcxta nota Alti. exem. H. tonu

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Schema tertium . jtfutattonu comfoftti thcmatu ex fixto tono in tertium tonumdurum.

SI porrd quis compofitum primo thema in fcxto tono in tertium tranfmurare vellet tonum luftuofum,&rebustriftibusaptum iIntentumisobtinebit,ficolumnath_« dauiumapplicaueritad columnamtonitcrtijfiuephrygij. Si cnimin penragrammis* literarum per numcros Mufarithmorum in columna clauium dcnotatarum loca , pun- ftisprimd,deindevti dicnjmeft, notismetromctrisfignaucrit ,prodibita!iud nouum cantionisgenusiuxtatoninaturam quaefitum ,vtitcrtia columna fyftematis fequcntis ulchre docct,obferuando tamen cum omni dibgcntia Ioca8fcmitoniorum,aut etia & b.iuxtaprxceptain prxccdentibus indicata_i.

Schemaquartum. Mutationis tbematis exfexto in auartum tonum .

I

MVtabis thcmaafTumptum in quartum tonum ,fi columnam ciauium appiicuens adcolumnam toniquarti.Si cnim Ioca Iitcrarum in pentagrammis pcr nu- meros Mufarithmorum indicatarum pun<ftis,deindcverdnotis appropriatis fignaueris prodibit tonus fletui & planftui aptus,quefitus. Videfchcma toni IV.fcquctis Syftema- tis. Quarequicumqucdic^amcantUcnam extonoin tonum qucmuis aliura mutandi in hifce quatuor tonis mcthodum rcsftc intcllexcrit ; is nullam quoquc in relicmis for- mandis ditficultatcm habcbit . Quare nihil reftat nifi vt fyftema generale mutationis af- furnptithematisfecundumduodecim tonos,vnica fynopfi ob oculos curiofo Leftori ponamus ; Ex hac cnim quomodo inreliquisproccdcndum, clare patcbit.

Syftemavniucrfalequoajjumftumthcmafer XII. tonos

mutatur effentiaiiter .

I. Tonij fiue dorij II. Toni hypodorij III. Toni phrygij

IV. To- 1

4m Artis Magrut Confini, & Dijfoni

IV. Toni hypophrygij V, Toni lydij VI, Toni hypolydij.

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X. Toni hypoionij XI. Toni Iaftij XII.Tonihypoiaftij.

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Lib. VIII. Mufurgia Mirifica . 6j

Habcs hic Leftor vnius thematis in omncs tonos transformationcra in vno fyfteraa- t£ demonftratam vt vel binc vidcas, immcnfam vcl vnius Mufarithmi varictatem ; qui- bus li acccdat diuerfus notarum valor , ciufdera mutatidnum varietas emerget prorfus mconccptibiIis,qux om nia ideo hic fufius oftendcre volui, vt artificij noftri <»0f Ajxirpoc apertiuspatcrct. Sed jam de valorcnotarurafiuedemutatione tcmporisajjquid dica- mns.

Schema V. Mutationu notarum metrometrarum .

QVi primc. partis huiuslibri caput S.rite expenderit,facile vidcbit mutationum ali- cuiusthcmatisiuxtadiuerfum tempus,vixeflefinem , Eftautcm duplex te- pusperfe&um & imperfeclum,de quo cumin Requifuotertio fat diftumfit, hicjongioreflc nolo,fedtandcm cxplicaboquomodoillud themati noftro varie appli- cari poflit. Notas tcmporis perfecti fingulis coIumnisMufarithmorum fubiunximus, quas & notas mctromctras appellamus, eo quod numcns Mufanthmorum,quoad nu- inerum&tcmpusperfecterefpondeantJ& priores quidem fine numero proportionis notatx fignificanf tempus impcrfcfturajEa vcr6 qu$ numcrum proportionistcmporis prxfixum habent, vocanturnot^tcmporispcrfe^tij&vulgotnpladicitur . Etquamuis vt fupra dixi , cx oc':o nctaiu in Kcquifito tcrtio explicatarum mutua intcr fe combina- tionc infinita prorfus varictas emanet, nos tamcn ad faciJitandam, vt ita dicam>Mufur- giamHoftram ex omnibus duodecim tantum elcgimus,quxabundead diftam confti- tucndarumraodulationura varietatemfufficient. Theraaitaque noftrum priraoaflum- ptum in prxcedcntifyftcmarc duodecics replicaru,toties cnim rcplicari poterit applica- do fingulis quatuor vocibusvnara notarumexduodecim quarumlibet lericm. Quod vt iiuelligas notandum cft ,quod cum boc loco contrapun&uin fimplicem tradamus Imx&rw id eftxquali tcmporc proccdcntcm,in quoexdern notx fingulis quatuor vo- cibus appliccnturj fufncerevnam notaium quatuorvocibusapplicandarum quamcu- cjucfcncm, ficnim quifpiamdiuerfasferiesdiucrfis vocibus applicaret , iara tota har- monia dcftrucretur,cumcatempusMufarithmis minimecongruum haberet. Hocita- quc prxnotato,vt vidcas modum applicationis,hicquc pcrfectius patcfiar ; nos bafin-. aflumpti thcmatis tantum d iucrfo valore notarum infignitum adducere voluimus . Na m rcli quas voccs eori efpondentes eadcm notarum ferie & ordinc infignire facile^ quiuis potcrit . Vnicaigiturfynopfiartificiumtibioboculos ponimusi Seruict enioi-» hxC tcmpoiis diuerii vnricras,ud variosin modulatione affeftus excitandos,- Nam vti aftcvftus triftiticjlanguonsjplanaufquc tarda, ita afTedtus gaudij, hilatitatis &diffolutio- nis, indignationifcrue,velocia,requirnnttcmpora_,.

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SjBema mutationu aflumfti thematis fufra ftxtum tonum comfofiti, quo admutationem notarum metrometrarumiuxta temfu<5 imferfecluntj .

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Eece vides hic ix mutariones notarum> omnesdiffercntes magifque principalcs,alijs innumerisreIiftis,quasMufice: peritis adiungcndasrelmquo. quamcumquc igitur ex bisduodccim fcricm bafifiuevoci infcriori applicaueris,eadem legcrcliquis vocibus eam ad Imxcplmt tenorem,applicandam noueris . Sediam temporis perfecti quoque^ paradigraa monftremus .

Schema temforis ferfecli fiue TrifU maioris .

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Schema temforis ferficli fiue trifU minoris, fiuehcmioU.

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Si quis igiturmodulationcm temporis imperfetfi in perfeclum murare velit, is vo- ces notafque methodo hic pofita fignabit, habebitque ctiam mutationcm ab omnibus reliquisdirTcrcnrem ihuiufmodi autem tempus in caJce tabularum rcpcnes , fub hoc ti- tulo: tnpla maior, rripla minor . Vtramuis igitur tibi feJigere poteris , vbi tamen notan vcJim,in metristripJam ptr fingulas ftrcphas continuandam , neque pcrmifcendam tc- pori imperfeclo,in vcrbis vero non metricis triplam arbitriocompofitorisrehnquimus.

Ex hiicc paucis nifaJJor fatis patet, artificij noftri mira vis, quo ex ijfdera numens trm Muraritnmorum Hon mutatis,tamingens&admirabiJis varietas enafcitur. Qu?cumq, igiturhucufqucdeajTumptirbcmatis melothefiadiAafunt , omnibusrcliquis lecutu- r?s operationibus communia funt; Nam modus operationis in omnibus idcm eft , vnde hicartirTcijmethodumplcncpertraAarevifum eft, neinfecuturiscandem rem toties xepeterc cogcremur, Lcclorem igitur huc fempcr remittemus .

His igitunta prarftitis, nihil reftat, nifi vt an tequam vlterius progrediamur, hic cautc - las qualdam apponamus, quas non mcrito Caoones totius artis appcllamus ; vt iuxta_» cos,omncsdimcirltatcsoccurrentcsfuperare poflimus,&ad perfeftam componendi notitiampcrucnire^.

CA-

Digitized by GoO<

Lib.Flll. Mufurgta Mtrtfca. ffg

C A P V T I V.

De Canonibus Mu{arithmicis,fiueCautelisin Melothe- ticis operationibus adhibendis .

NE Muiici aobis obijcere poflcnt , aiiquidin vniuerfo Muficx praftica* ambiru la- tere,quod auc non pratuiderimus » autalijs difficultatibus occurrentibus me- dcri non potuerimus , hicCanones totius artis direitorcs apponcndos duximus , qui- bus fingulari ftudio obfcruatis , nulla vnquam diificultas tanta occurret , quam non__. hc Ue Tyro ctiam Hpum fit fupcraturus .

c a n o N I.

De Characlerifmis fentagrammorum fiuc de modo fignationis uocum in faUmffefto fbonotailico .

CLaues harmonica», quasalij fcalamappcllant , variasfedcs in pentagrammis obti- ncnt,)deocautc fignationc lllavtendu n , Nc igitur Tyro huius arcis inincertu errct, ita opcrabitur compofiturusmclothcfiam quampiam , primofeliget fibiccrtum ex duodccim fupraprarfcriptistonum > vcrborum fignificationiapcum, vti fupradiclu eft. Quo peradto videat in lyftemate mutationis duodecim tonorum characlcrifmos pentagrammorum,fiue qua?clauiurnfeufcal.r conftitutio iit in columnatoniqucrry elegiti& hoc codem charaftcrifmopcnta»ramma fuainpalimpleftodelineatafignabit, fi durus fuerit characler:fmus,durOi fi mollis,rnolli luadercm tamcn Tyronibus , vcse- pcr accipercnt eam fignaturam fcalat , quam obtinenc in fyftemate vniucrfali fex ordi- ne coniiramediatclequcncesi Hic enira reddic canrum magis naturalcm , fingulifque vocibus magis congruum i Si quis enim cofcalae generevcacur,quamhabencprimus& tresvlcimiconi, hic voces rcddecpIuj^quoaltas&vocibusCancorum incongruas.in ijtamcn conisin quibus huiufmodi fignaturaoflendicur, relinquenda eft, fciasquoquc nos hic conos duodccim pofuifle paJfim in Ecclefia vflracos,& quos iudkaui noftropro- pofito optimos, non ignarus maximam de tonoi um quahtate controucrfum, quai» & in prajcedentibuslibnsfatis difcuffimus .

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C A N O N II.

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De Mufarithmi* eorumque ordinationc

QVidMufarithmusfit in pratce Jentibus declarauimus, cftenimcertumharmoni- corum nuraerorum aggrcgatum, quale contincnt fingul? cellulac fiueareej columnarum,inquatuornumerorumfcricsdiftributa?, quarum prima re- fcrt cantum fiueprimam vocem,fecundafccundam id cft AItum,certiacertiamideft Tcnorcm, & quaita quartam id cft Bafin i Atque Bafis fcrics immutabihs eft , nequc_> vnquam locum alterius vocis fubire,ficuti ncquc alterius cuiufuis vocisfcries in locum bafisfubire potcft .Tres tamcn feries vltrabaftn,prolibicu,fineceflicascompuleric, in- uiccm pcrmutari poterunr . Dixi ii neceflicas compulcric iCocingitcniminccrtisfub- mde tonis, vtvox quarpiam cx mufarithmis nuncaltior ,nuncprofundior euadat icui vtmederi polfis, voccspcrmutand^funt i V. g.fiCancus velTcnor nimis Alti forent, ajtcrutra vox in Altum mutanda foret , & Alti vox in Cantum vcl Tenorem fcilfcetal-

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* f Artis Magn* Con/oni, Diffori

terutramvocem. Vcriim rcm exemplo oftendamus . In fyftematis vniuerfaliscoliina quinto tono notataomncs voccsaltiuscquoaffurgunt ; vtcas igiturad mcdiocritatc quandam transfcras Cantus in Altum i Sc hic in Cantum mutari dcbct , Tcnor vcro o- cta«4o Infotenpbj^/khtbebis yoccs ad rraroralem ftitum redu&as, vt fcquitur .

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Ltb.Vlll. MuJurguxMmjica. 69

Pofuimus hic 8. columnas \ prima columna raonftrat exceflum vocum vltra natu- ralcra conftitutionem alcendentium, Sccunda columna vocum ad mediocritatem re- ductarum mutationem oftcndit ,itavidcs Alti vocem vtad mcdiocntatem redigatur fiibire dcbere locum Cantus, & CStus vt mediocritatem habeat debere cederc in locu Alti ; Tenorem verd fi mediocritatem non habeat, o&auainrraincederc dcberc*» . Quam rcgulam fi ftnc"tc feruaueris,nulJam amplius in proportionandis vocibus diffi- cultatem rcpcries \ Elt cnim ita comparatum vocibusa natura, vt vna excedenteme- diocritatcra, mutatio iIJius in aliam neccflario excefsu rcducat ad mediocritatem, qu? mutuatranstormatto maxime locumhabet in Altojfiueenim Tcnor ,fiue Cantusex- ceflcrit,altcrutra vox in Altum migrans admcdiocritaic rednc*ta ccnfcbitur.trafmigra- tiotameninoftauaTenorimelius conuenit,quamCantui ;fi tamen ita dcfcenderet profundc vt infra notas Bafis inccdcrct, vt in Tenorc accidit, tunc Cantus cum Tcnorc ledes fuas mutarc potcrit .

Porro hc.c rufius declaranda funt ; fi itaquequatuor voccs hanc conftitutionem ha- bcrc nt, cjuam tertia columna oAcndjt id eft plus $quo fingulc. dcfcendercnt; tunc mu- QHomo<,° tandxforcatinvoces inquarta columnaprimiscorrclpondcntes,itavidelicct Cantus vocumper- m Altum ; Altusin Cantum, Tenor & Baiis 8 fupra incedcre dcberent , vt quarta colii- agcn<ta_*. na monftrat . Pari pacto, fi voces altius xquo mcederent vt quinta columna demoftrat , tunc rautandxforent, in voccs, qualcsfexta columna monitrat . fcUicet Caatus m Al- tum ; Alxusin Cantum , Tcnor vel ra Altum vel vti & Bafis in ottauam infra mutari de- berct . Scd cumhafCcIarcexexcmpIjspateant,»jsnoojmmorabimur. iolum hic du- bium Tyroni occurrcre poflet, qua rationcftatim ilJe voces mutaripoflint .

Refpondto, nihil faclu faciliuseile. Si cnim loca dauium fiuc literarum in pentagram- mo Cantus, eadcm m pcntagrammo Alti vel altcriuscuiufuis vocis, puncftis notilque-f figncs, habebis quxfitum . Sunt cnim loca clauium fingulis quatuor vocibus commu- nia ,&idemprorluseft , fiuelocaclauium Alti ponas 111 Cantu, fiue Cantus vcl Te- noris ponas m Alto ; Vnde & fcquitur quod in quolibet Mufarithmo trium numeroru feries ad tres rcliquas poft Bafim voc.es pertinentcs funt indiflcrcntes , ita vt prima fc- ries tam Alto,quamTcnoricompetat,fecunda & tertia tam Cantui quam Alto & Tc- nori, IndirTerentia tantuminhocconfiftit, quodin vna voce fubindc altius autpro- fiindiusxqu6incedant,&hoccafu vocesdicto modo pcrmutandejunt . Vcrum vtTy- roni hic aliquam fatisfactionem de.mus , Sit vox Cantus in prc, cedenti exemplo ab cx- ceffu fuo ad mcdiocritatem redigenda, hoc eftin Altum mutanda fit ; ita operabcris, cum dux primx not$ Cantus confiftantinF, terrjain E,quartainC, quintainB,fexta Afeptima inC, &oftauain D. Vidcbisvbina in Altipcntagramo fintdiftaru clauium loca, m hifce enim notc. pofitc, dabunt in vocc Alti CantO ad mcdiocritare reduclum-.; ita in omnibus aJijs operaberis; Vbi etia notabisTenore" &Cantu,ira fimiles etTe,vt nul- lo prorfus fcrtipulo vnaproalterafumi poftit ; cfom in pentagramis non nifi vnicoin- tcruallo diftent. Solaigitur transformatto ex altcrutra in Altum ficri debct, qui a di- ctis vocibus, vt plurimum ditono aut diateflaron diftat .

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CANON III.

T>ejlgnis b b & X intra columruu Tonorum occurrcntibiu .

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N columnis Tonorum fubindc occurrunt in certis tonis hxc ilgna b & X. Quo o- ftendimus, illis litcris ,qux per numcrum cui hxc litera b. afcripta cft , indicari

quibufcumqucin pcntagj-ammis reperiantur, fempcrb. prxfigi dcbcre , idem diccndu eft de b quadrato, & de figno £ femitonij maior is; hoc cnim feraper fere 7. numcro af- fixum eit; litera ioiturquc. per huncfeptcnarium numerum infcala clauiu fignatur , no- tam hoc figno artcdamrequirit, non iemper quidcm fed tunc cum nota fcquens afcfc-

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derit, vel finahsfucrit,velpaufam habueritfcc*ucntem;fed vidcqua? de hifcefignis fu- fiustra&auimusinfchemate primo Mutatioms VI. toni,inpriroum. Vbi& exemphu, dcdimus • Sed in gratiam Tyronis repetemus excmplumfuprapofiti in fecundacolum- na fyftematis vniuerfalis .

Canrus Altus

Videsinhocexeroplovltimam cantus notam <quod finalisfit hocS not.irijln Aho vctdprimam&fcxtamhoceodemfigno. cumenimhocexemplumfecandi toni fit; fi columnam clauium columna? fecundi toni applices , ir uenies 7 hoc figno 35 affe£urn_. Fliteram denotarc;vbicumqucigiturin pentagrammis F cocurrerir, ibi notahocfigno affccbponenda eft, vt in prima &fexta Alti nc ta apparct. Prxterca in hoc tono,vti & primo,numero6.femperappofitum b molleefleinuenicsjtjuodcumE rcfpiciar, dcno- tatin omnibuspcntagrammis,vbihxclitcraoccurrcrit ,ibi notamaffeclam cflc debe- rcliterab. In primovero tono oftcndit notam in chorda b quantumuis dura,b roolli tamcnfignandam,vtin primitonifchcmatcfuperiorisfyftcmatisclare patet, vbiquin- ta notabafisb mollivti& 3.tenorishoc fignoaffeftafpeclatur . Scdhcc clarioraiunt , qtiam vtfufiustraclarimercantur.quare adalia_#.

C A N O N IV.

De Tonorum eleHione .

OMncsMufarithmifinguIisduodccimtonis prolibitu & promifcue adaptari nec dcbent necpoflunr, cura Mufjrithmi multi fint ,qui ccrtis tonis proptcr illici- torum intcruallorum ( dc quorum notitia poftea pluribus agcraus) oc urlum, applicari nonpoflunt. Hinc vt tonorum commoditaci facilitatiquc in operando coniulercmus, finguliscolumnisafcripfimustonosappropriatos mufarithmis diclarum columnarum ; quibus feruatisomnes procul dubio errorcs tacilcvirabuntur. Quartus&quintusrard in vfu funt, & paucis tanruro Mufarithmisaccommodantur , obfcquentem vti dixi illi- citorum interuallorura occurfum . Reliqui omnes in vfum facile venire pofTunt . Hinc fuadeo vt Tyro primd fe in fcx tonis potifllmum exerceat, vidclicet 1 . x. 3. 6. 7. 8. hi c- nim cumpnncipales finr, & fere cumfcx rcliquisconucniant,ad omnem harmonicam modulationemabunde fumcicnt,imo vixvllaaflignaripoteft cantilena,quc. non iuxta vnum cx his fcx tonis compofita fit . Si quis tamcn rchquis fex quoque tonis ad ma- iorcm vanctatem vti velit,illi non repugnamus, dummodd ea q ua diclum cft , cautehu proce-dac .rncjiusquoque fcceritTyto,vt priusinll.&VLtono fccxerceac

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C A N O N V.

Dc tllicttU intcruallis euitandu \

COntingit fubinde vt rautandotonum,Iiter$in illicitainteruaili incidant ,qu$ vt omniftudiocaueas,vclim.Suntenimmaximumin Mufica abfiurdun ,& aurcs mirurn in modumflagellant. Suntautcm fcqucntia-».

1/Itctta tntcrualla. 3 4

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	—	Sterz
53

Reduclio illtcitorum intcruallorumadlicita.

6

Prima fcrics intcruallorum oftendit intcrualla illkita: fccunda, mtcrualla reducT*-. . ln prima & fccunda columna vides mi contra Jfc, kf» contra «i abfurdiffimum intcr- uallum, rcduci pcr mutationem duriCantusin mollem.Intertia&quartacolurana-. vidcs nt contra^/i in primo tonoreduci pcr mutationemcantusduri in b. mollcm-» . In quinta &fcxta colunavides illicita interualla in cacu rooili.reduciper mutatione ca- tus mollis in durfi orailTo vtroq; b, vcl cxduro in mollt vtroq^dm»flo,& ficdc cceteris.

Vides i-iturquarationc prohibita interualla reducidcbcant. Quandocumquc igi- tur in vnum ex hifcc incidcris, vcl claufula mutanda eft cx duro in molicm,vcl cx mol- liin durumivelqnod confult.usiudicauerim, Mufarithraus rautandus erKrquod netj fialium qujcfiucnsMularithmumcuiusvltimiduo numcri inbafi,diucraaprioniint,« habcbis ncgotium totum, finc tanta mutarionc confeclum . Vndc canoncm ficrorma-

^Quandocunquc numcriMufarithmorurainprohibitainterualla inciderintitunc J x Mufcrithrausmutanduscft,quodfiet, fialium acceperis ,cuiusduo vlurai nuracri inbafidiucrfifint.cxcmplumhocfit. . lttmm

SintMufarithmobalisduovItimi numcri y.i. qui in columnaV. tom incioent 4 inFB &cantusfitdurus,habcbuntq,nota!cadcntiam,quarafccunda columna mon- fttat, fcilicct prohibitam. Quaercigituralium Mufarithmumbafiscuius numcri non-. habcant * . 1. fed v. g. 6. x. hos fiapplices cidem columnxclauiujn prodibunt duaeutc.

7-2 Artis oZMdgrne Conjbni, DiJJoni

rx G & C. pofitxijjitur in dictis. locisprodibit interualluro lkitum vt c latcre patct . Vcl filaborcm fugias in alio Mufarithmo quxrendo , om- niumfacilJimonegotiorcmexpedics,ficolumnamclauium vno gra- du altiiisproraoueas, vthice laterefadtumvides ; Nam primacolum- natonivitiofuminteruallumpr^ftatsaltcracolumnavno gradu altius promotaita vt %. literx G relpondeat, iim interuallum prohibitum_. rranslatum, licitum interuallumprxftabit , Sed hcc poftea fufiusprofe- quemur . Vides igitur quara diutrfis mocjs illicita interuallaemcnda- re poffiraus .

C A N O N VI.

De mutatione Tonorum in *vna & eadem cantilena Jtue

de mijiura ^Tonorum.

TT t -

NE Muficusquifpiam nobisobijccrepoflit,nosin Mufarith- misnoftrisnuJlambabcrc varictatera, circa mifturam., Tonorum hic cam traderc voluimusj vt autera hanc mifluranu! tonoruro intclligant Tyrones ,fciendum eft Muficara ita varic- tatisamantcm clfc,vt fiin vna&cademtantilcnaqualitcunique illafucrit,perpctuus afliimpti toni tcnor, & eademfempcr intcr- uallaferucntur, nccplaccre, nec auribus vllamiucunditatcm-j prxflare poflir , quin potius molcftia& txdium adfcrant . Hinc peritiores Mufurgi,diuerforura tonorum claufulis,veluti totide coloribus diucrfis fuas modulationescum raagna audicntiunu* iucunditate, exhibere folcnt. Ne igitur dic~ti Mufurgi putent no- flrum Mufurgicum artificium hoc modo ingeniosc intcrtexcn- ditonos priuaturn cflc ,hoccanonc monftrabo , qua radoncfi- milibustcxturis noflras Melothefias adornarepofliraus,nequic <juam in hac noftraMufurgia omififlTc vidercmur .

Nota itaque intcrualla principij & finisalicuius cantilenx s6- per ordui, & tcrminan dcbcrcin tono, quiprothematc afllim- pfuseft.Mediumautemdiucrforuratonorum claufulis Iuxu- nari pofle , dummodo fempcr ex hifce diucrfis tonis aflumptis , rcfleiitat in tonum proprium afiumprom : fier autem hxc muta. tio artificiofh hac methodo. Defcribarur duplexcolumna Tono- rum,eoquihic elatercvidcrurraodo, dcindc fit paradigma- tis loco Icquens hymnus, ldcm quifupii, fupra fcxtum ronum-, compofitus. :.;P .:.*:..• d -

Cunrr.r.x EpitemicX TotioTum,

Perioduj I.

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Etprimaftrophafiucperiodus ficfcxtitoni,vcIis autcm alium quemuis tonum cui cantus molhs competit, lecundc ftrophx accomraodare , ira agc : promoue coluronam toni vno gradu iurfum ita vt i non iam F fcd v/ G . refpondeat , & hoc perarto Mufa- rithmi quarauis ijdcm , qui pnrai iahum tamcn tonnm fortientur vidcJicct fccundum ;

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proucnietquc daufula vtin fecundaftropha patet, nos hoc loco tantum experimcnta in vna vocc bafis ponimus> reliqu? cnim voccscomponuntur cadem prorius ratione— *> quabafis. Siitcrumpromoucascolumnam numcrorum per j.gradus,ita vt i vcl8. rcfpodcatD. vt in columnaru fecuadaapplicationepatet,deinde iuxtahac metathefin pcntagrammis punfta impretTeris , prodibit II. toni miftura, & ad tertiam mctathefin-. IX. toni miftura prodibit , vt tcrtia periodus oftendrr, Quarta verd periodus > crit vt onor fcxti toni . Nam vtdiximusprincipium &finis femptr dcbent icipondere tono fupra qucm cantilena quxpiam principalitcrcompofiracft.

Vidcs igttur quam ftcili negotio tonorum fiat mixtura . In cantilenis igitur fupra_, tonum molliscantuscompofiti fummoftudiocaucndum cft,ncapplicatio fiuepromo- tio columnx numcroium contingatin gradu, qui propric cantui durocompetat,& ii cantilcna fa&afuerir in cantu molli ,toni qui durocantui competunt,mifcere nulla_* ratjone poiTunt aut debcnt, nifi ccrtis ijfque rariffimiscafibus,dum nimirum ingcntem mutationcm ex gaudioin triftitiam artificiose innuere volumus. Adagnofcendos vero tonos ritd pcrmixtibilcs hofce Canoncs i fcruato ,icd demusaliud cxemplum_..

Quandocunqifeligis pro quapiam compofitione pcrficienda tonum II. fcias eofdcm fecQdr toni mufarithmos tcr aut quatcr mutaripoflc per bacillos tranfpefitorios. fienim prima alicuiusMufarithmi notam vna tertiaaltius acceperis; habcbis nouam daufula & pcrfeftam rautationemtoni,itcm fivnaquartaaltiorcm pofuerisideindc vna quinta,&deni- quein pnorcm tonumrcucrfusfueris: ied in cxcmplo rcs dariusclucefcet. Sit huiufmodi Mu farithmus pt opofitus in_. notisfccundi toni.hunc limutari velis, applica columnarn-. numerorum mufarithmorum ad columnam dauium fiuc li- teraium muftcarum, itavt i. rcfpondeat primae norc. mula- rithmi,vidclicetinG. hoc paclo prodibit pro primo vcrfu ahcuius metri primadaufula fccundi toni.fi vcrdpromoueas columnae numcrumad B, ica vt i icfpondeatB, &dcmde_:» numcrosmufarithmorumin notas rcfolucris,habebisprima mutationem prioris claufulaevthicapparct.fi vcrdcolum- nam diclam numcrorum numcro fuo i liter$ C incolumna clauium appiicaucris, deinde iuxta hanc applicationem nu- mcros mufarithmorura in notas rclolueris , prodibit fecun- da mutatio claufuixvthic apparetifi verocolumnam nume- rorum numero fuoradicali applicaocris ad D & iuxta hac applicationc numerosinno- tas refolucris prodibit tcrtia mutatio , vthic apparct . Quarta vcro daufulacntcadcm cum prima .

I.MuCirirh.II.Toni Prima Mucatio SecundaMutatio Tcrtia Mutatio

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Vndc hanc formamusregula :In omni mufarithmo II. toni, quatuor mutationcs fic- ri poflunt.prima contingit, fi i numerum columnx numerorum appliccs vna tcrt»a,vna quai ta 3 & vna quinta altiorem primanota primi Mufarithmi ; proucnict cnim perfccu tonorum miftio.

cs4liud Exemplttm mutationn tonorum .

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C A N O N VII.

.81* ! V-

De Ditandu frohibitu interuaUit .

I. /^VVandocunquc cantilenaaliquaeftfignamcharaclcrifmocantus mollis, nu- V^/ ^ merus i . vcl 8. columna» memorata?, ncquaquam applicari dcbct fupra_, litcras A & E. cum cnim harc intcrualla propri£ cantus duri fint, pratcr quam quod diaerfae naturc ronisinfercr€tHr, ctiam in intcrualla iJlicita incidercnt . ad rcJiquas vcrd orrmcsliteras diclus numerus i .vcl 8. applicariporeft .

1 1. Si cantilcna fuerit fignara characlerifmo cantus duri , tunc numcrus i vcl 8. nc- quaquam ftatui debet fupra B. & fupra E, & hoc adhibitis fignis b nifi,non rufi raro: bas duas regulasfi ritc feruaris,finc pcriculo vlloin miftionc tonorumprogrcdicris .

C A N O N VIII.

De fofttionefignorum chromaticorum b Ir j;-

VErum in vtraquc columna dimera applicatoria inucnics figna chromatica tam li- tcrisquam numerisaffixa; quibusfignificauimus, quod, quandocunque tam_. numerusquamlitcraijfdem fignis notataoccurrunt,tunc notariftiufmodi fignurapr$- figendum , Si vcro alrcrutra ccllula columnaru ijs fucrit vacua, omittendum crit. Ita in primacolumna CJiteram fignoXaffeclam reperies. 5.autem numerum correfponde- tcm codempriuatum ,quo indicarc voluimus C non cfie afficicndum hoc figno , fcd prorfus omitrcndum. Iterum in cadem columna leptimum numcrum paritcr hoc figno Xaffcftum rcpcrics,cuiE refpondctcum pra?fixob. quia vcrd literapriuaturfignoSE& numerus 7 priuarur Jirera b. fignum tibi crit , vtrumque in hoc tono , tim literam b , quaroj&Omirreitdam.quayomniadiligentcr notandafunt. Promota verocolumna_» numerorum vno gradu v. g. cx F in G . rcpcrics numerum b fignatum »7 vcro figno Jgaffeclum.quibus numcris,cum E &Freipondcantijfdem fignis notatac indicabit tibi vti nt E prxhVendura b. itl F. praefigendum efTcX-adc6 vt haec vniucrfalisrcgula cfTcpoflit . Quandocumque tamhtcra», quam numericorrefpondcntcsijfdcm fignis af- fccli'occurrermt,tum literas poftularearfcclionem fignorum ■, fivcr6 altcrutratantum vd Jitera vcl numcrus hifcefignis affcctusfuerit, literam nulla rationc co figno notan- dam . Nota quoquc fignum X non fcmpcr, vti in Canone tertio monuimus poni dcbe- re,fed >unc,cum notafequensafccndcrit, autpaufaimmediate fequatur,autctiara fi- nalisfiierit. Sedh$c omniafufiusin fequcntcpartetraclabuntur.quarcedLcclorera

rcmittimus

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C A N O N IX.

De Multiflicationc Mufarithmorum .

VT maiorem varietatem in Mufurgia noftra monftraremus , hunc Canoncm ordi- nauimus. Confiftit autcm multiplicatio inhoc,ciim cx vno numcro alicuius Mufarithmi integrum Mufarithmum formemus . Sit procxcinplo logarithmas2fa/£rpro primo themate Paradigma.

affumptus fequens 5- 1 4 5 6 5 5 1 . cui refpondcnt g-A—

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quideiufi 5. pfliespro multitudinc fylhbarurainafluragtotheroate. Veni Creator Sp* ritusy ponas,id eftprimam notara in Cpofitam 8. rcplicesj&dcindealteramperioduni firailiter oftiesin F. & 3 . (imilitcr oclics in Bi & vltima vox ordinariam cadentiam Jir- uet . Verum cx fequenti cxcmplo mcntem noftram mclius percipics . fj

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Vidcs in hoc excmplo fuperioris paradigraatis primi notarn in Ceflc hic oftiesre- plicata iuxta o6to fyilabas, fecundam vcro notamhic in F paritcr oftics multiplicatam tcrtia,in B.fimilitcr, quaitainC. ita tamen vt 3 primas notasin C,duasfequetcsinD; & 2 inC,& vJtima tande in F ponas,vt m paradigmate.Nc vcro in notis mctroractris cr- res»acciperepoteris,praqualibetnotavnam cx duodecim notarum in caicc columnar ottofyHaboru contcntaru feriem.Sccud6fiintegra^period.os noIj^poterisMuiarjt^.mu, diuiderequouismodo.Vel enim primani notamparadigmatasinCdupldrcveltripIarC vd quadruplarc vcl quintuplarc &c. & iecundam notam in F. fcxtuplarc, vcl quin,tu- plarc, vcJ quadrpf lare, vcl triplare vcl duplare, \ t in lequenti cxempJo patct .

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Eccein hocparadigmatc cx infinitisrerecorr.binationibuspauculas tantum felcgi- mus;primx tres clauiiila? refpondent duabus notis fuperioris paradigmatis , vt in prc- cedCti pentagrammo bafispatet, quarta &quinta tribus notisfuperioris paradigmatis, fexta quinquereliquis, atquehex omnia mfinins vt dixi modis mutabiles& replica- biies fu nt;Sicut cnim primar,fic & vltim? multiphcabiles sut,idq;in tcmpore quouisda- to . Verum ciim dc hifccin fcquentibus fofius traftaruri fimus, hic fuperuacaneum cflfc ratus fum ijs longiiis im morari . Ex his fequitur quam facili negotio hac mcthodo con- centus illi quos vulgo [fnlfobordone ] vocant ficri poffint. Sint enim dati v. g. Mufarith- mi 1 5 1 .& 37 1 5 . in notas translati, vt hic patctconftctes,vt barbarcloquar,/a^«r»i bor- ^»f/w,fiprimaf & terticin primo membro.dcindeprimxin fccundo membro, & quar- tc noti valorem per longam exprimas,vt fequitur.

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Quibus quidem notis quofuis vcrborum hymnos,quofuis deniquepfalmosaccom- modarcpoteris . Atquc hoc harmodic; «enerc in pfalmis hymnifquc canundis Mufici pafiGm vtuntur» vtproindeciim vulganafintampliuspertraftandanonccnfeamiQua- re hurufmodiraiTos bordones componcndi mcthodum eantum tibunfinuafle fufliciat ; nc quKqyam in muficafu, in quod Mufurgia noftraimperiu luumextendcre dici non

C A N O N X.

De Vcrborum ad notai accommodatione .

jd nt ;nup4*i**4D «} *«o8 mimtiq j n»rrc; c« .Ditiljrcup . • .hmo\g r4»E»3l

INPinace I.pofuimuspolyfyllabaquorum penultimalonga ; InfecundoPinacee-» contra polyfyllaba pofujmus penultima brcui i Quotieicunque igitur vox alitjua-» quotcunquelyllabarum^occurrcntjCuius vltimalyllabalongatuericpnmi pinacis po- lyfyllabis vtens ; Si vero penulcima brcuisfuerit, fccundi pinacis prourriculus dcmon- ftrat, Mufarithmis vrerisi In calce vcr6 vtriufque rabulc ,hoc eft m calce vniufcurufque columnxnotx pofitxfunc Metromeerc, diftc^coquod datum qualecunque polyfyllabu perfe<fte & multis modis mctiantur . V.g. fi fie fupcr hxc vcr ba c omp o nc nd u m, Magni- ficat anima mea Dominum accipe in fecudo pinacc in columna cecrafyllabor u penulcima breuipro Magwficat» quemuisMuiarithmum.cuiincalccrcfpondcnt nocxmecromc- trf ; pro Anima mea% accipics in primopinacc in coiumna pentajyllaboru, quemuis Mu- fanthmum ,cui quxlibet in calce noearum mcrrometrarum feries reipondet. harc cnim ifyllaba etn penultima natura brcuem habeac,hab£c tamc quoad fonum longam.

C

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el pro libieu proAnima rriJyllabum ; Sc pro mea biflyllabo vti potcris . qux omnia tam

fupra declarata iune

O A P V T V.

DeMufurgiaPbetica metricaRhythmica, quse Contra- punclo fimplici vfitato fiue pari vocum progreffu conftruenda-» .

SYntagma Il.tabularum Mclorheeicarum contineejMuCu-iehmo^omnfsgenerisme- trisapplicatosatqucadco hocloco vniuerfam Muficam poeticam, quantum fieri poteft <*6'o A« tradabimus, vt nulla natio in mundo fit , qux non poflit fupra quoslibec verius m oatiuaJjngua cooftru&os S> mphoniasomnis gcncris (criamfiMuficxfucrint imperi' i) <;or*ft«*ucre . Quod tanto racio libentius.quanto non ica pndem hoc a Syris Sc Arflbibus^acParfflJUs noftris Indisalijfque diuerfarum Prouinciarum inftancius a mo fui t requ lfitum > acceffit quod a nemine id huc vfque prxfticumfciam . Nam cunj non fcmpef vbiuifiiocowjm, qutarccm mciotheticam nonntMagiftrircpcriantur,Cantilc- n$ tamenfiu<a4ckuotioncmhominum cxcitandam,fiucin vlus eheacralcs aut ctiatrt propriam recrcationem f«ruientes,fubindc nccefTaric. finti opcrx prccium mc facturum ouftimaui, iihocloco modum traderem , quoomncspopuli ieipiisfupra darisquof- Iibct in natiua lingua conftruclos verfus,quaslibct harmonias &quouisartificio ador- natascomponere polfint, Quod quidem nulia ratione mehusin cffec~tum deducipo- tuit, quam per Muiurgiam poeticam , quc cum oracionem fiue cenum verborum con-

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Ltb.VllL MuJurgiaMirifica. '77

tcxtum nen vagoac foluto ftylo ,fed cundcm mctrica quadam amuffi fub cctto fylla- barum pedumque numcroligct & conftnngatiMctra autcm ommbus Jinguis appiita- ripofluntiCcncidnobismagr.umfane ad propofitum noftrum pcrtiDgendum prx- bct compcndiQ, fcd omiflis veiborumambagibus ad rcmiplam progrcdumur a lati- msvcrfibusinitiumfaduri.

Sicutiigitur corpus cx varijs membris, tabella cx varijs piduris , & harmonia ex di- ucrfisvocibusoriuntur.itacx varijspcdibusvarij nafcuntur verlus,metrafeu Rhythmi, vt proinde verlus nihil aliud fit quam orario ccrtogcncrc atquc ordine pcdum aliigata, quorum quidem nouem fpeciesi nonnulli vigintiquatuor i ajij pJura ,paucioraaIijpo- fucru nt i dc quibus fingulis fusc parte fccu nda huius libri : n os rcJiiitis hiicc poctaftroru ahcrcationibus ,ea mctrorum gencra aflumcmus, qui & ad aniiru aflcdiones cxcitan- das pJus encrgia?, & ad Muficos numcros plus aptitudinis habere vidcbuntur . Ordinc igitur naturaJi progrcdicntcs , a minimis verfibus ad maximos vfque finsulis Muurith- mos aopropriatos pcr tabulas applicabim u s , vt fic dato quolibct vcrfu , ftatim pinax cfi Mufanthmis verfusdatiiimeniripoflit. Cum vcro plcrumque non vnusvcrfusautftro- pha» fcd plures fimul 3 coaceruentur,omnia vcrfuum gcnera in tctraftrophaid cft qua- tuor ftrophasparticmur, vt fic faciJion ncgotioin artc Mufurgicaproccoat Tyro .

Propofitio I.

Datumetru Adonus {$> certotono M elotbefiam quamuis infiniUL^

quadam varietate comfonere .

QVamuisAdoniusverfusnon nifiraropolyftrophusfit ifed vt plurimum fapphicis tnftrophis m fineadiungi foleat, nos tamen hic pro themate tctraftrophon_* ~ aflumpfimus , vt artcm noftram ilJi mcliusapplicarcpoflemus . Sit mctrum-. tctraftrophon Adontum datum, vtfcquitur .

Adonium Tetraftr.

Ttu\>i\>\M atrxU Condita, nuilum Fundere pojfuni Sydera lumen

Dadylicum Tetraftr.

Tolliee lumina Jd T/aga fidera Ctrnite tiumints Luctdamunera .

Petitur (iipcr hos verfus componi mufica> ita operaro.

T)Rimo,fcligaturTonusvetbisaptu$, exfyftematevniucrfali jvelexmenla Tono- X graphica^.

Sccund6,fignctur fyftemaphonotaclicum chara&erifmo cantus,quem tonus rcterr, duro fi durus,firaollis>mollj,ideft fingula quatuorvocum pentagramma fuis fcalis & dauibus vt in menfaTonograpJtiica praricripfimus» & infripatet>ugnanda funt .

Terti6,HocpcraftoaccipcPinacem III. antc tc , in quo prima columna Adonia_»i fccunda Daftylicacontinct» exccrpanturquc quatuorMuiaiithmiquatuor ftrophis da- us compctentcS) vtfequitur .

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HosMufarithraosnon ordincquoin columnafequuturexcerpfimus> fedpromifcuCjVt yidcret Tyro quoslibctMufarithmosaccipipofefine_> difcretione, &pcrinde eiTc liue ordinc reclo, fiue ordinc intcrrupto,fiuc tranfuerfo,fiue cti5 oblictuo eosaccipias.quii uisconfultius fecerit Tyro, fi ordincm naturajefrt columnarum feruct . Excerptis Mularitlimis>hac ptfaxleosin notasanimabis.

' <2uart6,frrtejflus Vl.fupra^uem mclothcfiaconitruendacftjquxre igUtir columnam hulustonj &iuxta cam appliccs columnam dauiuaL*. vtinmar«incj>atct.

Quinto ,accipeprimam Mularirhmiprin m numcrorum , vidcli- cct 5 5 3 5 5. & vidc cui iitera? in columna clauium refpondcant , & inuc- nics refponderc CC ACC, imprirne igitur in pemagnarnmo cantus duo pun&ain fpacio C, & vnuin A. in difcrctis pro tribusfyliabis [Nuybi,bus\ fpaci^vtvidesidcmdeduoahanunftainfpacioC.cjufdeirt pentagrammij in difcrctis pro duabusfy llabis|>/m] fpacijs. habcbjfquc pro primaflrophaconfonantiaruraloca dctcrminata,j .

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Sextd,pro Altoaccipcfecundam Mukrithmiprimi nnmerorumferiem 3 2878. & vi- dequibusincolumnadauiumJitcris hinumerirefpondcant, &repenes AGFEF.in_. fccundoigitur pentagrammo Alto in tribusfpacijs difcrctis fpacio AGF. corrcfportde- tibus triapunclaimprimcs>deindc vnurn Ipacio E. & dcnique vnum itcru m in ipacio F. habebifqueloca harmonicain pentagrammo Alti detcrminata .

Scptimo, prorenoreaccipetertiamMufarithmiprimi numcrorura fcriem 55- 123.& videquibusnamlitcrisincolumnaclauium illarefpondeanr,&inucnicsCCFGA.ira- primc igiturin totidem fpacijsdifcretis puncla in locis quibus litcrcj affixeTunt , vidcli-

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cetprima duo punclainfpacioCjtcrti^in F.quartuminG.&quintum in A.habcbif- quc loca harmonrca Tenoris deterrriina"ta_» .

Octauo, accipc pro Bafi quartam Mu farithmi pr imi numerorum fcriem 876 5 1 . & vi- dc quibuinam in columnaclauium Jitcns rclpondcat, repericfqueFEDCF.imprime^ itaque pun&atotidcm in fpacijs difcicrisjatquc iri locis, qua?dauibus correfpondcnt in pcntagrammo Bifli. & habcbis loca bafis decerminata, vt in prccedenrifchemate— > patet.

Non6,pofitispunctis notas ijsfuprapones, ea qua-fequitur methodo,accipe in calcc columnaequamcunquc notarum fcricm, norafquc fingulasfingulispunctisapplicabis, ita vt omnes notatin fingulisquatuorpentagrammis vnifyllaba? rcfpondentcsfintciuf- dem valoris; apparebitque prima ftropha harmonica , vt in fupcriori fchcmate patet .

Decimo, reliquas ftrophaseademprorfusratione & merhodo , quaprimamexpedi- uimus, expedics . Ncque enim vlla diucrfa operandiratio in illis occurrcre poteft. Da- to igitur metro Adomo tetraftropho, & dato tono cantilcnam aifiqnauimus,quod crat faciendum__.

Nota in fragmatiam feraclam .

NOta prirao,in huiufmodimetriciscompofitionibus,eafdcm prorfuscautelasrc- gulafqueobfcruandas efle, quasin pnecedcntibus iocanonibustradidimu6. Quosvt felicius in ncootio proerediaris,perfcde caJlerc dcbcs, vt fi difficu Jtas aliqua oc- currcrit, quid faciendu fit deliberare polfis ; Soluimus cnimin illis 10 canonibusquic- quid in vniuerfaMufurgia occurrere poteft difficultatis. Vcrum in iequentipropofitio- nc aliquas particularcs rcgulas aflignabimus ; quibus quicquid hic omiflum eft , vber- tim recompcnfabitur.

Nota fccundo , huiufmodi mufarithmosquibuslibettonisaccommodari poflc , ex- ccptisijs, quiobtritonumaut femidiapenteeosnon admittunr.

Notatcrti6,fcdcsfignoruraaccidcntaIium obferuandas.fine hiscnim facilc crror contingere poflet.

Nota quart6,vel per vnius mufarithmiad diuerfis tonisapplicarionem>eundcn__ cffeclum prodire, qui pcr 4 diucrfos mufarithmos diucrfis ftrophis accommodatos.

Notaquint6,admifturasronorum anificiofius in 2 & j ftrophainfercndas,ordinem columnarum naturalemferuandum; ita vt prima columna ftrophar prima»; fecundafc- cundac, tcrtiatcrtia:; quarta quartar correfpondeat,hoc enim paclo omnis in miftura to- norum error vitabitur; & cantilena naturaliproceflu conXtituta, dulcius aures fcriet . Qux omnia fummoftudio obfcruanda funt .

SequiturPinax Mufarithmorum .

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Propofitio I I.

Dato metrolambico Eunfed<co, dato tono quolibet fufra illud quzmltbet harmomam componere.

IAmbicum Euripcd xura mctrum hectafyllabumeft, cuius Mufarithmos in quatuor columnis PinacislV. Syntagmarisfecundiordine , velutintoridemcctiaft.opha^. otdinauimus,vt tituluscolumna.um demonftrat . ArTumamus pro thcmate mctrivul- gatiflimurn, facatiffimumqueilliimhymnum, quiJcquitur.

Aue maris sltlla DEl Matcrabna Atquc femper Virgo Felix caliporta .

Supcr hunc itaquc tctraftrophon quifpiam defidcrabit componcrc modulationcrru* quatuor vocibus dccantandamj isita proceder . Primdcolumnas rcfciflaseo ordine_*>> quo volucrit ordinabit vclctiam^Mufarithmos quatuor ftrophiscorrefpondcntescx- ccrpct feorfim i Sint autcm quatuor Mufarithmi ordinc iuxta ftropharum ordincm ex- cerpti, vt fcquitur .

II.Toni

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I'jitu6 , cxpedies ftrophc, pnmx Mufarithmum , deinde ordine reliquos . Vide igitur quibuslitcri-s m^ohnnnaclnUmnuefporldeantprirriiMiifarithmiprima numeroruau, fcncs 12, 413. & inuenfrs GABCAB. harumhtcra-ium loca quxre m pentagrammo Canrus, ibique puncla imprimes. vt vidcs,demde vide quibus litcris in columna clauiu relpondeatlecunda numeroruminprimoMufarijhmolcncs V7SS/ & repcrics DB.» GFG.harum htcrarum Itxaquxrcrapcntagrammo Ak»,ibiquc punfoimpritnc :tcr> rio vide quibus literis refpontrCHteimT>umerorum ferics $zi 1 ?f in eodcm Muia- rithmo, & reperieseam rciporfdcre BAGGDD. harum htcrarum luca quxrc m penta- grammoTenons , ibique punela imprimc . Quarto videquibus htens m columna cla- uium Bafis Mufarithmus 8764y8reipondeati peritfqneGFECDG.harum lireraium loca in pentagrammoBafisdihgentcr nota , ibique punclaimprimc . Quibus imprc:hs accipe quamcunquc notarum mctrometcaruin (quas in taicccolumnaiuminucnics) feriem;camque vnam & eandem fmgulis quatuor vocibusaccommoda,vidclic:ct »fu- prapuncta fingulispentagtammisimprc fla .Namhxcpunda oftcndunt fpacia in qui- bus notxnumero punftiiquccorrefpondeDtes poni dcbent,habebifque prioiam ftxo. pbam compofitami Reliquaso.rdinc ftrophas cadcm prorfus rationecxpedics .Dato i- gitur IambicoEuripedxotetraftropho & dato tonoqucfito,datam melodiam compo- fuiraus, quod erat facicndum_j .

J^ota in Pinacem IV.

I V 7Tftropharum mclodiafinccrioi habcatnr , mufirithmi exftropbarumcolum- V n's naturali ordine difpofitis excerpantur . Quod ideo monemus nc mulun- thmi hinc indcfine vllofelcdtuexcerpti,quofdam fuppcditent, quiminusfuaui mc- lodia influant. hinc prouidimus, vt muiarithmi naturali ordinc deprompti femper per- feclara harmornam , qucinexaciatonorum miftura confiftit, cxhiberent.quod «fu* pramonuimusVSein omoibusiccuturis pinacibusobfeii.an.dum cft.Hoc non ideodi- clarn velJm',quod in promilcuc depromptismuiarirhnus nulla haimoniaprodcat ;ea_, rnlw fetnper, quocunque ©rdine eos depropfcris emergct, fcd quod ij , non crTcctum_. parcmijs, qui excolumnisordinc naturali dcpromuntur ,exhibeant . Si quis tamcru* inhocncgotioexercitatior fiicritiiscx difpofitionenumerorumfacile quoqucinten- tutn, hmc inde eos deproracndo, effcftum confequetur .

II. LocaS&>. fummo ftudio,iuxtaprxceptainprxcedcntibustradita, obleruan-

da funt .

III. Velvnicusmufarithrnus fufficictad^ftropharum perfeftamharmoniam ;u vti m prxcedentibus diftum eft, per bacillos tranfpofitorios diuerfis tonis, vei quod idem cft diuerfisliteris in columna clauiura applicetur . hoc interim obferuando , vt vltima., itropha femper primx quoad tonum rclpondeat.

IV. Hofccprxdtftos4ftropharummufarithraosomnibustonis in capitecolumna- rum defcriptis applicarepoteris;hoc camen obfcruando,vt fiin voce quapiam vox al- uor aut dcprcifior,fuerititamcumalteravocc >vtin canonibusdiftum cft,commutcs.

PINAX

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Propofitio III.

Dato tetraflrofho monocolo Anacreontici metrijuper id quamuid har-

moniam fetitam comfonere.

Slt datura tetraftrophon vtfcquiturduplex Anaciconticumproprie diJhirm&Boc- tianum-.-

Oterquatcrqtxfchx Habet omnu hocvohiptas

Cicada^fupremis AnaCrConticum SttmuUs aghfurentes Boctianum. Jnarborumviretts 71 reu Apwmquc per volantum

Cantarc dulce gaudc: Ferit acJacordamorfu.

Quicunqucigiturftipcr hocmctrum harmoniam defideratcomponerei isitaproce- daLfittoDusVIII.datusproformacantus. Ton.VlIT. L Accipe quoslibctMufanthmosmxta4.ftrophasdilpoutosinictiue-

tipinace,vtinferiuspatet.

II. Sionenturpentagrammapalimpieftiphonotaclicbaracteriimocan- tus duri prout oftauustonus rcfert .

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16 Artis Magn* Conjont , Dijfoni

Propofitio I V.

Dato Tetrdftrophomonocolo metrilambici Archilochici4atoquetono

harmoniampetitam componere.

DAtum fit Tetraftrophon fcouens, hymnusfcilicct in Ecdcfia cantatiffimus Vexjlta Regij prodeunt Fulget cructs myjlerium Qua vita mortempertulit Et morte vitam protuht . SitqUctonusprimusdatus,fupcrqucm quifpiam defiderabit compo- nerc harmoniam,ita proccdct.

I. Applicacolumnamclauiumcolumn^ toni primi. Deindc fi^nabis quatuor vocum pentagrammijs in palimpfeftophonorafticoiuxta tonum primum, quicharadterifmiduri cft.

II. Accipe 4 Mufarithmos quofuis cx Pinace fcquenti ex quo nos 4 z- quales muiarithmos 4 ftrophis corrcfpondcntcs accepimus .

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Deinde opcrare punclando pentagramma , vt in prxcedentibus didum eft, deinde applica punftisquarumc unquc notarum in calcc columnarum fericm, nos hic triplam ciegimus,&prodibitharmonicum tetraftrophon quarfitum; vt hic apparet; diligentcr ob(cruando,pofiriQnttn fignorum c hromaticorura X & b. locis oportunis facicndam. Quomodoverd huiufmodicantilenaru Copofiti oncsinfinitis modis variari poflint,dixi- musin canonibus, quosconfulc,&inpropofitioncprima pinacisprimi . Intcrim cc su- mo ftudio notarc vclim* quod & fupra in Canonc II. monuimus ; Si voccs in aiiquo to-

nopIusa?quoaltiusautprorundiusdcfcendercnt,caspermutandasinter fe , vt cirato locofuscdocuimus.

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