TEXTS ON MUSIC IN ENGLISH
School of Music
University of Nebraska--Lincoln
Lincoln, NE 68588-0100
(phone: [402] 472-2507; Internet: plefferts1@unl.edu)

Data entry: Robin High
Checked by: Peter Slemon
Approved by: Peter M. Lefferts

Fn and Ft: SCOTA3B4_TEXT
Author: Anonymous
Title: The Scottish Anonymous
Source: Judson Dana Maynard, "An anonymous Scottish treatise on music from the sixteenth century, British Museum, Additional Manuscript 4911, edition and commentary," 2 vols. (Ph.D. dissertation, Indiana University, 1961), 2:333-69. Used by permission.
Graphics: SCOTA3B4 01GF-SCOTA3B4 18GF

[-333-] [fol. 113] HEIR BEGINIS THE THRID PART OF THIS LIBELL AND THE FOURT BUIK OF MUSIC

The first tua partis of this present libell beand formaly dressit [as] first in the beginnyng dedusit eftir the form and ordour, now it is nedfull to schew the process and discription of the ferd part of music callit proporcion musicall. Quhair[foir] it is necessar to be knawin:

CAPUT PRIMUM

Quhat is proportioun? Nicholas Barroducensis dois determ[ine] that proporcioun is of tua quantateis of the samyn kynd of ane till ane uther in equalitie or excess ane certain habitud. Thairfoir it is to be knawin that all proporcion is other equall or inequall.

Proporcion equall is quhair all equalitie in the proprie moderation keipis ane mesur and quantatie, that is to say, that equall proporcion is quhan tua numeris equall ar togidder assimulat, as tua contra [thrie crossed out] tua, 3 contra 3, 4 contra 4, 5 contra 5, and sa furth.

Inequall[t crossed out] proporcion is quhan tua quantateis inequall ar togidder comparit and maid alyk of quantatie, as 4 to 3 and 2 to 3, the quhilk proportion of inequalitie is dubill, that is to say, of the mair inequalitie and of the less inequalitie.

[fol. 113v] Proporcion of the mair inequalitie--quhat is it? It is quhan the mair [quha crossed out] quantatie is coequat and comparit to the less, as 4 to 3, 4 to 2, or saxt to 3.

[-334-] Proporcion of [the] less inequalitie--quhat is it? It is quhan the less quantatie is maid coequat to the mair, as 3 to 4, and 3 to 6, the quhilkis kyndis of mair and less inequalite musicians wyslie dois consider; fra the quhilkis inequaliteis fyve kyndis of proporcionis ar sprung and uprasit, that is to say, of the mair inequalitie, thrie sympill kindis and tua componit.

Of the mair inequalitie: Thir ar the 3

Multiplex

Superparticulare

Superparciens

Thir ar the 2

Multiplex superparticularis

Multiplex superparciens

Of the less inequalitie:

Submultiplex multipliciqueicans [sic]

Subsuperparticulare

Subsuperpartiens

Submultiplex superparticulans

Submultiplex superparciens

Th[e] first kynd of the mair inequalitie is callit multiplex and it is quhen the mair nummer contenis in him all the less nummer twyiss, thryss, or four tymes and say furth and, giff the mair nummer contenis [fol. 114] the less twyss, it is callit proportio dupla, as 2 to 1, 4 to 2, 6 to 3, or 8 to 4. Gif the mair numbre contenis the less thryss, than it is callit proporcio tripla, as 3 till ane, 6 to 3, and gif the mair numer contenis the less four tymes, than it is callit proporcio quadrupla, as 4 till 1, of the quhilk kynd thir proportionis eftir following everrie ane in thair awin quantatie of numer dois rewfully proceid.

[-335-]

dupla 2 till 1

tripla 3 till 1

quadrupla 4 till 1

quintupla 5 till 1

sextupla 6 till 1

septupla 7 till 1

octupla 8 till 1

nonupla 9 till 1

decupla 10 till 1

This ordur precedent is of the first kynd of the mair inequalitie--callit multiplex.

subdupla 1 to 2

subtripla 1 to 3

subquadrupla 1 to 4

subquintupla 1 to 5

subsextupla 1 to 6

subseptupla 1 to 7

suboctupla 1 to 8

subnonupla 1 till 9

subdecupla 1 to 10

This ordur precedent is of the first kynd of the less inequalitie and it is callit submultiplex.

Of [the] quhilkis fornemmit proportionis of multiplex gener sax of tham to modulation ar admittit, that ar to say, dupla, tripla, quadrupla, sextupla, octupla, and nonupla. The uther thrie, as quintupla, septupla and decupla, fro the fruition of musicians ar declynit for quhy thay may nocht formalie be inducit that men may plesandly sing tham as eftir [pars crossed out] wart pars aliquota sall declair. Nocht-the-les, thay suld nocht be expellit, for causs thay ar ry[c]th w[i]sly formmit and amangis the leif of proporcionis ordurly situat.

[fol. 114v] To produce intelligens of the rehersit kyndis of multiplex and submultiplie gener, the saiddis thrie declynit proporcionis beand excludit, viz., quintu[p]la, septupla, and decupla, thir decorit exemplis followand of diveris nummeris ar worthy to be amplexit and to memory commendit.

Gauforus Laudensis dois mak mention that all proportion is destroyit quhen eftir proporcionat notis the [sign] of perfyt or of imperfect tyme is desponit and attour gif subdupla or subtripla beis eftir tripla or dupla disponit be cyphris contray to tham, dupla and tripla salbe depryvit and in that place have na mair strynth. Subdupla [-336-] and subtripla fra that furtht in thair awin kindis salbe modulat ay and quhill ane uther proporcion or muid distroy tham. Thairfoir siclyk jugment of all utheris proporcionis is to be considerat, as the consequent speculation dois report:

[Anon., Scottish, 336; text: (Example 154.), 1, 2, dupla, sincopa, subdupla, quadrupla, [fol. 115]]. [SCOTA3B4 01GF]

[-337-] [Anon., Scottish, 337; text: subquadruple, octupla, quadrupla, suboctupla, tripla maior, subtripla, tripla, sextupla, subsextupla, tripla minor, [fol. 115v], nonupla]. [SCOTA3B4 02GF]

[-338-] [Anon., Scottish, 338; text: tripla, tripla maior, nonupla, subnonupla]. [SCOTA3B4 02GF]

The leiv, forsuith, of multiplie and submultiplie kyndis to the consideratioun and wisdom of musicians we leiff to be sersit and soch[t].

[-339-] THE SECUND CHAPTUR

The secund kynd of the mair inequalitie, as Franchinus sayis, is callit superparticulare. That is quhan the mair nummer to the less anis with the part aliquota of hym is comprehendit, that is to say, quhan the mair nummer in himself dois conten[i]t all the less numbre anenis and of him [self crossed out] the part aliquota beyond, or atouur quhilk is understand to be referrit to the said numer, equivalent in quantatie and mesur of tym.

[fol. 116] Quhat is pars aliquota? Pars aliquota is the part quhilk oft wyiss twa dois compleat the haill number allanerly, as 2 to 6, the quhilk twa thriss multiplicat dois fulfill the number sax.

Quhat is pars non aliquota? Pars non aliquota is the part quhilk oft syiss twae completis nocht the haill number, as 3 to 5, the quhilk thrie beand multiplicat comis never to fyve for quhy uther tua acceidis the numbre or thay ar within the number. Thairfoir, it is nocht pars aliquota.

Of the quhilk gener infinit kyndis ar to be sersit and fund, of the quhilk kynd thir proportionis eftir followand everry ane in thair awin [kynd crossed out] quantatie of number rewlfully dois proceid.

sesquialtera 3 for 2

sesquitercia 4 for 3

sesquiquarta 5 for 4

sesquiquinta 6 for 5

sesquisexta 7 for 6

sesquiseptima 8 for 7

[-340-] sesquioctava 9 for 8

sesquinona 10 for 9

This ordur precedent is of the of the [sic] secund kynd of the mair inequalitie--callit superparticulare.

[-339-] subsesquialtera 2 for 3

subsesquitercia 3 for 4

subsesquiquarta 4 for 5

subsesquiquinta 5 for 6

subsesquisexta 6 for 7

subsesquiseptima 7 for 8

[-340-] subsesquioctava 8 for 9

subsesquinona 9 for 10

This ordur precedent is of the secund kynd of the less inequ[a]litie--callit subsuperparticule.

The declar[at]ion of the foirnemmit and eftir nemmit proportionis with dyverss fyguris and exemplis dois eftir follow and quhow mony of the proporcions as we find that may be formaly inducit and reducit, say mony exemplis we hav practicit with the inductionis of tham.

[fol. 116v]

[Anon., Scottish, 340; text: proporcio dupla, diapason, sesquitercia, diatessaron, sesquioctava, tonus, sesquialtera, diapente, diapenthe, 6, 8, 9, 12]. [SCOTA3B4 03GF]

[-341-] [Anon., Scottish, 341,1; text: sesquialtera, quadrupla sesqualtera, dupla sesquiquarta, sesquitercia, dupla, tripla, 2, 3, 4, 9]. [SCOTA3B4 03GF]

[fol. 117]

[Anon., Scottish, 341,2; text: subdupla, subsesquialtera, subsesquitercia, quadrupla, dupla, tripla, 1, 2, 3, 4].[SCOTA3B4 01GF]. [SCOTA3B4 03GF]

[-342-] [Anon., Scottish, 342; text: (Example 155.), induccio, sesquitercia, dupla superbiparcienstercias, reduccio, [fol. 117v], tripla minor, sextupla, tripla maior, alteratio, diviso, sesquialtera maior, tripla maior decolorat, subsesquialtera]. [SCOTA3B4 04GF]

[-343-] [Anon., Scottish, 343; text: tripla maior colora, sesqualtera decollora minor, subsesquitercia, sesqualtera, tripla, induccio, subsuperbiparcienstercias, [fol. 118], sesquiquinta dimidia fra the precedent, reduccio, subduplasesquialtera] [SCOTA3B4 05GF]

[-344-] [Anon., Scottish, 344; text: induccio, subsesquiquarta, supertriparciensquintas, dimidia fra the precedent, tripla, sesquialtera, quadrupla sesquialtera, [fol. 118v], dupla sesquiquarta, sesquioctava maior]. [SCOTA3B4 06GF]

[-345-] Tripla maior and tripla minor, suppois thair be diversitie in the notting of tham, thay ar baytht alyk modulat in ane mesur and tym. Evin the samyn jugment is to be had of sesquialtera maior and minor as of tripla maior and minor.

The breve of dupla sesquiquarta and the breiff of sesquioctava ar boyth alyk of tym and mesur.

Dupla sesquiquarta is, as sesquialtera, song apone tua nottis of the sesquialtera precedent--the quhilk is induction to sesquioctava.

Sesquioctava maior is fund thrie maner of wayis; the first, be dupla superbiparcienstercias set contra tripla; secundlie, dupla sesquiquarta set contrar aucht mynny[m]is; thridly, be sesquitercia set contrar sesquialtera as this exemple dois furth schew:

[Anon., Scottish, 345; text: (Example 156.), The first exemple, dupla superbiparcienstercias contra tripla, [fol. 119] The secu[n]d, dupla sesquiquarta contra aucht mynnyms, The thrid, sesquialtera co[n]tra sesquitercia] [SCOTA3B4 07GF]

[-346-] THRID CHAPTUR

The t[h]rid kynd of the mair inequalitie is callit superparciens. That is quhan the mair nummer in him self dois contein the less anenis and a part attour, than the said numbir to the less is coequat in power and mesur of tym. And, gif the mair numbre dois contein the less anenis and tua partis beyond throw the quhilkis it is nocht pars aliquota in respect of the less numer, than it is callit superbiparciens, as 5 to 3; als[o], gif the mair numbre dois contein the less anyss and thrie partis beand nocht aliquotit, than it is callit in respect of the less numer supertriparciens, as 7 to 4; and, gif the mair numbre dois conten the less aneiss and four partis atouir nocht aliquotit, than it is callit superquatriparciens, as nyn to fyve and sua furth, till infinit be multiplicat.

Mairatouir, gif ony part of the forsaid partis be thrid part of the less numbre, than it sall hav denomination, tercias; and, gif it have the ferd part, than it sall have this denomination, quartas; [fol. 119v] and, gif it be the fyvft part, it sall haif this denomination, quintas and sua furth of the leiff, etc. Item, gif the less numbre be trynarie, than it is callit tercias and, gif it be quaternary, it is callit quartas and, gif it be quinary, it is callit quintas and [sua] furth, ascendent as this proporcion ta[k]ne betuix fyve and thrie, than it sall have this particle, bi, for quhy the mair numer dois contein the less aneiss and tua partis beyond throw quhilkis it is nocht pars aliquota in respect of the less numbre and sall hav this particle, tercias, for quhy everry unitie of thir partis atour contentit is the thrid part [-347-] of the less numer. Theirfoir, betuix fyve and thrie the proporcion is callit superbiparcienstercias. Item, gif the mair numbre dois contene the less aneiss and thrie partis atour throw quhilkis it is nocht pars aliquota in respect of the less numbre, than the proporcion is callit supertriparciensquartas, as sevin to four. Item, gif the mair numbre dois contein the less aneiss and four partis beyond nocht aliquotit, than the proporcion is callit superquadreparciensquintas, as nyn to fyve and so furth of the kindis of superparciens eftir the multiplication of sub and super, quhilkis till infinit may ascend.

Item, the foirnemmit proporcion superparciens may be callit superbiparcienstercias for quhy it is the sam proporcion and of the samyn nymbrie as betuix fyve and thrie as forsaidis. Item, the proporcion supertriparciens may be callit supertriparciensquartas and so furth of the leiff, etc. Ittem, Franchinus Laudens[i]s says, gif the parcient numbre and the partit partis eftir the denomination of the evinlyk number, be considerit nocht in the superparciens bot in the epymory, habitud dois convein, as sax to four. It is nocht, swythly, callit superbiparciensquartas bot it is callit sesquialtera. [fol. 120] Item, of superbiparciens ane is callit superbiparcienstercias, as 5 to 3; ane uther is callit superbiparciensquintas, as 7 to 5; ane uther superbiparciensseptias, as nyn to sevin and so furth. Item of supertriparciens siclyk ane is callit supertriparciensquartas, as 7 to 4; ane uther supertriparciensquintas, as aucht to fyv; ane uther supertriparciensseptias, as 9 to 7 [sic] and so furth. Item, of superquadriparciens ane is callit superquadriparciensquintas, as nyn to fyve; ane uther superquatriparciensseptias, as alevin to sevin; ane [-348-] uther superquatriparciensnonas, as threttin to nyn. Item of superquintuparciens, ane is callit superquintuparcienssextas, as alevin to sax; ane uther superquintuparciensseptias, as XII to VII; ane uther superquintuparciensoctavas, as 13 to 8; and [uther crossed out] in the same maner tho kyndis superparcient to infinit numer dois proceid as the ordour in this wiss is decryvit.

superbiparcienstercias 5 to 2 [sic]

superbiparciensquintas 7 to 5

superbiparciensseptias 9 to 7

supertriparciensquartas 7 to 4

supertriparciensquintas 8 to 5

supertriparciensseptias 10 to 7

superquatriparciensquintas 9 to 5

superquatriparciensseptias 11 to 7

superquatriparciensnonas 13 to 9

superquintuparcienssextas 11 to 6

superquintoparciensseptias 12 to 7

supersextuparciensseptias 13 to 7

subsuperbiparcienstercias 3 to 5

subsuperbiparciensquintas 5 to 7

subsuperbiparciensseptias 7 to 9

subsupertriparciensquartas 4 to 7

subsupertriparciensquintas 5 to 8

subsupertriparciensseptias 7 to 10

subsuperquatriparciensquintas 5 to 9

subsuperquatriparciensseptias 7 to 11

subsuperquatriparciensnonas 9 to 13

subsuperquintuparcienssextas 6 [to] 11

subsuperquintuparciensseptias 7 to 12

subsupersextuparciensseptias 7 to 13

[fol. 120v] This figur consequent of diverss greis is componit, in quhilk fyve cyphris dois proceid fro the uther circlis to the sax circle set in the middis of the figur. The proporcionis callaterall procedent fro cyphre to cyphre within the uther bordouris, suppois thay [-349-] be calculat in fyguris pre[ce]dent, heir thay fulfillis the lymeittis and makis the figur perfyct.

[Anon., Scottish, 349; text: quadrupla, dupla, sesquialtera, supla superbiparcienstercias, supertriparciensquintas, supduplasesquialtera, sesquiquinta, sesquitercia, 2, 3, 4, 5, 6, 8] [SCOTA3B4 08GF]

[-350-] [fol. 121] THE FERD CHAPTOUR

The ferd kynd of the mair inequalitie, as Franchinus dois writ, is callit [multiplex] superparticulare, that is to say, quhan the mair numer to the less comparit dois comprehend him oft syiss and attour ane aliquot part of hym, of the quhilk, forswyth, infinit kyndis of dyverss greis ar to be considerit.

The first grie dois proceid fro the first multiplie permixit superparticularis, eftir the naturall disposition of tham, as dupla sesqualtera, V to II; dupla sesquitercia, VII to III; dupla sesquiquarta, IX to IIII; dupla sesquiquinta, alevin to fyve, and so furth.

The secund [de crossed out] grie dois proceid fro the secund multiplie, susceptible of all superparticularis naturally disponit, as tripla sesqualtera, 7 to 2; tripla sesquitercia, ten to thrie; tripla sesquiquarta, XIII to IIII; tripla sesquiquinta, 21 [sic] to 5, and so furth.

The thrid grie is that all the habitudis of the superparticular kyndis to the thrid multiply ar conjunit, as quadrupla sesqualtera, 9 to 2; quadrupla sesquitercia, XIII to 3; quadrupla sesquiquarta, sevntein to four, quadrupla sesquiquinta, XXI to 5, and so furth.

The ferd grie is that all superparticularis to the ferd multiply dois adheir, as quintu[p]la sesqualtera, alevin to 2; quintupla sesquitercia, XVI to III; quintup[la] sesquiquarta, 21 to 4; quintupla sesquiquinta, 26 to 5; etc., and so infinit gries of this kynd dois proceid.

[-351-] [fol. 121v]

dupla sesqualtera 5 to 2

dupla sesquitercia 7 to 3

dupla sesquiqua[r]ta 9 to 4

dupla sesquiquinta XI to 5

tripla sesqualtera 7 to 2

tripla sesquitercia 10 to 3

tripla sesquiquarta 13 to 4

quadrupla sesqualtera 9 to 2

quadrupla sesquitercia 13 to 3

quadrupla sesquiquarta 17 to 4

quintupla sesqualtera 11 to 2

quintupla sesquitercia 16 to 3

quintupla sesquiquarta 21 to 4

subdupla sesqualtera 2 to 5

subdupla sesquitercia 3 to 7

subdupla sesquiquarta 4 to 9

subdupla sesquiquinta 5 to 11

subtripla sesqualtera 2 to 7

subtripla sesquitercia 3 to 10

subtripla s[es]quiquarta 4 to 13

subquadrupla sesqualtera 2 to 9

subquadrupla sesquitercia 3 to 13

[fol. 122] subquadrupla sesquiquarta 4 to 17

subquintupla sesqualtera 2 to 11

subquintupla sesquitercia 3 to 16

subquintupla sesquiquarta 4 to 21

[-352-] THE FIVFT CHAPTOUR

The fivft kind of the mair inequalitie, as Franchinus sayis, is quhan the mair numbre of the consequent nottis to the less numbre of the noittis precedent referrit dois contein the self numer oft syiss with ane aliquot part of him conducent mony aliquottis, of thy quhilk kynd infinit greis to evry multiplicis quhatsumever superparcientis dois proceid.

The first grie is maid of the first multiplie to everry superparcientis togidder knet, as dupla superbiparciens, dupla supertriparciens, dupla superquatriparciens. Thay kyndis ar callit subaltera, that is to say, that dois supplie the vice of utheris kyndis be alteration of tym and forther everry ane is convertit in the strenth of gener with connection. Of dowbill superbiparcientis, ane is dupla superbiparcienstercias, as VIII to 3, ane uther is dupla superbiparciensquintas, as XII to V, ane uther dupla superbiparciensseptias, as XVI to VII, ane uther dupla superbiparciensnonas, as XXIII [sic] to IX and so furth.

The secund grie dois conjune everray superparcientis of the secund multiplie, of the quhilk the ordour is subaltern and maist speciall, tripla [fol. 122v] superbiparcienstercias, as nyn [sic] to thrie; thripla superbiparciensquintas, as 17 to 5; tripla superbiparciensseptias, as 23 to 7, and so furth.

The thrid grie dois put the thrid multiplie to every superbiparcientis, of the quhilk the ordour is quadrupla superbiparcienstercias, as XIIII to 3; quadrupla superbiparciensquintas, as 22 to 5; quadrupla superbiparciensseptias, as threttie to sevin, and so furth.

The ferd grie is that everry superparcientis dois apply to the [-353-] ferd multiplie in this ordour: quintupla superbiparcienstercias, as 17 to 3; quintupla superbiparciensquintas, as 27 to 5; quintupla superbiparciensseptias, as 37 to 7. The process of the same oft syiss considerit be application of subaltern ar superparcientis to everry multiplis, as dupla superbiparciens, dupla supertriparcienss, dupla superquadriparciens and in the leiff diverss consideration dois gane and accord. Of the quhilk eftir is to be writtin.

dupla superbiparcienstercias 8 to 3

dupla superbiparciensquintas 12 to 5

dupla superbiparciensseptias 16 to 7

dupla superbiparciensnonas 20 to 9

dupla supertriparciensquartas 11 to 4

dupla supertriparciensquintas 13 to 5

tripla superbiparcienstercias 11 to 3

tripla superbiparciensquintas 17 to 5

tripla superbiparciensseptias 23 to 7

[fol. 123] thripla supertriparciensquartas 15 to 4

tripla supertriparciensquintas 18 to 5

quadrupla superbiparcienstercias 14 to 3

quadrupla superbiparciensquintas 22 to 5

quadrupla superbiparciensseptias 30 to 7

quadrupla supertriparciensquartas 19 to 4

quintupla superbiparcienstercias 17 to 3

quintupla superbiparciensquintas 27 to 5

quintupla superbiparciensseptias 37 to 7

subdupla superbiparcienstercias 3 to 8

subdupla superbiparciensquintas 5 to 12

subdupla superbiparciensseptias 7 to 16

subdupla superbiparciensnonas 9 to 20

subdupla supertriparciensquartas 4 to 11

subdupla supertriparciensquintas 5 to 13

subtripla superbiparcienstercias 3 to 11

subtripla superbiparciensquintas 5 to 18 [sic]

subtripla superbiparciensseptias 7 to 23

subtripla supertriparciensquartas 4 to 15

subtripla supertriparciensquintas 5 to 18

[-354-] subquadrupla superbiparcienstercias 3 to 14

subquadrupla superbiparciensquintas 5 to 22

subquadrupla superbiparciensseptias 7 to 30

subquadrupla supertriparciensquartas 4 to 19

subquintupla superbiparcienstercias 3 to 17

subquintupla superbiparciensquintas 5 to 27

subquintupupla superbiparciensseptias 7 to 37

[fol. 123v] Dyverss mudis ar proporcionat quhilkis ar conte[nit] in the levnt chaiptour of the first buk of sympill music, that is to say, tonus in soundis is proporcionat witht sesquioctava in numberis as 9 to 8. Diatessaron in soundis is proporcionat with sesquitercia in nummebris, quhilk is callit in Greik epytrica, as 4 to 3. Diapenthe in soundis is proporcionat with sesqualtera in numberis, quhilk is callit in Greik emiola, as 3 to 2. Diapason equison in soundis is proporcionat with dupla in numberis, quhilk is callit in Greik epogdoa, as 2 to 1. Diapenthe cum diapason in soundis is ordorit in the proporcion of tripla in numeris, as 3 to 1. Disdiapason is ordorit in the proporcion of quadrupla, as 4 to 1. It suld nocht be callit disdiapason bot it suld be callit disdiapason for quhy diapason is Greik and it is componit with dis, Grek, as disdiapason. Dis in Greik is als mekill to say as bis in Latin, thairfor thay faill that writtis it bisdiapason. Disdiapason is ane intervall be ane fyvftend within the quhilk natura hes befoir fixit diligently as ane mark to the voic humane somekill that the naturall voic beyond the bordouris of the sam ma nocht proceid nor passaig haif.

[-355-] Disdiapason Subdiapason Epydiapason

Disdiatessaron Subdiatessaron Epydiapenthe

Disdiapenthe Subdiapenthe Epydiatessaron

Of the quhilkis fornemit muidis, ane reall exemple in ane figur speculateve dois eftir follow:

[fol. 124]

[Anon., Scottish, 355; text: diapason, diapenthe, diatessaron, tonus, dupla, sesquialtera, sesquitercia, sesquioctava, 1, 2, 3, 4, 6, 8, 9, 12] [SCOTA3B4 09GF]

Thir ar the proportions quhilkis may be lichtly inducit to modulation, that is to say, of multiplie gener and submultiply:

dupla subdupla

tripla subtripla

quadrupla subquadrupla

sextupla subsextupla

octupla suboctupla

nonupla subnonupla

[-356-] [fol. 124v] Of the gener superparticular and subsuperparticular:

sesquialter subsesquialtera

sesquitercia subsesquitercia

subsesquiquarta 4 to 5

sesquiquinta 6 to 5

sesquioctava 9 to 8

Of gener superpacient and subsuperpacient:

subsuperbiparcienstercias 3 to 5

supertriparciensquintas 8 to 5

Of multiple superparticular and subsuperparticular:

subdupla sesquialtera 2 to 5

dupla sesquiquarta 9 to 4

quadrupla sesquialtera 9 to 2

Of multiplie superparcient:

dupla superbiparcienstercias 8 to 3

The remanentis of the proporcionis, except thir that ar put heir befoir, ar difissilt to be inducit, thairfoir we refer tham to mair subtill practicianis of music to be sersit and soich out and formally to modulation inducit.

The proporcions afoir nemmit beand all formaly put in ordour, ane schort canticle of thrie partis dois eftir follow, in the quhilk we have [-357-] inducit almoist all proporcions cantabill, so that thay may be lyghtly modulat nocht offendent the eyris of the auditouris.

[Anon., Scottish, 357; text: [fol. 125] (Example 157.), inductio, sesquitercia, subsesquialtera, dupla superbiparciens tercia, tripla] [SCOTA3B4 09GF]

[-358-] [Anon., Scottish, 358; text: sesquitercia, sesquialtera maior, quadrupla, [fol. 125v], quadrupla sesquialtera, inductio, subdupla sesquialtera, sesquiquarta, supertraparciensquintas diminutie fro the precedent, sextupla] [SCOTA3B4 10GF]

[-359-] [Anon., Scottish, 359; text: tripla maior, tripla minor, inductio, subsesquitercia, subsuperbiparcie[n]stercias, [fol. 126], sesquiquinta dimidat fro the precedent, tripla, sesquialtera, dupla sesquiquarta] [SCOTA3B4 11GF]

[-360-] [Anon., Scottish, 360,1; text: sesquioctava] [SCOTA3B4 11GF]

[Anon., Scottish, 360,2; text: [fol. 126v] (Example 158.)] [SCOTA3B4 12GF]

[-361-] [Anon., Scottish, 361,1; text: sesquioctav, sesquioctava] [SCOTA3B4 12GF]

[Anon., Scottish, 361,2; text: (Example 159.), [fol. 127]] [SCOTA3B4 13GF]

[-362-] [Anon., Scottish, 362; text: sesqualtera, quadrup sesqualtera] [SCOTA3B4 13GF]

[-363-] [Anon., Scottish, 363; text: (Example 160.), duple, diminucio simplex, simplex diminucio, quadrupla, duplex diminucio, diminucio duplex, duplex diminucio, duplex diminutio, tripla, sesquialtera, sesquialtera simplex] [SCOTA3B4 14GF]

[-364-] [Anon., Scottish, 364; text: quadrupla sesquialtera, dupla sesquiquarta, sesquialtera duplex, sesquitercia, dupla superbiparcienstercia, sesquialtera, inductio superbiparcienstercias] [SCOTA3B4 15GF]

[-365-] [Anon., Scottish, 365; text: [fol. 127v] (Example 161.)] [SCOTA3B4 16GF]

[-366-] [Anon., Scottish, 366,1] [SCOTA3B4 17GF]

[Anon., Scottish, 366,2; text: [fol. 128] (Example 162.)] [SCOTA3B4 17GF]

[-367-] [Anon., Scottish, 367] [SCOTA3B4 17GF]

It is to wit, that tua principall kyndis of proporcions ar nemmit, thay ar to say, dupla and tripla, fra the quhilkis ane plesand pluralitie of proportionis dois furth spring. Dupla for the numer binar, quhilk dois hald the place primordiall, quhairfra dyvess proporcions of the said kynd principall dois discend. Tripla fro the numbre trinar, quhilk dois hald the seit iniciall, quhairfra dyverss proporcionis of the said principall kynd dois descend, of the quhilkis tua kyndis of dupla and tripla the proporcions that may be inducit be ony of tham in exemplis precedent and subsequent ar plesandly practicat and convoyit.

[fol. 128v] Dupla, 2 to 1, 4 to 2, 6 to 3, 8 to 4.

Quadrupla, 4 to 1, 8 to 2, 12 to 3.

Octupla, 8 to 1, 16 to 2, 24 to 3.

Sesquitercia, 4 to 3, 8 to 6, 12 to 9.

Dupla superbiparcienstercias, 8 to 3.

Subsesquiquarta, 4 to 5.

Supertriparcienciens, 8 to 5, it is inducit with the diminucion of subsesquiquarta nix[t] procedent.

Thir proporcions, quhilkis respect has to the proporcion dupla, plesandly may be modulat.

[-368-] Tripla, 3 for 1, 6 for 2, 9 for 3, 12 for 4.

Sextupla, 6 for 1, 12 for 2.

Nonupla, 9 for 1.

Sesqualtera, 3 for 2, 6 for 4.

Subsuperbiparcienstercias, 3 for 5.

Sesquiquinta, 6 for 5. It is inducit with the diminucion of superbiparcienstercias nixt precident, the quhilk induction fra tripla dois descend.

Quadrupla sesquialtera, 9 for 2.

Dupla sesquiquarta, 9 for 4.

Sesquioctava, 9 for 8.

Subdupla sesquialtera, 2 for 5.

Thir proporcions prece[de]nt, quhilkis respect has to tripla, plesandly to modulation may be inducit.

[fol. 129]

[Anon., Scottish, 368; text: 9 for 8 sesquioctava, 9 for 2 quadrupla sesquialtera, 3 for 5 superbiparcienstercias, 3 for 2 sesquialtera, 4 for 3 sesquitercia, 2 for 1 dupla, 3 for 1 tripla, 4 for 1 quadrupla, 6 for 1 sextupla, 8 for 1 octupla, 9 for 1 nonupla, 6 for 5 sesquiquinta, 8 for 5 supertriparciensquintas, 4 for 5 sesquiquartas, 8 for 3 dupla superbiparciens tercia, 9 for 4 dupla sesquiquarta] [SCOTA3B4 18GF]

[-369-] This figur ostensive, quhilk last in ordur is situat, reser[v]at the secrettis of all proporcions thairto pertenig. The cyphris contra utheris upon t[h]e s[p]akis of the quheill inwith betuix the nave and the ryne calculat dois signifye the numberis of everie proporcion be thairself; upone the uter part of everry spaik, quhilk throw the ryne is persit, the nam of everry proporcioun ingravit. The tua circlis haill and half dois betakin muid perfyt and imperfyt of the fyguris and nottis upon the centrie of said nave ingravit, so:

[Anon., Scottish, 369] [SCOTA3B4 18GF]