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

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

Fn and Ft: DEPRPA1B_MLBLL763
Author: Anonymous
Title: On the nature of proportion
Source: London, British Library, Lansdowne 763, ff. 117r-118v.

[-f.117r-] HEre beginneth Tretises diuerse of musical proporcions. And of theire naturis. and denominacions. Ferst in englissh. and than in latyne.

NOW passid al maner sightis of Descant and with him wel replesshid. yt natural appetide not saturate sufficientli but feruentli desirithe mo musical conclusions as nou in special of Proporcions and of them to haue plein informacion. of the whech aftir myn vnderstonging ye shal haue opin declaracion. But for as moche as the namys of hem be more conuenientli and compendiusli sette in latin than in englissh therfor the namis of hem shal stonde stille in latin. and as breueli as I can declare the naturis of them in englissh.

Ferst ye shal vnderstonde that proporcion is a Comparison of .2o. thinges be encheson of numbir. or of quantite. like. or vnlike eythir to othir so that proporcion is seide in 2o. maner of wyse scilicet Equalitatis and Inequalitatis [.2tem. proportionem scilicet equalitatis. et inequalitatis in marg.] Proporcion of Equalite is whan .2o. euyn thingis be likenyd eythir sette togedir in Comparison as .2o. to .2o. or .4. to .4. and so of othir. Proporcion of Inequalite. is whan the more thinge is sette in Comparison to the lasse or the lasse to the more. as .2o. to .4. or .4. to .2o. or .3e. to .5e. or 5e. to .3e. And this proporcion of Inequalite hathe 5 spicis or naturis or keendis. whois namys be these in general [5e. genera nominum proporcionum in marg.] [.1. supra lin.] Multiplex [.2. supra lin.] Superparticularis [.3. supra lin.] Superparciens [.4. supra lin.] Multiplex superparticularis [.5. supra lin.] Multiplex superparciens The ferst spice eythir keende of Inequalite is callid Multiplex. that is [-f.117v-] to sey Manifolde. and that is whan the more numbir. conteynythe the lasse manyfolde. as twies .1. and that is callid in special Dupla id est tweyfold. as .2. to .1. or 4. to .2. or 6. to .3. and so forthe endlesli Yyf the more numbir conteyne thries the lasse. than it is callid in Special. Tripla. as .3. to .1. 6. to .2. 9. to .3. Yyf it be .4. times the lasse conteinid in the more than it is Quadrupla. as .4. to .1. 8. to .2. 12. to .3. and so forthe Qvindupla. Sexdupla. Sepdupla. Ocdupla. and so vpward endlesli. As for othir keendis ye shal vnderstonde. that ther be .2. maner of Parties. one is callid Aliquota and another is callid. Non aliquota Pars aliquota is whan that partie be ony maner of multiplicacion yeldithe his hole. as whanne betwene his hole and him is. proporcio Multiplex. As a vnite is Pars aliquota of euery numbir For be multiplicacion of that euery numbir wexith and tweyne. or dualite is pars aliquota of euery evyn numbir and thus this partye shal be namyd in special after the numbir on whom he is multiplied and yeldithe his hole. For yf he yeldethe his hole be multiplicacion. of .2. it is callid altera id est halfe. And yyf he yeldithe his hole. be multiplicacion of .3. it is callid Tercia id est the thirde parte. Sequitur exemplum. 2o. is the thirde parte of .6. and .3. of .9. and .4. of .12. And yf he yeldith his multiplicacion be .4. than is callid Quarta as .2o. for .8te. for .4. tymys .2o. is .8te. And yf it yeldith his hole be multiplicacion of .5. than it is callid Qvinta. An of .6. Sexta. and so forthe endlesli. Pars non aliquota. is whan that party be no maner of multiplicacion may yelde his hole. As .2o. is a parte of .5. but he is non aliquota. For hou so euer he be multiplied he makithe not euyn .5. For yf ye take [him supra lin.] twies it makithe [-f.118r-] but .4. And yf ye take him thries he passithe and makithe .6.

Proporcio superparticularis. is whan the more numbir conteynyth the lasse. and more ouer a party of him that is Aliquota and aftir the special name of that parties Aliquota. shal that proporcion be namyd in special. As betwene .6. and .4. is proporcio Sesquealtera. [exemplum et exposicionem de sesquealtera in marg.] Ses. in grew id est totum in latin. al in englisshe. so Sesquealtera is for to sey. al. and halfe. For the [more supra lin.] numbir conteynyth al the lasse. and halfe therof more ouer. Betwene .8. and .6. is proporcio Sesquetercia. For the more numbir conteynyth the lasse. and his 3de. parte ouer. Betwene .10. and 8te. is Sesquequarta. Betwene .12. and .10. is Sesquequinta. Betwene [.14. supra lin.] and .12. is Sesquesexta. et sic infinite.

Proporcio superparciens. is whan the more numbir conteynythe the lasse. and more ouer the whech excesse eyther superplu3 it not pars Aliquota of the lasse numbir As betwene .5. and .3. But than thu must loke to that excesse. whan the more numbir passithe the lasse. and deuyde it into sweche parties that be aliquota. And loke hou many ther be therof. and what is her special namys. and whether they be .3e. 4te. or .5te. and so forthe. And yf ther be .2o. parties Aliquote than thu shalt sey in special Superbiparciens. and yf ther be 3 Supertriparciens. and yf ther be .4. Superquartiparciens and so forthe. And ferthermore tho parties that be .tercie. than thu shalt sey alwey atte last ende. .tercias. And yf thei be .4te. .quartas. and so forthe endlesli. Sequitur exemplum. Betwene .5. and .3. is proporcio superbiparciens tercias. for the more numbir conteynyth the lasse. and .2o. parties ouer that be .tercie. But they bothe togedir be not pars aliquota. of the lasse numbir. [-f.118v-] Betwene .7. and .5. is Superbiparciens quintas. Betwene .7. and .3. is [Superquartiparciens tercias. del.] [dupla sesquetercias in marg. m. sec.] Betwene .9. and .5. is Superquartiparciens quintas. Betwene .10. and .6. is. Superbiparciens .tercias. And loke ye take goode hede. that ye deuyde the excesse into the grettest partyes aliquotas that ye may. as here in this last ensample .4. is deuydid into .2o. dualiteis that beene .tercie. of six. And take this for a general rwle. that the same proporcion [that supra lin.] is betwene .2o. smale numbris. the same is betwene here doubles and treblis and quatreblis and quiniblis and so forthe endlesly Sequitur exemplum. The same proporcion. that is betwene .5. and .3. is betwene 10. and 6. betwene .20. and 12. betwene 40. and 24. betwene 80. and 48. and so forthe endlesli. Multiplex superparticularis. is whan the more numbir conteynythe the lasse. and a partye of him that is Aliquota. as .5. and .2o. is Dupla sesquealtera. And so is .10. and .4. And so is .20. and 8te. But .7. and .3. is Dupla sesque .tercia. And so is .14. and 6. Multiplex superparciens. is whan the more numbir conteynyth the lasse and the parties that be ouer Aliquote. But thei alle togedir be not one parte Aliquota . As .8te. and .3. is Dupla superbiparciens tercias. And so is .16. and 6 . 32. and 12. Secuntur denominaciones.

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