Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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292280IO. BABPT. BENED. interualla ſuperant tonum ſeſquinonum, & ſi eſſent .10. commata ſuperarent tonum
ſeſquioctauum, eo quod aggregatum ex .9. commatibus continetur ſub iſtis duobus
terminis hoc eſt .150094635296999121. et .134217728000000000. quæ qui-
dem proportio maior eſt proportione ſeſquinona, ſumma verò .10. commatum con
tinetur ſub .12157665459056928801. et .10737418240000000000. quæ pro
portio maior eſt tono ſeſquioctauo, quod autem dico de aſcenſu cantilenæ, idem aſ-
ſero de eiuſdem deſcenſu, & hoc non tantum per interuallum illius commatis, quod
eſt differentia toni maioris à minori, ſed etiam per illud quod eſt differentia ſemito
nij maioris à minori, vt in ſecundo exemplo hic ſubſcripto videre eſt in deſcenſu
cantilenæ per comma & comma, vt differentia inter ſemitonia maiora & minora,
vbi in prima cellula diſcedens baſſus à quinta cum ſuperiori, & ab vniſono cum te-
nore deſcendens ad tertiam minorem cum ipſo tenore, facit cum ſuperiori ſeptimam
maiorem, quæ eſt vt .9. ad .5. ſuperquadripartiensquintas ſcilicet, à qua diſcedens
poſtea ſuperius, vt faciat cum baſſu ſextam maiorem, deſcendit per ſemitonium ma
ius, à qua ſexta maiori deſcendens baſſus, & aſcendens per quartam, efficit cum di-
cto ſuperiori tertiam maiorem, à qua diſcedens ſuperius, vt efficiat quartam cum ipſo
baſſu (qui quidem baſſus tranſit in tenorem) aſcendit per ſemitonium minus, diffe-
rens à ſemitonio maiori per vnum comma, vnde cantilena remanet depreſſa per
vnum comma.
cum deinde idem faciat inter tertiam, & quartam cellulam, per a-
liud comma deſcendit, & ſic toties facere poſſet, vt poſtremo valde deprimatur
cantilena à primo phthongo.
318[Figure 318]
Quod autem hic ſupradictum eſt, clrca inſtrumenta artificialia non accidit, qua
propter organa, & clauicimbula concordantur certo quodam ordine, ita vt omnes
conſonantiæ, excepta diapaſon, ſeu octaua, ſint imperfectæ, hoc eſt, aut diminutę,
aut ſuperantes à inſto, vt exempli gratia, omnes quintæ ſunt diminutæ, quartæ verò
ſunt exceſſiuę, quod quidem fit, vt tertiæ, & ſextæ, non multum auribus diſſonent,
eo quod ſi quintæ omnes, & quartæ, perfectæ eſſent,
tunc omnes ſextę, & tertiæ in-
tollerabiles eſſent, & à perfectis differrent per vnum comma, quod manifeſtum no-
bis erit hoc modo, accipiamus tres diapentes, ſeu quintas, conſequenter ſucceſſiuas
vnam poſt aliam, hoc eſt tres proportiones ſeſquialteras, quarum aggregatum erit
vt .27. ad .8. quæ proportio, dicitur tripla ſupertripartiensoctauas, & quæ à practicis

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