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]

Table of Notes

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                  interualla ſuperant tonum ſeſquinonum, & ſi eſſent .10. commata
                    <unsure/>
                  ſuperarent tonum
                    <lb/>
                  ſeſquioctauum, eo quod aggregatum ex .9. commatibus continetur ſub iſtis duobus
                    <lb/>
                  terminis hoc eſt .150094635296999121. et .134217728000000000. quæ qui-
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                  dem proportio maior eſt proportione ſeſquinona, ſumma verò .10. commatum con
                    <lb/>
                  tinetur ſub .12157665459056928801. et .10737418240000000000. quæ pro
                    <lb/>
                  portio maior eſt tono ſeſquioctauo, quod autem dico de aſcenſu cantilenæ, idem aſ-
                    <lb/>
                  ſero de eiuſdem deſcenſu, & hoc non tantum per interuallum illius commatis, quod
                    <lb/>
                  eſt differentia toni maioris à minori, ſed etiam per illud quod eſt differentia ſemito
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                  nij maioris à minori, vt in ſecundo exemplo hic ſubſcripto videre eſt in deſcenſu
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                  cantilenæ per comma & comma, vt differentia inter ſemitonia maiora
                    <unsure/>
                  & minora,
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                  vbi in prima cellula diſcedens baſſus à quinta cum ſuperiori, & ab vniſono cum te-
                    <lb/>
                  nore deſcendens ad tertiam minorem cum ipſo tenore, facit cum ſuperiori
                    <reg norm="ſeptimam" type="context">ſeptimã</reg>
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                  maiorem, quæ eſt vt .9. ad .5. ſuperquadripartiensquintas ſcilicet, à qua diſcedens
                    <lb/>
                  poſtea ſuperius, vt faciat cum baſſu ſextam maiorem, deſcendit per ſemitonium ma
                    <lb/>
                  ius, à qua ſexta maiori deſcendens baſſus, & aſcendens per quartam, efficit cum di-
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                  cto ſuperiori
                    <reg norm="tertiam" type="context">tertiã</reg>
                  maiorem, à qua diſcedens ſuperius, vt efficiat quartam cum ipſo
                    <lb/>
                  baſſu (qui quidem baſſus tranſit in tenorem) aſcendit per ſemitonium minus, diffe-
                    <lb/>
                  rens à ſemitonio maiori per vnum comma, vnde cantilena remanet depreſſa per
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                  vnum comma. </s>
                  <s xml:id="echoid-s3474" xml:space="preserve">cum deinde idem faciat inter tertiam, & quartam cellulam, per a-
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                  liud comma deſcendit, & ſic toties facere poſſet, vt poſtremo valde deprimatur
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                  cantilena à primo phthongo.</s>
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                  <s xml:id="echoid-s3475" xml:space="preserve">Quod autem hic ſupradictum eſt, clrca inſtrumenta artificialia non accidit, qua
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                  propter organa, & clauicimbula concordantur certo quodam ordine, ita vt omnes
                    <lb/>
                  conſonantiæ, excepta diapaſon, ſeu octaua, ſint imperfectæ, hoc eſt, aut diminutę,
                    <lb/>
                  aut ſuperantes à inſto, vt exempli gratia, omnes quintæ ſunt diminutæ, quartæ verò
                    <lb/>
                  ſunt exceſſiuę, quod quidem fit, vt tertiæ, & ſextæ, non multum auribus diſſonent,
                    <lb/>
                  eo quod ſi quintæ omnes, & quartæ, perfectæ eſſent, </s>
                  <s xml:id="echoid-s3476" xml:space="preserve">tunc omnes ſextę, & tertiæ in-
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                  tollerabiles eſſent, & à perfectis differrent per vnum comma, quod manifeſtum no-
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                  bis erit hoc modo, accipiamus tres diapentes, ſeu quintas, conſequenter ſucceſſiuas
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                  vnam poſt aliam, hoc eſt tres proportiones ſeſquialteras, quarum aggregatum erit
                    <lb/>
                  vt .27. ad .8. quæ proportio, dicitur tripla ſupertripartiensoctauas, & quæ à practicis </s>
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