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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EPISTOL AE.
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295
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0295
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ſeptima maiori, omnia ſibi inuicem ſunt proportionalia, idem etiam dico de reli-
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quis partibus, cum relatæ fuerint ad ſua tota.</
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<
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xml:space
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">Nec alienum mihi videtur à propoſito inſtituto, ſpeculari modum generationis
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ipſarum ſimplicium
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; </
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<
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">qui quidem modus fit ex quadam æquatione per
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@uſſionum, ſeu æquali concurſu vndarum aeris, vel conterminatione earum.</
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<
s
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">Nam, nulli dubium eſt, quin vniſonus ſit prima principalis
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amiciſſima,
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nec non magis propria conſonantia; </
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">& ſi intelligatur, vt punctus in linea, vel vnitas
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in numero, quam immediate ſequitur diapaſon, ei ſimillima, poſt hanc verò diapen
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te,
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. </
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<
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">Videamus igitur ordinem concurſus percuſſionum terminorum, ſeu
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vndarum aeris, vnde ſonus generatur.</
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<
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">Concipiatur igitur mente monochordus, hoc eſt chorda diſtenta, quæ cum diuiſa
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fuerit in duas æquales partes à ponticulo, </
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pars eundem ſonum pro-
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feret, & ambæ formabunt vniſonum, quia eodem tempore, tot percuſſiones in aere
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faciet vna partium illius chordæ, quot & altera: </
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<
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xml:space
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">ita vt vndæ aeris ſimul eant, & æqua
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liter concurrant, abſque ulla interſectione, vel fractione illarum inuicem.</
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<
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<
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">Sed cum ponticulus ita diuiſerit chordam, vt relicta ſit eius tertia pars ab vno la-
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tere, ab alio vero, duę tertię, </
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">tunc maior pars, dupla erit minori, &
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ipſam dia
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paſon conſonantiam, percuſſiones vero terminorum ipſius, tali proportione ſe inui-
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cem habebunt, ut in qualibet ſecunda percuſſione minoris portionis ipſius chordæ,
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maior percutiet, ſeu concurret cum minori, eodem temporis inſtanti, cum ne-
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mo ſit qui neſciat, quod quo longior eſt chorda, etiam tardius moueatur, </
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">quare
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cum longior dupla ſit breuiori, & eiuſdem intenſionis tam vna quam altera, tunc eo
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tempore, quo longior vnum interuallum tremoris perfecerit, breuior duo interual-
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la conficiet.</
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<
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">Cum autem ponticulus ita diuiſerit chordam, ut ab uno latere relinquantur duæ
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quintæ partes, ab alio verò tres quintæ, ex quibus partibus generatur conſonantia
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diapente; </
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<
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">tunc clarè patet, quod eadem proportione tardius erit vnum interuallu
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m
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tremoris maioris portionis, vno interuallo tremoris minoris portionis, quam ma-
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i
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or portio habet ad minorem; </
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<
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">hoc eſt tempus maioris interualli ad tempus minoris
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erit
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quare non
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ſimul, niſi perfectis tribus interuallis mino-
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ris portionis, & duobus maioris; </
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<
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xml:space
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">ita quod eadem proportio erit numeri interuallo-
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rum minoris portionis ad interualla maioris, quæ longitudinis maioris portionis ad
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longitudinem minoris; </
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<
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">vnde productum numeri portionis minoris ipſius chordæ
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in numerum interuallorum motus ipſius portionis, æquale erit producto numeri
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portionis maioris in numerum interuallorum ipſius maioris portionis; </
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<
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producta ita ſe habebunt, vt in diapaſon, ſit binarius numerus; </
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<
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ſenarius; </
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">in diateſſaron duodenarius, in hexachordo maiori quindenarius; </
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<
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tono vicenarius, in ſemiditono tricenarius, demum in hexachordo minori quadra
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genarius: </
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<
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">qui quidem numeri non abſque mirabili analogia conueniunt inuicem.</
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<
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">Voluptas autem, quam auditui afferunt conſonantiæ fit, quia leniuntur ſenſus,
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quemadmodum
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, dolor qui à diſſonantijs oritur, ab aſperitate naſcitur, id quod
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facilè vide
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re poteris cum conchordantur organorum fiſtulæ.</
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