Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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249
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Interuallum verò, quod inter chordam L D, & chordam H D, remanet, non
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habet proportionem ſeſquioctauam, ſed dimidio ferè minorem, & propte
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rea huiuſmodi interuallum ſemitonium, & etiam dieſis, ſiue diuiſio, appel
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latur. </
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<
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id
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s.004235
">Interuallum verò illud, quod inter puncta F, & E, remanet, diuiſe
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runt eodem modo, quo diuiſum fuit ſpatium inter C, & H, & repercerunt
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eaſdem iterum voces; ſint diuiſiones illæ punctis M, & N, notatæ; & pari
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ter hic etiam inter N, & E, ſiue inter Mi, & Fa, eſt alterum ſemitonium.
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<
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id
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s.004236
">ſunt igitur hæ octo voces, Vt, Re, Mi, Fa, Sol, Re, Mi, Fa, quæ totam Dia
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paſon componunt, vt enim ſupra dictum eſt inter Vt, & Fa,
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abbr
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vltimũ
">vltimum</
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, eſt con
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ſonantia diapaſon, ſiue dicamus inter chordam C D, vel A B, & chordam
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E D. ex interuallis autem,quæ ſunt inter voces, duo ſunt ſemitonia, ſcilicet
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vnum inter Mi, & Fa, notatum literis L, H. & alterum inter vltima Mi, &
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Fa, ſignatum notis N, E. reliqua
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quinq;
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interualla ſunt integri toni. </
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<
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id
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s.004237
">Aduer
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tendum præterea eſt, ab Vt,
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vſq;
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ad primum Sol, eſſe conſonantiam Dia
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pente, quæ continet tria interualla toniaca, & vnum ſemitonium; in vni
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uerſum tamen ſunt
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quinq;
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voces, Vt, Re, Mi, Fa, Sol.</
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s.004238
">Notandum etiam, quod à Sol,
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vſq;
">vſque</
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ad vltimum Fa, ſunt quatuor voces,
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Sol, Re, Mi, Fa,quæ omninò ſimiles ſunt primis quatuor, Vt, Re, Mi Fa. </
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<
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id
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s.004239
">hæ
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tamen ſunt grauiores, illæ verò acutiores, & quemadmodum ab Vt, ad pri
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mum Fa, eſt Diateſſaron, ita etiam à Sol,
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vſq;
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ad vltimum Fa, eſt altera Dia
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teſſaron. </
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<
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id
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">Ex quibus vltimò notandum ſequitur, duas conſonantias Diateſ
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ſaron, & Diapente totam conſtituere Diapaſon: ſiue Diapaſon diuidi in
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vnam Diateſſaron, & vnam Diapente; nam ab Vt, ad Sol, eſt Diapente; à
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Sol, verò in Fa, poſtremum, eſt Diateſſaron. </
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<
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id
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s.004241
">quod etiam aliter conſtabit, ſi
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dicamus ab Vt, ad primum Fa, eſſe Diateſſaron, vt patet ex chordæ diuiſio
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ne: ex Fa, autem primò ad vltimum Fa, eſſe Diapente: vt manifeſtum eſt
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ex quatuor ipſius interuallis, quorum tria ſunt Toni, reliquum verò ſemito
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nium, quæ etiam erant in altera Diapente inter Vt, & Sol, contenta.</
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<
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id
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">Nunc rurſus fiat tactus in I, eſt autem I D, quarta pars totius C D. per
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cutiantur ſimul A B, & I D;
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edeturq́
">edeturque</
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; ſuauiſſima conſonantia Diſdiapaſon
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appellata, propterea quod ex duabus Diapaſon conſtet; quarum prima eſt
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inter A B, ſiue C D, & E D: ſecunda verò inter ipſam E D, & I D. harum
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enim proportio dupla eſt, ſicuti illarum. </
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<
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id
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s.004243
">proportio huius eſt quadrupla, vt
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ex diuiſione conſtat; vulgò dicitur decimaquinta, quia à primo Vt,
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vſq;
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ad
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hanc vocem,quæ etiam Fa, nominatur, eſſent quindecim voces, ſi interual
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lum E I, eo modo diuideretur, quo diuiſum eſt primum C E.</
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<
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id
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">Poſtremò ſit G D, tertia pars totius C D,
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fiatq́
">fiatque</
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; in G, tactus, pulſentur ſi
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mul A B, G D. audietur ſuauis conſonantia, quæ Diapaſondiapente nomi
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natur, quod conſtet ex vna Diapaſon contenta interuallo C E, ſiue duabus
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chordis C D, E D, & vna Diapente contenta interuallo E G, ſiue chordis
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E D, G D; nam chorda E D, ad chordam G D, ſeſquialtera eſt; quæ propor
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tio naturam ipſius diapente conſtituit huius conſonantiæ proportio eſt tri
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pla, eſt enim chorda A B, vel C D, tripla ipſius G D. vulgò dicitur duode
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cima, cò quod inter Vt, & Sol, notatum litera G, ſint duodecim voces, ſi in
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teruallum E O, ſuas recipiat diuiſiones. </
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<
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id
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">ex quibus omnibus manifeſtum eſt
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auris experimento, eſſe omninò quinque conſonantias, tres ſimplices </
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