Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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            <p type="main">
              <s id="s.004234">
                <pb pagenum="249" xlink:href="009/01/249.jpg"/>
              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. </s>
              <s id="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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              </s>
              <s id="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,
                <expan abbr="vltimũ">vltimum</expan>
              , 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
                <expan abbr="quinq;">quinque</expan>
              interualla ſunt integri toni. </s>
              <s id="s.004237">Aduer­
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              tendum præterea eſt, ab Vt,
                <expan abbr="vſq;">vſque</expan>
              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
                <expan abbr="quinq;">quinque</expan>
              voces, Vt, Re, Mi, Fa, Sol.</s>
            </p>
            <p type="main">
              <s id="s.004238">Notandum etiam, quod à Sol,
                <expan abbr="vſq;">vſque</expan>
              ad vltimum Fa, ſunt quatuor voces,
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              Sol, Re, Mi, Fa,quæ omninò ſimiles ſunt primis quatuor, Vt, Re, Mi Fa. </s>
              <s id="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,
                <expan abbr="vſq;">vſque</expan>
              ad vltimum Fa, eſt altera Dia­
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              teſſaron. </s>
              <s id="s.004240">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. </s>
              <s id="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.</s>
            </p>
            <p type="main">
              <s id="s.004242">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;
                <expan abbr="edeturq́">edeturque</expan>
              ; 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. </s>
              <s id="s.004243">proportio huius eſt quadrupla, vt
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              ex diuiſione conſtat; vulgò dicitur decimaquinta, quia à primo Vt,
                <expan abbr="vſq;">vſque</expan>
              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.</s>
            </p>
            <p type="main">
              <s id="s.004244">Poſtremò ſit G D, tertia pars totius C D,
                <expan abbr="fiatq́">fiatque</expan>
              ; 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. </s>
              <s id="s.004245">ex quibus omnibus manifeſtum eſt
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              auris experimento, eſſe omninò quinque conſonantias, tres ſimplices </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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