Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.004708">
                <pb pagenum="269" xlink:href="009/01/269.jpg"/>
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              autem ex contrarijs vocibus conſiſtat, propterea in Diapaſon magadari ſolě)
                <emph.end type="italics"/>
              Hic
                <lb/>
              repetenda ſunt, quæ probl. </s>
              <s id="s.004709">17. annotaui, vbi quid Magadis, & Magadari
                <lb/>
              explicatum eſt. </s>
              <s id="s.004710">repetenda ſunt pariter, quæ in 35. probl. </s>
              <s id="s.004711">de præſtantia con­
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              ſonantiæ Diapaſon ſunt dicta. </s>
              <s id="s.004712">verba illa
                <emph type="italics"/>
              (Cum finiat ad dimidiam)
                <emph.end type="italics"/>
                <expan abbr="intelligē-da">intelligen­
                  <lb/>
                da</expan>
              ſunt de Diapente, cuius rationis termini ſunt 1 1/2. qui ad dimidium fi­
                <lb/>
              niunt; poſtea videtur aliquid addendum pro Diateſſaron, cuius
                <expan abbr="nimirū">nimirum</expan>
              ter­
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              mini ſunt 1 1/3. qui ad vnam tertiam finiunt; nequeunt igitur horum termi­
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              norum conſonantiæ Diapente, & Diateſſaron, eſſe eiuſdem facultatis cum
                <lb/>
              Diapaſon, cuius rationis termini ſunt integri, vt 2. ad 1. verba illa
                <emph type="italics"/>
              (Præte­
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              rea ipſi hypati accidit, & c.)
                <emph.end type="italics"/>
              vt intelligantur, vide problem. </s>
              <s id="s.004713">24. cum ſua ex­
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              plicatione.</s>
            </p>
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              <s id="s.004714">
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            <p type="margin">
              <s id="s.004715">
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              394</s>
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            <p type="main">
              <s id="s.004716">Probl. 41.
                <emph type="italics"/>
              (Cur ſuauius cantum audimus, quem ſcimus, quam quem ignora­
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              mus? </s>
              <s id="s.004717">Vtrum, quoniam cum
                <expan abbr="cantilenã">cantilenam</expan>
              agnoſcimus, manifeſtior eſt, qui veluti ſco­
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              pum, aſſequatur. </s>
              <s id="s.004718">cognoſcentium autem ſpeculatio ſuauis eſt. </s>
              <s id="s.004719">An quia accidit, vt
                <lb/>
              auditor vnà cum cantore afficiatur, qui notam cantat cantilenam, nam tunc audi­
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              tor illi quaſi ſuccinit. </s>
              <s id="s.004720">Solet autem quiſque alacriter canere, niſi ob aliquam neceſ­
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              ſitatem id faciat)
                <emph.end type="italics"/>
              Lege problem. </s>
              <s id="s.004721">5. eiuſque explicationem,
                <expan abbr="eritq́">eritque</expan>
              huic etiam
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              ſatisfactum.</s>
            </p>
            <p type="main">
              <s id="s.004722">
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              </s>
            </p>
            <p type="margin">
              <s id="s.004723">
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              395</s>
            </p>
            <p type="main">
              <s id="s.004724">Probl. 42.
                <emph type="italics"/>
              (Cur nec bis Diapente, nec bis Diateſſaron conſonant, ſed bis Dia­
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              paſon. </s>
              <s id="s.004725">An quod Diapente conſonantia est in proportione ſeſquialtera? </s>
              <s id="s.004726">quod ſi tres
                <lb/>
              ſeſquialteri, aut ſeſquitertij numeri ordine diſponantur, extremi
                <expan abbr="nullã">nullam</expan>
              inuicem pro­
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              portionem habebunt,
                <expan abbr="neq;">neque</expan>
              enim multiplices,
                <expan abbr="neq;">neque</expan>
              ſuperparticulares erunt: At con­
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              ſonantia Diapaſon, quoniam in dupla ratione conſiſtit, qua duplicata, quadruplam
                <lb/>
              extremi rationem obtinebunt. </s>
              <s id="s.004727">Itaque cum conſonantia ex ſonis conſiet proportio­
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              nem, habentibus,
                <expan abbr="proportionemq́">proportionemque</expan>
              ; habeant ij, qui interuallo bis Diapaſon compo­
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              nuntur; minimè autem, ij, qui bis Diateſſaron, aut bis Diapente interuallis conti­
                <lb/>
              nentur; idcirco ſoni bis Diapaſon conſoni ſunt, cæteri verò
                <expan abbr="nequaquã">nequaquam</expan>
              ob prædicta)
                <emph.end type="italics"/>
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              Quæ dicta ſunt ad probl. </s>
              <s id="s.004728">34. & 35. totum ferè hunc locum illuſtrant. </s>
              <s id="s.004729">Cæ­
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              terum
                <expan abbr="quãdo">quando</expan>
              Muſici volunt duas ſeſquialteras ratione ſimul addere, diſpo­
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              nunt ordine tres numeros habentes inuicem ſeſquialteram rationem, vt ſe­
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              quentes 9. 6. 4. quam deinde habent rationem extremi 9. & 4. eam dicunt
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                <expan abbr="compoſitã">compoſitam</expan>
              ex duabus ſeſquialteris: quæ quidem eſt dupla ſeſquiquarta, quæ
                <lb/>
              conſonantiæ faciendæ inepta eſt; ſiue quæ non eſt conſonantia harmonica;
                <lb/>
              vnde Muſici dicunt eoſdem numero nullam habere rationem, ideſt harmo­
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              nicam, cum omnis harmonica ſit, aut multiplex, aut ſuperparticularis, vn­
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              de patet cur bis Diapente nullam pariat conſonantiam. </s>
              <s id="s.004730">Similiter, duæ ra­
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              tiones ſeſquitertiæ, 16. 12. 9. additæ efficiunt rationem, quæ eſt inter 16. &
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              9. quæ non eſt harmonica, quia neque multiplex, neque ſuperpendicularis
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              eſt; ideo apud Muſicos nulla eſt; quamuis re vera ab Arithmeticis dicatur,
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              & ſit ſuperpartiens, & in ſpecie ſuperquintupartiens nonas. </s>
              <s id="s.004731">Duæ verò du­
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              plæ, vti 4. 2. 1. eo modo conflant rationem inter 4. & 1. quæ multiplex eſt,
                <lb/>
              & quadrupla dicitur, ideò harmonica eſt portio: vnde patet ratio, cur duæ
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              Diapaſon conſonant. </s>
              <s id="s.004732">talis autem conſonantia appellatur Diſdiapaſon, cu­
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              ius forma eſt in ratione quadrupla.</s>
            </p>
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            <p type="margin">
              <s id="s.004734">
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              396</s>
            </p>
            <p type="main">
              <s id="s.004735">Probl. 43.
                <emph type="italics"/>
              (Cur ſi quis
                <expan abbr="pſallẽs">pſallens</expan>
              neten apprehědat, ſola hypate ſubſonare videtur?
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              </s>
              <s id="s.004736">An
                <expan abbr="quoniã">quoniam</expan>
              nete deſinens & elangueſcens euadit hypate;
                <expan abbr="indiciũ">indicium</expan>
              , quòd poſt hypaten
                <emph.end type="italics"/>
              -</s>
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          </chap>
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