Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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              <s id="s.004595">
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              igitur alijs præſtet
                <expan abbr="ſitq́">ſitque</expan>
              ; ſui tetrachordi acutiſſima,
                <expan abbr="cõuenienter">conuenienter</expan>
              natura du­
                <lb/>
              ce fit, vt ab acuta voce cantum exordiamur. </s>
              <s id="s.004596">ideſt ſicut in tetrachoreo prin­
                <lb/>
              cipalis eſt acuta, ſiue principium tetrachordi eſt acutum, ita etiam princi­
                <lb/>
              pium cantus debet eſſe acutum. </s>
              <s id="s.004597">Quod ſi à graui cantandi principium fa­
                <lb/>
              ceremus, à fine potius, quàm à principio contra naturæ ordinem
                <expan abbr="principiũ">principium</expan>
                <lb/>
              faceremus. </s>
              <s id="s.004598">Theodorus Gaza vertit, primi tetrachordi, verum in vulgatis,
                <lb/>
              atque correctis codicibus græcis legitur,
                <foreign lang="grc">παράτετραχορδου,</foreign>
              quod non pri­
                <lb/>
              mum, ſed potius ſubſequens tetrachordum, ſignificare videtur. </s>
              <s id="s.004599">vtrumuis le­
                <lb/>
              gamus, explicatio allata ſufficere poteſt. </s>
              <s id="s.004600">Subdit poſtea aliam reſponſio­
                <lb/>
              nem, quod nimirum hoc modo grauis vox cantilenam claudens, quando ex
                <lb/>
              acuto quodammodo orta eſt, generoſior,
                <expan abbr="atq;">atque</expan>
              ſonantior euadit.</s>
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            <p type="main">
              <s id="s.004601">
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            <p type="margin">
              <s id="s.004602">
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              387</s>
            </p>
            <p type="main">
              <s id="s.004603">Probl. 34.
                <emph type="italics"/>
              (Cur bis Diapente, aut bis Diateſſaron
                <expan abbr="cõſonantia">conſonantia</expan>
                <expan abbr="cõponi">componi</expan>
              non poteſt,
                <lb/>
              bis
                <expan abbr="aũt">autem</expan>
              Diapaſon poteſt? </s>
              <s id="s.004604">An, quòd bis Diapente, non bis Diateſſaron eſt: ſed Dia­
                <lb/>
              teſſaron, & Diapente in vnă Diapaſon concurrunt)
                <emph.end type="italics"/>
              Quamuis textus
                <expan abbr="aliquantulũ">aliquantulum</expan>
                <lb/>
                <expan abbr="ẽt">et</expan>
              græcus corruptus ſit, verumtamen ſenſum Ariſt. ex ſequentibus percipie­
                <lb/>
              mus. </s>
              <s id="s.004605">Pro intelligentia igitur huius problematis placet hic deſcribere
                <expan abbr="demõ-ſtrationem">demon­
                  <lb/>
                ſtrationem</expan>
              16. lib. 3. doctiſſimi Fabri ſtapulentis, qua ipſe veſtigijs
                <expan abbr="antiquo-rũ">antiquo­
                  <lb/>
                rum</expan>
              inhærens optimè præſenti quæſtioni ſatisfacit. </s>
              <s id="s.004606">eſt
                <expan abbr="aũt">aut</expan>
              huiuſmodi: Biſdia­
                <lb/>
              teſſaron, aut bis
                <expan abbr="Diapẽte">Diapente</expan>
                <expan abbr="nullã">nullam</expan>
              conſonantiam
                <expan abbr="cõponere">componere</expan>
              poteſt, omnis
                <expan abbr="namq;">namque</expan>
                <lb/>
              conſonantia, aut in proportione multiplici, aut in ſuperparticulari collo­
                <lb/>
              canda eſt, ex Pythagoreorum,
                <expan abbr="aliorumq́">aliorumque</expan>
              ; Muſicorum traditione; ſed ſi duæ
                <lb/>
              Diateſſaron, aut duæ Diapente componantur,
                <expan abbr="neq;">neque</expan>
              multiplicem, neque ſu­
                <lb/>
              perarticularem creant rationem, ergò additæ nullam efficere valent
                <expan abbr="cõſo-nantiam">conſo­
                  <lb/>
                nantiam</expan>
              . </s>
              <s id="s.004607">duas Diapentes nullam facere rationem multiplicem, aut ſuper­
                <lb/>
              particularem patet ex numeris earum rationem continentibus ſimul addi­
                <lb/>
              tis, eo modo, quo Muſici ſolent addere. </s>
              <s id="s.004608">ratio Diapentes eſt ſeſquialtera, ſi
                <lb/>
              ergo duæ ſeſquialteræ ſimul continuentur, vt in his numeris. </s>
              <s id="s.004609">9. 6. 4. ratio
                <lb/>
              primi 9 ad vltimum 4. erit compoſita ex duabus ſeſquialteris; ratio autem
                <lb/>
              9. & 4.
                <expan abbr="neq;">neque</expan>
              eſt multiplex,
                <expan abbr="neq;">neque</expan>
              ſuperarticularis, vt oporteret, ſed eſt multi­
                <lb/>
              plex ſuperparticularis, quæ ad conſonantiam inepta eſt. </s>
              <s id="s.004610">propterea igitur
                <lb/>
              duæ Diapentæ additæ nullam faciunt conſonantiam. </s>
              <s id="s.004611">quod præterea expe­
                <lb/>
              rientia ipſa manifeſtat. </s>
              <s id="s.004612">ſed cur proprio multiplex, & ſuperarticularis ſunt
                <lb/>
              harmonicæ; multiplex verò ſuperarticularis, aut quælibet alia non? </s>
              <s id="s.004613">fortè
                <lb/>
              quia in illis maior ſeruatur integritas, quæ perfectio eſt: in cæteris verò mi­
                <lb/>
              nor integritas, quæ imperfectio eſt. </s>
              <s id="s.004614">quod melius in ſequenti problem. </s>
              <s id="s.004615">ex­
                <lb/>
              plicabitur. </s>
              <s id="s.004616">ſimiliter duas Diateſſaron nullam facere
                <expan abbr="rationẽ">rationem</expan>
              conſonantem,
                <lb/>
              patet ex numeris illarum additis: eorum proportio eſt ſeſquitertia,
                <expan abbr="addã-tur">addan­
                  <lb/>
                tur</expan>
              ; ergò duæ ſeſquitertiæ, vt in his numeris 16. 12. 9. ratio primi 16. ad
                <lb/>
              extremum 9. nec multiplex, nec ſuperparticularis eſt, vt oporteret: ergò
                <lb/>
              nullam conſonantiam efficient. </s>
              <s id="s.004617">At verò, ſi vna Diateſſaron, & vna Dia­
                <lb/>
              pente, componantur, efficiunt Diapaſon; quia ipſarum rationes additæ du­
                <lb/>
              plam, quæ eſt ratio Diapaſon, efficiunt: dupla autem eſt multiplex. </s>
              <s id="s.004618">
                <expan abbr="ponã-tur">ponan­
                  <lb/>
                tur</expan>
              hi tres numeri 6. 4. 3. proportio primi 6. & ſecundi 4. eſt ſeſquialtera,
                <lb/>
              pro Diapente. </s>
              <s id="s.004619">proportio ſecundi 4. & 3. eſt ſeſquitertia pro Diateſſaron.
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              </s>
              <s id="s.004620">Iam proportio inter primum 6. & vltimum 3. eſt dupla: quæ eſt ratio ipſius
                <lb/>
              perfectiſſimæ conſonantiæ Diapaſon. </s>
              <s id="s.004621">Ex quibus Ariſt. ſententia manifeſta </s>
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