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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                    <pb o="281" rhead="EPISTOL AE." n="293" file="0293" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0293"/>
                  appellaretur tertia decima maior, vt exempli gratia, eſſet Gamaut cum ſecundo ela
                    <lb/>
                  mi, </s>
                  <s xml:id="echoid-s3477" xml:space="preserve">tunc talis tertiadecima valde odioſa eſſet ſenſui auditus, à qua, ſi dempta ſuerit
                    <lb/>
                  diapaſon, ſeu octaua, remaneret quoddam hexachordum maius, ſeu ſexta maior, au-
                    <lb/>
                  ribus valde inimica, ſub proportione .13. ad 8. ſed hæc proportio differret à propor
                    <lb/>
                  tione ſuperbipartientetertias perfecti hexachordi maioris, hoc eſt ſextæ maioris
                    <lb/>
                  conſonantis, per proportionem ſeſquioctuageſimam, hoc eſt per vnum comma,
                    <lb/>
                  quod quidem eſt etiam differentia aggregati trium ſeſquialterarum, à tertiadeci-
                    <lb/>
                  ma maiori conſonanti, hoc eſt exceſſus proportionis triplæ ſupertripartientis octa-
                    <lb/>
                  uas, ſupra triplam ſeſquitertiam, quæ eſt ſumma ipſius duplæ cum ſuperbi partien-
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                  tetertias.</s>
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                <p>
                  <s xml:id="echoid-s3478" xml:space="preserve">A tali ſumma igitur trium ſeſquialterarum efficitur tertiadecima maior diſſonans
                    <lb/>
                  excedens conſonantem per vnum comma (cuius proportio eſt .81. ad .80.) quæ con-
                    <lb/>
                  fonans continetur in proportione .10. ad .3. vt ſupra dixi.</s>
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                <p>
                  <s xml:id="echoid-s3479" xml:space="preserve">Hæcigitur eſt vera ratio, propter quam debemus comma diſtribuere in organis
                    <lb/>
                  & clauicymbalis, cum ab aggregato trium quintarum producatur talis exceſſus ſu-
                    <lb/>
                  pra perfectam, ſeu conſonantem tertiamdecimam maiorem, quod quidem aggre-
                    <lb/>
                  gatum, cum demptum fuerit à quintadecima, relinquet nobis tertiam minorem
                    <lb/>
                  diſſonantem, & mancam, per eundem exceſſum à conſonanti. </s>
                  <s xml:id="echoid-s3480" xml:space="preserve">quæ quidem tertia
                    <lb/>
                  minor diſſonans ſubtracta à diapente ſeu quinta perfecta, relinquet nobis tertiam
                    <lb/>
                  maiorem diſſonantem, qu@ conſonantem excedit per eundem exceſſum comma-
                    <lb/>
                  tis, & hæc demum tertia maior diſſonans, dempta ex diapaſon, ſeu octaua, relin-
                    <lb/>
                  quet nobis hexachordum minus, hoc eſt ſextam minorem diſſonantem, & muti-
                    <lb/>
                  lam à conſonanti per eundem exceſſum commatis. </s>
                  <s xml:id="echoid-s3481" xml:space="preserve">De huiuſmodi verò commatis
                    <lb/>
                  diſtributione doctiſſimè ſcripſit Excellentiſſimus Zarlinus in ſecunda parte Inſtitu-
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                  tionum Harmonicarum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3482" xml:space="preserve">Sed quia ſenſus auditus non poteſt exactè cognoſcere debitam quantitatem ex-
                    <lb/>
                  ceſſus, vel defectus, intendendo vel remittendo chordas inſtrumentorum, ideo hanc
                    <lb/>
                  viam ſequutus ſum.</s>
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                <p>
                  <s xml:id="echoid-s3483" xml:space="preserve">Sit exempli gratia, hic ſubſcriptus ordo lignorum tangentium ſeu pinarum inci-
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                  piens ab
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                  deſinens ad
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                  ita quod inter ipſos terminos ſit ea conſonantia quæ vo-
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                  catur vigeſimaſecunda, quæro primum
                    <var>.b.</var>
                  inter
                    <var>.D.E.</var>
                  quod eſt nigrum ipſius Ela-
                    <lb/>
                  mi grauiſſimum, quod groſſo modo facio conſonans cum
                    <var>.G.</var>
                  grauiſſimo per ſex-
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                  tam
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                  , deinde
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                  ipſo pt
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                  imo
                    <var>.b.</var>
                  ipſius elami concordo ſuum octauum & quin-
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                  tumdecimum, quo perfectius poſſum, deinde accipio
                    <var>.b.</var>
                  molle ſecundum ipſius. b
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                  fabmi quod concordo cum
                    <var>.b.</var>
                  primo ipſius Elami per quintam imperfectam, dein-
                    <lb/>
                  de cum hoc
                    <var>.b.</var>
                  ſecundo ipſius bſabmi concordo ſecundum
                    <var>.f.</var>
                  per quintam ſimiliter
                    <lb/>
                  imperfectam, cum quo
                    <var>.f.</var>
                  poſtea concordo tertium
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                  per ſimilem quintam, quem
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                  tertium
                    <var>.c.</var>
                  poſtea confero
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                  ſecundo
                    <var>.b.</var>
                  ipſius elami, ita quod inter ſe conſonent per
                    <lb/>
                  ſextam maiorem tolerabilem, & ſi ſic inuenio, tunc nihil muto has treschordas hoc.
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                        <xhtml:td xml:space="preserve">G A B b C * D b E F * g * a b b c * d b e f * g * a b b c * d b e f * g *</xhtml:td>
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                        <xhtml:td xml:space="preserve">1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4.</xhtml:td>
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