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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EPISTOL AE.
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293
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0293
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appellaretur tertia decima maior, vt exempli gratia, eſſet Gamaut cum ſecundo ela
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mi, </
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<
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">tunc talis tertiadecima valde odioſa eſſet ſenſui auditus, à qua, ſi dempta ſuerit
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diapaſon, ſeu octaua, remaneret quoddam hexachordum maius, ſeu ſexta maior, au-
<
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ribus valde inimica, ſub proportione .13. ad 8. ſed hæc proportio differret à propor
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tione ſuperbipartientetertias perfecti hexachordi maioris, hoc eſt ſextæ maioris
<
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conſonantis, per proportionem ſeſquioctuageſimam, hoc eſt per vnum comma,
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quod quidem eſt etiam differentia aggregati trium ſeſquialterarum, à tertiadeci-
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ma maiori conſonanti, hoc eſt exceſſus proportionis triplæ ſupertripartientis octa-
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uas, ſupra triplam ſeſquitertiam, quæ eſt ſumma ipſius duplæ cum ſuperbi partien-
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tetertias.</
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<
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">A tali ſumma igitur trium ſeſquialterarum efficitur tertiadecima maior diſſonans
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excedens conſonantem per vnum comma (cuius proportio eſt .81. ad .80.) quæ con-
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fonans continetur in proportione .10. ad .3. vt ſupra dixi.</
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<
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<
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">Hæcigitur eſt vera ratio, propter quam debemus comma diſtribuere in organis
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& clauicymbalis, cum ab aggregato trium quintarum producatur talis exceſſus ſu-
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pra perfectam, ſeu conſonantem tertiamdecimam maiorem, quod quidem aggre-
<
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/>
gatum, cum demptum fuerit à quintadecima, relinquet nobis tertiam minorem
<
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diſſonantem, & mancam, per eundem exceſſum à conſonanti. </
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<
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">quæ quidem tertia
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minor diſſonans ſubtracta à diapente ſeu quinta perfecta, relinquet nobis tertiam
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maiorem diſſonantem, qu@ conſonantem excedit per eundem exceſſum comma-
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tis, & hæc demum tertia maior diſſonans, dempta ex diapaſon, ſeu octaua, relin-
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quet nobis hexachordum minus, hoc eſt ſextam minorem diſſonantem, & muti-
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lam à conſonanti per eundem exceſſum commatis. </
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<
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xml:space
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">De huiuſmodi verò commatis
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diſtributione doctiſſimè ſcripſit Excellentiſſimus Zarlinus in ſecunda parte Inſtitu-
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tionum Harmonicarum.</
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<
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<
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">Sed quia ſenſus auditus non poteſt exactè cognoſcere debitam quantitatem ex-
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ceſſus, vel defectus, intendendo vel remittendo chordas inſtrumentorum, ideo hanc
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viam ſequutus ſum.</
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<
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<
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xml:space
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">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
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>.b.</
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inter
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>.D.E.</
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>
quod eſt nigrum ipſius Ela-
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mi grauiſſimum, quod groſſo modo facio conſonans cum
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grauiſſimo per ſex-
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tam
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, deinde
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ipſo pt
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imo
<
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ipſius elami concordo ſuum octauum & quin-
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tumdecimum, quo perfectius poſſum, deinde accipio
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molle ſecundum ipſius. b
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fabmi quod concordo cum
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primo ipſius Elami per quintam imperfectam, dein-
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de cum hoc
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ſecundo ipſius bſabmi concordo ſecundum
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per quintam ſimiliter
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imperfectam, cum quo
<
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poſtea concordo tertium
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per ſimilem quintam, quem
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tertium
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poſtea confero
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ſecundo
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ipſius elami, ita quod inter ſe conſonent per
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ſextam maiorem tolerabilem, & ſi ſic inuenio, tunc nihil muto has treschordas hoc.
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<
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