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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[284] Pro Lunæ ortu. Ad lati .45.
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                <p>
                  <s xml:id="echoid-s3499" xml:space="preserve">
                    <pb o="283" rhead="EPISTOL AE." n="295" file="0295" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0295"/>
                  ſeptima maiori, omnia ſibi inuicem ſunt proportionalia, idem etiam dico de reli-
                    <lb/>
                  quis partibus, cum relatæ fuerint ad ſua tota.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3500" xml:space="preserve">Nec alienum mihi videtur à propoſito inſtituto, ſpeculari modum generationis
                    <lb/>
                  ipſarum ſimplicium
                    <reg norm="conſonantiarum" type="context">conſonantiarũ</reg>
                  ; </s>
                  <s xml:id="echoid-s3501" xml:space="preserve">qui quidem modus fit ex quadam æquatione per
                    <lb/>
                  @uſſionum, ſeu æquali concurſu vndarum aeris, vel conterminatione earum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3502" xml:space="preserve">Nam, nulli dubium eſt, quin vniſonus ſit prima principalis
                    <reg norm="audituque" type="simple">audituq́</reg>
                  amiciſſima,
                    <lb/>
                  nec non magis propria conſonantia; </s>
                  <s xml:id="echoid-s3503" xml:space="preserve">& ſi intelligatur, vt punctus in linea, vel vnitas
                    <lb/>
                  in numero, quam immediate ſequitur diapaſon, ei ſimillima, poſt hanc verò diapen
                    <lb/>
                  te,
                    <reg norm="cæteræque" type="simple">cæteræq́;</reg>
                  . </s>
                  <s xml:id="echoid-s3504" xml:space="preserve">Videamus igitur ordinem concurſus percuſſionum terminorum, ſeu
                    <lb/>
                  vndarum aeris, vnde ſonus generatur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3505" xml:space="preserve">Concipiatur igitur mente monochordus, hoc eſt chorda diſtenta, quæ cum diuiſa
                    <lb/>
                  fuerit in duas æquales partes à ponticulo, </s>
                  <s xml:id="echoid-s3506" xml:space="preserve">tunc
                    <reg norm="vnaquæque" type="simple">vnaquæq;</reg>
                  pars eundem ſonum pro-
                    <lb/>
                  feret, & ambæ formabunt vniſonum, quia eodem tempore, tot percuſſiones in aere
                    <lb/>
                  faciet vna partium illius chordæ, quot & altera: </s>
                  <s xml:id="echoid-s3507" xml:space="preserve">ita vt vndæ aeris ſimul eant, & æqua
                    <lb/>
                  liter concurrant, abſque ulla interſectione, vel fractione illarum inuicem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3508" xml:space="preserve">Sed cum ponticulus ita diuiſerit chordam, vt relicta ſit eius tertia pars ab vno la-
                    <lb/>
                  tere, ab alio vero, duę tertię, </s>
                  <s xml:id="echoid-s3509" xml:space="preserve">tunc maior pars, dupla erit minori, &
                    <reg norm="ſonabunt" type="context">ſonabũt</reg>
                  ipſam dia
                    <lb/>
                  paſon conſonantiam, percuſſiones vero terminorum ipſius, tali proportione ſe inui-
                    <lb/>
                  cem habebunt, ut in qualibet ſecunda percuſſione minoris portionis ipſius chordæ,
                    <lb/>
                  maior percutiet, ſeu concurret cum minori, eodem temporis inſtanti, cum ne-
                    <lb/>
                  mo ſit qui neſciat, quod quo longior eſt chorda, etiam tardius moueatur, </s>
                  <s xml:id="echoid-s3510" xml:space="preserve">quare
                    <lb/>
                  cum longior dupla ſit breuiori, & eiuſdem intenſionis tam vna quam altera, tunc eo
                    <lb/>
                  tempore, quo longior vnum interuallum tremoris perfecerit, breuior duo interual-
                    <lb/>
                  la conficiet.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3511" xml:space="preserve">Cum autem ponticulus ita diuiſerit chordam, ut ab uno latere relinquantur duæ
                    <lb/>
                  quintæ partes, ab alio verò tres quintæ, ex quibus partibus generatur conſonantia
                    <lb/>
                  diapente; </s>
                  <s xml:id="echoid-s3512" xml:space="preserve">tunc clarè patet, quod eadem proportione tardius erit vnum interuallu
                    <unsure/>
                  m
                    <lb/>
                  tremoris maioris portionis, vno interuallo tremoris minoris portionis, quam ma-
                    <lb/>
                  i
                    <unsure/>
                  or portio habet ad minorem; </s>
                  <s xml:id="echoid-s3513" xml:space="preserve">hoc eſt tempus maioris interualli ad tempus minoris
                    <lb/>
                  erit
                    <reg norm="ſeſquialterum" type="context">ſeſquialterũ</reg>
                  quare non
                    <reg norm="conuenient" type="context">cõuenient</reg>
                  ſimul, niſi perfectis tribus interuallis mino-
                    <lb/>
                  ris portionis, & duobus maioris; </s>
                  <s xml:id="echoid-s3514" xml:space="preserve">ita quod eadem proportio erit numeri interuallo-
                    <lb/>
                  rum minoris portionis ad interualla maioris, quæ longitudinis maioris portionis ad
                    <lb/>
                  longitudinem minoris; </s>
                  <s xml:id="echoid-s3515" xml:space="preserve">vnde productum numeri portionis minoris ipſius chordæ
                    <lb/>
                  in numerum interuallorum motus ipſius portionis, æquale erit producto numeri
                    <lb/>
                  portionis maioris in numerum interuallorum ipſius maioris portionis; </s>
                  <s xml:id="echoid-s3516" xml:space="preserve">quæ quidem
                    <lb/>
                  producta ita ſe habebunt, vt in diapaſon, ſit binarius numerus; </s>
                  <s xml:id="echoid-s3517" xml:space="preserve">in diapente verò
                    <lb/>
                  ſenarius; </s>
                  <s xml:id="echoid-s3518" xml:space="preserve">in diateſſaron duodenarius, in hexachordo maiori quindenarius; </s>
                  <s xml:id="echoid-s3519" xml:space="preserve">in di-
                    <lb/>
                  tono vicenarius, in ſemiditono tricenarius, demum in hexachordo minori quadra
                    <lb/>
                  genarius: </s>
                  <s xml:id="echoid-s3520" xml:space="preserve">qui quidem numeri non abſque mirabili analogia conueniunt inuicem.</s>
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                <p>
                  <s xml:id="echoid-s3521" xml:space="preserve">Voluptas autem, quam auditui afferunt conſonantiæ fit, quia leniuntur ſenſus,
                    <lb/>
                  quemadmodum
                    <reg norm="contra" type="context">cõtra</reg>
                  , dolor qui à diſſonantijs oritur, ab aſperitate naſcitur, id quod
                    <lb/>
                  facilè vide
                    <unsure/>
                  re poteris cum conchordantur organorum fiſtulæ.</s>
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