Vitruvius, De architectura libri decem, 1567

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              <s xml:id="echoid-s13479" xml:space="preserve">
                <pb o="175" file="514.01.207" n="207" rhead="QVINTVS."/>
              gnificabant, in quo enim conſtiterat uox, gradus dicebatur, diſcrimen uero inter du is uoces, interuallum, & </s>
              <s xml:id="echoid-s13480" xml:space="preserve">
                <lb/>
              ſpatium uocabant. </s>
              <s xml:id="echoid-s13481" xml:space="preserve">& </s>
              <s xml:id="echoid-s13482" xml:space="preserve">boc loco non caret reprehenſione Aristoxenus, qui grauitatem, & </s>
              <s xml:id="echoid-s13483" xml:space="preserve">acumen uocis in
                <lb/>
              qualitate, & </s>
              <s xml:id="echoid-s13484" xml:space="preserve">non in quantitate ponit. </s>
              <s xml:id="echoid-s13485" xml:space="preserve">Ex ijs, quæ dicta ſunt habemus alias ordinationes, & </s>
              <s xml:id="echoid-s13486" xml:space="preserve">ſcalas maiores eſ-
                <lb/>
              ſe, alias minores, maiores ſunt, quæ plures, minores, quæ pauciores habẽt gradus, unde maxima illa erit apud
                <lb/>
              antiquos, quæ quindecim gradus habebit. </s>
              <s xml:id="echoid-s13487" xml:space="preserve">Dico ſecundum antiquos, nam recentiores alios inſuper addidere,
                <lb/>
              nihil enim prohibet, quin ratione ducti ulterius progrediamur, præſertim in muſicis organis conficiendis, quo-
                <lb/>
              rum ſonitus acutiores humana uoce, altius conſcendere poſſunt. </s>
              <s xml:id="echoid-s13488" xml:space="preserve">hum ana enim uox ultra quindecim gradus
                <lb/>
              raro ſcandit, quin inepta, & </s>
              <s xml:id="echoid-s13489" xml:space="preserve">obſtrepens audiatur. </s>
              <s xml:id="echoid-s13490" xml:space="preserve">Cæterum & </s>
              <s xml:id="echoid-s13491" xml:space="preserve">ſi uelimus recte conſiderare, licet ultra de-
                <lb/>
              narium numerum progredi poſſimus, certe cum ad denarium deuentum est in numeris ad perfectam ſummam
                <lb/>
                <note position="left" xlink:label="note-514.01.207-01" xlink:href="note-514.01.207-01a" xml:space="preserve">10</note>
              nos deueniſſe cognoſcimus, & </s>
              <s xml:id="echoid-s13492" xml:space="preserve">eadem repetere cogimur, ſi ſupra ire uelimus. </s>
              <s xml:id="echoid-s13493" xml:space="preserve">ita cum in quint odecimo gradu
                <lb/>
              conſtiterimus, abſolutam ordinationem concentuum cognoſcemus, ultra quam ſi progredi uelimus, eaſdem
                <lb/>
              rationes innouabimus, quæ prius obuiam nobis uenere. </s>
              <s xml:id="echoid-s13494" xml:space="preserve">His poſitis, & </s>
              <s xml:id="echoid-s13495" xml:space="preserve">conſtitutis, iam ſcimus quid tetrachor-
                <lb/>
              dum, quid interuallum, quid ordinatio ſit. </s>
              <s xml:id="echoid-s13496" xml:space="preserve">Nunc ad alias uoces exponendas accedendum, quæ ſunt dieſis,
                <lb/>
              tonus, hemitonium, trihemitonium, ditonus, quæ ſunt interuallorum nomina. </s>
              <s xml:id="echoid-s13497" xml:space="preserve">Tonus igitur eſt conſonantiæ prin-
                <lb/>
              cipium, idest primus terminus, tanquam fundamentum concẽtus, & </s>
              <s xml:id="echoid-s13498" xml:space="preserve">ſymphoniæ ſeſquioctaua proportione con-
                <lb/>
              ſtans. </s>
              <s xml:id="echoid-s13499" xml:space="preserve">Concentus, & </s>
              <s xml:id="echoid-s13500" xml:space="preserve">ſymphonia est grauium, & </s>
              <s xml:id="echoid-s13501" xml:space="preserve">acutorum ſonorum permixtio temperata ad aures cum incun-
                <lb/>
              ditate pertinens. </s>
              <s xml:id="echoid-s13502" xml:space="preserve">Seſquioctauaratio eſt, cum quod plus eſt, continet quod minus est, ſemel, & </s>
              <s xml:id="echoid-s13503" xml:space="preserve">octauam eius
                <lb/>
              partem, quemadmodum nouennarius numerus octonarium ſemel continet, & </s>
              <s xml:id="echoid-s13504" xml:space="preserve">amplius unitatem, quæ octo-
                <lb/>
              narij octaua pars eſt. </s>
              <s xml:id="echoid-s13505" xml:space="preserve">Qui igitur ſonitus, uocesq́; </s>
              <s xml:id="echoid-s13506" xml:space="preserve">comparare, & </s>
              <s xml:id="echoid-s13507" xml:space="preserve">ratione temperare uoluerit, fpatia comparare,
                <lb/>
                <note position="left" xlink:label="note-514.01.207-02" xlink:href="note-514.01.207-02a" xml:space="preserve">20</note>
              & </s>
              <s xml:id="echoid-s13508" xml:space="preserve">ratione temperare studeat. </s>
              <s xml:id="echoid-s13509" xml:space="preserve">quiſpatia temperare uult adnumeros confugiat, & </s>
              <s xml:id="echoid-s13510" xml:space="preserve">ad numerorum rationes, & </s>
              <s xml:id="echoid-s13511" xml:space="preserve">
                <lb/>
              comparationes. </s>
              <s xml:id="echoid-s13512" xml:space="preserve">nam eadem ratio, quæ cadit inter ſpatium, & </s>
              <s xml:id="echoid-s13513" xml:space="preserve">ſpatium, cadit etiam inter ſonum, & </s>
              <s xml:id="echoid-s13514" xml:space="preserve">ſonum.
                <lb/>
              </s>
              <s xml:id="echoid-s13515" xml:space="preserve">Quare ubi ſpatium ſeſquioctaua proportione temperatum fuerit, ſonus quoque eandem habebit comparatio-
                <lb/>
              nem. </s>
              <s xml:id="echoid-s13516" xml:space="preserve">Accipio in exemplum, neruum unicum longum palmos nouem in abaco diftentum, ſitq́; </s>
              <s xml:id="echoid-s13517" xml:space="preserve">ille a, b, & </s>
              <s xml:id="echoid-s13518" xml:space="preserve">
                <lb/>
              in ſingulis palmis ſingulas notas appono. </s>
              <s xml:id="echoid-s13519" xml:space="preserve">I, 2, 3, 4, 5, 6, 7, 8, 9, tango illum, ſonitum dabit: </s>
              <s xml:id="echoid-s13520" xml:space="preserve">in
                <lb/>
              codem neruo tonum collocare uolo, pono fulcrum ſub nota prim
                <unsure/>
              palmi, a qua nota ad ſinem erunt octo palmi. </s>
              <s xml:id="echoid-s13521" xml:space="preserve">
                <lb/>
              dico ſi tetigero partem nerui a prima nota ad ultimam contentam, neruum illum mibi ſonum daturum, qui a
                <lb/>
              priori tono diſtabit: </s>
              <s xml:id="echoid-s13522" xml:space="preserve">ea igitur proportio, quæ cadit inter chordæ ſpatia, ea inquam cadit inter ſonos, qui a chor-
                <lb/>
              dæictu perueniunt. </s>
              <s xml:id="echoid-s13523" xml:space="preserve">quoniam igitur chorda integra ad partem I. </s>
              <s xml:id="echoid-s13524" xml:space="preserve">uſque ad ultimam reſpondet in ſeſquioctaua
                <lb/>
              comparatione, ideo & </s>
              <s xml:id="echoid-s13525" xml:space="preserve">ſonus qui a chorda integra icta prouenit, ſono, qui a prima nota ad ultimam efficitur,
                <lb/>
                <note position="left" xlink:label="note-514.01.207-03" xlink:href="note-514.01.207-03a" xml:space="preserve">30</note>
              ſeſquioctaua ratione comparatur. </s>
              <s xml:id="echoid-s13526" xml:space="preserve">& </s>
              <s xml:id="echoid-s13527" xml:space="preserve">quoniam tonus in ratione ſeſquioctaua ponitur, ideo illi ſonitus tono in-
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              uicem distabunt. </s>
              <s xml:id="echoid-s13528" xml:space="preserve">Cum uero unus & </s>
              <s xml:id="echoid-s13529" xml:space="preserve">idem uocis, & </s>
              <s xml:id="echoid-s13530" xml:space="preserve">ſoni tenor fit, absq́; </s>
              <s xml:id="echoid-s13531" xml:space="preserve">aſcenſu & </s>
              <s xml:id="echoid-s13532" xml:space="preserve">deſcenſu, vniſonum dici-
                <lb/>
              mus. </s>
              <s xml:id="echoid-s13533" xml:space="preserve">Vniſonum enim non eſt ſpatium aliquod, uel interuallum, ſed interuallorum, & </s>
              <s xml:id="echoid-s13534" xml:space="preserve">ſpatiorum fundamentum.
                <lb/>
              </s>
              <s xml:id="echoid-s13535" xml:space="preserve">Vnde notulæ omnes, quæ in eadem linea, uel in eodem ſpatio collocantur, uniſonum oſtendunt, quemadmodum
                <lb/>
              ut ut, re re, mi mi, fa fa, ſol ſol, la la, & </s>
              <s xml:id="echoid-s13536" xml:space="preserve">huiuſmodi. </s>
              <s xml:id="echoid-s13537" xml:space="preserve">Sed tonus eſt uocis interuallum. </s>
              <s xml:id="echoid-s13538" xml:space="preserve">ab una linea ad ſeqüens
                <lb/>
              ſpatium, aut ab uno ſpatio ad ſequentem lineam, quemadmodum ab ut, ad re, uel a re, ad ut, & </s>
              <s xml:id="echoid-s13539" xml:space="preserve">hoc quo que
                <lb/>
              loco reprehenditur Aristoxenus, qui numeris non utitur in notandis uocibus, ut rationes, & </s>
              <s xml:id="echoid-s13540" xml:space="preserve">proportiones col-
                <lb/>
              ligat, ſed in medio earum differentias ponit ita, ut ſpeculationem non in uocibus, ſed in eo, in quo differunt
                <lb/>
              uoces, collocet. </s>
              <s xml:id="echoid-s13541" xml:space="preserve">res quidem inconſiderata, dum putat earum uocum diſcrimina ſcire, quorum nec quantitatem,
                <lb/>
              nec menſuram ullam habet, omne iudicium auribus tribuens. </s>
              <s xml:id="echoid-s13542" xml:space="preserve">Deinde partitur tonum duas in partes æquales,
                <lb/>
              quas hemitonia uocat, uideturq́ue ignoraſſe nullam comparationem ſuprapartientem in duas poſſe æ qualiter
                <lb/>
                <note position="left" xlink:label="note-514.01.207-04" xlink:href="note-514.01.207-04a" xml:space="preserve">40</note>
              diuidi, & </s>
              <s xml:id="echoid-s13543" xml:space="preserve">propterea tonum, quia huiuſmodi comparatione conſtat, non poſſe pariter partiri. </s>
              <s xml:id="echoid-s13544" xml:space="preserve">ſed nos ſequamur
                <lb/>
              peritiores. </s>
              <s xml:id="echoid-s13545" xml:space="preserve">Tonus igitur cum in duas æquas partes ſecari non poſſit, in duas ſecabitur inæquales, quarum al-
                <lb/>
              tera hemitonium minus, item & </s>
              <s xml:id="echoid-s13546" xml:space="preserve">dieſis, altera hemitonium maius, & </s>
              <s xml:id="echoid-s13547" xml:space="preserve">apotome nominatur. </s>
              <s xml:id="echoid-s13548" xml:space="preserve">Hemitonium
                <lb/>
              minus est ea toni pars, qua ſeſquitertia comparatio duobus tonis maior eſt, duo toni autem ſunt duæ ſeſquio-
                <lb/>
              ctauæ. </s>
              <s xml:id="echoid-s13549" xml:space="preserve">Exemplum ſit huiuſmodi. </s>
              <s xml:id="echoid-s13550" xml:space="preserve">in monochordo neruum quàm longum eſt, in quatuor ſpatia diuidito, & </s>
              <s xml:id="echoid-s13551" xml:space="preserve">
                <lb/>
              ſuis notis quælibet, ſpatia ſignato, I, 2, 3, 4, ſub prima fulcrum collocato, dico neruum illum integrum,
                <lb/>
              cum parte illa ſub qua fulcrum erit poſitum ſeſquitertium ſonum editurum, nam ita ſpatium ſeſquitertia com-
                <lb/>
              paratione constat. </s>
              <s xml:id="echoid-s13552" xml:space="preserve">Siigitur duos continuos tonos in neruo poſueris, quemadmodum ſupra dictum eſt, ſeſquio-
                <lb/>
              ctaua proportione constantes, & </s>
              <s xml:id="echoid-s13553" xml:space="preserve">ſubijcies fulcrum, ubi ſecundi toni terminus eſt
                <unsure/>
              , dico ſpatium interceptum
                <lb/>
              inter priorem fulcrum, in quo erat ſeſquitertia proportio, & </s>
              <s xml:id="echoid-s13554" xml:space="preserve">notam ſub fulcro, quod ſecundi toni terminus erat,
                <lb/>
                <note position="left" xlink:label="note-514.01.207-05" xlink:href="note-514.01.207-05a" xml:space="preserve">50</note>
              eße ſpatium hemitonij minoris, ideſt illud amplius, quo duos continuatos tonos ſeſquitertia comparatio excedit,
                <lb/>
              cuiuſmodi est fpatium inter mi, & </s>
              <s xml:id="echoid-s13555" xml:space="preserve">fa; </s>
              <s xml:id="echoid-s13556" xml:space="preserve">hemitonium uero maius, ſeu apotome, eſt reliquum tertij toni ab ſeſqui-
                <lb/>
              tertia, nam continuatis in eodem neruo tribus tonis ſpatium interceptum inter notam ſeſquitertiæ, & </s>
              <s xml:id="echoid-s13557" xml:space="preserve">finem
                <lb/>
              tertijtoni, & </s>
              <s xml:id="echoid-s13558" xml:space="preserve">ſpatium hemitonij maioris. </s>
              <s xml:id="echoid-s13559" xml:space="preserve">Quo ſit ut hemitonij uocabulum, non ſignificet dimidiatum tonum
                <lb/>
              omnino, quemadmodum nec ſemiuocalis nomen dimidium uocalis innuat, ſed dimidium utrumque quaſi inter
                <lb/>
              extrema collocatum ſignificat, quemadmodum in ſuperiori uolumine ſemimetopia, & </s>
              <s xml:id="echoid-s13560" xml:space="preserve">ſemitriglyphos appel-
                <lb/>
              lauimus. </s>
              <s xml:id="echoid-s13561" xml:space="preserve">præterea licet tonus, & </s>
              <s xml:id="echoid-s13562" xml:space="preserve">hemitonium concentum non faciant, ſunt tamen in conſideratione habendi,
                <lb/>
              ium quia concentum interualla diſtinguunt, nam per eos tanquam gradibus ad conſonantias ferimur, tum quia
                <lb/>
              ijs ſolidæ conſonantiæ tanquam uinculis colligantur, & </s>
              <s xml:id="echoid-s13563" xml:space="preserve">utriſque ius datur affectuum mouendorum. </s>
              <s xml:id="echoid-s13564" xml:space="preserve">Numeri
                <lb/>
              ucro unius toni ſunt 8, & </s>
              <s xml:id="echoid-s13565" xml:space="preserve">9. </s>
              <s xml:id="echoid-s13566" xml:space="preserve">duorum 81, 72, 64, qui fiunt, ſi duas octo in ſe, item nouem in ſe, & </s>
              <s xml:id="echoid-s13567" xml:space="preserve">octo
                <lb/>
                <note position="left" xlink:label="note-514.01.207-06" xlink:href="note-514.01.207-06a" xml:space="preserve">60</note>
              </s>
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