Vitruvius, De architectura libri decem, 1567

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              <s xml:id="echoid-s13567" xml:space="preserve">
                <pb o="176" file="514.01.208" n="208" rhead="LIBER"/>
              in nouem. </s>
              <s xml:id="echoid-s13568" xml:space="preserve">numeri uero trium tonorum ſunt 729, 648, 512. </s>
              <s xml:id="echoid-s13569" xml:space="preserve">ducendo 81, 72, 64, per nouem, & </s>
              <s xml:id="echoid-s13570" xml:space="preserve">643
                <unsure/>
                <lb/>
              per octo, & </s>
              <s xml:id="echoid-s13571" xml:space="preserve">ita toni cum numeris continenter efficiuntur, in quibus maioris ad minus comparatio ſemper est
                <lb/>
              ſeſquioctaua. </s>
              <s xml:id="echoid-s13572" xml:space="preserve">Ditonus autem eſt ſpatium a linea ad lineam ſpatio unico interiecto, modo hemitonium non inter
                <lb/>
              iaceat. </s>
              <s xml:id="echoid-s13573" xml:space="preserve">oblect. </s>
              <s xml:id="echoid-s13574" xml:space="preserve">it quidem ſed non eſt c
                <unsure/>
              bſoluta conſonantia, & </s>
              <s xml:id="echoid-s13575" xml:space="preserve">a noſtris tertia maior nominatur, quemadmodum
                <lb/>
              eſt ab ut, ad mi, ſcandendo, uel a mi, ad ut, deſcendendo. </s>
              <s xml:id="echoid-s13576" xml:space="preserve">Trihemitonium, quod est ſeſquitonum, uocant, est
                <lb/>
              ſpatium toni, & </s>
              <s xml:id="echoid-s13577" xml:space="preserve">hemitonij minoris, quemadmodum ab re, ad fa, aſcendendo; </s>
              <s xml:id="echoid-s13578" xml:space="preserve">& </s>
              <s xml:id="echoid-s13579" xml:space="preserve">a fa, ad re, ſi deſcendas. </s>
              <s xml:id="echoid-s13580" xml:space="preserve">ad au-
                <lb/>
              res etiam cum ſuauitate peruenit, ſed nondum concentum facit: </s>
              <s xml:id="echoid-s13581" xml:space="preserve">a noſtris tertia minor appellatur, eſtq́; </s>
              <s xml:id="echoid-s13582" xml:space="preserve">ſpatiũ
                <lb/>
              a linea ad lineam hemitonio intercepto. </s>
              <s xml:id="echoid-s13583" xml:space="preserve">Conueniunt omnia ſupra dicta interualla, quia muſicæ deſeruiunt.
                <lb/>
              </s>
              <s xml:id="echoid-s13584" xml:space="preserve">Tonus, & </s>
              <s xml:id="echoid-s13585" xml:space="preserve">hemitonium tetrachordorum coniunctionibus tanquam fundamenta ſubſternuntur. </s>
              <s xml:id="echoid-s13586" xml:space="preserve">Trithemito-
                <lb/>
              nium, & </s>
              <s xml:id="echoid-s13587" xml:space="preserve">ditonus, quia delectant, & </s>
              <s xml:id="echoid-s13588" xml:space="preserve">quoniam in generum diuiſiones incidunt. </s>
              <s xml:id="echoid-s13589" xml:space="preserve">Delectant etiam alij ſoni, qui
                <lb/>
                <note position="left" xlink:label="note-514.01.208-01" xlink:href="note-514.01.208-01a" xml:space="preserve">10</note>
              tamen conſonantias abſolutas minime reddunt. </s>
              <s xml:id="echoid-s13590" xml:space="preserve">constat enim proportione ſuprapartiente, cuiuſmodi ſunt & </s>
              <s xml:id="echoid-s13591" xml:space="preserve">
                <lb/>
              iam dicti trihemitonium, & </s>
              <s xml:id="echoid-s13592" xml:space="preserve">ditonus. </s>
              <s xml:id="echoid-s13593" xml:space="preserve">item & </s>
              <s xml:id="echoid-s13594" xml:space="preserve">quæ ſexta maior a noſtris dicitur, hemitonio, & </s>
              <s xml:id="echoid-s13595" xml:space="preserve">diapente con-
                <lb/>
              stans, id eſt additione hemitonij ad ſeſquialteram, quæ ſit cum a quaque linea ad tertium ſpatium aſcendimus,
                <lb/>
              continens duo hemitonia uel dieſes, & </s>
              <s xml:id="echoid-s13596" xml:space="preserve">tres tonos, quemadmodum ab mi, ad fa, ſi per ſextam modulentur.
                <lb/>
              </s>
              <s xml:id="echoid-s13597" xml:space="preserve">Eſt etiam iucundus tonus cum diapente, a quaque linea ad tertium ſpatium progrediens, unico hemitonio in-
                <lb/>
              tercepto, tonis quatuor incidentibus, quemadmodum ab ut, ad la, per ſextam modulari, quam ſextam maio-
                <lb/>
              rem uocant. </s>
              <s xml:id="echoid-s13598" xml:space="preserve">Oblectat etiam ſeptima minor duabus dieſibus, & </s>
              <s xml:id="echoid-s13599" xml:space="preserve">quatuor tonis comprehenſa, quemadmodum
                <lb/>
              ab ut, ad mi, ab uno ſpatio ad quartum, uel ab una linea ad quartam progrediens. </s>
              <s xml:id="echoid-s13600" xml:space="preserve">Sunt & </s>
              <s xml:id="echoid-s13601" xml:space="preserve">alia interualla. </s>
              <s xml:id="echoid-s13602" xml:space="preserve">
                <lb/>
              exercentibus nota, qualia ſunt nona, decima, undecima, & </s>
              <s xml:id="echoid-s13603" xml:space="preserve">duodecima a nostris dicta, quorum incunditas
                <lb/>
              exercitio potius, quàm regulis cognoſcitur. </s>
              <s xml:id="echoid-s13604" xml:space="preserve">Sed hæc ſatis ad intellectnm eorum, quæ a Vitruuio dicuntur. </s>
              <s xml:id="echoid-s13605" xml:space="preserve">in-
                <lb/>
                <note position="left" xlink:label="note-514.01.208-02" xlink:href="note-514.01.208-02a" xml:space="preserve">20</note>
              quit enim Vitru.</s>
              <s xml:id="echoid-s13606" xml:space="preserve"/>
            </p>
            <figure number="71">
              <caption xml:id="echoid-caption28" xml:space="preserve">EXEMPLVM MONOCHORDI.</caption>
              <description xml:id="echoid-description40" xml:space="preserve">Vniſonum
                <lb/>
              Tonus
                <lb/>
              Semitonium
                <lb/>
              Ditonus
                <lb/>
              Semiditonus
                <lb/>
              Tuo no</description>
            </figure>
            <note position="left" xml:space="preserve">30</note>
            <note position="left" xml:space="preserve">40</note>
            <p style="it">
              <s xml:id="echoid-s13607" xml:space="preserve">{In tribus generibus diſſimiles eſſe tetrachordorum diſpoſitones} ratio eſt quoniam diuerſis rerum qualitati-
                <lb/>
              tibus corum temperamenta applicantur, & </s>
              <s xml:id="echoid-s13608" xml:space="preserve">ideas referunt diuerſas uel magnarum, uel mediocrium, uel infir-
                <lb/>
              marum rerum. </s>
              <s xml:id="echoid-s13609" xml:space="preserve">In ſingulis tetrachordis quatuor ſonitus, aut gradus uocis continentur, tribus autem inter-
                <lb/>
              uallis ſingula conſtant, & </s>
              <s xml:id="echoid-s13610" xml:space="preserve">inter imum, & </s>
              <s xml:id="echoid-s13611" xml:space="preserve">ſummum gradum ſeſquitertia proportio, & </s>
              <s xml:id="echoid-s13612" xml:space="preserve">comparatio habetur,
                <lb/>
              & </s>
              <s xml:id="echoid-s13613" xml:space="preserve">in omnibus eſt eadem ratio extremorum, ſed interualla media dißimilibus diſpoſitionibus conſtituuntur in
                <lb/>
              ſingulis. </s>
              <s xml:id="echoid-s13614" xml:space="preserve">Nam harmonicum tetracbordum a dimidia dieſi, ad dimidiam ſcandit, inde ad ditonum, quæ ſimul
                <lb/>
              poſita duos tonos, & </s>
              <s xml:id="echoid-s13615" xml:space="preserve">hemitonium minus, uel dieſim unam continent. </s>
              <s xml:id="echoid-s13616" xml:space="preserve">in quibus ſeſquitertia proportio habetur.
                <lb/>
              </s>
              <s xml:id="echoid-s13617" xml:space="preserve">Sed chromaticum primum interuallum hemitonij vel dieſeos, ſecundum bemitonij uel apotomes, tertium trihe-
                <lb/>
                <note position="left" xlink:label="note-514.01.208-05" xlink:href="note-514.01.208-05a" xml:space="preserve">50</note>
              mitonij, quæ omniatonos duos, & </s>
              <s xml:id="echoid-s13618" xml:space="preserve">dieſim unam referunt, quemadmodum, ſpatia harmonici generis referebat.
                <lb/>
              </s>
              <s xml:id="echoid-s13619" xml:space="preserve">Similiter diatonicum primo interuallo tonum, ſecundo item tonum, tertio dieſim continet, & </s>
              <s xml:id="echoid-s13620" xml:space="preserve">ipſum quoque duo-
                <lb/>
              bus tonis, & </s>
              <s xml:id="echoid-s13621" xml:space="preserve">dieſi ordinatur. </s>
              <s xml:id="echoid-s13622" xml:space="preserve">Atque hoc illud eſt, quod Vitr. </s>
              <s xml:id="echoid-s13623" xml:space="preserve">dicit. </s>
              <s xml:id="echoid-s13624" xml:space="preserve">{Ita in tribus generibus tetrachorda
                <lb/>
              cx duobus tonis, & </s>
              <s xml:id="echoid-s13625" xml:space="preserve">hemitonio ſunt peræquata} extremis enim conueniunt, ſed medijs differunt. </s>
              <s xml:id="echoid-s13626" xml:space="preserve">Armonicum
                <lb/>
              genus, quod Vitr. </s>
              <s xml:id="echoid-s13627" xml:space="preserve">harmoniam uocat, ex parte graui, & </s>
              <s xml:id="echoid-s13628" xml:space="preserve">ima, ad acuta, & </s>
              <s xml:id="echoid-s13629" xml:space="preserve">elatum ſcandit in ſui tetrachordi
                <lb/>
              diſpoſitione a dimidia dieſi. </s>
              <s xml:id="echoid-s13630" xml:space="preserve">in qua ponitur primum interuallum, ad aliam dimidiam, in qua ſecundum eſt inter-
                <lb/>
              uallum, inde ad ditonum, in qua tertium eſt interuallum. </s>
              <s xml:id="echoid-s13631" xml:space="preserve">Intelligebat Ariſto xenum dimidium uerum, ſed ita
                <lb/>
              non eſt (ut dixi) claudit ergo tetrachordum huiuſmodi concentum illum, quem diateſſaron Græci, noſtri quar-
                <lb/>
              tam uocænt. </s>
              <s xml:id="echoid-s13632" xml:space="preserve">Ordinatio igitur, & </s>
              <s xml:id="echoid-s13633" xml:space="preserve">ſcala harmonici tetrachordi conſtituta, uoce ima, & </s>
              <s xml:id="echoid-s13634" xml:space="preserve">graui ſcandit a pro-
                <lb/>
              portione ſeſquiquadrageſima quinta, ad ſeſquiuigeſimam tertiam, & </s>
              <s xml:id="echoid-s13635" xml:space="preserve">inde ad ſeſquiquartam terminatur, deſcen
                <lb/>
                <note position="left" xlink:label="note-514.01.208-06" xlink:href="note-514.01.208-06a" xml:space="preserve">60</note>
              </s>
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