Vitruvius
,
De architectura libri decem
,
1567
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514.01.207
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gnificabant, in quo enim conſtiterat uox, gradus dicebatur, diſcrimen uero inter du is uoces, interuallum, & </
s
>
<
s
xml:id
="
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xml:space
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<
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ſpatium uocabant. </
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>
<
s
xml:id
="
echoid-s13481
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xml:space
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">& </
s
>
<
s
xml:id
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"
xml:space
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">boc loco non caret reprehenſione Aristoxenus, qui grauitatem, & </
s
>
<
s
xml:id
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xml:space
="
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">acumen uocis in
<
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qualitate, & </
s
>
<
s
xml:id
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xml:space
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">non in quantitate ponit. </
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>
<
s
xml:id
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xml:space
="
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">Ex ijs, quæ dicta ſunt habemus alias ordinationes, & </
s
>
<
s
xml:id
="
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xml:space
="
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">ſcalas maiores eſ-
<
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ſe, alias minores, maiores ſunt, quæ plures, minores, quæ pauciores habẽt gradus, unde maxima illa erit apud
<
lb
/>
antiquos, quæ quindecim gradus habebit. </
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>
<
s
xml:id
="
echoid-s13487
"
xml:space
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">Dico ſecundum antiquos, nam recentiores alios inſuper addidere,
<
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/>
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
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raro ſcandit, quin inepta, & </
s
>
<
s
xml:id
="
echoid-s13489
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xml:space
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">obſtrepens audiatur. </
s
>
<
s
xml:id
="
echoid-s13490
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xml:space
="
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">Cæterum & </
s
>
<
s
xml:id
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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
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xlink:href
="
note-514.01.207-01a
"
xml:space
="
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">10</
note
>
nos deueniſſe cognoſcimus, & </
s
>
<
s
xml:id
="
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"
xml:space
="
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">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
="
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">comparare, & </
s
>
<
s
xml:id
="
echoid-s13507
"
xml:space
="
preserve
">ratione temperare uoluerit, fpatia comparare,
<
lb
/>
<
note
position
="
left
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xlink:label
="
note-514.01.207-02
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xlink:href
="
note-514.01.207-02a
"
xml:space
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">20</
note
>
& </
s
>
<
s
xml:id
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xml:space
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">ratione temperare studeat. </
s
>
<
s
xml:id
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echoid-s13509
"
xml:space
="
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">quiſpatia temperare uult adnumeros confugiat, & </
s
>
<
s
xml:id
="
echoid-s13510
"
xml:space
="
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">ad numerorum rationes, & </
s
>
<
s
xml:id
="
echoid-s13511
"
xml:space
="
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">
<
lb
/>
comparationes. </
s
>
<
s
xml:id
="
echoid-s13512
"
xml:space
="
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">nam eadem ratio, quæ cadit inter ſpatium, & </
s
>
<
s
xml:id
="
echoid-s13513
"
xml:space
="
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">ſpatium, cadit etiam inter ſonum, & </
s
>
<
s
xml:id
="
echoid-s13514
"
xml:space
="
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">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
="
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">ille a, b, & </
s
>
<
s
xml:id
="
echoid-s13518
"
xml:space
="
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">
<
lb
/>
in ſingulis palmis ſingulas notas appono. </
s
>
<
s
xml:id
="
echoid-s13519
"
xml:space
="
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">I, 2, 3, 4, 5, 6, 7, 8, 9, tango illum, ſonitum dabit: </
s
>
<
s
xml:id
="
echoid-s13520
"
xml:space
="
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">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
="
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">
<
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
="
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">uſque ad ultimam reſpondet in ſeſquioctaua
<
lb
/>
comparatione, ideo & </
s
>
<
s
xml:id
="
echoid-s13525
"
xml:space
="
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">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
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xlink:href
="
note-514.01.207-03a
"
xml:space
="
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">30</
note
>
ſeſquioctaua ratione comparatur. </
s
>
<
s
xml:id
="
echoid-s13526
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s13527
"
xml:space
="
preserve
">quoniam tonus in ratione ſeſquioctaua ponitur, ideo illi ſonitus tono in-
<
lb
/>
uicem distabunt. </
s
>
<
s
xml:id
="
echoid-s13528
"
xml:space
="
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">Cum uero unus & </
s
>
<
s
xml:id
="
echoid-s13529
"
xml:space
="
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">idem uocis, & </
s
>
<
s
xml:id
="
echoid-s13530
"
xml:space
="
preserve
">ſoni tenor fit, absq́; </
s
>
<
s
xml:id
="
echoid-s13531
"
xml:space
="
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">aſcenſu & </
s
>
<
s
xml:id
="
echoid-s13532
"
xml:space
="
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">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
>
</
p
>
</
div
>
</
div
>
</
text
>
</
echo
>