User:Xenllium/Xenllium's circulating scales: Difference between revisions

← Older edit

VisualWikitext

@@ Line 2: / Line 2: @@
 == Xentwelve ==
-'''Xentwelve''' is a 12-tone circulating scale based on [[12edo|12 equal temperament]]. In summary, it is close to [[1/3-comma meantone]] in the natural keys and [[Pythagorean tuning]] in the remote keys. The generator is a perfect fifth, which comes in three sizes, with eight pure fifths (at C–G, C♯–G♯, E♭–B♭, E–B, F–C, F♯–C♯, B♭–F and B–F♯, frequency ratio [[3/2]]), three 1/3-comma meantone fifths (at D–A, G–D and A–E), and one narrow schismic fifth (at G♯–D♯ (A♭–E♭), frequency ratio [[16384/10935]]). It derives two major thirds exact [[5/4]] (at C–E and G–B) and one minor third exact [[6/5]] (at E–G), with a pure major chord (at C–E–G) and a pure minor chord (at E–G–B).
+'''Xentwelve''' is a 12-tone circulating scale based on [[12edo|12 equal temperament]]. In summary, it is close to [[1/3-comma meantone]] in the natural keys and [[Pythagorean tuning]] in the remote keys. The generator is a perfect fifth, which comes in three sizes, with eight pure fifths (at C–G, C♯–G♯, E♭–B♭, E–B, F–C, F♯–C♯, B♭–F and B–F♯, frequency ratio [[3/2]]), three 1/3-comma meantone fifths (at D–A, G–D and A–E), and one schisma-compressed fifth (at G♯–D♯ (A♭–E♭), frequency ratio [[16384/10935]]). It derives two major thirds exact [[5/4]] (at C–E and G–B) and one minor third exact [[6/5]] (at E–G), with a pure major triad (at C–E–G) and a pure minor triad (at E–G–B).
 <pre>
@@ Line 8: / Line 8: @@
 !
 Xentwelve, Xenllium's 12-tone circulating scale, Central A
 !
 .56252207087
 .74123853187
 .47252380165
 .65124026264
 .21376233352
 .60752120549
 .78623766648
 .51752293626
 .69623939726
 .42752466704
 .60624112803
 .00000000000
 </pre>
+=== Intervals ===
+By the definition, there are no fifths larger than pure 3/2, no major thirds larger than Pythagorean 81/64, no minor thirds smaller than Pythagorean 32/27, and no whole tones larger than Pythagorean 9/8. Major thirds and minor thirds come in five sizes, whole tones and semitones come in four sizes respectively.
 <div class="toccolours mw-collapsible mw-collapsed" style="width:500px; overflow:auto;">
@@ Line 68: / Line 71: @@
 |}
 </div></div>
 <div class="toccolours mw-collapsible mw-collapsed" style="width:500px; overflow:auto;">
@@ Line 135: / Line 137: @@
 |}
 </div></div>
 <div class="toccolours mw-collapsible mw-collapsed" style="width:500px; overflow:auto;">
@@ Line 184: / Line 185: @@
 </div></div>
+=== Music ===
+* ''[https://youtube.com/watch?v=QOFBKfCYThI Xentwelve tuning]'' – demonstration of Xentwelve tuning
+* [https://youtube.com/watch?v=bbJ0HjPAuaA <span lang="ja" style="font-family:Yu Gothic UI, Yu Gothic, Meiryo, MS PGothic, sans-serif">【オリジナル曲】かなしいこと</span> / The sadness]
+== 31-tone circulating scales ==
+'''Xenthirtyone''' is a 31-tone circulating scale based on [[31edo|31 equal temperament]]. There are two circulating scales, named ''Xenthirtyone I'' and ''Xenthirtyone II'', generated by a major third, which comes in three sizes, with twenty-two pure major thirds, eight 1/4-Würschmidt-comma-stretched major thirds, and one luna-comma-stretched major third.
+=== Xenthirtyone I ===
+<pre>
+! xenthirtyone1.scl
+!
+Xenthirtyone I, Xenllium's 31-tone circulating scale
+!
+/125
+.53374935096
+/15
+/1875
+/234375
+/8192
+/64
+/5
+.11617794602
+/4
+/25
+.70878570247
+/3
+/375
+/46875
+/32768
+/256
+/2
+.29121429753
+/16
+/5
+.88382205398
+/3
+/75
+/9375
+/131072
+/1024
+/8
+.46625064904
+/64
+/1
+</pre>
+=== Xenthirtyone II ===
+<pre>
+! xenthirtyone2.scl
+!
+Xenthirtyone II, Xenllium's 31-tone circulating scale
+!
+/125
+.25639432431
+.45393024313
+.65146616195
+/234375
+/8192
+.72110610838
+.91864202720
+.11617794602
+/4
+/25
+.57010818915
+.76764410797
+.96518002679
+/46875
+/32768
+.03481997321
+.23235589203
+.42989181085
+/16
+/5
+.88382205398
+.08135797280
+.27889389162
+/9375
+/131072
+.34853383805
+.54606975687
+.74360567569
+/64
+/1
+</pre>
+[[Category:Pages with Scala files]]
 [[Category:12-tone scales]]
+[[Category:31-tone scales]]
 [[Category:Tempered scales]]