User:Userminusone/Userminusone's 11 limit 15 tone scale: Difference between revisions

(4 intermediate revisions by the same user not shown)

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This scale has 9 just perfect fifths, 5 just major thirds, 6 harmonic sevenths, and 5 11-limit superfourths. One interesting thing about this scale is that it has 3 chains of pseudo-5edo that only contain perfect fifths and harmonic sevenths. (This subset scale is 1/1, 9/8, 21/16, 3/2, 7/4, 2/1 or the chord 16:18:21:24:28:32.) In the same way that 15edo could be used as 5edo with a few extra ornamental notes, this scale could be used as pseudo-5edo with occasional 5-limit and 11-limit melodies/harmonies~~. If you see any other interesting properties that I missed, please let me know in this page's talk section~~.

This scale has 9 just perfect fifths, 5 just major thirds, 6 harmonic sevenths, and 5 11-limit superfourths. One interesting thing about this scale is that it has 3 chains of pseudo-5edo that only contain perfect fifths and harmonic sevenths. (This subset scale is 1/1, 9/8, 21/16, 3/2, 7/4, 2/1 or the chord 16:18:21:24:28:32.) In the same way that 15edo could be used as 5edo with a few extra ornamental notes, this scale could be used as pseudo-5edo with occasional 5-limit and 11-limit melodies/harmonies.

==Links==

[https://sevish.com/scaleworkshop/?data=33%2F32%0A35%2F32%0A9%2F8%0A77%2F64%0A5%2F4%0A21%2F16%0A11%2F8%0A45%2F32%0A3%2F2%0A99%2F64%0A105%2F64%0A7%2F4%0A231%2F128%0A15%2F8%0A2%2F1&freq=130.812783&midi=48&vert=-2&horiz=3&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=triangle&ampenv=organ Play along with Scale Workshop]

[http://terpstrakeyboard.com/web-app/keys.htm?fundamental=261.626&right=3&upright=1&size=30&rotation=0&instrument=piano&enum=false&equivSteps=31&spectrum_colors=false&fundamental_color=55FF55&no_labels=false&scale=33%2F32%0A35%2F32%0A9%2F8%0A77%2F64%0A5%2F4%0A21%2F16%0A11%2F8%0A45%2F32%0A3%2F2%0A99%2F64%0A105%2F64%0A7%2F4%0A231%2F128%0A15%2F8%0A2%2F1&names=C%0AC%0AD%0AD%0AEb%0AE%0AF%0AF%0AF%23%0AG%0AG%0AA%0ABb%0ABb%0AB&note_colors=ffffff%0Aff60c0%0A50b0ff%0Affffff%0A9030ff%0Affd000%0A5050ff%0Aff60c0%0Affd000%0Affffff%0Aff60c0%0A50b0ff%0A5050ff%0A9030ff%0Affd000 Play along with Terpstra Keyboard]

[http://terpstrakeyboard.com/web-app/keys.htm?fundamental=261.626&right=1&upright=7&size=30&rotation=0&instrument=piano&enum=false&equivSteps=31&spectrum_colors=false&fundamental_color=55FF55&no_labels=false&scale=3%2F2%0A9%2F4%0A%2F%0A%2F%0A%2F%0A%2F%0A7%2F4%0A21%2F8%0A%2F%0A11%2F8%0A33%2F16%0A99%2F32%0A%2F%0A%2F%0A%2F%0A%2F%0A77%2F32%0A231%2F64%0A%2F%0A5%2F4%0A15%2F8%0A45%2F16%0A%2F%0A%2F%0A%2F%0A%2F%0A35%2F16%0A105%2F32%0A%2F%0A2%2F1&names=C%0AG%0AD%0A%0A%0A%0A%0ABb%0AF%0A%0AF%0AC%0AG%0A%0A%0A%0A%0AEb%0ABb%0A%0AE%0AB%0AF%23%0A%0A%0A%0A%0AD%0AA%0A&note_colors=ffffff%0Affffff%0Affffff%0A202020%0A202020%0A202020%0A202020%0A5050ff%0A5050ff%0A202020%0Aff60c0%0Aff60c0%0Aff60c0%0A202020%0A202020%0A202020%0A202020%0A9030ff%0A9030ff%0A202020%0Affd000%0Affd000%0Affd000%0A202020%0A202020%0A202020%0A202020%0A50b0ff%0A50b0ff%0A202020 Play along with Terpstra Keyboard (lattice)]

[http://terpstrakeyboard.com/web-app/keys.htm?fundamental=261.626&right=3&upright=4&size=30&rotation=0&instrument=piano&enum=false&equivSteps=31&spectrum_colors=false&fundamental_color=55FF55&no_labels=false&scale=99%2F64%0A231%2F128%0A3%2F2%0A7%2F4%0A5%2F4%0A9%2F4%0A21%2F8%0A15%2F8%0A35%2F16%0A11%2F8%0A45%2F16%0A105%2F32%0A33%2F16%0A77%2F32%0A2%2F1&names=C%0AG%0ABb%0AG%0ABb%0AE%0AD%0AF%0AB%0AD%0AF%0AF%23%0AA%0AC%0AEb&note_colors=ffffff%0Aff60c0%0A9030ff%0Affffff%0A5050ff%0Affd000%0Affffff%0A5050ff%0Affd000%0A50b0ff%0Aff60c0%0Affd000%0A50b0ff%0Aff60c0%0A9030ff Play along with Terpstra Keyboard (compact lattice)]

[[Category:15-tone scales]]

[[Category:Just intonation scales]]

[[Category:Pages with Scala files]]

@@ Line 23: / Line 23: @@
 [[File:Userminusone15scalelattice.jpg|frameless|A lattice showing the structure of this scale|400px]] [[File:Userminusone15scalecolornames.jpg|frameless|A closer look at the note names, including their corresponding ratios|400x400px|alt=]]
-This scale has 9 just perfect fifths, 5 just major thirds, 6 harmonic sevenths, and 5 11-limit superfourths. One interesting thing about this scale is that it has 3 chains of pseudo-5edo that only contain perfect fifths and harmonic sevenths. (This subset scale is 1/1, 9/8, 21/16, 3/2, 7/4, 2/1 or the chord 16:18:21:24:28:32.) In the same way that 15edo could be used as 5edo with a few extra ornamental notes, this scale could be used as pseudo-5edo with occasional 5-limit and 11-limit melodies/harmonies. If you see any other interesting properties that I missed, please let me know in this page's talk section.
+This scale has 9 just perfect fifths, 5 just major thirds, 6 harmonic sevenths, and 5 11-limit superfourths. One interesting thing about this scale is that it has 3 chains of pseudo-5edo that only contain perfect fifths and harmonic sevenths. (This subset scale is 1/1, 9/8, 21/16, 3/2, 7/4, 2/1 or the chord 16:18:21:24:28:32.) In the same way that 15edo could be used as 5edo with a few extra ornamental notes, this scale could be used as pseudo-5edo with occasional 5-limit and 11-limit melodies/harmonies.
+==Links==
+[https://sevish.com/scaleworkshop/?data=33%2F32%0A35%2F32%0A9%2F8%0A77%2F64%0A5%2F4%0A21%2F16%0A11%2F8%0A45%2F32%0A3%2F2%0A99%2F64%0A105%2F64%0A7%2F4%0A231%2F128%0A15%2F8%0A2%2F1&freq=130.812783&midi=48&vert=-2&horiz=3&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=triangle&ampenv=organ Play along with Scale Workshop]
+[http://terpstrakeyboard.com/web-app/keys.htm?fundamental=261.626&right=3&upright=1&size=30&rotation=0&instrument=piano&enum=false&equivSteps=31&spectrum_colors=false&fundamental_color=55FF55&no_labels=false&scale=33%2F32%0A35%2F32%0A9%2F8%0A77%2F64%0A5%2F4%0A21%2F16%0A11%2F8%0A45%2F32%0A3%2F2%0A99%2F64%0A105%2F64%0A7%2F4%0A231%2F128%0A15%2F8%0A2%2F1&names=C%0AC%0AD%0AD%0AEb%0AE%0AF%0AF%0AF%23%0AG%0AG%0AA%0ABb%0ABb%0AB&note_colors=ffffff%0Aff60c0%0A50b0ff%0Affffff%0A9030ff%0Affd000%0A5050ff%0Aff60c0%0Affd000%0Affffff%0Aff60c0%0A50b0ff%0A5050ff%0A9030ff%0Affd000 Play along with Terpstra Keyboard]
+[http://terpstrakeyboard.com/web-app/keys.htm?fundamental=261.626&right=1&upright=7&size=30&rotation=0&instrument=piano&enum=false&equivSteps=31&spectrum_colors=false&fundamental_color=55FF55&no_labels=false&scale=3%2F2%0A9%2F4%0A%2F%0A%2F%0A%2F%0A%2F%0A7%2F4%0A21%2F8%0A%2F%0A11%2F8%0A33%2F16%0A99%2F32%0A%2F%0A%2F%0A%2F%0A%2F%0A77%2F32%0A231%2F64%0A%2F%0A5%2F4%0A15%2F8%0A45%2F16%0A%2F%0A%2F%0A%2F%0A%2F%0A35%2F16%0A105%2F32%0A%2F%0A2%2F1&names=C%0AG%0AD%0A%0A%0A%0A%0ABb%0AF%0A%0AF%0AC%0AG%0A%0A%0A%0A%0AEb%0ABb%0A%0AE%0AB%0AF%23%0A%0A%0A%0A%0AD%0AA%0A&note_colors=ffffff%0Affffff%0Affffff%0A202020%0A202020%0A202020%0A202020%0A5050ff%0A5050ff%0A202020%0Aff60c0%0Aff60c0%0Aff60c0%0A202020%0A202020%0A202020%0A202020%0A9030ff%0A9030ff%0A202020%0Affd000%0Affd000%0Affd000%0A202020%0A202020%0A202020%0A202020%0A50b0ff%0A50b0ff%0A202020 Play along with Terpstra Keyboard (lattice)]
+[http://terpstrakeyboard.com/web-app/keys.htm?fundamental=261.626&right=3&upright=4&size=30&rotation=0&instrument=piano&enum=false&equivSteps=31&spectrum_colors=false&fundamental_color=55FF55&no_labels=false&scale=99%2F64%0A231%2F128%0A3%2F2%0A7%2F4%0A5%2F4%0A9%2F4%0A21%2F8%0A15%2F8%0A35%2F16%0A11%2F8%0A45%2F16%0A105%2F32%0A33%2F16%0A77%2F32%0A2%2F1&names=C%0AG%0ABb%0AG%0ABb%0AE%0AD%0AF%0AB%0AD%0AF%0AF%23%0AA%0AC%0AEb&note_colors=ffffff%0Aff60c0%0A9030ff%0Affffff%0A5050ff%0Affd000%0Affffff%0A5050ff%0Affd000%0A50b0ff%0Aff60c0%0Affd000%0A50b0ff%0Aff60c0%0A9030ff Play along with Terpstra Keyboard (compact lattice)]
 [[Category:15-tone scales]]
 [[Category:Just intonation scales]]
 [[Category:Pages with Scala files]]