User:Userminusone/Userminusone's 11 limit 15 tone scale - Revision history

Userminusone at 22:15, 4 November 2021

2021-11-04T22:15:38Z

← Older revision		Revision as of 22:15, 4 November 2021
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=]]		[[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==		==Links==

Userminusone at 03:11, 28 March 2021

2021-03-28T03:11:14Z

← Older revision		Revision as of 03:11, 28 March 2021
Line 26:		Line 26:

	==Links==		==Links==
	[https://sevish.com/scaleworkshop/?~~name=&~~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=~~261~~.~~625565~~&midi=60&vert=1&horiz=3&colors=white%20black%20white%20white%20black%20white%20black%20white%20white%20black%20white%20black&waveform=triangle&ampenv=organ Play along with Scale Workshop]		[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=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]

Userminusone at 03:07, 28 March 2021

2021-03-28T03:07:19Z

← Older revision		Revision as of 03:07, 28 March 2021
Line 26:		Line 26:

	==Links==		==Links==
			[https://sevish.com/scaleworkshop/?name=&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=261.625565&midi=60&vert=1&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=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]

Userminusone at 03:01, 28 March 2021

2021-03-28T03:01:57Z

← Older revision		Revision as of 03:01, 28 March 2021
Line 29:		Line 29:
	[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=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:15-tone scales]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	[[Category:Pages with Scala files]]		[[Category:Pages with Scala files]]

Userminusone at 01:44, 28 March 2021

2021-03-28T01:44:12Z

← Older revision		Revision as of 01:44, 28 March 2021
Line 24:		Line 24:

	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. If you see any other interesting properties that I missed, please let me know in this page's talk section.

			==Links==

			[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]

	[[Category:15-tone scales]]		[[Category:15-tone scales]]
	[[Category:Just intonation scales]]		[[Category:Just intonation scales]]
	[[Category:Pages with Scala files]]		[[Category:Pages with Scala files]]

Userminusone: Created page with "

 33/32 35/32 9/8 77/64 5/4 21/16 11/8 45/32 3/2 99/64 105/64 7/4 231/128 15/8 2/1

This scale only uses harmonics of the fundamental up to the 11 prime limit. It c..."

2021-03-14T03:52:52Z

Created page with "<pre> 33/32 35/32 9/8 77/64 5/4 21/16 11/8 45/32 3/2 99/64 105/64 7/4 231/128 15/8 2/1 </pre> This scale only uses harmonics of the fundamental up to the 11 prime limit. It c..."

New page

<pre>
33/32
35/32
9/8
77/64
5/4
21/16
11/8
45/32
3/2
99/64
105/64
7/4
231/128
15/8
2/1
</pre>

This scale only uses harmonics of the fundamental up to the 11 prime limit. It can be interpreted as the chord 128:132:140:144:154:160:168:176:180:192:198:210:224:231:240:256.

==Details about scale structure==

[[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.

[[Category:15-tone scales]]
[[Category:Just intonation scales]]
[[Category:Pages with Scala files]]