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→Musical Mad Science Musings on Diatonicized Sixth-Tone Sub-Chromaticism(?): Added table of odd harmonics for various EDO values supporting 17L 2s
→Musical Mad Science Musings on Diatonicized Chromaticism: Added table of odd harmonics for various EDO values supporting 11L 2s; also change ToDo from formal to informal so this page doesn't clutter the formal ToDo category
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I didn't do the 7th harmonic, because Ivan Wyschnegradsky himself wrote in the text at the beginning of the ''24 Quarter-Tone Preludes for two pianos'' linked above that you really need something more than 24edo to get the 7th harmonic (his choice for this in almost all of his compositions that could have reasonably dealt with it was 36edo or 72edo, although he also wrote a single [[31edo]] composition for the Fokker organ; but none of those support his diatonicized chromatic scale, other than 72edo in redundant form (being 3 * 24edo).  It would be interesting to do as a future back-extension to the 24 & 37 temperament, but it is understandable why he didn't use it, since 24edo has a bad 7th harmonic, and you have to go to either the superhard (46edo) region or the soft region (37edo through 50edo) to get a good 7th harmonic within the 11L 2s tuning spectrum.
I didn't do the 7th harmonic, because Ivan Wyschnegradsky himself wrote in the text at the beginning of the ''24 Quarter-Tone Preludes for two pianos'' linked above that you really need something more than 24edo to get the 7th harmonic (his choice for this in almost all of his compositions that could have reasonably dealt with it was 36edo or 72edo, although he also wrote a single [[31edo]] composition for the Fokker organ; but none of those support his diatonicized chromatic scale, other than 72edo in redundant form (being 3 * 24edo).  It would be interesting to do as a future back-extension to the 24 & 37 temperament, but it is understandable why he didn't use it, since 24edo has a bad 7th harmonic, and you have to go to either the superhard (46edo) region or the soft region (37edo through 50edo) to get a good 7th harmonic within the 11L 2s tuning spectrum.
==== That's all for now ====


Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:18, 25 January 2025 (UTC)<br>
Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:18, 25 January 2025 (UTC)<br>
(Fixed some links) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:04, 25 January 2025 (UTC)<br>
Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 9 April 2025 (UTC)
(Added a few words to the immediately previous paragraph to avoid confusion about Ivan Wyschnegradsky's compositions going beyond 24edo) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:02, 12 March 2025 (UTC)<br>
Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:08, 13 March 2025 (UTC)


=== Comma for getting the fifth on the circle of 11/8 or 16/11 in the middle of the 11L 2s tuning spectrum ===
=== Comma for getting the fifth on the circle of 11/8 or 16/11 in the middle of the 11L 2s tuning spectrum ===
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Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:04, 16 February 2025 (UTC)<br>
Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:04, 16 February 2025 (UTC)<br>
Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:40, 3 April 2025 (UTC)


{{Todo|complete section|inline=1|text=Need comma for back-extension to 5th harmonic and maybe back extension to 7th harmonic}}
Still need comma for back-extension to 5th harmonic and maybe back extension to 7th harmonic.
 
Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 9 April 2025 (UTC)


=== Rationale for leaving some of this on the Talk:11L 2s page ===
=== Rationale for leaving some of this on the Talk:11L 2s page ===
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Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:29, 18 March 2025 (UTC)
Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:29, 18 March 2025 (UTC)
=== Table of odd harmonics for various EDO values supporting 17L&nbsp;2s ===
This table (actually a collection of tables for now) is for tracking trends in odd harmonics along the tuning spectrum of [[11L&nbsp;2s]]; it is intended to match the organization of [[11L_2s#Scale_tree|the corresponding scale tree]], except for omitting the right-most column other than the top and bottom extremes:
{{Harmonics in equal|13|intervals=odd|prec=2|columns=28|title=[[13edo]] (L=1, s=1, [[16/11]] is 7) &mdash; Equalized 11L&nbsp;2s}}
{{Harmonics in equal|76|intervals=odd|prec=2|columns=28|title=[[76edo]] (L=6, s=5, 16/11 is 41)}}
{{Harmonics in equal|63|intervals=odd|prec=2|columns=28|title=[[63edo]] (L=5, s=4, 16/11 is 34)}}
{{Harmonics in equal|50|intervals=odd|prec=2|columns=28|title=[[50edo]] (L=4, s=3, 16/11 is 27) &mdash; Supersoft 11L&nbsp;2s}}
{{Harmonics in equal|87|intervals=odd|prec=2|columns=28|title=[[87edo]] (L=7, s=5, 16/11 is 47)}}
{{Harmonics in equal|37|intervals=odd|prec=2|columns=28|title=[[37edo]] (L=3, s=2, 16/11 is 20) &mdash; Soft 11L&nbsp;2s}}
{{Harmonics in equal|98|intervals=odd|prec=2|columns=28|title=[[98edo]] (L=8, s=5, 16/11 is 53)}}
{{Harmonics in equal|61|intervals=odd|prec=2|columns=28|title=[[61edo]] (L=5, s=3, 16/11 is 33) &mdash; Semisoft 11L&nbsp;2s}}
{{Harmonics in equal|85|intervals=odd|prec=2|columns=28|title=[[85edo]] (L=7, s=4, 16/11 is 46)}}
{{Harmonics in equal|24|intervals=odd|prec=2|columns=28|title=[[24edo]] (L=2, s=1, 16/11 is 13) &mdash; Basic 11L&nbsp;2s}}
{{Harmonics in equal|83|intervals=odd|prec=2|columns=28|title=[[83edo]] (L=7, s=3, 16/11 is 45)}}
{{Harmonics in equal|59|intervals=odd|prec=2|columns=28|title=[[59edo]] (L=5, s=2, 16/11 is 32) &mdash; Semihard 11L&nbsp;2s}}
{{Harmonics in equal|94|intervals=odd|prec=2|columns=28|title=[[94edo]] (L=8, s=3, 16/11 is 51)}}
{{Harmonics in equal|35|intervals=odd|prec=2|columns=28|title=[[35edo]] (L=3, s=1, 16/11 is 19) &mdash; Hard 11L&nbsp;2s}}
{{Harmonics in equal|81|intervals=odd|prec=2|columns=28|title=[[81edo]] (L=7, s=2, 16/11 is 44)}}
{{Harmonics in equal|46|intervals=odd|prec=2|columns=28|title=[[46edo]] (L=4, s=1, 16/11 is 25) &mdash; Superhard 11L&nbsp;2s}}
{{Harmonics in equal|57|intervals=odd|prec=2|columns=28|title=[[57edo]] (L=5, s=1, 16/11 is 31)}}
{{Harmonics in equal|68|intervals=odd|prec=2|columns=28|title=[[68edo]] (L=6, s=1, 16/11 is 37)}}
{{Harmonics in equal|11|intervals=odd|prec=2|columns=28|title=[[11edo]] (L=1, s=0, 16/11 is 6) &mdash; Collapsed 11L&nbsp;2s}}
(Need a way to combine the collection of tables into a single table for better readability.)
Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:00, 9 April 2025 (UTC)


== Musical Mad Science Musings on Diatonicized Sixth-Tone Sub-Chromaticism(?) ==
== Musical Mad Science Musings on Diatonicized Sixth-Tone Sub-Chromaticism(?) ==
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