Talk:11L 2s: Difference between revisions

Line 31:

On the hard side, this already quits working for 35edo, for which the 5/4 major third is fairly flat (you instead get a very sharp alternative major third, a bit sharp of a Pythagorean major third, and almost up to 33/26). For 46edo, it gets even worse, giving an alternate-alternate sharp major third (the patent 5/4 (sub-)major third is already slightly sharp), actually more like 14/11. For 59edo, the situation is similar, even though the 59edo 5/4 (sub-)maor third is just barely sharp of just, instead giving 19/15. So even the mildly hard side of the 11L 2s tuning spectrum doesn't work for the 5th harmonic, despite working for the third harmonic.

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 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 ====

[[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)

(Fixed some links) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:04, 25 January 2025 (UTC)<br>

(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)

=== Comma for getting the fifth on the circle of 11/8 or 16/11 in the middle of the 11L 2s tuning spectrum ===

The comma |-33 -1 0 0 10⟩ (11.224¢) equates a stack of ten 11/8 (octave-reduced) to 3/2. However, this only gives the patent fifth in more or less the range 35EDO to 37EDO. For 50EDO (as noted above) it gives the Blackwood (pentatonic) fifth; while for 46EDO it gives the 23EDO flat fifth. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:04, 16 February 2025 (UTC) Edited [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:06, 16 February 2025 (UTC)

@@ Line 31: / Line 31: @@
 On the hard side, this already quits working for 35edo, for which the 5/4 major third is fairly flat (you instead get a very sharp alternative major third, a bit sharp of a Pythagorean major third, and almost up to 33/26).  For 46edo, it gets even worse, giving an alternate-alternate sharp major third (the patent 5/4 (sub-)major third is already slightly sharp), actually more like 14/11.  For 59edo, the situation is similar, even though the 59edo 5/4 (sub-)maor third is just barely sharp of just, instead giving 19/15.  So even the mildly hard side of the 11L 2s tuning spectrum doesn't work for the 5th harmonic, despite working for the third harmonic.
-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 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 ====
 [[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)
+(Fixed some links) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:04, 25 January 2025 (UTC)<br>
+(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)
 === Comma for getting the fifth on the circle of 11/8 or 16/11 in the middle of the 11L 2s tuning spectrum ===
 The comma |-33 -1 0 0 10⟩ (11.224¢) equates a stack of ten 11/8 (octave-reduced) to 3/2.  However, this only gives the patent fifth in more or less the range 35EDO to 37EDO.  For 50EDO (as noted above) it gives the Blackwood (pentatonic) fifth; while for 46EDO it gives the 23EDO flat fifth.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:04, 16 February 2025 (UTC) Edited [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 11:06, 16 February 2025 (UTC)