User talk:Aura: Difference between revisions

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::: Yes, working with the 11/8 paramajor fourth is inherently weird- it takes either the 16/15 diatonic semitone or the 5/4 major third to set it up, and it really seems to like being a chord root in a 1/1-25/22-14/11-3/2 chord. Have you tried working with this stuff? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:29, 6 April 2025 (UTC)

:::: I haven't worked with it myself, but I am trying to gain an understanding. Obviously it isn't easy -- Ivan Wyschnegradsky and a very few others figured it out, but only a very few others. But you gave me an idea of things to test, with the 1/1-25/22-14/11-3/2 chord. Although keep in mind that in 24edo (which Ivan Wyschnegradsky used most of the time, along with Alois Hába and a few compositions of Charles Ives), 14/11 maps down to the same as 5/4 (8\24) due to 24edo's badly flat 7th harmonic, while 25/22 maps not to the closest interval 9/8 as 4\24, but up to the same as 22/19 as 5\24, because its 5th harmonic is sharp (but not sharp enough for mapping as 25 instead of 5^2). But then again, I don't know whether Alois Hába or Charles Ives (ore much more recently, Scott Crothers) ever used 11L 2s as opposed to other ways of using 24edo; 11L 2s may be unique to Ivan Wyschnegradsky. Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:44, 6 April 2025 (UTC) Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:34, 7 April 2025 (UTC)

:::: I haven't worked with it myself, but I am trying to gain an understanding. Obviously it isn't easy — Ivan Wyschnegradsky and a very few others figured it out, but only a very few others. But you gave me an idea of things to test, with the 1/1-25/22-14/11-3/2 chord. Although keep in mind that in 24edo (which Ivan Wyschnegradsky used most of the time, along with Alois Hába and a few compositions of Charles Ives), 14/11 maps down to the same as 5/4 (8\24) due to 24edo's badly flat 7th harmonic, while 25/22 maps not to the closest interval 9/8 as 4\24, but up to the same as 22/19 as 5\24, because its 5th harmonic is sharp (but not sharp enough for mapping as 25 instead of 5^2). But then again, I don't know whether Alois Hába or Charles Ives (ore much more recently, Scott Crothers) ever used 11L 2s as opposed to other ways of using 24edo; 11L 2s may be unique to Ivan Wyschnegradsky. Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:44, 6 April 2025 (UTC) Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:34, 7 April 2025 (UTC)

::::: Oddly enough, my experiments with how to handle the 11/8 paramajor fourth relative to the tonic have been largely carried out in 159edo, but I must say that even in 24edo, that 11/8 wants to go to either 3/2 relative to the tonic, or, to 4/3 relative to the tonic- at least in terms of chord roots. It should be noted that the 11/8 seems to literally bring in its own set of related accidentals relative to the key you're in- I've already hinted at 25/16 being dragged in, and the same is true with the 7/4, which, in this capacity, acts like an ultramajor sixth relative to the tonic. Naturally, the 33/32 will likely be dragged in as well, but what I didn't tell you is that 75/64 wants to rear its head in scalar motion on a tIV chord- the only two default scale degrees relative to the tonic that can be used with a tIV chord are the 5/4, and the 15/8. Otherwise, if you use an 11/8, it has to either be part of a 1/1-11/8-3/2 suspension on the tonic, or as part of a 1/1-5/4-3/2-55/32 built on the 8/5 relative to the tonic. There are other chords I know, such as the 1/1-11/8-15/8 built on the tonic, or the 1/1-11/8-7/4 built on the tonic, but these tend to be harder to set up and follow up properly. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:50, 7 April 2025 (UTC)

:::::: Keep in mind that 159edo is going to be a LOT different from the low to mid (and even upper-mid) double digits EDOs. You get literally a lot finer control over how your chords sound. Of course, the downside is that you need an instrument (or group thereof) that can play that many pitches (or you need to be REALLY GOOD on a continuous-pitch instrument). Another thing I noticed is that in 11L 2s it is hard to choose a mode that lets you hit common 5-limit intervals without going off-scale with accidentals. (I need to see how that plays out with 7-limit intervals in an EDO that supports the 7-limit better than 24edo, like 37edo or 59edo or 61edo, although I noticed that if you go all the way afield to 50edo or 46edo, this scale shoots itself in the foot by not mapping intervals of ANY mode to 3/2 or 4/3, which map differently than in 11L 2s EDOs closer to 24EDO in the tuning spectrum. Not sure yet, but I think 17L 2s operating in in the 2.3.7... subgroup may have less of that problem.) [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:03, 7 April 2025 (UTC)

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 ::: Yes, working with the 11/8 paramajor fourth is inherently weird- it takes either the 16/15 diatonic semitone or the 5/4 major third to set it up, and it really seems to like being a chord root in a 1/1-25/22-14/11-3/2 chord.  Have you tried working with this stuff? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:29, 6 April 2025 (UTC)
-:::: I haven't worked with it myself, but I am trying to gain an understanding.  Obviously it isn't easy -- Ivan Wyschnegradsky and a very few others figured it out, but only a very few others.  But you gave me an idea of things to test, with the 1/1-25/22-14/11-3/2 chord.  Although keep in mind that in 24edo (which Ivan Wyschnegradsky used most of the time, along with Alois Hába and a few compositions of Charles Ives), 14/11 maps down to the same as 5/4 (8\24) due to 24edo's badly flat 7th harmonic, while 25/22 maps not to the closest interval 9/8 as 4\24, but up to the same as 22/19 as 5\24, because its 5th harmonic is sharp (but not sharp enough for mapping as 25 instead of 5^2).  But then again, I don't know whether Alois Hába or Charles Ives (ore much more recently, Scott Crothers) ever used 11L&nbsp;2s as opposed to other ways of using 24edo; 11L&nbsp;2s may be unique to Ivan Wyschnegradsky.  Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:44, 6 April 2025 (UTC)  Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:34, 7 April 2025 (UTC)
+:::: I haven't worked with it myself, but I am trying to gain an understanding.  Obviously it isn't easy &mdash; Ivan Wyschnegradsky and a very few others figured it out, but only a very few others.  But you gave me an idea of things to test, with the 1/1-25/22-14/11-3/2 chord.  Although keep in mind that in 24edo (which Ivan Wyschnegradsky used most of the time, along with Alois Hába and a few compositions of Charles Ives), 14/11 maps down to the same as 5/4 (8\24) due to 24edo's badly flat 7th harmonic, while 25/22 maps not to the closest interval 9/8 as 4\24, but up to the same as 22/19 as 5\24, because its 5th harmonic is sharp (but not sharp enough for mapping as 25 instead of 5^2).  But then again, I don't know whether Alois Hába or Charles Ives (ore much more recently, Scott Crothers) ever used 11L&nbsp;2s as opposed to other ways of using 24edo; 11L&nbsp;2s may be unique to Ivan Wyschnegradsky.  Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 19:44, 6 April 2025 (UTC)  Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 00:34, 7 April 2025 (UTC)
 ::::: Oddly enough, my experiments with how to handle the 11/8 paramajor fourth relative to the tonic have been largely carried out in 159edo, but I must say that even in 24edo, that 11/8 wants to go to either 3/2 relative to the tonic, or, to 4/3 relative to the tonic- at least in terms of chord roots.  It should be noted that the 11/8 seems to literally bring in its own set of related accidentals relative to the key you're in- I've already hinted at 25/16 being dragged in, and the same is true with the 7/4, which, in this capacity, acts like an ultramajor sixth relative to the tonic.  Naturally, the 33/32 will likely be dragged in as well, but what I didn't tell you is that 75/64 wants to rear its head in scalar motion on a tIV chord- the only two default scale degrees relative to the tonic that can be used with a tIV chord are the 5/4, and the 15/8.  Otherwise, if you use an 11/8, it has to either be part of a 1/1-11/8-3/2 suspension on the tonic, or as part of a 1/1-5/4-3/2-55/32 built on the 8/5 relative to the tonic.  There are other chords I know, such as the 1/1-11/8-15/8 built on the tonic, or the 1/1-11/8-7/4 built on the tonic, but these tend to be harder to set up and follow up properly. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:50, 7 April 2025 (UTC)
+:::::: Keep in mind that 159edo is going to be a LOT different from the low to mid (and even upper-mid) double digits EDOs.  You get literally a lot finer control over how your chords sound.  Of course, the downside is that you need an instrument (or group thereof) that can play that many pitches (or you need to be REALLY GOOD on a continuous-pitch instrument).  Another thing I noticed is that in 11L&nbsp;2s it is hard to choose a mode that lets you hit common 5-limit intervals without going off-scale with accidentals.  (I need to see how that plays out with 7-limit intervals in an EDO that supports the 7-limit better than 24edo, like 37edo or 59edo or 61edo, although I noticed that if you go all the way afield to 50edo or 46edo, this scale shoots itself in the foot by not mapping intervals of ANY mode to 3/2 or 4/3, which map differently than in 11L&nbsp;2s EDOs closer to 24EDO in the tuning spectrum.  Not sure yet, but I think 17L&nbsp;2s operating in in the 2.3.7... subgroup may have less of that problem.)  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:03, 7 April 2025 (UTC)