User talk:Overthink: Difference between revisions

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:: You'd be right about that, but you'd also be right if you decided on a 159-note MOS of [[frameshift]]. Fortunately, 159edo itself tempers out both the nexus comma and the frameshift comma. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:37, 25 October 2025 (UTC)

: It would be nice if the 2.3.5.11 subgroup was more connected. Prime 5 is equated to -8 fifths octave reduced, which is relatively close, but three 11/8s reach the original chain of fifths +28/-25 fifths away, which is almost exactly the opposite side of the circle. Three 11/10's return only a single fifth down, but unfortunately intervals with 3 factors of 5 are (just barely) inconsistent. There doesn't seem to be a very simple way to connect 2.3.11 to prime 5, but think I found a solution: Prime 17! The 4 intervals closest to the 12edo semitone in 159edo are 256/243, '''18/17''', '''17/16''', and 2187/2048. Prime 17 could be quite useful in classical music, such as in the 17:20:24 diminished chord. Prime 5 is found much more easily and consistently, as simply 3/2 minus 3 17/16s, and nothing of this simplicity is in 2.3.5.11. I believe it would be a good idea to devise a system of 2.3.17 analogous to alpharabian tuning, and you could easily just add back prime 11. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 04:24, 16 November 2025 (UTC)

Revision as of 17:37, 25 October 2025 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 6,010 edits No edit summary ← Older edit		Revision as of 04:24, 16 November 2025 view source Overthink (talk \| contribs) autopatrolled 2,762 edits →23-limit in 159edo: Prime 17 is a miracle Newer edit →
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	:: You'd be right about that, but you'd also be right if you decided on a 159-note MOS of [[frameshift]]. Fortunately, 159edo itself tempers out both the nexus comma and the frameshift comma. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 17:37, 25 October 2025 (UTC)		:: You'd be right about that, but you'd also be right if you decided on a 159-note MOS of [[frameshift]]. Fortunately, 159edo itself tempers out both the nexus comma and the frameshift comma. --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 17:37, 25 October 2025 (UTC)

			: It would be nice if the 2.3.5.11 subgroup was more connected. Prime 5 is equated to -8 fifths octave reduced, which is relatively close, but three 11/8s reach the original chain of fifths +28/-25 fifths away, which is almost exactly the opposite side of the circle. Three 11/10's return only a single fifth down, but unfortunately intervals with 3 factors of 5 are (just barely) inconsistent. There doesn't seem to be a very simple way to connect 2.3.11 to prime 5, but think I found a solution: Prime 17! The 4 intervals closest to the 12edo semitone in 159edo are 256/243, '''18/17''', '''17/16''', and 2187/2048. Prime 17 could be quite useful in classical music, such as in the 17:20:24 diminished chord. Prime 5 is found much more easily and consistently, as simply 3/2 minus 3 17/16s, and nothing of this simplicity is in 2.3.5.11. I believe it would be a good idea to devise a system of 2.3.17 analogous to alpharabian tuning, and you could easily just add back prime 11. --[[User:Overthink\|Overthink]] ([[User talk:Overthink\|talk]]) 04:24, 16 November 2025 (UTC)