Talk:19edo: Difference between revisions

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The latest revision says that 19edo is "slightly worse in terms of relative error" than 12edo. This is arguably untrue, as TE relative error and maximum 9-odd-limit relative error are both lower in 19edo than in 12edo. I think this is because the error of primes 3, 5, and 7 are in the same direction, resulting in some cancellations of error involving prime 3 where it would add up in 12edo. How would this sentence best be written?--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 22:55, 13 February 2026 (UTC)

: I just went by the relative error listed in the table of harmonics. Let me know if you think of something better, or if you want me to just undo it. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:48, 13 February 2026 (UTC)

: Also, playing around with [http://terpstrakeyboard.com/play-it-now/ the online Terpstra keyboard] to generate barbershop chords (4:5:6:7) in harpsichord timbre, the 12edo version definitely sounds better than the 19edo version, even though 19edo sounds better than 12edo when leaving off the A♯, and this matches my experience with other sound sources. Not only that, playing around with it some more, 19d (use B♭ instead of A♯) sounds better in 19edo than doing it according to the patent val, even though it is mathematically a lot further off. Just to prove I wasn't crazy or suddenly tone-deaf, doing the barbershop chord in 31edo sounds better than any of those, even though I don't like the fifth in 31edo (falls in that in-between zone of too flat for 3/2 and too sharp for 112/75). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:19, 14 February 2026 (UTC)

:: I think that's just because you're used to 12edo. The 12edo "harmonic seventh chord" sounds better because it is the familiar dominant seventh chord, but IMO it doesn't really represent 4:5:6:7. Personally both the 12edo and 19edo versions sound quite different from 4:5:6:7, but the 19edo one is somewhat closer. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 07:55, 14 February 2026 (UTC)

::: That's why I included 31edo in the comparison — if it was just a matter of being used to 12edo, then 31edo's barbershop chord wouldn't sound good. The 12edo version is a fudge for 4:5:6:7, with substitution of a pretty good 16/9 for the 7/4 (it still fits in the general vicinity of a minor seventh), whereas 19edo doesn't offer a substitute that fits in the right interval zone (just intervals 26/15 and especially 19/11 are close to 15\19, but they sound more like slightly stretched major sixths). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 17:56, 14 February 2026 (UTC)

:::: In my opinion 7/4 sounds more like a seventh than a sixth, but still somewhat ambiguous. 19edo captures (and exaggerates) that ambiguous nature, but 12edo makes it clearly a minor seventh. The 19edo ~4:5:6:7 still sounds off, but still closer to 4:5:6:7 than the 12edo one, even if it doesn't sound as "good" as 12edo because the ~7/4 doesn't sound like as much of a seventh.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 18:07, 14 February 2026 (UTC)

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 The latest revision says that 19edo is "slightly worse in terms of relative error" than 12edo. This is arguably untrue, as TE relative error and maximum 9-odd-limit relative error are both lower in 19edo than in 12edo. I think this is because the error of primes 3, 5, and 7 are in the same direction, resulting in some cancellations of error involving prime 3 where it would add up in 12edo. How would this sentence best be written?--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 22:55, 13 February 2026 (UTC)
+: I just went by the relative error listed in the table of harmonics.  Let me know if you think of something better, or if you want me to just undo it.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 23:48, 13 February 2026 (UTC)
+: Also, playing around with [http://terpstrakeyboard.com/play-it-now/ the online Terpstra keyboard] to generate barbershop chords (4:5:6:7) in harpsichord timbre, the 12edo version definitely sounds better than the 19edo version, even though 19edo sounds better than 12edo when leaving off the A♯, and this matches my experience with other sound sources.  Not only that, playing around with it some more, 19d (use B♭ instead of A♯) sounds better in 19edo than doing it according to the patent val, even though it is mathematically a lot further off.  Just to prove I wasn't crazy or suddenly tone-deaf, doing the barbershop chord in 31edo sounds better than any of those, even though I don't like the fifth in 31edo (falls in that in-between zone of too flat for 3/2 and too sharp for 112/75).  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:19, 14 February 2026 (UTC)
+:: I think that's just because you're used to 12edo. The 12edo "harmonic seventh chord" sounds better because it is the familiar dominant seventh chord, but IMO it doesn't really represent 4:5:6:7. Personally both the 12edo and 19edo versions sound quite different from 4:5:6:7, but the 19edo one is somewhat closer. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 07:55, 14 February 2026 (UTC)
+::: That's why I included 31edo in the comparison &mdash; if it was just a matter of being used to 12edo, then 31edo's barbershop chord wouldn't sound good.  The 12edo version is a fudge for 4:5:6:7, with substitution of a pretty good 16/9 for the 7/4 (it still fits in the general vicinity of a minor seventh), whereas 19edo doesn't offer a substitute that fits in the right interval zone (just intervals 26/15 and especially 19/11 are close to 15\19, but they sound more like slightly stretched major sixths).  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 17:56, 14 February 2026 (UTC)
+:::: In my opinion 7/4 sounds more like a seventh than a sixth, but still somewhat ambiguous. 19edo captures (and exaggerates) that ambiguous nature, but 12edo makes it clearly a minor seventh. The 19edo ~4:5:6:7 still sounds off, but still closer to 4:5:6:7 than the 12edo one, even if it doesn't sound as "good" as 12edo because the ~7/4 doesn't sound like as much of a seventh.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 18:07, 14 February 2026 (UTC)