Talk:44edo: Difference between revisions

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:::: Well I don't think any inconsistency implies there's a point to treat the edo as dual-prime. The question of a dual-prime edo is rather if the two interpretations are about as valid, and in this case I don't think so. For 2.3.7, consider that 39edo, which has an even sharper 7, isn't treated as dual-7 on this wiki, which I think is very fair and should be taken as a sign that the archy mapping prevails over semaphore in this range. The flat 5 here isn't enough to shift the sharp tendency to justify a flat mapping of 7. This is confirmed in Graham Breed's temperament finder, where 44d doesn't come up in the 7-limit at all and 44e comes before 44d in the 11- to 19-limit. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:50, 9 May 2026 (UTC)

:::::: 39edo has the advantage that all of the flat harmonics (at least up to 23) are flat enough that you can just wart them all and call it a day. But 44edo has some harmonics that are just moderately sharp or moderately flat (not really working with a wart), so since 7 is far enough off to be wartable, might as well make it dual. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 16:04, 9 May 2026 (UTC)

::::: 39edo has the advantage that all of the flat harmonics (at least up to 23) are flat enough that you can just wart them all and call it a day. But 44edo has some harmonics that are just moderately sharp or moderately flat (not really working with a wart), so since 7 is far enough off to be wartable, might as well make it dual. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 16:04, 9 May 2026 (UTC)

:::::: I'd say even for the full 7-limit, and up to the 19-limit, the 7 isn't ambiguous. Note that only 7/5 and 11/7 are made closer by switching to the flat mapping, at the cost of all the rest. Another thing that clearly favors the sharp mapping is that it achieves 19-odd-limit monotonicity whereas the flat mapping fails at 14/13 and 15/14. Finally, as I said, 44e has a lower error than 44d, so if 44e isn't reasonable to consider, neither is 44d. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:26, 9 May 2026 (UTC)

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 :::: Well I don't think any inconsistency implies there's a point to treat the edo as dual-prime. The question of a dual-prime edo is rather if the two interpretations are about as valid, and in this case I don't think so. For 2.3.7, consider that 39edo, which has an even sharper 7, isn't treated as dual-7 on this wiki, which I think is very fair and should be taken as a sign that the archy mapping prevails over semaphore in this range. The flat 5 here isn't enough to shift the sharp tendency to justify a flat mapping of 7. This is confirmed in Graham Breed's temperament finder, where 44d doesn't come up in the 7-limit at all and 44e comes before 44d in the 11- to 19-limit. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:50, 9 May 2026 (UTC)
-:::::: 39edo has the advantage that all of the flat harmonics (at least up to 23) are flat enough that you can just wart them all and call it a day.  But 44edo has some harmonics that are just moderately sharp or moderately flat (not really working with a wart), so since 7 is far enough off to be wartable, might as well make it dual.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 16:04, 9 May 2026 (UTC)
+::::: 39edo has the advantage that all of the flat harmonics (at least up to 23) are flat enough that you can just wart them all and call it a day. But 44edo has some harmonics that are just moderately sharp or moderately flat (not really working with a wart), so since 7 is far enough off to be wartable, might as well make it dual.  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 16:04, 9 May 2026 (UTC)
+:::::: I'd say even for the full 7-limit, and up to the 19-limit, the 7 isn't ambiguous. Note that only 7/5 and 11/7 are made closer by switching to the flat mapping, at the cost of all the rest. Another thing that clearly favors the sharp mapping is that it achieves 19-odd-limit monotonicity whereas the flat mapping fails at 14/13 and 15/14. Finally, as I said, 44e has a lower error than 44d, so if 44e isn't reasonable to consider, neither is 44d. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 18:26, 9 May 2026 (UTC)