Talk:44edo: Difference between revisions

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:::::: 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)

::::::: The 11th harmonic has only -21.5¢ relative error, so flipping it is going to introduce much more relative error than flipping the 7th harmonic, which has +47.6¢ relative error. If you were going to apply a wart to just 1 harmonic and use only the warted val, it might make sense to flip the 11th harmonic (as done with 27e), but you wouldn't want to use 44d alone, but in strategic alternation with 44 patent (thus, dual-7 rather than solely alternate-7). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:00, 10 May 2026 (UTC)

Revision as of 18:26, 9 May 2026 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 25,457 edits No edit summary ← Older edit		Revision as of 12:00, 10 May 2026 view source Lucius Chiaraviglio (talk \| contribs) 2,915 edits →Dual-7 edo?: dual-7 rather than solely alternate-7 Newer edit →
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	:::::: 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)		:::::: 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)

			::::::: The 11th harmonic has only -21.5¢ relative error, so flipping it is going to introduce much more relative error than flipping the 7th harmonic, which has +47.6¢ relative error. If you were going to apply a wart to just 1 harmonic and use only the warted val, it might make sense to flip the 11th harmonic (as done with 27e), but you wouldn't want to use 44d alone, but in strategic alternation with 44 patent (thus, dual-7 rather than solely alternate-7). [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 12:00, 10 May 2026 (UTC)