Talk:Meantone: Difference between revisions

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:::: Looked at this a little bit more, and seeing that the 13th harmonic is very badly represented by the remaining EDOs other than 67EDO (even when considered independently of any rank-2+ temperaments), maybe the thing to do is declare no-13s when checking higher limits? And then Worsetone could be the name for the version that doesn't exclude the 13th harmonic? [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 10:04, 8 January 2025 (UTC)

:::: Looked at the 17th harmonic -- that's easy, it's equated to the diatonic semitone, so fifthspan -5. And the 19th harmonic is almost as easy, equated to the minor third, so fifthspan -3, except that if I haven't botched something by being in a hurry and up way too late, it actually doesn't quite work in 122EDO, so we get a ch wart here (EDO list: 12, 55, 67, 122ch -- most are close, but 122ch has high relative error). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 12:00, 8 January 2025 (UTC)

Revision as of 10:04, 8 January 2025 view source Lucius Chiaraviglio (talk \| contribs) 2,927 edits →Unlisted strong 7-limit Meantone extension (provisional name Mildtone)?: Looking at the 13-limit a bit more -- maybe no-13s is the way to go for the next higher limit(s)? ← Older edit		Revision as of 12:00, 8 January 2025 view source Lucius Chiaraviglio (talk \| contribs) 2,927 edits →Unlisted strong 7-limit Meantone extension (provisional name Mildtone)?: Looking at the No-13s 19-limit. Newer edit →
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	:::: Looked at this a little bit more, and seeing that the 13th harmonic is very badly represented by the remaining EDOs other than 67EDO (even when considered independently of any rank-2+ temperaments), maybe the thing to do is declare no-13s when checking higher limits? And then Worsetone could be the name for the version that doesn't exclude the 13th harmonic? [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 10:04, 8 January 2025 (UTC)		:::: Looked at this a little bit more, and seeing that the 13th harmonic is very badly represented by the remaining EDOs other than 67EDO (even when considered independently of any rank-2+ temperaments), maybe the thing to do is declare no-13s when checking higher limits? And then Worsetone could be the name for the version that doesn't exclude the 13th harmonic? [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 10:04, 8 January 2025 (UTC)

			:::: Looked at the 17th harmonic -- that's easy, it's equated to the diatonic semitone, so fifthspan -5. And the 19th harmonic is almost as easy, equated to the minor third, so fifthspan -3, except that if I haven't botched something by being in a hurry and up way too late, it actually doesn't quite work in 122EDO, so we get a ch wart here (EDO list: 12, 55, 67, 122ch -- most are close, but 122ch has high relative error). [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 12:00, 8 January 2025 (UTC)