Talk:Meantone family: Difference between revisions

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:: It wasn't originally my question, but let me try rephrasing it: Why is the POTE generator for it specified as being so close to 7\12 when 12edo is way out of the range for which Sharptone is optimal (unless you need it for pitch-bending the 7/4 up on a standard 12edo fretted instrument), and 5edo is the crossover point between Dominant and Sharptone, and Sharptone would give the most just 7/4 or 8/7 with a fifth somewhat sharp of the diatonic range of Meantone temperament? [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:49, 10 July 2025 (UTC)

::: ~~Meantone~~ clearly makes no sense beyond 3\5. Dominant doesn't make much sense beyond 10\17. I described the range of dominant as 7\12 to 10\17 in the Arhcytas clan page, which I hope you like. Unfortunately 10\17 isn't a natural boundary for meantone extensions, so maybe we'll keep 7\12 to 3\5 for dominant as we discuss it in this article. As for sharptone, the only 7-odd-limit monotone range of it is the singleton of 3\5, right? So that's the case for tuning it to 3\5. Our conventional optimization methods are least squares, which also make sense, but they obviously don't take those constraints into account. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:21, 11 July 2025 (UTC)

::: Classical (5-limit) meantone clearly makes no sense beyond 3\5. Dominant doesn't make much sense beyond 10\17. I described the range of dominant as 7\12 to 10\17 in the Arhcytas clan page, which I hope you like. Unfortunately 10\17 isn't a natural boundary for meantone extensions, so maybe we'll keep 7\12 to 3\5 for dominant as we discuss it in this article. As for sharptone, the only 7-odd-limit monotone range of it is the singleton of 3\5, right? So that's the case for tuning it to 3\5. Our conventional optimization methods are least squares, which also make sense, but they obviously don't take those constraints into account. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:21, 11 July 2025 (UTC)

:::: . . . Which leaves me wishing that the name Sharptone hadn't been taken for what is really an exotemperament extension of Meantone, so that it could have been used for something more fitting as a counterpart to Flattone, like the strong extension that gives the patent 7th harmonic for 55edo, 67edo, and 122edo (to which I gave the placeholder name Mildtone inn [[Talk:Meantone]]). [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:28, 11 July 2025 (UTC)

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 :: It wasn't originally my question, but let me try rephrasing it:  Why is the POTE generator for it specified as being so close to 7\12 when 12edo is way out of the range for which Sharptone is optimal (unless you need it for pitch-bending the 7/4 up on a standard 12edo fretted instrument), and 5edo is the crossover point between Dominant and Sharptone, and Sharptone would give the most just 7/4 or 8/7 with a fifth somewhat sharp of the diatonic range of Meantone temperament?  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 22:49, 10 July 2025 (UTC)
-::: Meantone clearly makes no sense beyond 3\5. Dominant doesn't make much sense beyond 10\17. I described the range of dominant as 7\12 to 10\17 in the Arhcytas clan page, which I hope you like. Unfortunately 10\17 isn't a natural boundary for meantone extensions, so maybe we'll keep 7\12 to 3\5 for dominant as we discuss it in this article. As for sharptone, the only 7-odd-limit monotone range of it is the singleton of 3\5, right? So that's the case for tuning it to 3\5. Our conventional optimization methods are least squares, which also make sense, but they obviously don't take those constraints into account. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:21, 11 July 2025 (UTC)
+::: Classical (5-limit) meantone clearly makes no sense beyond 3\5. Dominant doesn't make much sense beyond 10\17. I described the range of dominant as 7\12 to 10\17 in the Arhcytas clan page, which I hope you like. Unfortunately 10\17 isn't a natural boundary for meantone extensions, so maybe we'll keep 7\12 to 3\5 for dominant as we discuss it in this article. As for sharptone, the only 7-odd-limit monotone range of it is the singleton of 3\5, right? So that's the case for tuning it to 3\5. Our conventional optimization methods are least squares, which also make sense, but they obviously don't take those constraints into account. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:21, 11 July 2025 (UTC)
 :::: . . . Which leaves me wishing that the name Sharptone hadn't been taken for what is really an exotemperament extension of Meantone, so that it could have been used for something more fitting as a counterpart to Flattone, like the strong extension that gives the patent 7th harmonic for 55edo, 67edo, and 122edo (to which I gave the placeholder name Mildtone inn [[Talk:Meantone]]).  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:28, 11 July 2025 (UTC)