Talk:Golden meantone: Difference between revisions

Line 19:

--[[User:Bozu|Bozu]] ([[User talk:Bozu|talk]]) 19:29, 30 January 2020 (UTC)

: With 131edo, you can sort of ~~quint~~ at it just right and say that you get better overall consistency of harmonics 3 and 5 by using the second-best (flat) fifth, and you get some added utility by being able to support a [[17L 2s]] scale that splits the 3/1 into 3 equal parts, and of having the diatonic and chromatic semitones in very close to the right ratio to each other. But yes, after a certain point, meantone (even golden) stops being the best use of the tonal resources you get from going to the trouble to support all those notes.

: With 131edo, you can sort of squint at it just right and say that you get better overall consistency of harmonics 3 and 5 by using the second-best (flat) fifth, and you get some added utility by being able to support a [[17L 2s]] scale that splits the 3/1 into 3 equal parts, and of having the diatonic and chromatic semitones in very close to the right ratio to each other. But yes, after a certain point, meantone (even golden) stops being the best use of the tonal resources you get from going to the trouble to support all those notes.

: Unless given some reason as above to go further, I would normally say to stop at 50edo, which has amazing consistency up to high limits — just 1 pair inconsistent intervals in the 19-odd-limit — and no larger meantone maps both 9/8 and 10/9 consistently.

: Unless given some reason as above to go further, I would normally say to stop at 50edo, which has amazing consistency up to high limits — just 1 pair inconsistent intervals in the 19-odd-limit — and no larger meantone maps both 9/8 and 10/9 consistently. And [https://www.youtube.com/watch?v=r7RmbC-hRFE it sounds good], too.

: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:02, 7 January 2026 (UTC)

: Added: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:02, 7 January 2026 (UTC)

: Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:13, 7 January 2026 (UTC)

==OEIS==

The OEIS sequence [https://oeis.org/A001060 A001060] seems to represent the sequence of edos that approximate golden meantone better and better. Can this be added in? <span style="display: inline-block;transform: rotate(15deg);background:#E1EBF2;font-family:Verdana;text-shadow: 3px 3px 4px #0008;">[[User:Hotcrystal0|hotcrysta]][[User talk: Hotcrystal0|l0]]</span> 16:55, 6 January 2026 (UTC)

@@ Line 19: / Line 19: @@
 --[[User:Bozu|Bozu]] ([[User talk:Bozu|talk]]) 19:29, 30 January 2020 (UTC)
-: With 131edo, you can sort of quint at it just right and say that you get better overall consistency of harmonics 3 and 5 by using the second-best (flat) fifth, and you get some added utility by being able to support a [[17L&nbsp;2s]] scale that splits the 3/1 into 3 equal parts, and of having the diatonic and chromatic semitones in very close to the right ratio to each other. But yes, after a certain point, meantone (even golden) stops being the best use of the tonal resources you get from going to the trouble to support all those notes.
+: With 131edo, you can sort of squint at it just right and say that you get better overall consistency of harmonics 3 and 5 by using the second-best (flat) fifth, and you get some added utility by being able to support a [[17L&nbsp;2s]] scale that splits the 3/1 into 3 equal parts, and of having the diatonic and chromatic semitones in very close to the right ratio to each other. But yes, after a certain point, meantone (even golden) stops being the best use of the tonal resources you get from going to the trouble to support all those notes.
-: Unless given some reason as above to go further, I would normally say to stop at 50edo, which has amazing consistency up to high limits &mdash; just 1 pair inconsistent intervals in the 19-odd-limit &mdash; and no larger meantone maps both 9/8 and 10/9 consistently.
+: Unless given some reason as above to go further, I would normally say to stop at 50edo, which has amazing consistency up to high limits &mdash; just 1 pair inconsistent intervals in the 19-odd-limit &mdash; and no larger meantone maps both 9/8 and 10/9 consistently. And [https://www.youtube.com/watch?v=r7RmbC-hRFE it sounds good], too.
-: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:02, 7 January 2026 (UTC)
+: Added:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:02, 7 January 2026 (UTC)
+: Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 08:13, 7 January 2026 (UTC)
 ==OEIS==
 The OEIS sequence [https://oeis.org/A001060 A001060] seems to represent the sequence of edos that approximate golden meantone better and better. Can this be added in? <span style="display: inline-block;transform: rotate(15deg);background:#E1EBF2;font-family:Verdana;text-shadow: 3px 3px 4px #0008;">[[User:Hotcrystal0|hotcrysta]][[User talk: Hotcrystal0|l0]]</span> 16:55, 6 January 2026 (UTC)