Talk:Meantone: Difference between revisions

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: Last modified: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:46, 20 December 2025 (UTC) (diatonic Lumatone mapping also works as long as you don't run out of notes)

:: Related to the above, if you relax the requirement to be able to divide the fifth into 8 parts and instead 4 parts like Tetracot, you get white might be the [https://x31eq.com/pyscript/uv.html?uvs=81%2F80%0D%0A130321%2F129654&limit=2.3.5.7.19 Meantone relative of Tetracot] like Superpine is the Meantone relative of Porcupine: 2.3.5.7.19 unison vectors [-4, 4, -1, 0, 0⟩ (81/80), [-1, -3, 0, -4, 4⟩ (130321/129654)

:: Related to the above, if you relax the requirement to be able to divide the fifth into 8 parts and instead 4 parts like Tetracot, you get white might be the [https://x31eq.com/pyscript/uv.html?uvs=81%2F80%0D%0A130321%2F129654&limit=2.3.5.7.19 Meantone relative of Tetracot] like Superpine is the Meantone relative of Porcupine: 2.3.5.7.19 unison vectors [-4, 4, -1, 0, 0⟩ (81/80), [-1, -3, 0, -4, 4⟩ (130321/129654) (the last comma currently has no article, but it equates a stack of 4 [[21/19]]s with [[3/2]] without colliding with the 2.3.5 subgroup temperament specifications laid down by the normal Tetracot comma).

:: {BEGIN x31eq OUTPUT}

:: Equal Temperaments

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: The same would be true if anybody had come up with an even less-flattened meantone to use as-is with a likewise finite subset of the helix of fifths being shoehorned into circle (and no purposely-resized second size of fifth). I don't know of anything other than 1/6-comma meantone being used that way in actual practice, but the [[historical temperaments]] page here mentions Romieu and 1/7-comma meantone (of which the 12 note subset would be more circulation-friendly than 12 note 1/6-comma meantone), so depending upon whether that got into actual performance, that might be another example.

: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:08, 17 June 2025 (UTC)

== Synch-meantone ==

I took a listen to the major triad of Synch-meantone (fifth 695.632{{c}}), and it sounds ''much'' more in tune than [[quarter-comma meantone]], as well as tunings like [[55edo]]. This tuning deserves to be mentioned in this page.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 00:48, 19 January 2026 (UTC)

I did a bit more fine-tuning, and I found the optimum to actually be a bit sharp of this (fifth 695.8{{c}}), close to 2/7-comma. I likely overlooked this because even [[50edo]] didn't replicate it well enough. And yes, I notice such differences; the harmonic JND is ''tiny''.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 00:54, 19 January 2026 (UTC)

IDK, such tiny differences are perceptible, but I'm not sure. I think 50edo actually ''is'' good enough, and the "optima" I described are just the results of a few tests that might just influence ''each other''. Still, there should be more info in the tunings section, like there is on the page of [[superpyth]].--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 01:03, 19 January 2026 (UTC)

I just realized that the program has a precision limit of 1 cent. Nevermind much of this. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 01:10, 19 January 2026 (UTC)

: For what it's worth, the [[69edo]] page says that 69edo is a very close approximation of synch-meantone.

: From the point of view of Duke Ellington's rule about music (as relayed by Peter Schickele), "If it sounds good, it is good". To this end, you can find amazing sound samples on both sides of the 2/7-comma meantone divide, [https://www.youtube.com/watch?v=r7RmbC-hRFE in 50edo] and [https://www.youtube.com/watch?v=ZAqPonAHuUM in 69edo]. For [[50edo]] this is understandable since it just misses being consistent all the way to the 21-odd-limit (11/9 and 18/11 come out slightly inconsistent)), but apparently the [[devichromic chords]] of 69edo at least partly make up for its consistency shortcomings. You seem to be looking for something in between, but I don't know of any sound samples for [[119edo]].

: I am on the cusp of wanting to propose a meantone extension for meantone EDOs that have a corresponding c val on tetracot the way superpine tunings have a corresponding c val on porcupine, but the series 55*, 62, 69*, 76 ... 14c* does weird things with some of the mappings.

: *These are also octacot, and temper out the [[400/399|devichroma]], although in some cases needing one or more warts.

: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:41, 19 January 2026 (UTC)

@@ Line 401: / Line 401: @@
 : Last modified:  [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 09:46, 20 December 2025 (UTC) (diatonic Lumatone mapping also works as long as you don't run out of notes)
-:: Related to the above, if you relax the requirement to be able to divide the fifth into 8 parts and instead 4 parts like Tetracot, you get white might be the [https://x31eq.com/pyscript/uv.html?uvs=81%2F80%0D%0A130321%2F129654&limit=2.3.5.7.19 Meantone relative of Tetracot] like Superpine is the Meantone relative of Porcupine:  2.3.5.7.19 unison vectors [-4, 4, -1, 0, 0⟩ (81/80), [-1, -3, 0, -4, 4⟩ (130321/129654)
+:: Related to the above, if you relax the requirement to be able to divide the fifth into 8 parts and instead 4 parts like Tetracot, you get white might be the [https://x31eq.com/pyscript/uv.html?uvs=81%2F80%0D%0A130321%2F129654&limit=2.3.5.7.19 Meantone relative of Tetracot] like Superpine is the Meantone relative of Porcupine:  2.3.5.7.19 unison vectors [-4, 4, -1, 0, 0⟩ (81/80), [-1, -3, 0, -4, 4⟩ (130321/129654) (the last comma currently has no article, but it equates a stack of 4 [[21/19]]s with [[3/2]] without colliding with the 2.3.5 subgroup temperament specifications laid down by the normal Tetracot comma).
 :: {BEGIN x31eq OUTPUT}
 :: Equal Temperaments
@@ Line 417: / Line 417: @@
 : The same would be true if anybody had come up with an even less-flattened meantone to use as-is with a likewise finite subset of the helix of fifths being shoehorned into circle (and no purposely-resized second size of fifth).  I don't know of anything other than 1/6-comma meantone being used that way in actual practice, but the [[historical temperaments]] page here mentions Romieu and 1/7-comma meantone (of which the 12 note subset would be more circulation-friendly than 12 note 1/6-comma meantone), so depending upon whether that got into actual performance, that might be another example.
 : [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:08, 17 June 2025 (UTC)
+== Synch-meantone ==
+I took a listen to the major triad of Synch-meantone (fifth 695.632{{c}}), and it sounds ''much'' more in tune than [[quarter-comma meantone]], as well as tunings like [[55edo]]. This tuning deserves to be mentioned in this page.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 00:48, 19 January 2026 (UTC)
+I did a bit more fine-tuning, and I found the optimum to actually be a bit sharp of this (fifth 695.8{{c}}), close to 2/7-comma. I likely overlooked this because even [[50edo]] didn't replicate it well enough. And yes, I notice such differences; the harmonic JND is ''tiny''.--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 00:54, 19 January 2026 (UTC)
+IDK, such tiny differences are perceptible, but I'm not sure. I think 50edo actually ''is'' good enough, and the "optima" I described are just the results of a few tests that might just influence ''each other''. Still, there should be more info in the tunings section, like there is on the page of [[superpyth]].--[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 01:03, 19 January 2026 (UTC)
+I just realized that the program has a precision limit of 1 cent. Nevermind much of this. --[[User:Overthink|Overthink]] ([[User talk:Overthink|talk]]) 01:10, 19 January 2026 (UTC)
+: For what it's worth, the [[69edo]] page says that 69edo is a very close approximation of synch-meantone.
+: From the point of view of Duke Ellington's rule about music (as relayed by Peter Schickele), "If it sounds good, it is good".  To this end, you can find amazing sound samples on both sides of the 2/7-comma meantone divide, [https://www.youtube.com/watch?v=r7RmbC-hRFE in 50edo] and [https://www.youtube.com/watch?v=ZAqPonAHuUM in 69edo]. For [[50edo]] this is understandable since it just misses being consistent all the way to the 21-odd-limit (11/9 and 18/11 come out slightly inconsistent)), but apparently the [[devichromic chords]] of 69edo at least partly make up for its consistency shortcomings. You seem to be looking for something in between, but I don't know of any sound samples for [[119edo]].
+: I am on the cusp of wanting to propose a meantone extension for meantone EDOs that have a corresponding c val on tetracot the way superpine tunings have a corresponding c val on porcupine, but the series 55<sup>*</sup>, 62, 69<sup>*</sup>, 76 ... 14c<sup>*</sup> does weird things with some of the mappings.
+: <sup>*</sup>These are also octacot, and temper out the [[400/399|devichroma]], although in some cases needing one or more warts.
+: [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 07:41, 19 January 2026 (UTC)