Talk:Golden meantone - Revision history

Lucius Chiaraviglio: /* 131edo... and other notes */ Add sound sample; fix typo

2026-01-07T08:13:25Z

131edo... and other notes: Add sound sample; fix typo

← Older revision		Revision as of 08:13, 7 January 2026
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	--[[User:Bozu\|Bozu]] ([[User talk:Bozu\|talk]]) 19:29, 30 January 2020 (UTC)		--[[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==		==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)		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)

Lucius Chiaraviglio: /* 131edo... and other notes */ The Golden Meantone series: where to stop

2026-01-07T08:02:08Z

131edo... and other notes: The Golden Meantone series: where to stop

← Older revision		Revision as of 08:02, 7 January 2026
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	--[[User:Bozu\|Bozu]] ([[User talk:Bozu\|talk]]) 19:29, 30 January 2020 (UTC)		--[[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.
			: 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.
			: [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 08:02, 7 January 2026 (UTC)

	==OEIS==		==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)		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)

Hotcrystal0 at 16:55, 6 January 2026

2026-01-06T16:55:57Z

← Older revision		Revision as of 16:55, 6 January 2026
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	--[[User:Bozu\|Bozu]] ([[User talk:Bozu\|talk]]) 19:29, 30 January 2020 (UTC)		--[[User:Bozu\|Bozu]] ([[User talk:Bozu\|talk]]) 19:29, 30 January 2020 (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)

Xenwolf: Xenwolf moved page Talk:Golden Meantone to Talk:Golden meantone: Rule: only first letter capitalized. Reason: less typing when referenced

2020-06-08T11:40:44Z

Xenwolf moved page Talk:Golden Meantone to Talk:Golden meantone: Rule: only first letter capitalized. Reason: less typing when referenced

← Older revision	Revision as of 11:40, 8 June 2020
(No difference)

Bozu: /* 131edo... and other notes */ new section

2020-01-30T19:29:08Z

131edo... and other notes: new section

← Older revision		Revision as of 19:29, 30 January 2020
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	{{WSArchiveLink}}		{{WSArchiveLink}}

			== 131edo... and other notes ==

			I am a little confused at how 131edo is "meantone." 77\131 seems to be the representation of the fifth, which is 1.3 cents sharp, so it doesn't temper out the syntonic comma. If you use 76\131 instead, the fifth is noticeably more out, but it sort of works. I think Kornerup also acknowledged the discrepancy in his book, if I'm not mistaken (I do not own a copy of his book).

			The other note, is that I noticed an arithmetic series, as I'm sure almost every editor here has before, of (most of) the lower-numbered meantone edo tunings: 7, 12, 19, 31, 50, 81 - but, I don't see it mentioned how the fifth is represented in each of these systems also follows an arithmetic series (I'll get to why this is interesting to me in a minute): 4\7, 7\12, 11\19, 18\31, 29\50, 47\81.

			The series is a1 = 4, a2 = 7, an = an-1 + an-2 ... 4, 7, 4+7 = 11, 7+11 = 18, 11+18 = 29, 18+29 = 47.

			Going further through the series, after 131edo (50+81 = 131), there's 212edo, 343edo, 555edo, 898edo, etc., and most of these are not meantone the way I understand meantone (but I don't understand a lot of things). Representing the fifth in each of these, though...

			29+47 = 76 (this is the more sour fifth in 131edo that makes a meantone tuning, at least the way I understand the terminology)

			47+76 = 123, but the fifth in 212edo is represented by 124\212. So as disappointing as it is, I believe that the pattern of series breaks down beyond 81edo.

			Beyond that, just for fun... 76+123 = 199, but 76+124 = 200. 201\343 is the better fifth, but 200\343 fit meantone better.

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

Mike Battaglia: 1 revision imported: Moving archived Wikispaces discussion to subpage

2018-10-01T18:02:36Z

1 revision imported: Moving archived Wikispaces discussion to subpage

← Older revision	Revision as of 18:02, 1 October 2018
(No difference)

WikispacesArchive>Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-10-01T18:01:16Z

Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' <span style="color:#800000">''...

← Older revision		Revision as of 18:01, 1 October 2018
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	~~= ARCHIVED WIKISPACES DISCUSSION BELOW =~~		{{WSArchiveLink}}
	~~'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''~~

	~~<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.~~

	~~----~~

	~~== Problems with math ==~~
	The math expression rendering seems to be unstable. I encounter errors when loading fonts. Mostly, I see [Math Processing Error] instead of formulas, that's why I suggest not to mix math expressions into sentences. It's becoming unreadable, for example:

	~~<em>This makes the Golden fifth exactly [Math Processing Error] octave, or [Math Processing Error] cents, approximately 696.214 cents.</em>~~

	~~- '''xenwolf''' February 23, 2015, 12:56:58 AM UTC-0800~~
	~~----~~

Mike Battaglia: Text replacement - "'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''" to "'''All discussion below is archived from the Wikispaces export in its original unaltered form.''' ''...

2018-09-20T07:00:49Z

← Older revision		Revision as of 07:00, 20 September 2018
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	= ARCHIVED WIKISPACES DISCUSSION BELOW =		= ARCHIVED WIKISPACES DISCUSSION BELOW =
	'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''		'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''

			<span style="color:#800000">'''PLEASE MAKE ANY NEW COMMENTS <u>ABOVE</u> THIS SECTION.'''</span> Anything below here is for archival purposes only.

	----		----

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

New page

= ARCHIVED WIKISPACES DISCUSSION BELOW =
'''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
----

== Problems with math ==
The math expression rendering seems to be unstable. I encounter errors when loading fonts. Mostly, I see [Math Processing Error] instead of formulas, that's why I suggest not to mix math expressions into sentences. It's becoming unreadable, for example:

<em>This makes the Golden fifth exactly [Math Processing Error] octave, or [Math Processing Error] cents, approximately 696.214 cents.</em>

- '''xenwolf''' February 23, 2015, 12:56:58 AM UTC-0800
----