Meantone - Revision history

FloraC: /* Intervals */ short category names should suffice

2026-03-22T09:42:26Z

Intervals: short category names should suffice

Overthink: /* Intervals */ + Interval names and caption

2026-03-22T03:46:46Z

Intervals: + Interval names and caption

← Older revision		Revision as of 03:46, 22 March 2026
Line 56:		Line 56:

	<div style="display: inline-grid; margin-right: 25px;">		<div style="display: inline-grid; margin-right: 25px;">
	{\| class="wikitable sortable center-1 right-2"		{\| class="wikitable sortable center-1 right-3"
			\|+ style="font-size: 105%;" \| Intervals fifthward
	\|-		\|-
	! #		! #
			! class="unsortable" \| Name
	! Cents*		! Cents*
	! class="unsortable" \| Approximate ratios		! class="unsortable" \| Approximate ratios
	\|-		\|-
	\| 0		\| 0
			\| Unison
	\| 0.0		\| 0.0
	\| '''1/1'''		\| '''1/1'''
	\|-		\|-
	\| 1		\| 1
			\| Perfect 5th
	\| 696.7		\| 696.7
	\| '''3/2'''		\| '''3/2'''
	\|-		\|-
	\| 2		\| 2
			\| Major 2nd
	\| 193.3		\| 193.3
	\| '''9/8''', 10/9, 28/25		\| '''9/8''', 10/9, 28/25
	\|-		\|-
	\| 3		\| 3
			\| Major 6th
	\| 890.0		\| 890.0
	\| 5/3		\| 5/3
	\|-		\|-
	\| 4		\| 4
			\| Major 3rd
	\| 386.6		\| 386.6
	\| '''5/4'''		\| '''5/4'''
	\|-		\|-
	\| 5		\| 5
			\| Major 7th
	\| 1083.3		\| 1083.3
	\| '''15/8''', 28/15		\| '''15/8''', 28/15
	\|-		\|-
	\| 6		\| 6
			\| Aug. 4th
	\| 579.9		\| 579.9
	\| 7/5, 25/18		\| 7/5, 25/18
	\|-		\|-
	\| 7		\| 7
			\| Aug. 1sn
	\| 76.6		\| 76.6
	\| 21/20, 25/24, 28/27		\| 21/20, 25/24, 28/27
	\|-		\|-
	\| 8		\| 8
			\| Aug. 5th
	\| 773.2		\| 773.2
	\| 14/9, 25/16		\| 14/9, 25/16
	\|-		\|-
	\| 9		\| 9
			\| Aug. 2nd
	\| 269.9		\| 269.9
	\| 7/6		\| 7/6
	\|-		\|-
	\| 10		\| 10
			\| Aug. 6th
	\| 966.6		\| 966.6
	\| '''7/4'''		\| '''7/4'''
	\|-		\|-
	\| 11		\| 11
			\| Aug. 3nd
	\| 463.2		\| 463.2
	\| 21/16		\| 21/16
	\|-		\|-
	\| 12		\| 12
			\| Aug. 7th
	\| 1159.9		\| 1159.9
	\| 35/18, 49/25, 63/32		\| 35/18, 49/25, 63/32
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	</div>		</div>
	<div style="display: inline-grid; margin-right: 25px;">		<div style="display: inline-grid; margin-right: 25px;">
	{\| class="wikitable sortable center-1 right-2"		{\| class="wikitable sortable center-1 right-3"
			\|+ style="font-size: 105%;" \| Intervals fourthward
	\|-		\|-
	! #		! #
			! class="unsortable" \| Name
	! Cents*		! Cents*
	! class="unsortable" \| Approximate ratios		! class="unsortable" \| Approximate ratios
	\|-		\|-
	\| 0		\| 0
			\| Unison
	\| 0.0		\| 0.0
	\| '''1/1'''		\| '''1/1'''
	\|-		\|-
	\| −1		\| −1
			\| Perfect 4th
	\| 503.3		\| 503.3
	\| 4/3		\| 4/3
	\|-		\|-
	\| −2		\| −2
			\| Minor 7th
	\| 1006.7		\| 1006.7
	\| 9/5, 16/9, 25/14		\| 9/5, 16/9, 25/14
	\|-		\|-
	\| −3		\| −3
			\| Minor 3rd
	\| 310.0		\| 310.0
	\| 6/5		\| 6/5
	\|-		\|-
	\| −4		\| −4
			\| Minor 6th
	\| 813.4		\| 813.4
	\| 8/5		\| 8/5
	\|-		\|-
	\| −5		\| −5
			\| Minor 2nd
	\| 116.7		\| 116.7
	\| 15/14, 16/15		\| 15/14, 16/15
	\|-		\|-
	\| −6		\| −6
			\| Dim. 5th
	\| 620.1		\| 620.1
	\| 10/7, 36/25		\| 10/7, 36/25
	\|-		\|-
	\| −7		\| −7
			\| Dim. 8ve
	\| 1123.4		\| 1123.4
	\| 27/14, 40/21, 48/25		\| 27/14, 40/21, 48/25
	\|-		\|-
	\| −8		\| −8
			\| Dim. 4th
	\| 426.8		\| 426.8
	\| 9/7, 32/25		\| 9/7, 32/25
	\|-		\|-
	\| −9		\| −9
			\| Dim. 7th
	\| 930.1		\| 930.1
	\| 12/7		\| 12/7
	\|-		\|-
	\| −10		\| −10
			\| Dim. 3rd
	\| 233.4		\| 233.4
	\| 8/7		\| 8/7
	\|-		\|-
	\| −11		\| −11
			\| Dim. 6th
	\| 736.8		\| 736.8
	\| 32/21		\| 32/21
	\|-		\|-
	\| −12		\| −12
			\| Dim. 2nd
	\| 40.1		\| 40.1
	\| 36/35, 50/49, 64/63		\| 36/35, 50/49, 64/63

Overthink: /* Septimal meantone */ Expand on 11-limit extensions

2026-02-17T04:39:53Z

Septimal meantone: Expand on 11-limit extensions

← Older revision		Revision as of 04:39, 17 February 2026
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	{{Wikipedia\| Septimal meantone temperament }}		{{Wikipedia\| Septimal meantone temperament }}

	'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth (+10 fifths, C–A♯), and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh, as the diesis represents [[36/35]]~[[64/63]]. In septimal meantone, 7/5 is an augmented fourth, 7/6 is an augmented second, and [[9/7]] is a diminished fourth. Notably, septimal meantone equates the interval of a diminished fifth between the third and the seventh of a [[dominant seventh chord]] to [[10/7]], making it a [[9-odd-limit]] [[essentially tempered chord]]. Septimal meantone is best tuned close to [[31edo]].		'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth (+10 fifths, C–A♯), and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh, as the diesis represents [[36/35]]~[[64/63]]. In septimal meantone, 7/5 is an augmented fourth, 7/6 is an augmented second, and [[9/7]] is a diminished fourth. Notably, septimal meantone equates the interval of a diminished fifth between the third and the seventh of a [[dominant seventh chord]] to [[10/7]], making it a [[9-odd-limit]] [[essentially tempered chord]]. Septimal meantone is best tuned close to [[31edo]] or [[Quarter-comma meantone\|1/4-comma]].

	~~See~~ [[huygens vs meanpop]] ~~for a comparison of undecimal~~ (11-~~limit~~) ~~extensions~~.		Extending meantone to the [[11-limit]] is not as simple. For one, there is the factorization of 81/80 as ([[121/120]])*([[243/242]]), and tempering both out leads to [[mohaha]] in the [[2.3.5.11 subgroup]], which splits the perfect fifth into two [[11/9]]~[[27/22]] neutral thirds. Adding back the septimal meantone mapping of 7 (+20 neutral thirds) gives [[migration]], but mohaha has an alternative mapping of [[7/4]] at the semi-diminished seventh (-13 neutral thirds), known as [[mohajira]]. Extensions to prime 11 generated by the perfect fifth are trickier. If 121/120 and 243/242 are not tempered out, then one of them must be mapped positively, and the other negatively. Since 121/120 is the difference between [[11/10]] and [[12/11]], it makes more sense to map it positively, and thus 243/242 negatively, leading 11/9 to be mapped wider than 27/22 and causing inconsistencies. Nonetheless, 31edo supports septimal meantone well while also having a neutral third, and there are two extensions generated by the fifth which map 11/9 to the neutral third. [[Undecimal meantone]] (also known as ''huygens'') maps 11/9 to +16 fifths (C–D𝄪) and 11/8 to +18 fifths (C–E𝄪), tempering out [[99/98]], [[176/175]], and [[441/440]]. Huygens works in the range from 31edo (696.8{{C}}) to 12edo (700{{C}}). The other extension is [[meanpop]], which maps 11/9 to -15 fifths (C–F𝄫) and 11/8 to -13 fifths (C–G𝄫), tempering out [[385/384]] and [[540/539]]. Tunings of meanpop range from 19edo (694.7{{C}}) to 31edo (696.8{{C}}).

	=== Other septimal extensions ===		=== Other septimal extensions ===

FloraC: Cleanup on infobox

2026-02-09T08:50:00Z

Cleanup on infobox

← Older revision		Revision as of 08:50, 9 February 2026
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	\| Subgroups = 2.3.5, 2.3.5.7		\| Subgroups = 2.3.5, 2.3.5.7
	\| Comma basis = [[81/80]] (2.3.5); <br>[[81/80]], [[126/125]] (2.3.5.7)		\| Comma basis = [[81/80]] (2.3.5); <br>[[81/80]], [[126/125]] (2.3.5.7)
	\| ~~Generator~~ = 3/2		\| Edo join 1 = 12 \| Edo join 2 = 19
	\| Mapping = 1; 1 4 10		\| Mapping = 1; 1 4 10
			\| Generators = 3/2
			\| Generators tuning = 696.7
			\| Optimization method = CWE
			\| MOS scales = [[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]]
	\| Pergen = (P8, P5)		\| Pergen = (P8, P5)
	\| Color name = Guti		\| Color name = Guti
	~~\| Edo join 1 = 12 \| Edo join 2 = 19~~
	~~\| Optimization method = CWE~~
	~~\| Generator tuning = 696.7~~
	~~\| MOS scales = [[2L 3s]], [[5L 2s]], [[7L 5s]], [[12L 7s]]~~
	\| Odd limit 1 = 5 \| Mistuning 1 = 5.4 \| Complexity 1 = 5		\| Odd limit 1 = 5 \| Mistuning 1 = 5.4 \| Complexity 1 = 5
	\| Odd limit 2 = 9 \| Mistuning 2 = 10.8 \| Complexity 2 = 12		\| Odd limit 2 = 9 \| Mistuning 2 = 10.8 \| Complexity 2 = 12

Overthink: better linking

2026-01-12T23:53:19Z

better linking

← Older revision		Revision as of 23:53, 12 January 2026
Line 18:		Line 18:
	\| Odd limit 2 = 9 \| Mistuning 2 = 10.8 \| Complexity 2 = 12		\| Odd limit 2 = 9 \| Mistuning 2 = 10.8 \| Complexity 2 = 12
	}}		}}
	'''Meantone''' is a familiar ~~historical~~ [[temperament]] based on a [[chain of fifths]] (or fourths), possessing two [[generator\|generating intervals]]: the [[octave]] and the [[3/2\|fifth]], from which all pitches are composed. This qualifies it as a [[rank-2 temperament]]. The octave is typically pure or close to pure, and the fifth is a few [[cents]] narrower than pure. The rationale for narrowing the fifth is to temper out the [[syntonic comma]], 81/80, which means that stacking four fifths (such as {{dash\|C, G, D, A, E\|hair\|med}}) results in a major third (C–E) that is close to the just interval [[5/4]] rather than the more complex Pythagorean interval [[81/64]]; good tunings of meantone also lead to soft [[diatonic]] and [[Chromatic scale\|chromatic]] scales, which are desirable for interval categorization.		'''Meantone''' is a familiar [[Historical temperaments\|historical temperament]] based on a [[chain of fifths]] (or fourths), possessing two [[generator\|generating intervals]]: the [[octave]] and the [[3/2\|fifth]], from which all pitches are composed. This qualifies it as a [[rank-2 temperament]]. The octave is typically pure or close to pure, and the fifth is a few [[cents]] narrower than pure. The rationale for narrowing the fifth is to temper out the [[syntonic comma]], 81/80, which means that stacking four fifths (such as {{dash\|C, G, D, A, E\|hair\|med}}) results in a major third (C–E) that is close to the just interval [[5/4]] rather than the more complex Pythagorean interval [[81/64]]; good tunings of meantone also lead to soft [[diatonic]] and [[Chromatic scale\|chromatic]] scales, which are desirable for interval categorization.

	[[Meantone intervals\|Intervals in meantone]] have standard names based on the number of steps of the diatonic scale they span (this corresponds to the [[val]] {{val\| 7 11 16 }}), with a modifier {…"double diminished", "diminished", "minor", "major", "augmented", "double augmented"…} that tells you the specific interval in increments of a chromatic semitone. Note that in a general meantone system, all of these intervals are distinct. For example, a diminished fourth is a different interval from a major third.		[[Meantone intervals\|Intervals in meantone]] have standard names based on the number of steps of the diatonic scale they span (this corresponds to the [[val]] {{val\| 7 11 16 }}), with a modifier {…"double diminished", "diminished", "minor", "major", "augmented", "double augmented"…} that tells you the specific interval in increments of a chromatic semitone. Note that in a general meantone system, all of these intervals are distinct. For example, a diminished fourth is a different interval from a major third.

Xenllium at 12:58, 3 January 2026

2026-01-03T12:58:40Z

← Older revision		Revision as of 12:58, 3 January 2026
Line 55:		Line 55:
	In the following tables, odd harmonics 1–15 are labeled in '''bold'''.		In the following tables, odd harmonics 1–15 are labeled in '''bold'''.

	~~<div>~~<div style="display: inline-grid; margin-right: 25px;">		<div style="display: inline-grid; margin-right: 25px;">
	{\| class="wikitable sortable center-1 right-2"		{\| class="wikitable sortable center-1 right-2"
	\|-		\|-
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	\| [[9/5]]		\| [[9/5]]
	\| 691.202		\| 691.202
	\| [[1/2-comma meantone\|1/2 comma]], tunings flatter than this do not fit the original sense of meantone, since their whole tones are no longer between 9/8 and 10/9, a.k.a. lower bound of 9-odd-limit diamond tradeoff		\| [[1/2-comma meantone\|1/2-comma]], tunings flatter than this do not fit the original sense of meantone, since their whole tones are no longer between 9/8 and 10/9, a.k.a. lower bound of 9-odd-limit diamond tradeoff
	\|-		\|-
	\| [[59edo\|34\59]]		\| [[59edo\|34\59]]
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	\| [[27/25]]		\| [[27/25]]
	\| 693.352		\| 693.352
	\| [[2/5-comma meantone\|2/5 comma]]		\| [[2/5-comma meantone\|2/5-comma]]
	\|-		\|-
	\|		\|
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	\| {{nowrap\| ''f''<sup>4</sup> − 2''f'' − 2 {{=}} 0 }}		\| {{nowrap\| ''f''<sup>4</sup> − 2''f'' − 2 {{=}} 0 }}
	\| 695.630		\| 695.630
	\| 1–3–5 equal-beating tuning, Wilson's "metameantone" ([[DR]] 4:5:6), virtually 5/17 comma		\| 1–3–5 equal-beating tuning, Wilson's "metameantone" ([[DR]] 4:5:6), virtually 5/17-comma
	\|-		\|-
	\| [[69edo\|40\69]]		\| [[69edo\|40\69]]
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	\| [[25/24]]		\| [[25/24]]
	\| 695.810		\| 695.810
	\| [[2/7-comma meantone\|2/7 comma]], virtually also [[DR]] 10:12:15		\| [[2/7-comma meantone\|2/7-comma]], virtually also [[DR]] 10:12:15
	\|-		\|-
	\|		\|
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	\|-		\|-
	\|		\|
	\|		\| 3125/2304
	\| 695.981		\| 695.981
	\| [[5/18-comma meantone\|5/18 comma]]		\| [[5/18-comma meantone\|5/18-comma]]
	\|-		\|-
	\|		\|
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	\| [[78125/73728]]		\| [[78125/73728]]
	\| 696.165		\| 696.165
	\| [[7/26-comma meantone\|7/26 comma]], 5-odd-limit least squares		\| [[7/26-comma meantone\|7/26-comma]], 5-odd-limit least squares
	\|-		\|-
	\| {{nowrap\| (8 − φ)\11 }}		\| {{nowrap\| (8 − φ)\11 }}
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	\|-		\|-
	\|		\|
	\| [[1875/1024]]		\| 1875/1024
	\| 696.895		\| 696.895
	\| [[4/17-comma meantone\|4/17 comma]]; 5-limit [[CEE]] tuning		\| [[4/17-comma meantone\|4/17-comma]]; 5-limit [[CEE]] tuning
	\|-		\|-
	\|		\|
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	\| [[75/64]]		\| [[75/64]]
	\| 697.176		\| 697.176
	\| [[2/9-comma meantone\|2/9 comma]]		\| [[2/9-comma meantone\|2/9-comma]]
	\|-		\|-
	\|		\|
	\| {{nowrap\|''f''<sup>4</sup> + 2''f'' − 8 {{=}} 0}}		\| {{nowrap\|''f''<sup>4</sup> + 2''f'' − 8 {{=}} 0}}
	\| 697.278		\| 697.278
	\| 1–3–5 equal-beating tuning ([[DR]] 3:4:5), virtually 5/23 comma		\| 1–3–5 equal-beating tuning ([[DR]] 3:4:5), virtually 5/23-comma
	\|-		\|-
	\| [[74edo\|43\74]]		\| [[74edo\|43\74]]
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	\|-		\|-
	\|		\|
	\|		\| 1125/1024
	\| 697.347		\| 697.347
	\| [[3/14-comma meantone\|3/14 comma]]		\| [[3/14-comma meantone\|3/14-comma]]
	\|-		\|-
	\| {{nowrap\|(√(10) − 2)\2}}		\| {{nowrap\|(√(10) − 2)\2}}
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	\| [[15/8]]		\| [[15/8]]
	\| 697.654		\| 697.654
	\| [[1/5-comma meantone\|1/5 comma]]		\| [[1/5-comma meantone\|1/5-comma]]
	\|-		\|-
	\| [[43edo\|25\43]]		\| [[43edo\|25\43]]
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	\| [[45/32]]		\| [[45/32]]
	\| 698.371		\| 698.371
	\| [[1/6-comma meantone\|1/6 comma]]		\| [[1/6-comma meantone\|1/6-comma]]
	\|-		\|-
	\| [[67edo\|39\67]]		\| [[67edo\|39\67]]
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	\|-		\|-
	\|		\|
	\|		\| {{monzo\|-23 9 4}}
	\| 698.514		\| 698.514
	\| [[4/25-comma meantone\|4/25 comma]]		\| [[4/25-comma meantone\|4/25-comma]]
	\|-		\|-
	\|		\|
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	\| [[135/128]]		\| [[135/128]]
	\| 698.883		\| 698.883
	\| [[1/7-comma meantone\|1/7 comma]]		\| [[1/7-comma meantone\|1/7-comma]]
	\|-		\|-
	\| [[91edo\|53\91]]		\| [[91edo\|53\91]]
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	\|		\|
	\| '''700.000'''		\| '''700.000'''
	\| '''Upper bound of 7- and 9-odd-limit diamond monotone''', 1/12 Pythagorean comma, virtually [[1/11-comma meantone\|1/11 comma]]†		\| '''Upper bound of 7- and 9-odd-limit diamond monotone''', 1/12 Pythagorean comma, virtually [[1/11-comma meantone\|1/11-comma]]†
	\|-		\|-
	\|		\|

Overthink: /* Extensions */ more notes

2026-01-02T05:51:36Z

Extensions: more notes

← Older revision		Revision as of 05:51, 2 January 2026
Line 33:		Line 33:
	{{Wikipedia\| Septimal meantone temperament }}		{{Wikipedia\| Septimal meantone temperament }}

	'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth (+10 fifths), and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh, as the diesis represents [[36/35]]~[[64/63]]. In septimal meantone, 7/5 is an augmented fourth, 7/6 is an augmented second, and [[9/7]] is a diminished fourth. Notably, septimal meantone equates the interval of a diminished fifth between the third and the seventh of a [[dominant seventh chord]] to [[10/7]], making it a [[9-odd-limit]] [[essentially tempered chord]]. Septimal meantone is best tuned close to [[31edo]].		'''Septimal meantone''' or '''7-limit meantone''' is a natural extension of meantone which also addresses septimal intervals including but not limited to [[7/4]], [[7/5]], and [[7/6]]. By extending the [[circle of fifths]], consonant septimal intervals start to appear. For example, 7/4 is represented by an augmented sixth (+10 fifths, C–A♯), and is notably present in the augmented sixth chord; it can also be seen as a diesis-flat minor seventh, as the diesis represents [[36/35]]~[[64/63]]. In septimal meantone, 7/5 is an augmented fourth, 7/6 is an augmented second, and [[9/7]] is a diminished fourth. Notably, septimal meantone equates the interval of a diminished fifth between the third and the seventh of a [[dominant seventh chord]] to [[10/7]], making it a [[9-odd-limit]] [[essentially tempered chord]]. Septimal meantone is best tuned close to [[31edo]].

	See [[huygens vs meanpop]] for a comparison of undecimal (11-limit) extensions.		See [[huygens vs meanpop]] for a comparison of undecimal (11-limit) extensions.
Line 43:		Line 43:
	{{Main\| Flattone }}		{{Main\| Flattone }}

	Flattone is an alternative extension of meantone, which represents 7/4 as a diminished seventh rather than an augmented sixth. The fifth interval is adjusted narrower, nine of which give 8/7 and thirteen of which give 10/7 with octave reduction. Alternatively, stacking three minor thirds results in a diminished seventh that is close to 7/4.		Flattone is an alternative extension of meantone, which represents 7/4 as a diminished seventh rather than an augmented sixth. The fifth interval is adjusted narrower, nine of which give 8/7 and thirteen of which give 10/7 with octave reduction. Alternatively, stacking three minor thirds results in a diminished seventh that is close to 7/4. While less accurate than septimal meantone, flattone extends much more easily to the [[11-limit\|11-]] and [[13-limit\|13-]][[limit]]s, with [[11/8]] being an augmented fourth (+6 fifths, C–F♯) and [[13/8]] being a minor sixth (-4 fifths, C–A♭).

	==== Dominant ====		==== Dominant ====
	{{Main\| Dominant (temperament) }}		{{Main\| Dominant (temperament) }}

	Dominant is an alternative extension of meantone, which represents 7/4 as a minor seventh rather than an augmented sixth. This equates 6/5 with 7/6 and 5/4 with 9/7, tempering out [[36/35]] (septimal quarter tone) and [[64/63]] (Archytas' comma).		Dominant is an alternative extension of meantone, which represents 7/4 as a minor seventh rather than an augmented sixth. This equates 6/5 with 7/6 and 5/4 with 9/7, tempering out [[36/35]] (septimal quarter tone) and [[64/63]] (Archytas' comma). Dominant was named because the [[dominant seventh chord]] of the [[5L 2s\|diatonic]] scale represents [[4:5:6:7]] in it.

	== Intervals ==		== Intervals ==

FloraC: /* Tunings */ 17/16 as A1 has been removed

2026-01-01T16:43:52Z

Tunings: 17/16 as A1 has been removed

← Older revision		Revision as of 16:43, 1 January 2026
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	\| '''700.000'''		\| '''700.000'''
	\| '''Upper bound of 7- and 9-odd-limit diamond monotone''', 1/12 Pythagorean comma, virtually [[1/11-comma meantone\|1/11 comma]]†		\| '''Upper bound of 7- and 9-odd-limit diamond monotone''', 1/12 Pythagorean comma, virtually [[1/11-comma meantone\|1/11 comma]]†
	\|-
	\|
	~~\| [[17/9]]~~
	~~\| 700.209~~
	~~\| As M7~~
	\|-		\|-
	\|		\|

FloraC: /* Tunings */ - excessive highlight

2026-01-01T16:41:29Z

Tunings: - excessive highlight

← Older revision		Revision as of 16:41, 1 January 2026
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	\| [[9/5]]		\| [[9/5]]
	\| 691.202		\| 691.202
	\| ~~'''Lower bound of 9-odd-limit diamond tradeoff'''<br>~~[[1/2-comma meantone\|1/2 comma]], tunings flatter than this do not fit the original sense of meantone, since their whole tones are no longer between 9/8 and 10/9		\| [[1/2-comma meantone\|1/2 comma]], tunings flatter than this do not fit the original sense of meantone, since their whole tones are no longer between 9/8 and 10/9, a.k.a. lower bound of 9-odd-limit diamond tradeoff
	\|-		\|-
	\| [[59edo\|34\59]]		\| [[59edo\|34\59]]

Overthink: /* Other septimal extensions */ sharptone is clearly exo; avoid mentioning

2025-12-27T12:44:28Z

Other septimal extensions: sharptone is clearly exo; avoid mentioning

← Older revision		Revision as of 12:44, 27 December 2025
Line 38:		Line 38:

	=== Other septimal extensions ===		=== Other septimal extensions ===
	There are some alternative mappings of the 7-limit meantone, including flattone, dominant ~~and sharptone~~.		There are some alternative mappings of the 7-limit meantone, including flattone and dominant.

	==== Flattone ====		==== Flattone ====