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Meantone: Difference between revisions

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→Tuning spectrum: Also added sharp 1/5 limma and whole ptolemisma
Revert unjustified additions -- never heard of anyone using 2/3- or 3/4-comma; they make no sense whatsoever. Improve the vals since this table assumes septimal meantone. -11-limit tunings, -overprecise entries in the flattone and dominant range (these should go to the respective pages).
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| '''685.714'''
| '''685.714'''
| '''Lower bound of 5-odd-limit diamond monotone'''; 1/7 [[2187/2048|apotome]]
| '''Lower bound of 5-odd-limit diamond monotone'''
|-
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|[[8000/6561]]
|685.825
|[[3/4 comma]]
|-
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|[[243/200]]
|687.617
|[[2/3 comma]]
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| 690.909
| 690.909
|(33c — the patent val is not meantone)<br>Lower bound of reasonable tunings for [[meantone family#flattertone|flattertone]], the flattest 7-limit meantone extension with non-7edo patent vals. At this point, 5/4 tuned is to 363.6 cents.
| 33cddd val
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|-
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| 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
|-
| [[92edo|53\92]]
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| 691.304
|(92bcccd — the patent val is not meantone)
|-
|-
| [[59edo|34\59]]
| [[59edo|34\59]]
|
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| 691.525
| 691.525
|(59bc — the patent val is not meantone)
| 59bcddddd val
|-
|-
| [[26edo|15\26]]
| [[26edo|15\26]]
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| 693.333
| 693.333
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| 45dd val
|-
|-
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| 695.455
| 695.455
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| 88dd val
|-
|-
| 1\2 + 1\(4π)
| 1\2 + 1\(4π)
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| 695.652
| 695.652
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| 69d val
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|-
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| 698.182
| 698.182
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| 55d val
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|-
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| 698.507
| 698.507
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| 67d val
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|-
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| 698.734
| 698.734
|(79c — the patent val is not meantone)
| 79cdd val
|-
|-
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| 698.901
| 698.901
|(91c — the patent val is not meantone)
| 91cddd val
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|-
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| '''700.000'''
| '''700.000'''
| '''Upper bound of 7- and 9-odd-limit diamond monotone''', exactly 1/12 Pythagorean comma, virtually 1/11 syntonic comma (the difference is too small to appear in the digits provided here)
| '''Upper bound of 7- and 9-odd-limit diamond monotone''', 1/12 Pythagorean comma, virtually 1/11 syntonic comma (the difference is too small to appear in the digits provided here)
|-
|
|[[16384/10935]]
|700.001
|Full schisma (ptolemaic diminished sixth/Kirnberger fifth)
|-
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|-
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|[[17edo|10\17]]
| '''[[5edo|3\5]]'''
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|705.882
|(17c — the patent val is not meantone)
|-
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|[[25/24]]
|705.889
|Sharp 1/12 [[Immunity comma]]
|-
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|[[50/33]]
|719.354
|Sharp whole [[100/99|ptolemisma]]
|-
|'''[[5edo|3\5]]'''
|
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|'''720.000'''
| '''720.000'''
|'''Upper bound of 5-odd-limit diamond monotone''' (sharp 1/5 [[Pythagorean limma]])
| '''Upper bound of 5-odd-limit diamond monotone'''
|}
|}


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