Diaschismic family: Difference between revisions
→Seven limit extensions: improve readability |
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* strict range: [701.955, 706.843] | * strict range: [701.955, 706.843] | ||
{{Val list|legend=1| 34, 46, 80, 206c, 286bc }} | {{Val list|legend=1| 12, 34, 46, 80, 206c, 286bc }} | ||
[[Badness]]: 0.020033 | |||
== Seven limit extensions == | == Seven limit extensions == | ||
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= Srutal = | = Srutal = | ||
[[Comma list]]: 2048/2025, 4375/4374 | |||
strict range: [703.448, 705.882] | [[Tuning ranges]]: | ||
* valid range: [703.448, 705.882] (58 to 34d) | |||
* nice range: [701.955, 706.843] | |||
* strict range: [703.448, 705.882] | |||
POTE generator: ~3/2 = 704.814 | POTE generator: ~3/2 = 704.814 | ||
[[Mapping]]: [<2 0 11 -42|, <0 1 -2 15|] | |||
Wedgie: <<2 -4 30 -11 42 81|| | Wedgie: <<2 -4 30 -11 42 81|| | ||
{{Val list|legend=1| 46, 80, 126, 206cd, 332bcd }} | |||
Badness: 0.0915 | [[Badness]]: 0.0915 | ||
== 11-limit == | == 11-limit == | ||
Comma list: 176/175, 896/891, 1331/1323 | |||
valid range: [704.348, 705.882] (46 to 34d) | Tuning ranges: | ||
* valid range: [704.348, 705.882] (46 to 34d) | |||
nice range: [701.955, 706.843] | * nice range: [701.955, 706.843] | ||
* strict range: [704.348, 705.882] | |||
strict range: [704.348, 705.882] | |||
POTE generator: ~3/2 = 704.856 | POTE generator: ~3/2 = 704.856 | ||
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Map: [<2 0 11 -42 -28|, <0 1 -2 15 11|] | Map: [<2 0 11 -42 -28|, <0 1 -2 15 11|] | ||
Vals: {{Val list| 46, 80, 126, 206cd }} | |||
Badness: 0.0353 | Badness: 0.0353 | ||
== 13-limit == | == 13-limit == | ||
Comma list: 169/168, 176/175, 325/324, 364/363 | |||
valid range: [704.348, 705.882] (46 to 34d) | Tuning ranges: | ||
* valid range: [704.348, 705.882] (46 to 34d) | |||
nice range: [701.955, 706.843] | * nice range: [701.955, 706.843] | ||
* strict range: [704.348, 705.882] | |||
strict range: [704.348, 705.882] | |||
POTE generator: ~3/2 = 704.881 | POTE generator: ~3/2 = 704.881 | ||
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Map: [<2 0 11 -42 -28 -18|, <0 1 -2 15 11 8|] | Map: [<2 0 11 -42 -28 -18|, <0 1 -2 15 11 8|] | ||
Vals: {{Val list| 34d, 46, 80, 206cd, 286bcde }} | |||
Badness: 0.0253 | Badness: 0.0253 | ||
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Pajara extends nicely to an 11-limit version, for which the 56 tuning can be used, but a good alternative is to make the major thirds pure by setting the fifth to be 706.843 cents. Now 99/98, 100/99, 176/175 and 896/891 are being tempered out. | Pajara extends nicely to an 11-limit version, for which the 56 tuning can be used, but a good alternative is to make the major thirds pure by setting the fifth to be 706.843 cents. Now 99/98, 100/99, 176/175 and 896/891 are being tempered out. | ||
[[Comma list]]: 50/49, 64/63 | |||
valid range: [700.000, 720.000] (12 to 10) | [[Tuning ranges]]: | ||
* valid range: [700.000, 720.000] (12 to 10) | |||
nice range: [701.955, 715.587] | * nice range: [701.955, 715.587] | ||
* strict range: [701.955, 715.587] | |||
strict range: [701.955, 715.587] | |||
[[POTE_tuning|POTE generator]]: 707.048 | [[POTE_tuning|POTE generator]]: 707.048 | ||
[[Mapping]]: [<2 0 11 12|, <0 1 -2 -2|] | |||
{{Val list|legend=1| 10, 12, 22, 34d, 56d }} | |||
Badness: 0.0200 | [[Badness]]: 0.0200 | ||
== 11-limit == | == 11-limit == | ||
Comma list: 50/49, 64/63, 99/98 | |||
strict range: [701.955, 709.091] | Tuning ranges: | ||
* valid range: [700.000, 709.091] (12 to 22) | |||
* nice range: [701.955, 715.587] | |||
* strict range: [701.955, 709.091] | |||
[[POTE_tuning|POTE generator]]: 706.885 | [[POTE_tuning|POTE generator]]: 706.885 | ||
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=== 13-limit === | === 13-limit === | ||
Comma list: 50/49, 64/63, 65/63, 99/98 | |||
strict range: [] | Tuning ranges: | ||
* valid range: [700.000, 709.091] | |||
* nice range: [701.955, 738.573] | |||
* strict range: [701.955, 709.091] | |||
POTE generator: ~3/2 = 708.919 | POTE generator: ~3/2 = 708.919 | ||