Meantone family: Difference between revisions
→Septimal meantone: Meantone can not be considered the "main article" for 'Septimal meantone' temperament, improve interwiki link |
Cmloegcmluin (talk | contribs) update tuning range links |
||
| Line 24: | Line 24: | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* | * [[diamond monotone]] range: [685.714, 720.000] (4\7 to 3\5) | ||
* | * [[diamond pure]] range: [694.786, 701.955] (1/3 comma to Pythagorean) | ||
* strict range: [694.786, 701.955] | * [[diamond strict]] range: [694.786, 701.955] | ||
{{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }} | {{Val list|legend=1| 5, 7, 12, 19, 31, 50, 81, 131b, 212bb, 293bb }} | ||
| Line 70: | Line 70: | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* | * [[diamond monotone]] range: [694.737, 700.000] (11\19 to 7\12) | ||
* | * [[diamond pure]] range: [694.786, 701.955] (1/3 comma to Pythagorean) | ||
* strict range: [694.786, 700.000] | * [[diamond strict]] range: [694.786, 700.000] | ||
[[Algebraic generator]]: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, 503.4257 cents. The recurrence converges quickly. | [[Algebraic generator]]: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, 503.4257 cents. The recurrence converges quickly. | ||
| Line 99: | Line 99: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: [696.774, 700.000] (18\31 to 7\12) | ||
* | * [[diamond pure]] range: [691.202, 701.955] | ||
* strict range: [696.774, 700.000] | * [[diamond strict]] range: [696.774, 700.000] | ||
Algebraic generator: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents. | Algebraic generator: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents. | ||
| Line 137: | Line 137: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: [696.774, 700.000] (18\31 to 7\12) | ||
* | * [[diamond pure]] range: [691.202, 701.955] | ||
* strict range: [696.774, 700.000] | * [[diamond strict]] range: [696.774, 700.000] | ||
{{Val list|legend=1| 12, 19ef, 31, 43, 74 }} | {{Val list|legend=1| 12, 19ef, 31, 43, 74 }} | ||
| Line 192: | Line 192: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: [694.737, 696.774] (11\19 to 18\31) | ||
* | * [[diamond pure]] range: [691.202, 701.955] | ||
* strict range: [694.737, 696.774] | * [[diamond strict]] range: [694.737, 696.774] | ||
Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge. | Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge. | ||
| Line 219: | Line 219: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: [694.737, 696.774] (11\19 to 18\31) | ||
* | * [[diamond pure]] range: [691.202, 701.955] | ||
* strict range: [694.737, 696.774] | * [[diamond strict]] range: [694.737, 696.774] | ||
{{Val list|legend=1| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }} | {{Val list|legend=1| 12ef, 19, 31, 50, 81, 131bd, 212bbddf }} | ||
| Line 506: | Line 506: | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* | * [[diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19) | ||
* | * [[diamond pure]] range: [692.353, 701.955] | ||
* strict range: [692.353, 694.737] | * [[diamond strict]] range: [692.353, 694.737] | ||
Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4. | Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4. | ||
| Line 529: | Line 529: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19) | ||
* | * [[diamond pure]] range: [682.502, 701.955] | ||
* strict range: [692.308, 694.737] | * [[diamond strict]] range: [692.308, 694.737] | ||
{{Val list|legend=1| 7, 19, 26, 45, 71bc, 116bcde }} | {{Val list|legend=1| 7, 19, 26, 45, 71bc, 116bcde }} | ||
| Line 550: | Line 550: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: [692.308, 694.737] (15\26 to 11\19) | ||
* | * [[diamond pure]] range: [682.502, 701.955] | ||
* strict range: [692.308, 694.737] | * [[diamond strict]] range: [692.308, 694.737] | ||
{{Val list|legend=1| 7, 19, 26, 45f, 71bcf, 116bcdef }} | {{Val list|legend=1| 7, 19, 26, 45f, 71bcf, 116bcdef }} | ||
| Line 575: | Line 575: | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* | * [[diamond monotone]] range: [700.000, 720.000] (7\12 to 3\5) | ||
* | * [[diamond pure]] range: [694.786, 715.587] | ||
* strict range: [700.000, 715.587] | * [[diamond strict]] range: [700.000, 715.587] | ||
{{Val list|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }} | {{Val list|legend=1| 5, 7, 12, 41cd, 53cdd, 65ccddd }} | ||
| Line 592: | Line 592: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: [700.000, 705.882] (7\12 to 10\17) | ||
* | * [[diamond pure]] range: [691.202, 715.587] | ||
* strict range: [700.000, 705.882] | * [[diamond strict]] range: [700.000, 705.882] | ||
POTE generator: ~3/2 = 703.254 | POTE generator: ~3/2 = 703.254 | ||
| Line 613: | Line 613: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: 705.882 (10\17) | ||
* | * [[diamond pure]] range: [691.202, 715.587] | ||
* strict range: 705.882 | * [[diamond strict]] range: 705.882 | ||
{{Val list|legend=1| 12f, 17c, 29cdef }} | {{Val list|legend=1| 12f, 17c, 29cdef }} | ||
| Line 909: | Line 909: | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* | * [[diamond monotone]] range: [240.000, 257.143] (1\5 to 3\14) | ||
* | * [[diamond pure]] range: [231.174, 266.871] | ||
* strict range: [240.000, 257.143] | * [[diamond strict]] range: [240.000, 257.143] | ||
{{Val list|legend=1| 5, 14c, 19 }} | {{Val list|legend=1| 5, 14c, 19 }} | ||
| Line 930: | Line 930: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: [252.632, 257.143] (4\19 to 3\14) | ||
* | * [[diamond pure]] range: [231.174, 266.871] | ||
* strict range: [252.632, 257.143] | * [[diamond strict]] range: [252.632, 257.143] | ||
{{Val list|legend=1| 14c, 19, 33cd, 52cd }} | {{Val list|legend=1| 14c, 19, 33cd, 52cd }} | ||
| Line 951: | Line 951: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: 694.737 (4\19) | ||
* | * [[diamond pure]] range: [621.581, 737.652] | ||
* strict range: 694.737 | * [[diamond strict]] range: 694.737 | ||
{{Val list|legend=1| 14cf, 19, 33cdff, 52cdf }} | {{Val list|legend=1| 14cf, 19, 33cdff, 52cdf }} | ||
| Line 1,040: | Line 1,040: | ||
[[Tuning ranges]]: | [[Tuning ranges]]: | ||
* | * [[diamond monotone]] range: [685.714, 700.000] (8\14 to 7\12) | ||
* | * [[diamond pure]] range: [688.957, 701.955] | ||
* strict range: [688.957, 700.000] | * [[diamond strict]] range: [688.957, 700.000] | ||
{{Multival|legend=1| 2 8 8 8 7 -4 }} | {{Multival|legend=1| 2 8 8 8 7 -4 }} | ||
| Line 1,066: | Line 1,066: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: [685.714, 700.000] (8\14 to 7\12) | ||
* | * [[diamond pure]] range: [682.458, 701.955] | ||
* strict range: [685.714, 700.000] | * [[diamond strict]] range: [685.714, 700.000] | ||
{{Val list|legend=1| 12, 14c, 26, 90bce, 116bcce }} | {{Val list|legend=1| 12, 14c, 26, 90bce, 116bcce }} | ||
| Line 1,087: | Line 1,087: | ||
Tuning ranges: | Tuning ranges: | ||
* | * [[diamond monotone]] range: 692.308 (15\26) | ||
* | * [[diamond pure]] range: [682.458, 701.955] | ||
* strict range: 692.308 (15\26) | * [[diamond strict]] range: 692.308 (15\26) | ||
{{Val list|legend=1| 12f, 14cf, 26, 38e }} | {{Val list|legend=1| 12f, 14cf, 26, 38e }} | ||