Straddle cluster temperaments: Difference between revisions
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'''Straddle cluster temperaments''' are a subset of cluster temperaments, which have generators very close to an equal temperament. They [[Straddle primes|straddle]] ratios approximated by those equal temperaments. If a small equal temperament contains a vague approximation of a subgroup, its cluster temperaments will be useful for straddling that subgroup. | '''Straddle cluster temperaments''' are a subset of cluster temperaments, which have generators very close to an equal temperament. They [[Straddle primes|straddle]] ratios approximated by those equal temperaments. If a small equal temperament contains a vague approximation of a subgroup, its cluster temperaments will be useful for straddling that subgroup. | ||
== 5edo == | |||
5edo is an excellent approximation of 2.3.7 for its size, making it a good example for straddle cluster temperaments. It has four in this subgroup: | |||
* "Subcloud" (flat of 1\5) | |||
* "Supercloud" (sharp of 1\5) | |||
* Straddle Buzzard (flat of 2\5) | |||
* Straddle Hemiseven (sharp of 2\5) | |||
== Quartertone == | |||
Half-octave temperaments generated by ~11/8 are especially good at straddling the 11-limit. The foremost examples are '''Subgauss''' (found in 74edo) and '''Supergauss''' (found in 86edo, generated by the flat 11). They are named for 9801/9800, which equates two Gauss's tritones to an octave. | |||
== Paddle == | == Paddle == | ||
Revision as of 23:55, 27 July 2026
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Straddle cluster temperaments are a subset of cluster temperaments, which have generators very close to an equal temperament. They straddle ratios approximated by those equal temperaments. If a small equal temperament contains a vague approximation of a subgroup, its cluster temperaments will be useful for straddling that subgroup.
5edo
5edo is an excellent approximation of 2.3.7 for its size, making it a good example for straddle cluster temperaments. It has four in this subgroup:
- "Subcloud" (flat of 1\5)
- "Supercloud" (sharp of 1\5)
- Straddle Buzzard (flat of 2\5)
- Straddle Hemiseven (sharp of 2\5)
Quartertone
Half-octave temperaments generated by ~11/8 are especially good at straddling the 11-limit. The foremost examples are Subgauss (found in 74edo) and Supergauss (found in 86edo, generated by the flat 11). They are named for 9801/9800, which equates two Gauss's tritones to an octave.
Paddle
Paddle, short for "Passion straddle", is a 2.-3.+3.5.7 straddle version of Passion. It is especially useful for generating the aberration scale trackdye (5L2m8s), along with a straddle variant of Undecimation. It may be extended with Pentagoth.
| ¦| | ¦ | ¦| | | | ¦| | ¦ | ¦| | ¦¦ | ¦¦| | ¦¦¦ | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2\25 | 7\87 | 5\62 | 8\99 | 3\37 | 7\86 | 4\49 | 5\61 | 6\73 | 7\85 | 8\97 | 1\12 | |
| -12 | 48.0 | 41.4 | 38.7 | 36.4 | 32.4 | 27.9 | 24.5 | 19.7 | 16.4 | 14.1 | 12.4 | 0.0 |
| -11 | 144.0 | 137.9 | 135.5 | 133.3 | 129.7 | 125.6 | 122.4 | 118.0 | 115.1 | 112.9 | 111.3 | 100.0 |
| -10 | 240.0 | 234.5 | 232.3 | 230.3 | 227.0 | 223.3 | 220.4 | 216.4 | 213.7 | 211.8 | 210.3 | 200.0 |
| -9 | 336.0 | 331.0 | 329.0 | 327.3 | 324.3 | 320.9 | 318.4 | 314.8 | 312.3 | 310.6 | 309.3 | 300.0 |
| -8 | 432.0 | 427.6 | 425.8 | 424.2 | 421.6 | 418.6 | 416.3 | 413.1 | 411.0 | 409.4 | 408.2 | 400.0 |
| -7 | 528.0 | 524.1 | 522.6 | 521.2 | 518.9 | 516.3 | 514.3 | 511.5 | 509.6 | 508.2 | 507.2 | 500.0 |
| -6 | 624.0 | 620.7 | 619.4 | 618.2 | 616.2 | 614.0 | 612.2 | 609.8 | 608.2 | 607.1 | 606.2 | 600.0 |
| -5 | 720.0 | 717.2 | 716.1 | 715.2 | 713.5 | 711.6 | 710.2 | 708.2 | 706.8 | 705.9 | 705.2 | 700.0 |
| -4 | 816.0 | 813.8 | 812.9 | 812.1 | 810.8 | 809.3 | 808.2 | 806.6 | 805.5 | 804.7 | 804.1 | 800.0 |
| -3 | 912.0 | 910.3 | 909.7 | 909.1 | 908.1 | 907.0 | 906.1 | 904.9 | 904.1 | 903.5 | 903.1 | 900.0 |
| -2 | 1008.0 | 1006.9 | 1006.5 | 1006.1 | 1005.4 | 1004.7 | 1004.1 | 1003.3 | 1002.7 | 1002.4 | 1002.1 | 1000.0 |
| -1 | 1104.0 | 1103.4 | 1103.2 | 1103.0 | 1102.7 | 1102.3 | 1102.0 | 1101.6 | 1101.4 | 1101.2 | 1101.0 | 1100.0 |
| 0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| 1 | 96.0 | 96.6 | 96.8 | 97.0 | 97.3 | 97.7 | 98.0 | 98.4 | 98.6 | 98.8 | 99.0 | 100.0 |
| 2 | 192.0 | 193.1 | 193.5 | 193.9 | 194.6 | 195.3 | 195.9 | 196.7 | 197.3 | 197.6 | 197.9 | 200.0 |
| 3 | 288.0 | 289.7 | 290.3 | 290.9 | 291.9 | 293.0 | 293.9 | 295.1 | 295.9 | 296.5 | 296.9 | 300.0 |
| 4 | 384.0 | 386.2 | 387.1 | 387.9 | 389.2 | 390.7 | 391.8 | 393.4 | 394.5 | 395.3 | 395.9 | 400.0 |
| 5 | 480.0 | 482.8 | 483.9 | 484.8 | 486.5 | 488.4 | 489.8 | 491.8 | 493.2 | 494.1 | 494.8 | 500.0 |
| 6 | 576.0 | 579.3 | 580.6 | 581.8 | 583.8 | 586.0 | 587.8 | 590.2 | 591.8 | 592.9 | 593.8 | 600.0 |
| 7 | 672.0 | 675.9 | 677.4 | 678.8 | 681.1 | 683.7 | 685.7 | 688.5 | 690.4 | 691.8 | 692.8 | 700.0 |
| 8 | 768.0 | 772.4 | 774.2 | 775.8 | 778.4 | 781.4 | 783.7 | 786.9 | 789.0 | 790.6 | 791.8 | 800.0 |
| 9 | 864.0 | 869.0 | 871.0 | 872.7 | 875.7 | 879.1 | 881.6 | 885.2 | 887.7 | 889.4 | 890.7 | 900.0 |
| 10 | 960.0 | 965.5 | 967.7 | 969.7 | 973.0 | 976.7 | 979.6 | 983.6 | 986.3 | 988.2 | 989.7 | 1000.0 |
| 11 | 1056.0 | 1062.1 | 1064.5 | 1066.7 | 1070.3 | 1074.4 | 1077.6 | 1082.0 | 1084.9 | 1087.1 | 1088.7 | 1100.0 |
| 12 | 1152.0 | 1158.6 | 1161.3 | 1163.6 | 1167.6 | 1172.1 | 1175.5 | 1180.3 | 1183.6 | 1185.9 | 1187.6 | 0.0 |
