Scala analysis: xen18-schulter-707-24
Temperament with fifth of 707.22045
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63.898 cents 63.897750 2: 86.645 cents 86.645400 3: 150.543 cents 150.543150 4: 214.441 cents 214.440900 5: 278.339 cents 278.338650 6: 301.086 cents 301.086300 7: 342.236 cents 342.236400 8: 364.984 cents 364.984050 9: 428.882 cents 428.881800 10: 492.780 cents 492.779550 11: 556.677 cents 556.677300 12: 579.425 cents 579.424950 13: 643.323 cents 643.322700 14: 707.220 cents 707.220450 15: 771.118 cents 771.118200 16: 793.866 cents 793.865850 17: 835.016 cents 835.015950 18: 857.764 cents 857.763600 19: 921.661 cents 921.661350 20: 985.559 cents 985.559100 21: 1049.457 cents 1049.456850 22: 1072.205 cents 1072.204500 23: 1136.102 cents 1136.102250 24: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 63.8978 cents 63.8978 1: 63.8977 cents 63.8977 2: 22.7477 cents 22.7477 3: 63.8977 cents 63.8977 4: 63.8978 cents 63.8978 5: 63.8977 cents 63.8977 6: 22.7477 cents 22.7477 7: 41.1501 cents 41.1501 8: 22.7476 cents 22.7476 9: 63.8977 cents 63.8977 10: 63.8978 cents 63.8978 11: 63.8977 cents 63.8977 12: 22.7476 cents 22.7476 13: 63.8978 cents 63.8978 14: 63.8977 cents 63.8977 15: 63.8977 cents 63.8977 16: 22.7476 cents 22.7476 17: 41.1501 cents 41.1501 18: 22.7476 cents 22.7476 19: 63.8978 cents 63.8978 20: 63.8977 cents 63.8977 21: 63.8977 cents 63.8977 22: 22.7477 cents 22.7477 23: 63.8977 cents 63.8977 24: 63.8978 cents 63.8978
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 22.74765 cents 1: 2 41.15010 cents 1: 15 63.89775 cents 2: 4 63.89775 cents 2: 10 86.64540 cents 2: 10 127.79550 cents 3: 2 86.64540 cents 3: 4 127.79550 cents 3: 13 150.54315 cents 3: 5 191.69325 cents 4: 4 150.54315 cents 4: 4 191.69325 cents 4: 16 214.44090 cents 5: 6 214.44090 cents 5: 5 237.18855 cents 5: 4 255.59100 cents 5: 9 278.33865 cents 6: 12 278.33865 cents 6: 6 301.08630 cents 6: 6 342.23640 cents 7: 4 301.08630 cents 7: 10 342.23640 cents 7: 7 364.98405 cents 7: 3 406.13415 cents 8: 8 364.98405 cents 8: 8 406.13415 cents 8: 8 428.88180 cents 9: 12 428.88180 cents 9: 3 451.62945 cents 9: 6 470.03190 cents 9: 3 492.77955 cents 10: 20 492.77955 cents 10: 2 515.52720 cents 10: 2 556.67730 cents 11: 6 515.52720 cents 11: 1 533.92965 cents 11: 14 556.67730 cents 11: 2 579.42495 cents 11: 1 620.57505 cents 12: 2 556.67730 cents 12: 10 579.42495 cents 12: 10 620.57505 cents 12: 2 643.32270 cents 13: 1 579.42495 cents 13: 2 620.57505 cents 13: 14 643.32270 cents 13: 1 666.07035 cents 13: 6 684.47280 cents 14: 2 643.32270 cents 14: 2 684.47280 cents 14: 20 707.22045 cents 15: 3 707.22045 cents 15: 6 729.96810 cents 15: 3 748.37055 cents 15: 12 771.11820 cents 16: 8 771.11820 cents 16: 8 793.86585 cents 16: 8 835.01595 cents 17: 3 793.86585 cents 17: 7 835.01595 cents 17: 10 857.76360 cents 17: 4 898.91370 cents 18: 6 857.76360 cents 18: 6 898.91370 cents 18: 12 921.66135 cents 19: 9 921.66135 cents 19: 4 944.40900 cents 19: 5 962.81145 cents 19: 6 985.55910 cents 20: 16 985.55910 cents 20: 4 1008.30675 cents 20: 4 1049.45685 cents 21: 5 1008.30675 cents 21: 13 1049.45685 cents 21: 4 1072.20450 cents 21: 2 1113.35460 cents 22: 10 1072.20450 cents 22: 10 1113.35460 cents 22: 4 1136.10225 cents 23: 15 1136.10225 cents 23: 2 1158.84990 cents 23: 7 1177.25235 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.56522 = 82/23
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0.0 : 63.9 86.6 150.5 214.4 278.3 301.1 342.2 365.0 428.9 492.8 556.7 579.4 643.3 707.2 771.1 793.9 835.0 857.8 921.7 985.6 1049.5 1072.2 1136.1 1200.0 63.9 : 22.7 86.6 150.5 214.4 237.2 278.3 301.1 365.0 428.9 492.8 515.5 579.4 643.3 707.2 730.0 771.1 793.9 857.8 921.7 985.6 1008.3 1072.2 1136.1 1200.0 86.6 : 63.9 127.8 191.7 214.4 255.6 278.3 342.2 406.1 470.0 492.8 556.7 620.6 684.5 707.2 748.4 771.1 835.0 898.9 962.8 985.6 1049.5 1113.4 1177.3 1200.0 150.5 : 63.9 127.8 150.5 191.7 214.4 278.3 342.2 406.1 428.9 492.8 556.7 620.6 643.3 684.5 707.2 771.1 835.0 898.9 921.7 985.6 1049.5 1113.4 1136.1 1200.0 214.4 : 63.9 86.6 127.8 150.5 214.4 278.3 342.2 365.0 428.9 492.8 556.7 579.4 620.6 643.3 707.2 771.1 835.0 857.8 921.7 985.6 1049.5 1072.2 1136.1 1200.0 278.3 : 22.7 63.9 86.6 150.5 214.4 278.3 301.1 365.0 428.9 492.8 515.5 556.7 579.4 643.3 707.2 771.1 793.9 857.8 921.7 985.6 1008.3 1072.2 1136.1 1200.0 301.1 : 41.2 63.9 127.8 191.7 255.6 278.3 342.2 406.1 470.0 492.8 533.9 556.7 620.6 684.5 748.4 771.1 835.0 898.9 962.8 985.6 1049.5 1113.4 1177.3 1200.0 342.2 : 22.7 86.6 150.5 214.4 237.2 301.1 365.0 428.9 451.6 492.8 515.5 579.4 643.3 707.2 730.0 793.9 857.8 921.7 944.4 1008.3 1072.2 1136.1 1158.8 1200.0 365.0 : 63.9 127.8 191.7 214.4 278.3 342.2 406.1 428.9 470.0 492.8 556.7 620.6 684.5 707.2 771.1 835.0 898.9 921.7 985.6 1049.5 1113.4 1136.1 1177.3 1200.0 428.9 : 63.9 127.8 150.5 214.4 278.3 342.2 365.0 406.1 428.9 492.8 556.7 620.6 643.3 707.2 771.1 835.0 857.8 921.7 985.6 1049.5 1072.2 1113.4 1136.1 1200.0 492.8 : 63.9 86.6 150.5 214.4 278.3 301.1 342.2 365.0 428.9 492.8 556.7 579.4 643.3 707.2 771.1 793.9 857.8 921.7 985.6 1008.3 1049.5 1072.2 1136.1 1200.0 556.7 : 22.7 86.6 150.5 214.4 237.2 278.3 301.1 365.0 428.9 492.8 515.5 579.4 643.3 707.2 730.0 793.9 857.8 921.7 944.4 985.6 1008.3 1072.2 1136.1 1200.0 579.4 : 63.9 127.8 191.7 214.4 255.6 278.3 342.2 406.1 470.0 492.8 556.7 620.6 684.5 707.2 771.1 835.0 898.9 921.7 962.8 985.6 1049.5 1113.4 1177.3 1200.0 643.3 : 63.9 127.8 150.5 191.7 214.4 278.3 342.2 406.1 428.9 492.8 556.7 620.6 643.3 707.2 771.1 835.0 857.8 898.9 921.7 985.6 1049.5 1113.4 1136.1 1200.0 707.2 : 63.9 86.6 127.8 150.5 214.4 278.3 342.2 365.0 428.9 492.8 556.7 579.4 643.3 707.2 771.1 793.9 835.0 857.8 921.7 985.6 1049.5 1072.2 1136.1 1200.0 771.1 : 22.7 63.9 86.6 150.5 214.4 278.3 301.1 365.0 428.9 492.8 515.5 579.4 643.3 707.2 730.0 771.1 793.9 857.8 921.7 985.6 1008.3 1072.2 1136.1 1200.0 793.9 : 41.2 63.9 127.8 191.7 255.6 278.3 342.2 406.1 470.0 492.8 556.7 620.6 684.5 707.2 748.4 771.1 835.0 898.9 962.8 985.6 1049.5 1113.4 1177.3 1200.0 835.0 : 22.7 86.6 150.5 214.4 237.2 301.1 365.0 428.9 451.6 515.5 579.4 643.3 666.1 707.2 730.0 793.9 857.8 921.7 944.4 1008.3 1072.2 1136.1 1158.8 1200.0 857.8 : 63.9 127.8 191.7 214.4 278.3 342.2 406.1 428.9 492.8 556.7 620.6 643.3 684.5 707.2 771.1 835.0 898.9 921.7 985.6 1049.5 1113.4 1136.1 1177.3 1200.0 921.7 : 63.9 127.8 150.5 214.4 278.3 342.2 365.0 428.9 492.8 556.7 579.4 620.6 643.3 707.2 771.1 835.0 857.8 921.7 985.6 1049.5 1072.2 1113.4 1136.1 1200.0 985.6 : 63.9 86.6 150.5 214.4 278.3 301.1 365.0 428.9 492.8 515.5 556.7 579.4 643.3 707.2 771.1 793.9 857.8 921.7 985.6 1008.3 1049.5 1072.2 1136.1 1200.0 1049.5: 22.7 86.6 150.5 214.4 237.2 301.1 365.0 428.9 451.6 492.8 515.5 579.4 643.3 707.2 730.0 793.9 857.8 921.7 944.4 985.6 1008.3 1072.2 1136.1 1200.0 1072.2: 63.9 127.8 191.7 214.4 278.3 342.2 406.1 428.9 470.0 492.8 556.7 620.6 684.5 707.2 771.1 835.0 898.9 921.7 962.8 985.6 1049.5 1113.4 1177.3 1200.0 1136.1: 63.9 127.8 150.5 214.4 278.3 342.2 365.0 406.1 428.9 492.8 556.7 620.6 643.3 707.2 771.1 835.0 857.8 898.9 921.7 985.6 1049.5 1113.4 1136.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.7477 .. 63.8977 cents 41.15010 cents 22.74765 cents 2: 63.8978 .. 127.7955 cents 63.89775 cents 1/1, 0.0000 cents 3: 86.6454 .. 191.6932 cents 105.04785 cents -41.15010 cents 4: 150.5431 .. 214.4409 cents 63.89775 cents -41.15010 cents 5: 214.4409 .. 278.3386 cents 63.89775 cents 1/1, 0.0000 cents 6: 278.3387 .. 342.2364 cents 63.89775 cents 1/1, 0.0000 cents 7: 301.0863 .. 406.1341 cents 105.04785 cents -41.15010 cents 8: 364.9841 .. 428.8818 cents 63.89775 cents -41.15010 cents 9: 428.8818 .. 492.7796 cents 63.89775 cents 1/1, 0.0000 cents 10: 492.7796 .. 556.6773 cents 63.89775 cents 1/1, 0.0000 cents 11: 515.5272 .. 620.5751 cents 105.04785 cents -41.15010 cents 12: 556.6773 .. 643.3227 cents 86.64540 cents -63.89775 cents 13: 579.4249 .. 684.4728 cents 105.04785 cents -63.89775 cents 14: 643.3227 .. 707.2205 cents 63.89775 cents -41.15010 cents 15: 707.2204 .. 771.1182 cents 63.89775 cents 1/1, 0.0000 cents 16: 771.1182 .. 835.0159 cents 63.89775 cents 1/1, 0.0000 cents 17: 793.8658 .. 898.9137 cents 105.04785 cents -41.15010 cents 18: 857.7636 .. 921.6613 cents 63.89775 cents -41.15010 cents 19: 921.6613 .. 985.5591 cents 63.89775 cents 1/1, 0.0000 cents 20: 985.5591 .. 1049.4569 cents 63.89775 cents 1/1, 0.0000 cents 21: 1008.3068 .. 1113.3546 cents 105.04785 cents -41.15010 cents 22: 1072.2045 .. 1136.1022 cents 63.89775 cents -41.15010 cents 23: 1136.1022 .. 1177.2523 cents 41.15010 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 22.74765 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 63.89775 cents Average / Smallest step : 2.198029 Largest / Average step : 1.277955 Largest / Smallest step : 2.808982 Median interval of one step : 63.89775 cents, amount: 15 Most common interval of one step : 63.89775 cents, amount: 15 Least squares average step : 49.36178 cents, oct.: 1184.68270 cents Scale is not proper Scale is a mode of a 1108-tone equal temperament with octave 1200.000 cents degrees: 59 80 139 198 257 278 316 337 396 455 514 535 594 653 712 733 771 792 851 910 969 990 1049 1108 Least number of segments generator : 555 of 601.083 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 653 of 707.220 cents and inv. generated superset size: 24 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABCBAAABAAABCBAAABAA Step pattern size order : LSLLLSMSLLLSLLLSMSLLLSLL Scale is not a Constant Structure Scale diversity : 1.183638 Lumma stability : 0.037913 Lumma impropriety factor : 0.415122 Rothenberg efficiency : 0.694444 redundancy: 0.305556 Efficiency x scale size : 16.666667 Number of different interval sizes : 46 = 2.00000 / class Number of one step interval sizes : 3 Highest interval variety : 5 Mean interval variety : 3.56522 = 82/23 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 18.40245 cents Most common intervals : 492.77955 cents & inv., amount: 23 Scale has Generated (pseudo-Myhill) property, generator: 707.220 cents and inv. Most common triad is 0.0 492.780 707.220 cents, amount: 22 Number of recognisable fifths : 23, average 707.2205 cents Scale contains two identical conjunct "tetrachords" of 11 notes Formal octave complements present : 19 = 79.1667% Limited inverse transpositions : 23 Inversional symmetry on intervals : 11-12 23-24 -- Rational properties --
FIT/MODE
24: 1 1 1 1 2 0 1 0 2 1 1 1 1 1 1 1 1 0 1 2 1 0 2 1 N SD: 13.7400 c. M: 22.2045 c. 26: 1 1 1 2 1 1 0 1 1 2 1 1 1 1 2 0 1 1 1 1 2 0 2 1 N SD: 13.2171 c. M:-21.9906 c. 27: 1 1 1 2 1 1 1 0 2 1 2 0 1 2 1 1 1 0 2 1 2 0 2 1 N SD: 12.6772 c. M: 21.1005 c. 32: 1 1 2 1 2 1 1 0 2 2 2 0 2 2 1 1 1 1 1 2 2 0 2 2 N SD: 14.5392 c. M: 27.4841 c. 33: 2 0 2 2 1 1 1 1 2 1 2 1 1 2 2 1 1 0 2 2 2 0 2 2 N SD: 12.6424 c. M: 25.1409 c. 34: 2 0 2 2 2 1 1 0 2 2 2 0 2 2 2 0 2 0 2 2 2 0 2 2 N SD: 9.6846 c. M: 17.3953 c. 36: 2 1 2 1 2 1 1 1 2 2 2 0 2 2 2 1 1 1 2 2 1 1 2 2 N SD: 9.4496 c. M:-16.1235 c. 37: 2 1 2 2 2 0 2 0 2 2 2 1 2 2 2 0 2 0 2 2 2 1 2 2 N SD: 9.6071 c. M: 15.4875 c. 39: 2 1 2 2 2 1 1 1 2 2 2 1 2 2 2 1 1 1 2 2 2 1 2 2 N SD: 3.4728 c. M:-6.6060 c. 56: 3 1 3 3 3 1 2 1 3 3 3 1 3 3 3 1 2 1 3 3 3 1 3 3 N G SD: 0.5711 c. M: 1.0863 c. 151: 8 3 8 8 8 3 5 3 8 8 8 3 8 8 8 3 5 3 8 8 8 3 8 8 N G SD: 0.4734 c. M:-0.9005 c. 207: 11 4 11 11 11 4 7 4 11 11 11 4 11 11 11 4 7 4 11 11 11 4 11 11 N G SD: 0.1908 c. M:-0.3630 c. 263: 14 5 14 14 14 5 9 5 14 14 14 5 14 14 14 5 9 5 14 14 14 5 14 14 N G SD: 0.0286 c. M:-0.0544 c. 845: 45 16 45 45 45 16 29 16 45 45 45 16 45 45 45 16 29 16 45 45 45 16 45 45 N G SD: 0.0112 c. M: 0.0212 c. 1108: 59 21 59 59 59 21 38 21 59 59 59 21 59 59 59 21 38 21 59 59 59 21 59 59 N G SD: 0.0017 c. M: 0.0033 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.6327 cents 3 .. 6 match: 3 H SD: 9.0371 cents 4 .. 8 match: 4 H SD: 6.9042 cents 5 .. 10 match: 5 H SD: 8.0730 cents 6 .. 12 match: 6 H SD: 4.9841 cents 7 .. 14 match: 7 H SD: 5.0448 cents 8 .. 16 match: 8 H SD: 4.3134 cents 9 .. 18 match: 9 H SD: 5.8826 cents 10 .. 20 match: 10 H SD: 5.6010 cents 11 .. 22 match: 11 H SD: 4.1517 cents 12 .. 24 match: 12 H SD: 4.1053 cents 13 .. 26 match: 13 H SD: 4.4962 cents 14 .. 28 match: 14 H SD: 4.1645 cents 15 .. 30 match: 14 S SD: 4.9278 cents 16 .. 32 match: 16 H SD: 3.4095 cents 17 .. 34 match: 17 H SD: 3.9212 cents 18 .. 36 match: 17 SD: 3.2267 cents 19 .. 38 match: 17 SD: 4.5299 cents 20 .. 40 match: 18 SD: 3.6885 cents 21 .. 42 match: 17 SD: 2.8338 cents 22 .. 44 match: 20 SD: 2.6485 cents 23 .. 46 match: 19 SD: 2.9688 cents 24 .. 48 match: 21 SD: 2.6970 cents 25 .. 50 match: 20 SD: 2.9181 cents 26 .. 52 match: 18 SD: 2.8660 cents 27 .. 54 match: 19 SD: 2.8125 cents 28 .. 56 match: 20 SD: 2.6593 cents 29 .. 58 match: 22 SD: 2.3232 cents 30 .. 60 match: 21 SD: 2.4033 cents 31 .. 62 match: 22 SD: 2.1647 cents 32 .. 64 match: 22 SD: 2.4336 cents 33 .. 66 match: 20 SD: 2.1907 cents 34 .. 68 match: 23 SD: 2.1167 cents 35 .. 70 match: 21 SD: 2.2094 cents 36 .. 72 match: 22 SD: 1.7255 cents 38 .. 76 match: 22 SD: 2.0587 cents 39 .. 78 match: 21 SD: 2.0337 cents 40 .. 80 match: 22 SD: 1.6393 cents 41 .. 82 match: 22 SD: 1.9243 cents 42 .. 84 match: 22 SD: 1.4621 cents 43 .. 86 match: 22 SD: 1.4066 cents 44 .. 88 match: 20 SD: 1.7347 cents 45 .. 90 match: 23 SD: 1.5695 cents 46 .. 92 match: 22 SD: 1.4469 cents 47 .. 94 match: 23 SD: 1.3380 cents 48 .. 96 match: 23 SD: 1.5626 cents 49 .. 98 match: 22 SD: 1.9871 cents 50 .. 100 match: 23 SD: 1.4987 cents 51 .. 102 match: 24 SD: 1.3769 cents 52 .. 104 match: 24 SD: 1.3005 cents 53 .. 106 match: 23 SD: 1.1152 cents 55 .. 110 match: 23 SD: 0.9923 cents 67 .. 134 match: 23 SD: 1.0918 cents 68 .. 136 match: 23 SD: 0.9359 cents 73 .. 146 match: 24 SD: 0.9194 cents 76 .. 152 match: 24 SD: 0.8652 cents 77 .. 154 match: 24 SD: 0.8274 cents 78 .. 156 match: 24 SD: 0.7553 cents 97 .. 194 match: 24 SD: 0.6886 cents 98 .. 196 match: 24 SD: 0.6121 cents 100 .. 200 match: 24 SD: 0.5999 cents 111 .. 222 match: 24 SD: 0.5597 cents 121 .. 242 match: 24 SD: 0.5266 cents 131 .. 262 match: 24 SD: 0.4637 cents 136 .. 272 match: 24 SD: 0.4595 cents 137 .. 274 match: 24 SD: 0.4439 cents 142 .. 284 match: 24 SD: 0.4416 cents 153 .. 306 match: 24 SD: 0.3846 cents 174 .. 348 match: 24 SD: 0.3663 cents 179 .. 358 match: 24 SD: 0.3525 cents 184 .. 368 match: 24 SD: 0.3336 cents 189 .. 378 match: 24 SD: 0.2882 cents 206 .. 412 match: 24 SD: 0.2881 cents 218 .. 436 match: 24 SD: 0.2801 cents 234 .. 468 match: 24 SD: 0.2470 cents 242 .. 484 match: 24 SD: 0.2297 cents 274 .. 548 match: 24 SD: 0.1976 cents 289 .. 578 match: 24 SD: 0.1852 cents 349 .. 698 match: 24 SD: 0.1529 cents 374 .. 748 match: 24 SD: 0.1450 cents 395 .. 790 match: 24 SD: 0.1350 cents 426 .. 852 match: 24 SD: 0.1349 cents 448 .. 896 match: 24 SD: 0.1347 cents 452 .. 904 match: 24 SD: 0.1319 cents 485 .. 970 match: 24 SD: 0.1084 cents 562 .. 1124 match: 24 SD: 0.0925 cents 583 .. 1166 match: 24 SD: 0.0903 cents