Scala analysis: hemiwuer24
Hemiwurschmidt[24] in 229-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.843 cents 83.842795 2: 120.524 cents 120.524017 3: 157.205 cents 157.205240 4: 193.886 cents 193.886463 5: 277.729 cents 277.729258 6: 314.410 cents 314.410480 7: 351.092 cents 351.091703 8: 387.773 cents 387.772926 9: 508.297 cents 508.296943 10: 544.978 cents 544.978166 11: 581.659 cents 581.659389 12: 618.341 cents 618.340611 13: 702.183 cents 702.183406 14: 738.865 cents 738.864629 15: 775.546 cents 775.545852 16: 812.227 cents 812.227074 17: 896.070 cents 896.069869 18: 932.751 cents 932.751092 19: 969.432 cents 969.432314 20: 1006.114 cents 1006.113537 21: 1089.956 cents 1089.956332 22: 1126.638 cents 1126.637555 23: 1163.319 cents 1163.318777 24: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 36.6812 cents 36.6812 1: 83.8428 cents 83.8428 2: 36.6812 cents 36.6812 3: 36.6812 cents 36.6812 4: 36.6812 cents 36.6812 5: 83.8428 cents 83.8428 6: 36.6812 cents 36.6812 7: 36.6812 cents 36.6812 8: 36.6812 cents 36.6812 9: 120.5240 cents 120.5240 10: 36.6812 cents 36.6812 11: 36.6812 cents 36.6812 12: 36.6812 cents 36.6812 13: 83.8428 cents 83.8428 14: 36.6812 cents 36.6812 15: 36.6812 cents 36.6812 16: 36.6812 cents 36.6812 17: 83.8428 cents 83.8428 18: 36.6812 cents 36.6812 19: 36.6812 cents 36.6812 20: 36.6812 cents 36.6812 21: 83.8428 cents 83.8428 22: 36.6812 cents 36.6812 23: 36.6812 cents 36.6812 24: 36.6812 cents 36.6812
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 18 36.68122 cents 1: 5 83.84279 cents 1: 1 120.52402 cents 2: 12 73.36245 cents 2: 10 120.52402 cents 2: 2 157.20524 cents 3: 6 110.04367 cents 3: 15 157.20524 cents 3: 3 193.88646 cents 4: 20 193.88646 cents 4: 4 230.56768 cents 5: 15 230.56769 cents 5: 3 267.24891 cents 5: 4 277.72926 cents 5: 2 314.41048 cents 6: 10 267.24891 cents 6: 2 303.93013 cents 6: 8 314.41048 cents 6: 4 351.09170 cents 7: 5 303.93013 cents 7: 1 340.61135 cents 7: 12 351.09170 cents 7: 6 387.77293 cents 8: 16 387.77293 cents 8: 8 424.45415 cents 9: 12 424.45415 cents 9: 6 461.13537 cents 9: 3 471.61572 cents 9: 3 508.29694 cents 10: 8 461.13537 cents 10: 4 497.81659 cents 10: 6 508.29694 cents 10: 6 544.97817 cents 11: 4 497.81659 cents 11: 2 534.49782 cents 11: 9 544.97817 cents 11: 9 581.65939 cents 12: 12 581.65939 cents 12: 12 618.34061 cents 13: 9 618.34061 cents 13: 9 655.02183 cents 13: 2 665.50218 cents 13: 4 702.18341 cents 14: 6 655.02183 cents 14: 6 691.70306 cents 14: 4 702.18341 cents 14: 8 738.86463 cents 15: 3 691.70306 cents 15: 3 728.38428 cents 15: 6 738.86463 cents 15: 12 775.54585 cents 16: 8 775.54585 cents 16: 16 812.22707 cents 17: 6 812.22707 cents 17: 12 848.90830 cents 17: 1 859.38865 cents 17: 5 896.06987 cents 18: 4 848.90830 cents 18: 8 885.58952 cents 18: 2 896.06987 cents 18: 10 932.75109 cents 19: 2 885.58952 cents 19: 4 922.27074 cents 19: 3 932.75109 cents 19: 15 969.43231 cents 20: 4 969.43232 cents 20: 20 1006.11354 cents 21: 3 1006.11354 cents 21: 15 1042.79476 cents 21: 6 1089.95633 cents 22: 2 1042.79476 cents 22: 10 1079.47598 cents 22: 12 1126.63755 cents 23: 1 1079.47598 cents 23: 5 1116.15721 cents 23: 18 1163.31878 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.30435 = 76/23
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 : 83.8 120.5 157.2 193.9 277.7 314.4 351.1 387.8 508.3 545.0 581.7 618.3 702.2 738.9 775.5 812.2 896.1 932.8 969.4 1006.1 1090.0 1126.6 1163.3 1200.0 83.8 : 36.7 73.4 110.0 193.9 230.6 267.2 303.9 424.5 461.1 497.8 534.5 618.3 655.0 691.7 728.4 812.2 848.9 885.6 922.3 1006.1 1042.8 1079.5 1116.2 1200.0 120.5 : 36.7 73.4 157.2 193.9 230.6 267.2 387.8 424.5 461.1 497.8 581.7 618.3 655.0 691.7 775.5 812.2 848.9 885.6 969.4 1006.1 1042.8 1079.5 1163.3 1200.0 157.2 : 36.7 120.5 157.2 193.9 230.6 351.1 387.8 424.5 461.1 545.0 581.7 618.3 655.0 738.9 775.5 812.2 848.9 932.8 969.4 1006.1 1042.8 1126.6 1163.3 1200.0 193.9 : 83.8 120.5 157.2 193.9 314.4 351.1 387.8 424.5 508.3 545.0 581.7 618.3 702.2 738.9 775.5 812.2 896.1 932.8 969.4 1006.1 1090.0 1126.6 1163.3 1200.0 277.7 : 36.7 73.4 110.0 230.6 267.2 303.9 340.6 424.5 461.1 497.8 534.5 618.3 655.0 691.7 728.4 812.2 848.9 885.6 922.3 1006.1 1042.8 1079.5 1116.2 1200.0 314.4 : 36.7 73.4 193.9 230.6 267.2 303.9 387.8 424.5 461.1 497.8 581.7 618.3 655.0 691.7 775.5 812.2 848.9 885.6 969.4 1006.1 1042.8 1079.5 1163.3 1200.0 351.1 : 36.7 157.2 193.9 230.6 267.2 351.1 387.8 424.5 461.1 545.0 581.7 618.3 655.0 738.9 775.5 812.2 848.9 932.8 969.4 1006.1 1042.8 1126.6 1163.3 1200.0 387.8 : 120.5 157.2 193.9 230.6 314.4 351.1 387.8 424.5 508.3 545.0 581.7 618.3 702.2 738.9 775.5 812.2 896.1 932.8 969.4 1006.1 1090.0 1126.6 1163.3 1200.0 508.3 : 36.7 73.4 110.0 193.9 230.6 267.2 303.9 387.8 424.5 461.1 497.8 581.7 618.3 655.0 691.7 775.5 812.2 848.9 885.6 969.4 1006.1 1042.8 1079.5 1200.0 545.0 : 36.7 73.4 157.2 193.9 230.6 267.2 351.1 387.8 424.5 461.1 545.0 581.7 618.3 655.0 738.9 775.5 812.2 848.9 932.8 969.4 1006.1 1042.8 1163.3 1200.0 581.7 : 36.7 120.5 157.2 193.9 230.6 314.4 351.1 387.8 424.5 508.3 545.0 581.7 618.3 702.2 738.9 775.5 812.2 896.1 932.8 969.4 1006.1 1126.6 1163.3 1200.0 618.3 : 83.8 120.5 157.2 193.9 277.7 314.4 351.1 387.8 471.6 508.3 545.0 581.7 665.5 702.2 738.9 775.5 859.4 896.1 932.8 969.4 1090.0 1126.6 1163.3 1200.0 702.2 : 36.7 73.4 110.0 193.9 230.6 267.2 303.9 387.8 424.5 461.1 497.8 581.7 618.3 655.0 691.7 775.5 812.2 848.9 885.6 1006.1 1042.8 1079.5 1116.2 1200.0 738.9 : 36.7 73.4 157.2 193.9 230.6 267.2 351.1 387.8 424.5 461.1 545.0 581.7 618.3 655.0 738.9 775.5 812.2 848.9 969.4 1006.1 1042.8 1079.5 1163.3 1200.0 775.5 : 36.7 120.5 157.2 193.9 230.6 314.4 351.1 387.8 424.5 508.3 545.0 581.7 618.3 702.2 738.9 775.5 812.2 932.8 969.4 1006.1 1042.8 1126.6 1163.3 1200.0 812.2 : 83.8 120.5 157.2 193.9 277.7 314.4 351.1 387.8 471.6 508.3 545.0 581.7 665.5 702.2 738.9 775.5 896.1 932.8 969.4 1006.1 1090.0 1126.6 1163.3 1200.0 896.1 : 36.7 73.4 110.0 193.9 230.6 267.2 303.9 387.8 424.5 461.1 497.8 581.7 618.3 655.0 691.7 812.2 848.9 885.6 922.3 1006.1 1042.8 1079.5 1116.2 1200.0 932.8 : 36.7 73.4 157.2 193.9 230.6 267.2 351.1 387.8 424.5 461.1 545.0 581.7 618.3 655.0 775.5 812.2 848.9 885.6 969.4 1006.1 1042.8 1079.5 1163.3 1200.0 969.4 : 36.7 120.5 157.2 193.9 230.6 314.4 351.1 387.8 424.5 508.3 545.0 581.7 618.3 738.9 775.5 812.2 848.9 932.8 969.4 1006.1 1042.8 1126.6 1163.3 1200.0 1006.1: 83.8 120.5 157.2 193.9 277.7 314.4 351.1 387.8 471.6 508.3 545.0 581.7 702.2 738.9 775.5 812.2 896.1 932.8 969.4 1006.1 1090.0 1126.6 1163.3 1200.0 1090.0: 36.7 73.4 110.0 193.9 230.6 267.2 303.9 387.8 424.5 461.1 497.8 618.3 655.0 691.7 728.4 812.2 848.9 885.6 922.3 1006.1 1042.8 1079.5 1116.2 1200.0 1126.6: 36.7 73.4 157.2 193.9 230.6 267.2 351.1 387.8 424.5 461.1 581.7 618.3 655.0 691.7 775.5 812.2 848.9 885.6 969.4 1006.1 1042.8 1079.5 1163.3 1200.0 1163.3: 36.7 120.5 157.2 193.9 230.6 314.4 351.1 387.8 424.5 545.0 581.7 618.3 655.0 738.9 775.5 812.2 848.9 932.8 969.4 1006.1 1042.8 1126.6 1163.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.6812 .. 120.5240 cents 83.84279 cents 36.68122 cents 2: 73.3624 .. 157.2052 cents 83.84279 cents -47.16157 cents 3: 110.0437 .. 193.8865 cents 83.84279 cents -47.16157 cents 4: 193.8865 .. 230.5677 cents 36.68122 cents 1/1, 0.0000 cents 5: 230.5677 .. 314.4105 cents 83.84279 cents 1/1, 0.0000 cents 6: 267.2489 .. 351.0917 cents 83.84279 cents -47.16157 cents 7: 303.9301 .. 387.7729 cents 83.84279 cents -47.16157 cents 8: 387.7729 .. 424.4541 cents 36.68122 cents 1/1, 0.0000 cents 9: 424.4541 .. 508.2969 cents 83.84279 cents 0.00000 cents 10: 461.1354 .. 544.9782 cents 83.84280 cents -47.16157 cents 11: 497.8166 .. 581.6594 cents 83.84280 cents -47.16157 cents 12: 581.6594 .. 618.3406 cents 36.68122 cents 1/1, 0.0000 cents 13: 618.3406 .. 702.1834 cents 83.84279 cents 0.00000 cents 14: 655.0218 .. 738.8646 cents 83.84280 cents -47.16157 cents 15: 691.7031 .. 775.5459 cents 83.84280 cents -47.16157 cents 16: 775.5459 .. 812.2271 cents 36.68122 cents 1/1, 0.0000 cents 17: 812.2271 .. 896.0699 cents 83.84280 cents 1/1, 0.0000 cents 18: 848.9083 .. 932.7511 cents 83.84279 cents -47.16157 cents 19: 885.5895 .. 969.4323 cents 83.84279 cents -47.16157 cents 20: 969.4323 .. 1006.1135 cents 36.68122 cents 0.00000 cents 21: 1006.1135 .. 1089.9563 cents 83.84279 cents 1/1, 0.0000 cents 22: 1042.7948 .. 1126.6376 cents 83.84279 cents -47.16157 cents 23: 1079.4760 .. 1163.3188 cents 83.84279 cents -47.16157 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 36.68122 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 120.52402 cents Average / Smallest step : 1.363095 Largest / Average step : 2.410480 Largest / Smallest step : 3.285714 Median interval of one step : 36.68122 cents, amount: 18 Most common interval of one step : 36.68122 cents, amount: 18 Least squares average step : 51.45852 cents, oct.: 1235.00437 cents Scale is not proper Scale is a mode of a 229-tone equal temperament with octave 1200.000 cents degrees: 16 23 30 37 53 60 67 74 97 104 111 118 134 141 148 155 171 178 185 192 208 215 222 229 Least number of segments generator : 118 of 618.341 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 192 of 1006.114 cents and inv. generated superset size: 24 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBBABBBCBBBABBBABBBABBB Step pattern size order : MSSSMSSSLSSSMSSSMSSSMSSS Scale is not a Constant Structure Scale diversity : 1.153153 Lumma stability : 0.061135 Lumma impropriety factor : 0.419214 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 : 4 Mean interval variety : 3.30435 = 76/23 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 10.48035 cents Most common intervals : 193.88646 cents & inv., amount: 23 Scale has Generated (pseudo-Myhill) property, generator: 1006.114 cents and inv. Most common triad is 0.0 193.886 1006.114 cents, amount: 22 Number of recognisable fifths : 17, average 696.6350 cents Formal octave complements present : 7 = 29.1667% Limited inverse transpositions : 17 Inversional symmetry on intervals : 8-9 20-21 -- Rational properties --
FIT/MODE
24: 2 0 1 1 2 0 1 1 2 1 1 0 2 1 1 0 2 1 0 1 2 1 0 1 N T3 SD: 14.1731 c. M:-24.4541 c. 25: 2 1 0 1 2 1 0 1 3 0 1 1 2 0 1 1 2 0 1 1 2 0 1 1 N SD: 14.1276 c. M:-23.4760 c. 26: 2 1 0 1 2 1 1 0 3 1 1 0 2 1 1 1 1 1 1 1 2 0 1 1 N SD: 13.1723 c. M: 19.1468 c. 27: 2 1 1 0 2 1 1 1 2 1 1 1 2 1 0 1 2 1 1 1 2 0 1 1 N SD: 12.5078 c. M:-21.1548 c. 29: 2 1 1 1 2 1 0 1 3 1 1 1 2 1 1 1 2 1 0 1 2 1 1 1 N SD: 11.6375 c. M: 20.0572 c. 31: 2 1 1 1 2 1 1 1 3 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 N D3 SD: 3.7060 c. M: 6.7615 c. 68: 5 2 2 2 5 2 2 2 7 2 2 2 5 2 2 2 5 2 2 2 5 2 2 2 N G SD: 2.5343 c. M:-4.6237 c. 99: 7 3 3 3 7 3 3 3 10 3 3 3 7 3 3 3 7 3 3 3 7 3 3 3 N G SD: 0.5802 c. M:-1.0586 c. 130: 9 4 4 4 9 4 4 4 13 4 4 4 9 4 4 4 9 4 4 4 9 4 4 4 N G SD: 0.4419 c. M: 0.8062 c. 229: 16 7 7 7 16 7 7 7 23 7 7 7 16 7 7 7 16 7 7 7 16 7 7 7 N G SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.1142 cents 3 .. 6 match: 3 H SD: 5.1882 cents 4 .. 8 match: 4 H SD: 0.3992 cents 5 .. 10 match: 5 H SD: 2.3343 cents 6 .. 12 match: 6 H SD: 7.4685 cents 7 .. 14 match: 7 H SD: 9.0476 cents 8 .. 16 match: 8 H SD: 3.8466 cents 9 .. 18 match: 9 H SD: 3.6144 cents 10 .. 20 match: 10 H SD: 5.9661 cents 11 .. 22 match: 11 H SD: 6.4013 cents 12 .. 24 match: 11 SD: 3.1515 cents 13 .. 26 match: 13 H SD: 6.2258 cents 14 .. 28 match: 14 H SD: 5.5126 cents 15 .. 30 match: 14 SD: 3.2234 cents 16 .. 32 match: 16 H SD: 3.9381 cents 17 .. 34 match: 13 SD: 3.0479 cents 18 .. 36 match: 17 S SD: 3.3144 cents 19 .. 38 match: 16 SD: 3.6831 cents 20 .. 40 match: 17 SD: 3.2212 cents 21 .. 42 match: 18 SD: 2.8228 cents 22 .. 44 match: 18 SD: 3.0426 cents 23 .. 46 match: 19 SD: 2.3081 cents 24 .. 48 match: 20 SD: 2.1493 cents 25 .. 50 match: 20 SD: 2.1949 cents 26 .. 52 match: 20 SD: 2.7929 cents 27 .. 54 match: 21 SD: 2.4170 cents 28 .. 56 match: 21 SD: 2.1063 cents 29 .. 58 match: 20 SD: 2.7587 cents 30 .. 60 match: 24 SD: 2.4109 cents 31 .. 62 match: 22 SD: 2.6269 cents 32 .. 64 match: 22 SD: 1.6519 cents 33 .. 66 match: 22 SD: 2.2623 cents 34 .. 68 match: 23 SD: 2.2115 cents 35 .. 70 match: 23 SD: 1.6603 cents 36 .. 72 match: 23 S SD: 2.0689 cents 37 .. 74 match: 23 SD: 2.1455 cents 39 .. 78 match: 24 SD: 1.8445 cents 40 .. 80 match: 24 SD: 1.2810 cents 52 .. 104 match: 24 SD: 1.2094 cents 56 .. 112 match: 24 SD: 1.1233 cents 60 .. 120 match: 24 SD: 1.1046 cents 62 .. 124 match: 24 SD: 1.0745 cents 65 .. 130 match: 24 SD: 1.0196 cents 67 .. 134 match: 24 SD: 1.0093 cents 70 .. 140 match: 24 SD: 0.9743 cents 74 .. 148 match: 24 SD: 0.9681 cents 75 .. 150 match: 24 SD: 0.8262 cents 80 .. 160 match: 24 SD: 0.7895 cents 84 .. 168 match: 24 SD: 0.6880 cents 100 .. 200 match: 24 SD: 0.6561 cents 105 .. 210 match: 24 SD: 0.6545 cents 108 .. 216 match: 24 SD: 0.6175 cents 115 .. 230 match: 24 SD: 0.5582 cents 116 .. 232 match: 24 SD: 0.5571 cents 120 .. 240 match: 24 SD: 0.5043 cents 124 .. 248 match: 24 SD: 0.5016 cents 126 .. 252 match: 24 SD: 0.4976 cents 136 .. 272 match: 24 SD: 0.4825 cents 137 .. 274 match: 24 SD: 0.4417 cents 156 .. 312 match: 24 SD: 0.3859 cents 160 .. 320 match: 24 SD: 0.3819 cents 167 .. 334 match: 24 SD: 0.3805 cents 168 .. 336 match: 24 SD: 0.3552 cents 178 .. 356 match: 24 SD: 0.3516 cents 179 .. 358 match: 24 SD: 0.3338 cents 195 .. 390 match: 24 SD: 0.3275 cents 196 .. 392 match: 24 SD: 0.3049 cents 218 .. 436 match: 24 SD: 0.3022 cents 219 .. 438 match: 24 SD: 0.2965 cents 220 .. 440 match: 24 SD: 0.2674 cents 235 .. 470 match: 24 SD: 0.2498 cents 240 .. 480 match: 24 SD: 0.2494 cents 246 .. 492 match: 24 SD: 0.2476 cents 262 .. 524 match: 24 SD: 0.2437 cents 263 .. 526 match: 24 SD: 0.2248 cents 276 .. 552 match: 24 SD: 0.2006 cents 306 .. 612 match: 24 SD: 0.1944 cents 316 .. 632 match: 24 SD: 0.1898 cents 338 .. 676 match: 24 SD: 0.1611 cents 378 .. 756 match: 24 SD: 0.1434 cents 430 .. 860 match: 24 SD: 0.1385 cents 454 .. 908 match: 24 SD: 0.1338 cents 462 .. 924 match: 24 SD: 0.1307 cents 466 .. 932 match: 24 SD: 0.1283 cents 471 .. 942 match: 24 SD: 0.1234 cents 481 .. 962 match: 24 SD: 0.1179 cents 506 .. 1012 match: 24 SD: 0.1063 cents 566 .. 1132 match: 24 SD: 0.0980 cents 598 .. 1196 match: 24 SD: 0.0950 cents