Scala analysis: schismatic12
Schismatic[12] in 171-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 91.228 cents 91.228070 2: 203.509 cents 203.508772 3: 294.737 cents 294.736842 4: 385.965 cents 385.964912 5: 498.246 cents 498.245614 6: 589.474 cents 589.473684 7: 701.754 cents 701.754386 8: 792.982 cents 792.982456 9: 884.211 cents 884.210526 10: 996.491 cents 996.491228 11: 1087.719 cents 1087.719298 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 112.2807 cents 112.2807 1: 91.2281 cents 91.2281 2: 112.2807 cents 112.2807 3: 91.2281 cents 91.2281 4: 91.2281 cents 91.2281 5: 112.2807 cents 112.2807 6: 91.2281 cents 91.2281 7: 112.2807 cents 112.2807 8: 91.2281 cents 91.2281 9: 91.2281 cents 91.2281 10: 112.2807 cents 112.2807 11: 91.2281 cents 91.2281 12: 112.2807 cents 112.2807
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 91.22807 cents 1: 5 112.28070 cents 2: 2 182.45614 cents 2: 10 203.50877 cents 3: 9 294.73684 cents 3: 3 315.78947 cents 4: 4 385.96491 cents 4: 8 407.01754 cents 5: 11 498.24561 cents 5: 1 519.29825 cents 6: 6 589.47368 cents 6: 6 610.52632 cents 7: 1 680.70175 cents 7: 11 701.75439 cents 8: 8 792.98246 cents 8: 4 814.03509 cents 9: 3 884.21053 cents 9: 9 905.26316 cents 10: 10 996.49123 cents 10: 2 1017.54386 cents 11: 5 1087.71930 cents 11: 7 1108.77193 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 91.2 203.5 294.7 386.0 498.2 589.5 701.8 793.0 884.2 996.5 1087.7 1200.0 91.2 : 112.3 203.5 294.7 407.0 498.2 610.5 701.8 793.0 905.3 996.5 1108.8 1200.0 203.5 : 91.2 182.5 294.7 386.0 498.2 589.5 680.7 793.0 884.2 996.5 1087.7 1200.0 294.7 : 91.2 203.5 294.7 407.0 498.2 589.5 701.8 793.0 905.3 996.5 1108.8 1200.0 386.0 : 112.3 203.5 315.8 407.0 498.2 610.5 701.8 814.0 905.3 1017.5 1108.8 1200.0 498.2 : 91.2 203.5 294.7 386.0 498.2 589.5 701.8 793.0 905.3 996.5 1087.7 1200.0 589.5 : 112.3 203.5 294.7 407.0 498.2 610.5 701.8 814.0 905.3 996.5 1108.8 1200.0 701.8 : 91.2 182.5 294.7 386.0 498.2 589.5 701.8 793.0 884.2 996.5 1087.7 1200.0 793.0 : 91.2 203.5 294.7 407.0 498.2 610.5 701.8 793.0 905.3 996.5 1108.8 1200.0 884.2 : 112.3 203.5 315.8 407.0 519.3 610.5 701.8 814.0 905.3 1017.5 1108.8 1200.0 996.5 : 91.2 203.5 294.7 407.0 498.2 589.5 701.8 793.0 905.3 996.5 1087.7 1200.0 1087.7: 112.3 203.5 315.8 407.0 498.2 610.5 701.8 814.0 905.3 996.5 1108.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 91.2281 .. 112.2807 cents 21.05263 cents 91.22807 cents 2: 182.4561 .. 203.5088 cents 21.05263 cents 70.17544 cents 3: 294.7368 .. 315.7895 cents 21.05263 cents 91.22807 cents 4: 385.9649 .. 407.0175 cents 21.05263 cents 70.17544 cents 5: 498.2456 .. 519.2982 cents 21.05263 cents 91.22807 cents 6: 589.4737 .. 610.5263 cents 21.05263 cents 70.17544 cents 7: 680.7018 .. 701.7544 cents 21.05263 cents 70.17544 cents 8: 792.9825 .. 814.0351 cents 21.05263 cents 91.22807 cents 9: 884.2105 .. 905.2632 cents 21.05263 cents 70.17544 cents 10: 996.4912 .. 1017.5439 cents 21.05263 cents 91.22807 cents 11: 1087.7193 .. 1108.7719 cents 21.05263 cents 70.17544 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 91.22807 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 112.28070 cents Average / Smallest step : 1.096154 Largest / Average step : 1.122807 Largest / Smallest step : 1.230769 Median interval of one step : 91.22807 cents, amount: 7 Most common interval of one step : 91.22807 cents, amount: 7 Least squares average step : 99.22807 cents, oct.: 1190.73684 cents Scale is strictly proper Scale has Myhill's property chromas: 21.05263 cents and 70.17544 cents, ratio: 3.333333 generators: 5 of 498.24561 cents and 7 of 701.75439 cents ET pair of linear temperament : 12&53 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 171-tone equal temperament with octave 1200.000 cents degrees: 13 29 42 55 71 84 100 113 126 142 155 171 generators: 71 and 100 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABAB Step pattern size order : SLSSLSLSSLSL Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 5 0 0 0 0 0 0 0 0 0 2 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 3 0 0 0 0 0 0 0 0 0 4 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 11 0 0 1 0 0 0 0 0 0 0 0 0 6 0 ] Scale is a Constant Structure, by a margin of 70.17544 cents Ratio Whole / Half tone : 2.230769 Scale diversity : 1.141824 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.807018 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 21.05263 cents Most common intervals : 498.24561 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 91.228 701.754 cents Most common triad is 0.0 498.246 701.754 cents, amount: 10 Number of recognisable fifths : 11, average 701.7544 cents Scale contains two identical conjunct hexachords Best fifths form a closed circle Formal octave complements present : 5 = 41.6667% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.6245 c. M:-15.7895 c. Twelve-tone Chromatic (1/11-comma) 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 8.3271 c. M: 15.2450 c. Schismic-12 40: 3 4 3 3 4 3 3 3 3 4 3 4 SP D3 SD: 8.8834 c. M: 14.2105 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 3.3657 c. M: 6.1617 c. Schismic-12 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 0.6509 c. M: 1.1917 c. Schismic-12 118: 9 11 9 9 11 9 11 9 9 11 9 11 SP M DE SD: 0.2924 c. M:-0.5352 c. Schismic-12 171: 13 16 13 13 16 13 16 13 13 16 13 16 SP M DE SD: 0.0000 c. M:-0.0000 c. Schismic-12
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.1003 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0831 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.9171 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.3744 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.9019 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.7130 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.0332 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.9506 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.0733 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 11.3077 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.7079 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 9.3857 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.6523 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.2771 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 4.7850 cents 22:23:25:26:27:29:31:33:35:37:39:41:44 SD: 4.1258 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.2916 cents 32:34:36:38:40:43:45:48:51:53:57:60:64 SD: 2.1905 cents 39:41:44:46:49:52:55:58:62:65:69:73:78 SD: 2.1012 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 2.0215 cents 48:51:54:57:60:64:67:72:76:80:85:90:96 SD: 1.6706 cents 54:57:61:64:67:72:76:81:85:90:96:101:108 SD: 1.4327 cents 64:67:72:76:80:85:90:96:101:107:114:120:128 SD: 1.3153 cents 71:75:80:84:89:95:100:106:112:118:126:133:142 SD: 1.2463 cents 72:76:81:85:90:96:101:108:114:120:128:135:144 SD: 0.7454 cents 96:101:108:114:120:128:135:144:152:160:171:180:192 SD: 0.4968 cents 144:152:162:171:180:192:202:216:228:240:256:270:288 SD: 0.4808 cents 167:176:188:198:209:223:235:250:264:278:297:313:334 SD: 0.4726 cents 168:177:189:199:210:224:236:252:266:280:299:315:336 SD: 0.3126 cents 258:272:290:306:322:344:363:387:408:430:459:484:516 SD: 0.3002 cents 264:278:297:313:330:352:371:396:417:440:469:495:528 SD: 0.2518 cents 296:312:333:351:370:395:416:444:468:493:526:555:592 SD: 0.1815 cents 384:405:432:455:480:512:540:576:607:640:683:720:768 SD: 0.1553 cents 441:465:496:523:551:588:620:661:697:735:784:827:882 SD: 0.1489 cents 464:489:522:550:580:619:652:696:734:773:825:870:928 SD: 0.1483 cents 480:506:540:569:600:640:675:720:759:800:854:900:960 SD: 0.1269 cents 572:603:643:678:715:763:804:858:904:953:1017:1072:1144 SD: 0.1251 cents 576:607:648:683:720:768:810:864:911:960:1024:1080:1152 SD: 0.1223 cents 594:626:668:704:742:792:835:891:939:990:1056:1113:1188 SD: 0.1158 cents