Scala analysis: sevish159
159et tempered version of Sevish JI scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52.830 cents 52.830190 2: 203.774 cents 203.773580 3: 264.151 cents 264.150940 4: 384.906 cents 384.905660 5: 467.925 cents 467.924530 6: 550.943 cents 550.943400 7: 701.887 cents 701.886790 8: 815.094 cents 815.094340 9: 883.019 cents 883.018870 10: 905.660 cents 905.660380 11: 966.038 cents 966.037740 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 233.9623 cents 233.9623 1: 52.8302 cents 52.8302 2: 150.9434 cents 150.9434 3: 60.3774 cents 60.3774 4: 120.7547 cents 120.7547 5: 83.0189 cents 83.0189 6: 83.0189 cents 83.0189 7: 150.9434 cents 150.9434 8: 113.2075 cents 113.2075 9: 67.9245 cents 67.9245 10: 22.6415 cents 22.6415 11: 60.3774 cents 60.3774 12: 233.9623 cents 233.9623
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22.64151 cents 1: 1 52.83019 cents 1: 2 60.37736 cents 1: 1 67.92453 cents 1: 2 83.01887 cents 1: 1 113.20755 cents 1: 1 120.75472 cents 1: 2 150.94339 cents 1: 1 233.96226 cents 2: 1 83.01887 cents 2: 1 90.56604 cents 2: 1 166.03774 cents 2: 2 181.13208 cents 2: 2 203.77358 cents 2: 1 211.32075 cents 2: 1 233.96226 cents 2: 1 264.15094 cents 2: 1 286.79245 cents 2: 1 294.33962 cents 3: 1 150.94340 cents 3: 1 203.77359 cents 3: 2 264.15094 cents 3: 1 286.79246 cents 3: 2 316.98113 cents 3: 2 332.07547 cents 3: 2 347.16981 cents 3: 1 437.73584 cents 4: 1 264.15095 cents 4: 1 347.16982 cents 4: 1 354.71698 cents 4: 1 369.81132 cents 4: 2 384.90566 cents 4: 2 415.09434 cents 4: 1 430.18868 cents 4: 1 437.73585 cents 4: 2 498.11320 cents 5: 1 415.09434 cents 5: 2 437.73585 cents 5: 1 467.92453 cents 5: 4 498.11321 cents 5: 1 520.75471 cents 5: 1 550.94340 cents 5: 1 558.49056 cents 5: 1 618.86792 cents 6: 1 498.11321 cents 6: 1 520.75472 cents 6: 2 550.94340 cents 6: 1 581.13207 cents 6: 1 588.67924 cents 6: 1 611.32076 cents 6: 1 618.86793 cents 6: 2 649.05660 cents 6: 1 679.24528 cents 6: 1 701.88679 cents 7: 1 581.13208 cents 7: 1 641.50944 cents 7: 1 649.05660 cents 7: 1 679.24529 cents 7: 4 701.88679 cents 7: 1 732.07547 cents 7: 2 762.26415 cents 7: 1 784.90566 cents 8: 2 701.88680 cents 8: 1 762.26415 cents 8: 1 769.81132 cents 8: 2 784.90566 cents 8: 2 815.09434 cents 8: 1 830.18868 cents 8: 1 845.28302 cents 8: 1 852.83018 cents 8: 1 935.84905 cents 9: 1 762.26416 cents 9: 2 852.83019 cents 9: 2 867.92453 cents 9: 2 883.01887 cents 9: 1 913.20754 cents 9: 2 935.84906 cents 9: 1 996.22641 cents 9: 1 1049.05660 cents 10: 1 905.66038 cents 10: 1 913.20755 cents 10: 1 935.84906 cents 10: 1 966.03774 cents 10: 1 988.67925 cents 10: 2 996.22642 cents 10: 2 1018.86792 cents 10: 1 1033.96226 cents 10: 1 1109.43396 cents 10: 1 1116.98113 cents 11: 1 966.03774 cents 11: 2 1049.05661 cents 11: 1 1079.24528 cents 11: 1 1086.79245 cents 11: 2 1116.98113 cents 11: 1 1132.07547 cents 11: 2 1139.62264 cents 11: 1 1147.16981 cents 11: 1 1177.35849 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 8.90909 = 98/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 52.8 203.8 264.2 384.9 467.9 550.9 701.9 815.1 883.0 905.7 966.0 1200.0 52.8 : 150.9 211.3 332.1 415.1 498.1 649.1 762.3 830.2 852.8 913.2 1147.2 1200.0 203.8 : 60.4 181.1 264.2 347.2 498.1 611.3 679.2 701.9 762.3 996.2 1049.1 1200.0 264.2 : 120.8 203.8 286.8 437.7 550.9 618.9 641.5 701.9 935.8 988.7 1139.6 1200.0 384.9 : 83.0 166.0 317.0 430.2 498.1 520.8 581.1 815.1 867.9 1018.9 1079.2 1200.0 467.9 : 83.0 234.0 347.2 415.1 437.7 498.1 732.1 784.9 935.8 996.2 1117.0 1200.0 550.9 : 150.9 264.2 332.1 354.7 415.1 649.1 701.9 852.8 913.2 1034.0 1117.0 1200.0 701.9 : 113.2 181.1 203.8 264.2 498.1 550.9 701.9 762.3 883.0 966.0 1049.1 1200.0 815.1 : 67.9 90.6 150.9 384.9 437.7 588.7 649.1 769.8 852.8 935.8 1086.8 1200.0 883.0 : 22.6 83.0 317.0 369.8 520.8 581.1 701.9 784.9 867.9 1018.9 1132.1 1200.0 905.7 : 60.4 294.3 347.2 498.1 558.5 679.2 762.3 845.3 996.2 1109.4 1177.4 1200.0 966.0 : 234.0 286.8 437.7 498.1 618.9 701.9 784.9 935.8 1049.1 1117.0 1139.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.6415 .. 233.9623 cents 211.32075 cents 22.64151 cents 2: 83.0189 .. 294.3396 cents 211.32075 cents -150.94339 cents 3: 150.9434 .. 437.7358 cents 286.79244 cents -143.39622 cents 4: 264.1509 .. 498.1132 cents 233.96225 cents -173.58489 cents 5: 415.0943 .. 618.8679 cents 203.77358 cents -83.01886 cents 6: 498.1132 .. 701.8868 cents 203.77358 cents -120.75471 cents 7: 581.1321 .. 784.9057 cents 203.77358 cents -120.75471 cents 8: 701.8868 .. 935.8491 cents 233.96225 cents -83.01886 cents 9: 762.2642 .. 1049.0566 cents 286.79244 cents -173.58489 cents 10: 905.6604 .. 1116.9811 cents 211.32075 cents -143.39622 cents 11: 966.0377 .. 1177.3585 cents 211.32075 cents -150.94339 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 22.64151 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 233.96226 cents Average / Smallest step : 4.416667 Largest / Average step : 2.339623 Largest / Smallest step : 10.333333 Median interval of one step : 83.01887 cents, amount: 2 Least squares average step : 95.23367 cents, oct.: 1142.80407 cents Scale is not proper Scale is a mode of a 159-tone equal temperament with octave 2/1 degrees: 7 27 35 51 62 73 93 108 117 120 128 159 Least number of segments generator : 80 of 603.774 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 128 of 966.038 cents and inv. generated superset size: 59 = 47 more = 491.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEEBFGHCI Step pattern size order : BHCGEEHFDACI Interval vector is [ 0 0 1 0 0 0 1 2 1 0 3 1 0 0 1 1 0 0 0 3 0 1 0 2 0 0 3 1 0 0 2 0 0 0 4 0 0 2 1 0 0 2 0 2 0 3 1 0 1 0 2 0 0 0 3 0 1 4 0 0 0 1 0 0 0 7 0 0 2 0 0 0 3 1 0 0 2 1 0 ] Scale is not a Constant Structure Scale diversity : 1.611493 Lumma stability : 0.037736 Lumma impropriety factor : 0.861635 Rothenberg efficiency : 0.278451 redundancy: 0.721549 Efficiency x scale size : 3.341414 Number of different interval sizes : 66 = 6.00000 / class Number of one step interval sizes : 9 Highest interval variety : 10 Mean interval variety : 8.90909 = 98/11 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 7.54716 cents Most common intervals : 498.11320 cents & inv., amount: 7 Number of recognisable fifths : 7, average 701.8868 cents Formal octave complements present : 3 = 25.0000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 0 1 2 N T3 SD: 27.2226 c. M:-49.0566 c. 13: 1 1 1 1 1 1 2 1 1 0 1 2 N D3 SD: 26.3155 c. M:-49.3469 c. 15: 1 2 0 2 1 1 2 1 1 0 1 3 N SD: 19.0382 c. M:-36.2264 c. 16: 1 2 1 1 1 1 2 2 1 0 1 3 N SD: 19.4539 c. M:-35.8491 c. 18: 1 2 1 2 1 1 3 1 1 1 0 4 N SD: 18.4188 c. M: 32.7044 c. 19: 1 2 1 2 1 2 2 2 1 0 1 4 N SD: 13.9885 c. M: 25.8193 c. 20: 1 2 1 2 2 1 3 2 1 0 1 4 N SD: 16.8101 c. M:-24.9057 c. 22: 1 3 1 2 2 1 3 2 1 1 1 4 N SD: 12.0260 c. M:-22.9846 c. 24: 1 3 1 3 1 2 3 2 2 0 1 5 N SD: 11.4801 c. M: 17.9245 c. 26: 1 3 2 2 2 2 3 3 1 1 1 5 N SD: 11.3937 c. M: 19.1582 c. 28: 1 4 1 3 2 2 3 3 2 0 2 5 N SD: 10.3288 c. M:-19.6765 c. 31: 1 4 2 3 2 2 4 3 2 0 2 6 N SD: 8.0125 c. M: 15.3378 c. 37: 2 4 2 4 2 3 5 3 2 1 2 7 N SD: 7.7650 c. M: 13.8705 c. 40: 2 5 2 4 3 2 5 4 2 1 2 8 N SD: 8.2722 c. M: 13.0189 c. 41: 2 5 2 4 3 3 5 4 2 1 2 8 N SD: 3.2640 c. M:-5.7064 c. 72: 3 9 4 7 5 5 9 7 4 1 4 14 N SD: 2.4510 c. M: 5.6604 c. 87: 4 11 4 9 6 6 11 8 5 2 4 17 N SD: 2.0284 c. M:-4.6844 c. 94: 4 12 5 9 7 6 12 9 5 2 5 18 N SD: 2.4579 c. M:-4.4159 c. 106: 5 13 5 11 7 8 13 10 6 2 5 21 N SD: 2.4358 c. M: 3.7736 c. 113: 5 14 6 11 8 8 14 11 6 2 6 22 N SD: 1.6885 c. M: 3.0055 c. 118: 5 15 6 12 8 8 15 11 7 2 6 23 N SD: 1.1341 c. M: 1.9827 c. 159: 7 20 8 16 11 11 20 15 9 3 8 31 N SD: 0.0000 c. M:-0.0000 c.
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: 0.0341 cents 3 x x x x 4 x x x 5 x x 6 S SD: 10.0501 cents 4 x x x 5 x x 6 x x x 7:8 S SD: 0.7811 cents 5 x x 6 x x 7 x 8 x x 9:10 S SD: 15.8847 cents 6 x x 7 x 8 x 9 x 10 x x 12 S SD: 6.0546 cents 7 x 8 x x 9:10 x 11 x 12 x 14 S SD: 14.9767 cents 8 x 9 x 10 x 11:12:13 x x 14:16 S SD: 3.6611 cents 9 x 10 x 11:12 x x 14:15 x 16:18 S SD: 11.2421 cents 10 x 11:12 x 13:14:15:16 x 17 x 20 SD: 9.2782 cents 11 x 12:13:14 x 15:17 x 18 x 19:22 SD: 11.6644 cents 12 x x 14:15:16:17:18:19:20 x 21:24 S SD: 7.0429 cents 13:14 x 15:16:17:18:20:21 x 22:23:26 SD: 9.7124 cents 14:15:16 x 17:18:19:21:22:23:24 x 28 SD: 10.7303 cents 15:16:17 x 19:20:21:23:24:25 x 26:30 SD: 8.8198 cents 16:17:18:19:20:21:22:24:26 x 27:28:32 S SD: 6.0950 cents 18:19:20:21:22:24:25:27:29:30 x 31:36 SD: 6.7358 cents 19:20:21:22:24:25:26:29:30 x 32:33:38 SD: 6.0620 cents 20:21 x 23:25:26:27:30:32:33:34:35:40 SD: 5.0656 cents 21:22:24 x 26:28:29:32:34:35 x 37:42 SD: 6.3569 cents 22:23:25:26:27:29:30:33:35 x 37:38:44 SD: 5.2178 cents 23:24:26:27:29:30:32:35:37:38:39:40:46 SD: 4.1377 cents 24:25:27:28:30:31:33:36:38:40 x 42:48 SD: 3.3233 cents 25:26:28:29:31:33:34:38:40 x 42:44:50 SD: 3.8011 cents 28:29:32:33:35:37:38:42:45 x 47:49:56 SD: 4.1300 cents 29:30:33:34:36:38:40:44:46:48:49:51:58 SD: 3.3462 cents 30:31:34:35:37:39:41:45:48:50:51:52:60 SD: 3.0269 cents 31:32:35:36:39:41:43:47:50 x 52:54:62 SD: 3.3557 cents 32:33:36:37:40:42:44:48:51:53:54:56:64 SD: 1.5362 cents 34:35:38:40:42:45:47:51:54 x 57:59:68 SD: 3.6942 cents 35:36:39:41:44:46:48:53:56:58:59:61:70 SD: 2.5296 cents 37:38:42:43:46:48:51:56:59:62 x 65:74 SD: 3.1356 cents 38:39:43:44:47:50:52:57:61:63:64:66:76 SD: 2.4564 cents 40:41:45:47:50:52:55:60:64:67 x 70:80 SD: 2.2769 cents 42:43:47:49:52:55:58:63:67:70:71:73:84 SD: 2.1493 cents 48:49:54:56:60:63:66:72:77:80:81:84:96 SD: 1.5148 cents 62:64:70:72:77:81:85:93:99:103:105:108:124 SD: 1.5075 cents 64:66:72:75:80:84:88:96:102:107:108:112:128 SD: 1.2898 cents 72:74:81:84:90:94:99:108:115:120:121:126:144 SD: 1.0404 cents 80:82:90:93:100:105:110:120:128:133:135:140:160 SD: 0.9957 cents 90:93:101:105:112:118:124:135:144:150:152:157:180 SD: 0.8725 cents 96:99:108:112:120:126:132:144:154:160:162:168:192 SD: 0.5075 cents 128:132:144:149:160:168:176:192:205:213:216:224:256 SD: 0.3872 cents 194:200:218:226:242:254:267:291:311:323:327:339:388 SD: 0.3842 cents 200:206:225:233:250:262:275:300:320:333:337:349:400 SD: 0.3491 cents 224:231:252:261:280:294:308:336:359:373:378:391:448 SD: 0.3305 cents 230:237:259:268:287:301:316:345:368:383:388:402:460 SD: 0.3256 cents 248:256:279:289:310:325:341:372:397:413:418:433:496 SD: 0.2945 cents 254:262:286:296:317:333:349:381:407:423:429:444:508 SD: 0.2928 cents 256:264:288:298:320:335:352:384:410:426:432:447:512 SD: 0.2902 cents 286:295:322:333:357:375:393:429:458:476:483:500:572 SD: 0.2756 cents 290:299:326:338:362:380:399:435:464:483:489:507:580 SD: 0.2633 cents 296:305:333:345:370:388:407:444:474:493:499:517:592 SD: 0.2247 cents 326:336:367:380:407:427:448:489:522:543:550:570:652 SD: 0.2129 cents 352:363:396:410:440:461:484:528:564:586:594:615:704 SD: 0.1805 cents 442:456:497:515:552:579:608:663:708:736:746:772:884 SD: 0.1767 cents 448:462:504:522:560:587:616:672:717:746:756:783:896 SD: 0.1643 cents 454:468:511:529:567:595:624:681:727:756:766:793:908 SD: 0.1122 cents 582:600:655:678:727:763:800:873:932:969:982:1017:1164 SD: 0.1110 cents