Scala analysis: keemun11
Keemun[11] = Hanson[11] = Kleismic[11] in 53-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67.925 cents 67.924528 2: 135.849 cents 135.849057 3: 316.981 cents 316.981132 4: 384.906 cents 384.905660 5: 566.038 cents 566.037736 6: 633.962 cents 633.962264 7: 701.887 cents 701.886792 8: 883.019 cents 883.018868 9: 950.943 cents 950.943396 10: 1018.868 cents 1018.867925 11: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 181.1321 cents 181.1321 1: 67.9245 cents 67.9245 2: 67.9245 cents 67.9245 3: 181.1321 cents 181.1321 4: 67.9245 cents 67.9245 5: 181.1321 cents 181.1321 6: 67.9245 cents 67.9245 7: 67.9245 cents 67.9245 8: 181.1321 cents 181.1321 9: 67.9245 cents 67.9245 10: 67.9245 cents 67.9245 11: 181.1321 cents 181.1321
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 67.92453 cents 1: 4 181.13208 cents 2: 3 135.84906 cents 2: 8 249.05660 cents 3: 10 316.98113 cents 3: 1 430.18868 cents 4: 6 384.90566 cents 4: 5 498.11321 cents 5: 2 452.83019 cents 5: 9 566.03774 cents 6: 9 633.96226 cents 6: 2 747.16981 cents 7: 5 701.88679 cents 7: 6 815.09434 cents 8: 1 769.81132 cents 8: 10 883.01887 cents 9: 8 950.94340 cents 9: 3 1064.15094 cents 10: 4 1018.86793 cents 10: 7 1132.07547 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 0.0 : 67.9 135.8 317.0 384.9 566.0 634.0 701.9 883.0 950.9 1018.9 1200.0 67.9 : 67.9 249.1 317.0 498.1 566.0 634.0 815.1 883.0 950.9 1132.1 1200.0 135.8 : 181.1 249.1 430.2 498.1 566.0 747.2 815.1 883.0 1064.2 1132.1 1200.0 317.0 : 67.9 249.1 317.0 384.9 566.0 634.0 701.9 883.0 950.9 1018.9 1200.0 384.9 : 181.1 249.1 317.0 498.1 566.0 634.0 815.1 883.0 950.9 1132.1 1200.0 566.0 : 67.9 135.8 317.0 384.9 452.8 634.0 701.9 769.8 950.9 1018.9 1200.0 634.0 : 67.9 249.1 317.0 384.9 566.0 634.0 701.9 883.0 950.9 1132.1 1200.0 701.9 : 181.1 249.1 317.0 498.1 566.0 634.0 815.1 883.0 1064.2 1132.1 1200.0 883.0 : 67.9 135.8 317.0 384.9 452.8 634.0 701.9 883.0 950.9 1018.9 1200.0 950.9 : 67.9 249.1 317.0 384.9 566.0 634.0 815.1 883.0 950.9 1132.1 1200.0 1018.9: 181.1 249.1 317.0 498.1 566.0 747.2 815.1 883.0 1064.2 1132.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9245 .. 181.1321 cents 113.20755 cents 67.92453 cents 2: 135.8491 .. 249.0566 cents 113.20755 cents -45.28302 cents 3: 316.9811 .. 430.1887 cents 113.20755 cents 67.92453 cents 4: 384.9057 .. 498.1132 cents 113.20755 cents -45.28302 cents 5: 452.8302 .. 566.0377 cents 113.20755 cents -45.28302 cents 6: 633.9623 .. 747.1698 cents 113.20755 cents 67.92453 cents 7: 701.8868 .. 815.0943 cents 113.20755 cents -45.28302 cents 8: 769.8113 .. 883.0189 cents 113.20755 cents -45.28302 cents 9: 950.9434 .. 1064.1509 cents 113.20755 cents 67.92453 cents 10: 1018.8679 .. 1132.0755 cents 113.20755 cents -45.28302 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 67.92453 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 181.13208 cents Average / Smallest step : 1.606061 Largest / Average step : 1.660377 Largest / Smallest step : 2.666667 Median interval of one step : 67.92453 cents, amount: 7 Most common interval of one step : 67.92453 cents, amount: 7 Least squares average step : 105.51122 cents, oct.: 1160.62346 cents Scale is not proper Scale has Myhill's property chromas: 113.20755 cents and 45.28302 cents, ratio: 2.500000 generators: 3 of 316.98113 cents and 8 of 883.01887 cents ET pair of linear temperament : 15&19 Scale is distributional even Scale is a mode of a 53-tone equal temperament with octave 1200.000 cents degrees: 3 6 14 17 25 28 31 39 42 45 53 generators: 14 and 39 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 53-tone equal temperament Step pattern alph. order: AABABAABAAB Step pattern size order : SSLSLSSLSSL Interval vector is [ 0 0 7 0 0 3 0 4 0 0 8 0 0 10 0 0 6 0 1 2 0 5 0 0 9 0 ] Scale is a Constant Structure, by a margin of 22.64151 cents Scale diversity : 1.241814 Lumma stability : 0.283019 Lumma impropriety factor : 0.226415 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 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 : 22.64151 cents Most common intervals : 316.98113 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 498.113 883.019 cents Most common triad is 0.0 316.981 883.019 cents, amount: 9 Number of recognisable fifths : 5, average 701.8868 cents Formal octave complements present : 5 = 45.4545% Limited inverse transpositions : 7 Inversional symmetry on degrees : 9 Inversional symmetry on intervals : 3-4 -- Rational properties --
FIT/MODE
11: 0 1 1 1 2 0 1 2 0 1 2 N T3 SD: 57.6095 c. M: 98.7993 c. 12: 1 0 2 1 2 0 1 2 1 0 2 N T3 SD: 27.2889 c. M:-49.0566 c. 15: 1 1 2 1 2 1 1 2 1 1 2 P M ME S SD: 13.1589 c. M:-24.1509 c. Kleismic-11 19: 1 1 3 1 3 1 1 3 1 1 3 N M DE S SD: 5.1943 c. M: 9.5333 c. Kleismic-11 34: 2 2 5 2 5 2 2 5 2 2 5 N M DE S SD: 2.9027 c. M:-5.3274 c. Kleismic-11 53: 3 3 8 3 8 3 3 8 3 3 8 N M DE S SD: 0.0000 c. M: 0.0000 c. Kleismic-11
FIT/HARMONIC
1 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 4 S SD: 0.0341 cents 3 x x x x 4 x x 5 x x 6 S SD: 22.6686 cents 4 x x x 5 x x 6 x 7 x 8 S SD: 4.4845 cents 5 x x 6 x 7 x x 8 x 9:10 S SD: 14.2574 cents 6 x x 7 x 8 x 9:10 x 11:12 S SD: 14.9683 cents 7 x x 8:9 x 10:11 x 12:13:14 S SD: 20.0805 cents 8 x 9 x 10:11 x 12:13:14 x 16 S SD: 11.9320 cents 9 x 10:11 x 12:13:14:15 x 16:18 S SD: 13.8160 cents 10 x 11:12 x 14 x 15 x 17:18:20 SD: 6.6521 cents 11 x 12:13:14:15:16:17:18:19:20:22 S SD: 8.3679 cents 12 x 13:14:15 x 17:18:20:21:22:24 SD: 7.6422 cents 13 x 14 x 16:18:19:20:22 x 23:26 SD: 8.7571 cents 14 x 15:17 x 19:20:21:23:24:25:28 SD: 6.4809 cents 15 x 16:18:19:21:22:23:25:26:27:30 SD: 6.1249 cents 16 x 17:19:20:22:23:24:27:28:29:32 SD: 5.0407 cents 17:18 x 20:21:24:25:26:28:29:31:34 SD: 8.5645 cents 18:19 x 22 x 25:26:27:30:31:32:36 SD: 5.2310 cents 20:21:22:24:25:28:29:30:33:35:36:40 SD: 4.1308 cents 24:25:26:29:30:33:35:36:40:42:43:48 SD: 3.0485 cents 34:35:37:41:42:47:49:51:57:59:61:68 SD: 2.9644 cents 36:37:39:43:45:50:52:54:60:62:65:72 SD: 2.3107 cents 44:46:48:53:55:61:63:66:73:76:79:88 SD: 2.1974 cents 45:47:49:54:56:62:65:67:75:78:81:90 SD: 2.0966 cents 48:50:52:58:60:67:69:72:80:83:86:96 SD: 1.7885 cents 49:51:53:59:61:68:71:73:82:85:88:98 SD: 1.7348 cents 50:52:54:60:62:69:72:75:83:87:90:100 SD: 1.6751 cents 52:54:56:62:65:72:75:78:87:90:94:104 SD: 1.6540 cents 60:62:65:72:75:83:87:90:100:104:108:120 SD: 1.4244 cents 70:73:76:84:87:97:101:105:117:121:126:140 SD: 1.2672 cents 72:75:78:86:90:100:104:108:120:125:130:144 SD: 1.1284 cents 75:78:81:90:94:104:108:112:125:130:135:150 SD: 0.9774 cents 96:100:104:115:120:133:138:144:160:166:173:192 SD: 0.8202 cents 100:104:108:120:125:139:144:150:167:173:180:200 SD: 0.7217 cents 120:125:130:144:150:166:173:180:200:208:216:240 SD: 0.5926 cents 124:129:134:149:155:172:179:186:207:215:223:248 SD: 0.5520 cents 150:156:162:180:187:208:216:225:250:260:270:300 SD: 0.5085 cents 170:177:184:204:212:236:245:255:283:294:306:340 SD: 0.4809 cents 174:181:188:209:217:241:251:261:290:301:313:348 SD: 0.4718 cents 176:183:190:211:220:244:254:264:293:305:317:352 SD: 0.4547 cents 194:202:210:233:242:269:280:291:323:336:349:388 SD: 0.3822 cents 220:229:238:264:275:305:317:330:366:381:396:440 SD: 0.3373 cents 246:256:266:295:307:341:355:369:410:426:443:492 SD: 0.3327 cents 248:258:268:298:310:344:358:372:413:430:447:496 SD: 0.3272 cents 254:264:275:305:317:352:366:381:423:440:458:508 SD: 0.3225 cents 258:268:279:310:322:358:372:387:430:447:465:516 SD: 0.3057 cents 269:280:291:323:336:373:388:403:448:466:485:538 SD: 0.2769 cents 294:306:318:353:367:408:424:441:490:509:530:588 SD: 0.2657 cents 298:310:322:358:372:413:430:447:496:516:537:596 SD: 0.2558 cents 318:331:344:382:397:441:459:477:530:551:573:636 SD: 0.2484 cents 328:341:355:394:410:455:473:492:546:568:591:656 SD: 0.2045 cents 378:393:409:454:472:524:545:567:630:655:681:756 SD: 0.1825 cents 418:435:452:502:522:580:603:627:696:724:753:836 SD: 0.1525 cents 478:497:517:574:597:663:689:717:796:828:861:956 SD: 0.1057 cents 574:597:621:689:717:796:828:861:956:994:1034:1148 SD: 0.0973 cents