Scala analysis: wreck_b
Wreckmeister B temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 122.222 cents 122.222222 2: 188.889 cents 188.888889 3: 311.111 cents 311.111111 4: 388.889 cents 388.888889 5: 500.000 cents 500.000000 6: 577.778 cents 577.777778 7: 700.000 cents 700.000000 8: 811.111 cents 811.111111 9: 888.889 cents 888.888889 10: 1011.111 cents 1011.111111 11: 1077.778 cents 1077.777778 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 122.2222 cents 122.2222 1: 122.2222 cents 122.2222 2: 66.6667 cents 66.6667 3: 122.2222 cents 122.2222 4: 77.7778 cents 77.7778 5: 111.1111 cents 111.1111 6: 77.7778 cents 77.7778 7: 122.2222 cents 122.2222 8: 111.1111 cents 111.1111 9: 77.7778 cents 77.7778 10: 122.2222 cents 122.2222 11: 66.6667 cents 66.6667 12: 122.2222 cents 122.2222
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 66.66667 cents 1: 3 77.77778 cents 1: 2 111.11111 cents 1: 5 122.22222 cents 2: 7 188.88889 cents 2: 3 200.00000 cents 2: 1 233.33333 cents 2: 1 244.44444 cents 3: 3 266.66667 cents 3: 9 311.11111 cents 4: 3 377.77778 cents 4: 5 388.88889 cents 4: 1 422.22222 cents 4: 3 433.33333 cents 5: 1 455.55556 cents 5: 7 500.00000 cents 5: 4 511.11111 cents 6: 6 577.77778 cents 6: 6 622.22222 cents 7: 4 688.88889 cents 7: 7 700.00000 cents 7: 1 744.44444 cents 8: 3 766.66667 cents 8: 1 777.77778 cents 8: 5 811.11111 cents 8: 3 822.22222 cents 9: 9 888.88889 cents 9: 3 933.33333 cents 10: 1 955.55556 cents 10: 1 966.66667 cents 10: 3 1000.00000 cents 10: 7 1011.11111 cents 11: 5 1077.77778 cents 11: 2 1088.88889 cents 11: 3 1122.22222 cents 11: 2 1133.33333 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 122.2 188.9 311.1 388.9 500.0 577.8 700.0 811.1 888.9 1011.1 1077.8 1200.0 122.2 : 66.7 188.9 266.7 377.8 455.6 577.8 688.9 766.7 888.9 955.6 1077.8 1200.0 188.9 : 122.2 200.0 311.1 388.9 511.1 622.2 700.0 822.2 888.9 1011.1 1133.3 1200.0 311.1 : 77.8 188.9 266.7 388.9 500.0 577.8 700.0 766.7 888.9 1011.1 1077.8 1200.0 388.9 : 111.1 188.9 311.1 422.2 500.0 622.2 688.9 811.1 933.3 1000.0 1122.2 1200.0 500.0 : 77.8 200.0 311.1 388.9 511.1 577.8 700.0 822.2 888.9 1011.1 1088.9 1200.0 577.8 : 122.2 233.3 311.1 433.3 500.0 622.2 744.4 811.1 933.3 1011.1 1122.2 1200.0 700.0 : 111.1 188.9 311.1 377.8 500.0 622.2 688.9 811.1 888.9 1000.0 1077.8 1200.0 811.1 : 77.8 200.0 266.7 388.9 511.1 577.8 700.0 777.8 888.9 966.7 1088.9 1200.0 888.9 : 122.2 188.9 311.1 433.3 500.0 622.2 700.0 811.1 888.9 1011.1 1122.2 1200.0 1011.1: 66.7 188.9 311.1 377.8 500.0 577.8 688.9 766.7 888.9 1000.0 1077.8 1200.0 1077.8: 122.2 244.4 311.1 433.3 511.1 622.2 700.0 822.2 933.3 1011.1 1133.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 122.2222 cents 55.55556 cents 66.66667 cents 2: 188.8889 .. 244.4444 cents 55.55556 cents 66.66667 cents 3: 266.6667 .. 311.1111 cents 44.44444 cents 22.22222 cents 4: 377.7778 .. 433.3333 cents 55.55556 cents 66.66667 cents 5: 455.5556 .. 511.1111 cents 55.55556 cents 22.22222 cents 6: 577.7778 .. 622.2222 cents 44.44444 cents 66.66667 cents 7: 688.8889 .. 744.4444 cents 55.55556 cents 66.66667 cents 8: 766.6667 .. 822.2222 cents 55.55556 cents 22.22222 cents 9: 888.8889 .. 933.3333 cents 44.44444 cents 66.66667 cents 10: 955.5556 .. 1011.1111 cents 55.55556 cents 22.22222 cents 11: 1077.7778 .. 1133.3333 cents 55.55556 cents 66.66667 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 66.66667 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 122.22222 cents Average / Smallest step : 1.500000 Largest / Average step : 1.222222 Largest / Smallest step : 1.833333 Median interval of one step : 111.11111 cents, amount: 2 Most common interval of one step : 122.22222 cents, amount: 5 Least squares average step : 99.55556 cents, oct.: 1194.66667 cents Scale is strictly proper Scale is a mode of a 108-tone equal temperament with octave 2/1 degrees: 11 17 28 35 45 52 63 73 80 91 97 108 Least number of segments generator : 59 of 655.556 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 91 of 1011.111 cents and inv. generated superset size: 35 = 23 more = 291.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACDCADCABA Step pattern size order : DADBCBDCBDAD Interval vector is [ 0 0 0 0 0 2 3 0 0 2 5 0 0 0 0 0 7 3 0 0 1 1 0 3 0 0 0 9 0 0 0 0 0 3 5 0 0 1 3 0 1 0 0 0 7 4 0 0 0 0 0 6 0 0 ] Scale is a Constant Structure, by a margin of 22.22222 cents Scale diversity : 1.308130 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.518519 Rothenberg efficiency : 0.419108 redundancy: 0.580892 Efficiency x scale size : 5.029293 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 11.11111 cents Most common intervals : 311.11111 cents & inv., amount: 9 Most common triad is 0.0 311.111 888.889 cents, amount: 6 Number of recognisable fifths : 11, average 695.9596 cents Best fifths form a closed circle Formal octave complements present : 11 = 91.6667% Limited inverse transpositions with margin 55.5556 cents: 7 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.6083 c. M:-22.2222 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 1 2 2 1 2 1 2 P M ME SD: 5.9061 c. M: 9.9415 c. Genus diatonico-chromaticum, Yasser's Supradiatonic inverse 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 3.6199 c. M: 6.0932 c. Genus diatonico-chromaticum 50: 5 3 5 3 5 3 5 5 3 5 3 5 SP M DE SD: 3.0792 c. M: 4.8889 c. 58: 6 3 6 4 5 4 6 5 4 6 3 6 SP SD: 2.6545 c. M: 4.2146 c. 77: 8 4 8 5 7 5 8 7 5 8 4 8 SP SD: 1.4574 c. M: 2.4531 c. 89: 9 5 9 6 8 6 9 8 6 9 5 9 SP SD: 1.2609 c. M: 2.1223 c. 108: 11 6 11 7 10 7 11 10 7 11 6 11 SP 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: 0.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 1.6447 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.6022 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 1.9144 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.8078 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.0244 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.6031 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.7797 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9025 cents 11:12 x 13:14:15 x 16 x 18:20:21:22 S SD: 10.9604 cents 12:13 x 14:15:16:17:18:19:20 x 22:24 S SD: 6.2808 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.7896 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.7886 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.3987 cents 21 x 23:25:26:28:29:31:34:35:38:39:42 SD: 5.2209 cents 23:25:26:28:29:31:32:34:37:38:41:43:46 SD: 4.9885 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.5266 cents 25:27:28:30:31:33:35:37:40:42:45:47:50 SD: 3.4151 cents 27:29:30:32:34:36:38:40:43:45:48:50:54 SD: 3.1317 cents 28:30:31:34:35:37:39:42:45:47:50:52:56 SD: 3.1006 cents 30:32:33:36:38:40:42:45:48:50:54:56:60 SD: 2.9136 cents 35:38:39:42:44:47:49:52:56:58:63:65:70 SD: 2.7888 cents 36:39:40:43:45:48:50:54:58:60:65:67:72 SD: 2.3509 cents 40:43:45:48:50:53:56:60:64:67:72:75:80 SD: 2.0876 cents 42:45:47:50:53:56:59:63:67:70:75:78:84 SD: 1.9665 cents 45:48:50:54:56:60:63:67:72:75:81:84:90 SD: 1.8649 cents 51:55:57:61:64:68:71:76:81:85:91:95:102 SD: 1.7122 cents 52:56:58:62:65:69:73:78:83:87:93:97:104 SD: 1.4864 cents 60:64:67:72:75:80:84:90:96:100:108:112:120 SD: 1.3145 cents 68:73:76:81:85:91:95:102:109:114:122:127:136 SD: 1.1542 cents 80:86:89:96:100:107:112:120:128:134:143:149:160 SD: 1.0160 cents 86:92:96:103:108:115:120:129:137:144:154:160:172 SD: 0.9501 cents 95:102:106:114:119:127:133:142:152:159:170:177:190 SD: 0.8211 cents 96:103:107:115:120:128:134:144:153:160:172:179:192 SD: 0.6421 cents 122:131:136:146:153:163:170:183:195:204:219:227:244 SD: 0.5400 cents 146:157:163:175:183:195:204:219:233:244:262:272:292 SD: 0.5200 cents 147:158:164:176:184:196:205:220:235:246:264:274:294 SD: 0.4858 cents 164:176:183:196:205:219:229:246:262:274:294:306:328 SD: 0.3965 cents 179:192:200:214:224:239:250:268:286:299:321:334:358 SD: 0.3894 cents 207:222:231:248:259:276:289:310:331:346:371:386:414 SD: 0.3240 cents 219:235:244:262:274:292:306:328:350:366:393:408:438 SD: 0.2999 cents 243:261:271:291:304:324:339:364:388:406:436:453:486 SD: 0.2953 cents 285:306:318:341:357:380:398:427:455:476:511:531:570 SD: 0.2551 cents 301:323:336:360:377:402:420:451:481:503:540:561:602 SD: 0.2251 cents 313:336:349:375:392:418:437:469:500:523:561:583:626 SD: 0.2141 cents 329:353:367:394:412:439:459:493:526:550:590:613:658 SD: 0.2041 cents 381:409:425:456:477:509:532:571:609:637:683:710:762 SD: 0.1811 cents 397:426:443:475:497:530:554:595:634:663:712:740:794 SD: 0.1656 cents 452:485:504:541:566:603:631:677:722:755:811:842:904 SD: 0.1647 cents 477:512:532:571:597:637:666:715:762:797:855:889:954 SD: 0.1236 cents 492:528:549:589:616:657:687:737:786:822:882:917:984 SD: 0.1215 cents 600:644:669:718:751:801:838:899:959:1003:1076:1118:1200 SD: 0.1170 cents