Scala analysis: wreck_a
Wreckmeister A temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 77.778 cents 77.777778 2: 233.333 cents 233.333333 3: 311.111 cents 311.111111 4: 388.889 cents 388.888889 5: 500.000 cents 500.000000 6: 622.222 cents 622.222222 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: 1122.222 cents 1122.222222 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 77.7778 cents 77.7778 1: 77.7778 cents 77.7778 2: 155.5556 cents 155.5556 3: 77.7778 cents 77.7778 4: 77.7778 cents 77.7778 5: 111.1111 cents 111.1111 6: 122.2222 cents 122.2222 7: 77.7778 cents 77.7778 8: 111.1111 cents 111.1111 9: 77.7778 cents 77.7778 10: 122.2222 cents 122.2222 11: 111.1111 cents 111.1111 12: 77.7778 cents 77.7778
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 77.77778 cents 1: 3 111.11111 cents 1: 2 122.22222 cents 1: 1 155.55556 cents 2: 2 155.55556 cents 2: 4 188.88889 cents 2: 2 200.00000 cents 2: 4 233.33333 cents 3: 3 266.66667 cents 3: 9 311.11111 cents 4: 8 388.88889 cents 4: 4 422.22222 cents 5: 3 466.66667 cents 5: 6 500.00000 cents 5: 1 511.11111 cents 5: 2 544.44444 cents 6: 6 577.77778 cents 6: 6 622.22222 cents 7: 2 655.55556 cents 7: 1 688.88889 cents 7: 6 700.00000 cents 7: 3 733.33333 cents 8: 4 777.77778 cents 8: 8 811.11111 cents 9: 9 888.88889 cents 9: 3 933.33333 cents 10: 4 966.66667 cents 10: 2 1000.00000 cents 10: 4 1011.11111 cents 10: 2 1044.44444 cents 11: 1 1044.44444 cents 11: 2 1077.77778 cents 11: 3 1088.88889 cents 11: 6 1122.22222 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 77.8 233.3 311.1 388.9 500.0 622.2 700.0 811.1 888.9 1011.1 1122.2 1200.0 77.8 : 155.6 233.3 311.1 422.2 544.4 622.2 733.3 811.1 933.3 1044.4 1122.2 1200.0 233.3 : 77.8 155.6 266.7 388.9 466.7 577.8 655.6 777.8 888.9 966.7 1044.4 1200.0 311.1 : 77.8 188.9 311.1 388.9 500.0 577.8 700.0 811.1 888.9 966.7 1122.2 1200.0 388.9 : 111.1 233.3 311.1 422.2 500.0 622.2 733.3 811.1 888.9 1044.4 1122.2 1200.0 500.0 : 122.2 200.0 311.1 388.9 511.1 622.2 700.0 777.8 933.3 1011.1 1088.9 1200.0 622.2 : 77.8 188.9 266.7 388.9 500.0 577.8 655.6 811.1 888.9 966.7 1077.8 1200.0 700.0 : 111.1 188.9 311.1 422.2 500.0 577.8 733.3 811.1 888.9 1000.0 1122.2 1200.0 811.1 : 77.8 200.0 311.1 388.9 466.7 622.2 700.0 777.8 888.9 1011.1 1088.9 1200.0 888.9 : 122.2 233.3 311.1 388.9 544.4 622.2 700.0 811.1 933.3 1011.1 1122.2 1200.0 1011.1: 111.1 188.9 266.7 422.2 500.0 577.8 688.9 811.1 888.9 1000.0 1077.8 1200.0 1122.2: 77.8 155.6 311.1 388.9 466.7 577.8 700.0 777.8 888.9 966.7 1088.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.7778 .. 155.5556 cents 77.77778 cents 77.77778 cents 2: 155.5556 .. 233.3333 cents 77.77778 cents 0.00000 cents 3: 266.6667 .. 311.1111 cents 44.44444 cents 33.33333 cents 4: 388.8889 .. 422.2222 cents 33.33333 cents 77.77778 cents 5: 466.6667 .. 544.4444 cents 77.77778 cents 44.44444 cents 6: 577.7778 .. 622.2222 cents 44.44444 cents 33.33333 cents 7: 655.5556 .. 733.3333 cents 77.77778 cents 33.33333 cents 8: 777.7778 .. 811.1111 cents 33.33333 cents 44.44444 cents 9: 888.8889 .. 933.3333 cents 44.44444 cents 77.77778 cents 10: 966.6667 .. 1044.4444 cents 77.77778 cents 33.33333 cents 11: 1044.4444 .. 1122.2222 cents 77.77778 cents 0.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 77.77778 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 155.55556 cents Average / Smallest step : 1.285714 Largest / Average step : 1.555556 Largest / Smallest step : 2.000000 Median interval of one step : 94.44444 cents, amount: 0 Most common interval of one step : 77.77778 cents, amount: 6 Least squares average step : 100.78632 cents, oct.: 1209.43590 cents Scale is proper Scale is a mode of a 108-tone equal temperament with octave 2/1 degrees: 7 21 28 35 45 56 63 73 80 91 101 108 Least number of segments generator : 59 of 655.556 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 101 of 1122.222 cents and inv. generated superset size: 23 = 11 more = 191.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAACDACADCA Step pattern size order : ADAABCABACBA Interval vector is [ 0 0 0 0 0 0 6 0 0 3 2 0 0 3 0 0 4 2 0 0 4 0 0 3 0 0 0 9 0 0 0 0 0 0 8 0 0 4 0 0 0 3 0 0 6 1 0 0 2 0 0 6 0 0 ] Scale is not a Constant Structure Scale diversity : 1.315316 Rothenberg stability : 0.954545 = 21/22 Lumma stability : 0.444444 Rothenberg efficiency : 0.441763 redundancy: 0.558237 Efficiency x scale size : 5.301154 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 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 : 7, average 698.4127 cents Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 7-8 -- 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: 16.3551 c. M: 33.3333 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 1 1 1 2 1 1 1 2 1 1 P B ME SD: 14.1712 c. M:-28.8889 c. 19: 1 3 1 1 2 2 1 2 1 2 2 1 N D3 SD: 9.9358 c. M:-19.2982 c. Starling-12 27: 2 3 2 2 2 3 2 2 2 3 2 2 SP B ME SD: 9.0722 c. M:-11.1111 c. Starling-12 31: 2 4 2 2 3 3 2 3 2 3 3 2 P D3 SD: 2.2857 c. M: 4.6595 c. Starling-12 77: 5 10 5 5 7 8 5 7 5 8 7 5 P SD: 0.9202 c. M:-1.8759 c. Starling-12 108: 7 14 7 7 10 11 7 10 7 11 10 7 P 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: 8.1144 cents 6 x 7 x x 8 x 9 x 10:11 x 12 S SD: 8.5247 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.3632 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.6917 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.2636 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.7066 cents 11:12 x 13:14:15:16 x x 18:20:21:22 S SD: 11.4224 cents 12:13:14 x 15:16:17:18:19:20:22:23:24 S SD: 7.5771 cents 13:14:15 x 16:17:19 x 21:22:23:25:26 SD: 8.7113 cents 14:15:16:17:18:19:20:21:22:23:25:27:28 SD: 7.1241 cents 15:16:17:18:19:20:21:22:24:25:27:29:30 SD: 6.0348 cents 16:17:18:19:20:21:23:24:26:27:29:31:32 SD: 5.7161 cents 19:20:22:23:24:25:27:28:30:32:34:36:38 SD: 5.0459 cents 20:21:23:24:25:27:29:30:32:33:36:38:40 SD: 3.3606 cents 30:31:34:36:38:40:43:45:48:50:54:57:60 SD: 3.0651 cents 35:37:40:42:44:47:50:52:56:58:63:67:70 SD: 2.6648 cents 36:38:41:43:45:48:52:54:58:60:65:69:72 SD: 2.5550 cents 39:41:45:47:49:52:56:58:62:65:70:75:78 SD: 2.4260 cents 40:42:46:48:50:53:57:60:64:67:72:76:80 SD: 2.0130 cents 42:44:48:50:53:56:60:63:67:70:75:80:84 SD: 1.7578 cents 48:50:55:57:60:64:69:72:77:80:86:92:96 SD: 1.6279 cents 60:63:69:72:75:80:86:90:96:100:108:115:120 SD: 1.2938 cents 67:70:77:80:84:89:96:100:107:112:120:128:134 SD: 1.1996 cents 72:75:82:86:90:96:103:108:115:120:129:138:144 SD: 1.1465 cents 82:86:94:98:103:109:117:123:131:137:147:157:164 SD: 1.1205 cents 83:87:95:99:104:111:119:124:133:139:149:159:166 SD: 1.0015 cents 90:94:103:108:113:120:129:135:144:150:161:172:180 SD: 0.8640 cents 92:96:105:110:115:123:132:138:147:154:165:176:184 SD: 0.7244 cents 111:116:127:133:139:148:159:166:177:185:199:212:222 SD: 0.6252 cents 131:137:150:157:164:175:188:196:209:219:235:250:262 SD: 0.5453 cents 132:138:151:158:165:176:189:198:211:221:237:252:264 SD: 0.5261 cents 146:153:167:175:183:195:209:219:233:244:262:279:292 SD: 0.4924 cents 152:159:174:182:190:203:218:228:243:254:273:291:304 SD: 0.4536 cents 173:181:198:207:217:231:248:259:276:289:310:331:346 SD: 0.4176 cents 174:182:199:208:218:232:249:261:278:291:312:333:348 SD: 0.3937 cents 194:203:222:232:243:259:278:291:310:324:348:371:388 SD: 0.2528 cents 305:319:349:365:382:407:437:457:487:510:547:583:610 SD: 0.1623 cents 437:457:500:523:547:583:626:655:698:730:784:836:874 SD: 0.1499 cents 477:499:546:571:597:637:683:715:762:797:855:912:954 SD: 0.1453 cents 499:522:571:597:625:666:715:748:797:834:895:954:998 SD: 0.1370 cents 504:527:577:603:631:673:722:755:805:842:904:964:1008 SD: 0.1360 cents 568:594:650:680:711:758:814:851:907:949:1019:1086:1136 SD: 0.1297 cents