Scala analysis: didymus9
A distributionally even scale in didymus (81/80 planar) temperament, aabacabac
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 192.700 cents 192.700000 2: 385.400 cents 385.400000 3: 461.680 cents 461.680000 4: 654.380 cents 654.380000 5: 697.040 cents 697.040000 6: 889.740 cents 889.740000 7: 966.020 cents 966.020000 8: 1158.720 cents 1158.720000 9: 1201.380 cents 1201.380000
SHOW/INTERVAL
0: 42.6600 cents 42.6600 1: 192.7000 cents 192.7000 2: 192.7000 cents 192.7000 3: 76.2800 cents 76.2800 4: 192.7000 cents 192.7000 5: 42.6600 cents 42.6600 6: 192.7000 cents 192.7000 7: 76.2800 cents 76.2800 8: 192.7000 cents 192.7000 9: 42.6600 cents 42.6600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 42.66000 cents 1: 2 76.28000 cents 1: 5 192.70000 cents 2: 4 235.36000 cents 2: 4 268.98000 cents 2: 1 385.40000 cents 3: 3 311.64000 cents 3: 3 428.06000 cents 3: 3 461.68000 cents 4: 7 504.34000 cents 4: 1 620.76000 cents 4: 1 654.38000 cents 5: 1 547.00000 cents 5: 1 580.62000 cents 5: 7 697.04000 cents 6: 3 739.70000 cents 6: 3 773.32000 cents 6: 3 889.74000 cents 7: 1 815.98000 cents 7: 4 932.40000 cents 7: 4 966.02000 cents 8: 5 1008.68000 cents 8: 2 1125.10000 cents 8: 2 1158.72000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 192.7 385.4 461.7 654.4 697.0 889.7 966.0 1158.7 1201.4 192.7 : 192.7 269.0 461.7 504.3 697.0 773.3 966.0 1008.7 1201.4 385.4 : 76.3 269.0 311.6 504.3 580.6 773.3 816.0 1008.7 1201.4 461.7 : 192.7 235.4 428.1 504.3 697.0 739.7 932.4 1125.1 1201.4 654.4 : 42.7 235.4 311.6 504.3 547.0 739.7 932.4 1008.7 1201.4 697.0 : 192.7 269.0 461.7 504.3 697.0 889.7 966.0 1158.7 1201.4 889.7 : 76.3 269.0 311.6 504.3 697.0 773.3 966.0 1008.7 1201.4 966.0 : 192.7 235.4 428.1 620.8 697.0 889.7 932.4 1125.1 1201.4 1158.7: 42.7 235.4 428.1 504.3 697.0 739.7 932.4 1008.7 1201.4 1201.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.6600 .. 192.7000 cents 150.04000 cents 42.66000 cents 2: 235.3600 .. 385.4000 cents 150.04000 cents 42.66000 cents 3: 311.6400 .. 461.6800 cents 150.04000 cents -73.76000 cents 4: 504.3400 .. 654.3800 cents 150.04000 cents 42.66000 cents 5: 547.0000 .. 697.0400 cents 150.04000 cents -107.38000 cents 6: 739.7000 .. 889.7400 cents 150.04000 cents 42.66000 cents 7: 815.9800 .. 966.0200 cents 150.04000 cents -73.76000 cents 8: 1008.6800 .. 1158.7200 cents 150.04000 cents 42.66000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 42.66000 cents, class 1 Average step (divided formal octave): 133.4867 cents Largest one step interval : 192.70000 cents Average / Smallest step : 3.129083 Largest / Average step : 1.443590 Largest / Smallest step : 4.517112 Median interval of one step : 192.70000 cents, amount: 5 Most common interval of one step : 192.70000 cents, amount: 5 Least squares average step : 142.57551 cents, oct.: 1283.17958 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2394-tone equal temperament with octave 1201.380 cents degrees: 384 768 920 1304 1389 1773 1925 2309 2394 Least number of segments generator : 1199 of 601.694 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2327 of 1167.757 cents and inv. generated superset size: 61 = 52 more = 677.778% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABACABAC Step pattern size order : LLMLSLMLS Scale is a Constant Structure, by a margin of 40.14000 cents Scale diversity : 1.373398 Lumma stability : 0.213055 Lumma impropriety factor : 0.212173 Rothenberg efficiency : 0.525132 redundancy: 0.474868 Efficiency x scale size : 4.726190 Number of different interval sizes : 24 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 33.62000 cents Most common intervals : 504.34000 cents & inv., amount: 7 Scale is a chain of 4 triads 0.0 268.980 504.340 cents Most common triad is 0.0 504.340 697.040 cents, amount: 5 Number of recognisable fifths : 7, average 697.0400 cents Number of recognisable fourths : 7, average 504.3400 cents Formal octave complements present : 1 = 11.1111% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
9: 1 2 0 2 0 2 0 2 0 N T3 SD: 38.5029 c. M: 61.2200 c. 10: 2 1 1 1 1 1 1 2 0 P D3 S SD: 34.8255 c. M: 53.6900 c. 11: 2 2 0 2 0 2 1 2 0 N SD: 29.8748 c. M:-51.4655 c. 12: 2 2 1 2 0 2 1 2 0 N T3 SD: 28.1807 c. M:-46.4250 c. 15: 2 3 1 2 1 2 1 2 1 N T3 SD: 20.8000 c. M: 37.4320 c. 16: 3 2 1 3 0 3 1 2 1 N SD: 19.6499 c. M:-32.5588 c. 18: 3 3 1 3 0 3 1 3 1 N SD: 19.5156 c. M: 31.6133 c. 19: 3 3 1 3 1 3 1 3 1 N M DE S SD: 13.5412 c. M: 22.0747 c. Godzilla-9 24: 4 4 1 4 1 4 1 4 1 N M DE S SD: 9.6644 c. M:-15.0600 c. Godzilla-9 26: 4 4 2 4 1 4 2 4 1 N T3 SD: 7.8332 c. M: 15.7446 c. 31: 5 5 2 5 1 5 2 5 1 N T3 SD: 2.6453 c. M:-4.4413 c. 81: 13 13 5 13 3 13 5 13 3 N T3 SD: 1.2478 c. M: 1.9496 c. 112: 18 18 7 18 4 18 7 18 4 N T3 SD: 0.4374 c. M:-0.7579 c. 281: 45 45 18 45 10 45 18 45 10 N T3 SD: 0.3041 c. M: 0.6164 c. 312: 50 50 20 50 11 50 20 50 11 N T3 SD: 0.2860 c. M:-0.4748 c. 393: 63 63 25 63 14 63 25 63 14 N T3 SD: 0.1326 c. M: 0.2247 c. 424: 68 68 27 68 15 68 27 68 15 N T3 SD: 0.1128 c. M:-0.1842 c. 505: 81 81 32 81 18 81 32 81 18 N T3 SD: 0.1071 c. M: 0.1632 c. 536: 86 86 34 86 19 86 34 86 19 N T3 SD: 0.0700 c. M:-0.1175 c. 929: 149 149 59 149 33 149 59 149 33 N T3 SD: 0.0157 c. M: 0.0273 c. 1465: 235 235 93 235 52 235 93 235 52 N T3 SD: 0.0157 c. M:-0.0257 c. 2394: 384 384 152 384 85 384 152 384 85 N T3 SD: 0.0036 c. M:-0.0058 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 1.3800 cents 2 x x x x 3 x x x 4 S SD: 2.5525 cents 3 x x 4 x x 5 x x 6 S SD: 12.2623 cents 4 x 5 x x 6 x 7 x 8 S SD: 1.4741 cents 5 x 6 x 7 x 8:9 x 10 S SD: 27.1864 cents 6:7 x 8 x 9:10 x x 12 S SD: 16.5877 cents 7:8 x 9:10 x x 12 x 14 S SD: 13.6123 cents 8:9:10 x x 12:13:14 x 16 S SD: 8.4694 cents 9:10:11:12:13 x 15:16 x 18 SD: 9.1723 cents 10:11 x 13 x 15:17 x x 20 SD: 8.2077 cents 11:12:14 x 16 x 18:19:21:22 SD: 11.2019 cents 12:13:15:16 x 18:20:21:23:24 SD: 9.1564 cents 13:15:16:17:19 x 22:23:25:26 SD: 9.1360 cents 15:17:19:20:22 x 25:26:29:30 SD: 6.9202 cents 16:18:20:21:23:24:27:28:31:32 SD: 4.1157 cents 17:19:21:22:25 x 28:30:33:34 SD: 5.4096 cents 19:21:24:25:28 x 32:33:37:38 SD: 4.8428 cents 20:22:25:26:29:30:33:35:39:40 SD: 4.3128 cents 21:23:26:27:31 x 35:37:41:42 SD: 6.6490 cents 22:25:27:29:32:33:37:38:43:44 SD: 5.6708 cents 23:26:29:30 x 34:38:40:45:46 SD: 4.9195 cents 24:27:30:31:35:36:40:42:47:48 SD: 2.6296 cents 36:40:45:47:53:54:60:63:70:72 SD: 2.3762 cents 40:45:50:52:58:60:67:70:78:80 SD: 2.0989 cents 43:48:54:56:63:64:72:75:84:86 SD: 1.7294 cents 52:58:65:68:76:78:87:91:102:104 SD: 1.2310 cents 68:76:85:89:99:102:114:119:133:136 SD: 1.1086 cents 76:85:95:99:111:114:127:133:148:152 SD: 0.9824 cents 85:95:106:111:124:127:142:149:166:170 SD: 0.7885 cents 109:122:136:142:159:163:182:190:213:218 SD: 0.7859 cents 111:124:139:145:162:166:186:194:217:222 SD: 0.6970 cents 127:142:159:166:185:190:212:222:248:254 SD: 0.6766 cents 128:143:160:167:187:191:214:224:250:256 SD: 0.6433 cents 137:153:171:179:200:205:229:239:268:274 SD: 0.5532 cents 153:171:191:200:223:229:256:267:299:306 SD: 0.5176 cents 161:180:201:210:235:241:269:281:314:322 SD: 0.4709 cents 170:190:212:222:248:254:284:297:332:340 SD: 0.4680 cents 177:198:221:231:258:265:296:309:346:354 SD: 0.4635 cents 189:211:236:247:276:283:316:330:369:378 SD: 0.4458 cents 196:219:245:256:286:293:328:342:383:392 SD: 0.4090 cents 213:238:266:278:311:319:356:372:416:426 SD: 0.3425 cents 272:304:340:355:397:407:455:475:531:544 SD: 0.2642 cents 281:314:351:367:410:420:470:491:549:562 SD: 0.2589 cents 305:341:381:398:445:456:510:533:596:610 SD: 0.2524 cents 333:372:416:435:486:498:557:582:650:667 SD: 0.2505 cents 341:381:426:445:498:510:570:596:666:683 SD: 0.2402 cents 357:399:446:466:521:534:597:624:697:715 SD: 0.1639 cents 442:494:552:577:645:661:739:772:863:885 SD: 0.1307 cents 494:552:617:645:721:739:826:863:965:989 SD: 0.1154 cents