Scala analysis: well270c
270 et ordinaire 2*156+2*157+8*158
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88.889 cents 88.888889 2: 191.111 cents 191.111111 3: 293.333 cents 293.333333 4: 382.222 cents 382.222222 5: 497.778 cents 497.777778 6: 586.667 cents 586.666667 7: 697.778 cents 697.777778 8: 791.111 cents 791.111111 9: 884.444 cents 884.444444 10: 995.556 cents 995.555556 11: 1084.444 cents 1084.444444 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 115.5556 cents 115.5556 1: 88.8889 cents 88.8889 2: 102.2222 cents 102.2222 3: 102.2222 cents 102.2222 4: 88.8889 cents 88.8889 5: 115.5556 cents 115.5556 6: 88.8889 cents 88.8889 7: 111.1111 cents 111.1111 8: 93.3333 cents 93.3333 9: 93.3333 cents 93.3333 10: 111.1111 cents 111.1111 11: 88.8889 cents 88.8889 12: 115.5556 cents 115.5556
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 88.88889 cents 1: 2 93.33333 cents 1: 2 102.22222 cents 1: 2 111.11111 cents 1: 2 115.55556 cents 2: 1 186.66667 cents 2: 2 191.11111 cents 2: 2 200.00000 cents 2: 7 204.44444 cents 3: 6 293.33333 cents 3: 2 297.77778 cents 3: 2 306.66667 cents 3: 2 315.55556 cents 4: 1 382.22222 cents 4: 2 386.66667 cents 4: 2 395.55556 cents 4: 2 404.44445 cents 4: 5 408.88889 cents 5: 8 497.77778 cents 5: 2 502.22222 cents 5: 2 506.66667 cents 6: 3 586.66667 cents 6: 2 591.11111 cents 6: 2 600.00000 cents 6: 2 608.88889 cents 6: 3 613.33333 cents 7: 2 693.33333 cents 7: 2 697.77778 cents 7: 8 702.22222 cents 8: 5 791.11111 cents 8: 2 795.55556 cents 8: 2 804.44444 cents 8: 2 813.33333 cents 8: 1 817.77778 cents 9: 2 884.44444 cents 9: 2 893.33333 cents 9: 2 902.22222 cents 9: 6 906.66667 cents 10: 7 995.55556 cents 10: 2 1000.00000 cents 10: 2 1008.88889 cents 10: 1 1013.33333 cents 11: 2 1084.44444 cents 11: 2 1088.88889 cents 11: 2 1097.77778 cents 11: 2 1106.66667 cents 11: 4 1111.11111 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.27273 = 47/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 88.9 191.1 293.3 382.2 497.8 586.7 697.8 791.1 884.4 995.6 1084.4 1200.0 88.9 : 102.2 204.4 293.3 408.9 497.8 608.9 702.2 795.6 906.7 995.6 1111.1 1200.0 191.1 : 102.2 191.1 306.7 395.6 506.7 600.0 693.3 804.4 893.3 1008.9 1097.8 1200.0 293.3 : 88.9 204.4 293.3 404.4 497.8 591.1 702.2 791.1 906.7 995.6 1097.8 1200.0 382.2 : 115.6 204.4 315.6 408.9 502.2 613.3 702.2 817.8 906.7 1008.9 1111.1 1200.0 497.8 : 88.9 200.0 293.3 386.7 497.8 586.7 702.2 791.1 893.3 995.6 1084.4 1200.0 586.7 : 111.1 204.4 297.8 408.9 497.8 613.3 702.2 804.4 906.7 995.6 1111.1 1200.0 697.8 : 93.3 186.7 297.8 386.7 502.2 591.1 693.3 795.6 884.4 1000.0 1088.9 1200.0 791.1 : 93.3 204.4 293.3 408.9 497.8 600.0 702.2 791.1 906.7 995.6 1106.7 1200.0 884.4 : 111.1 200.0 315.6 404.4 506.7 608.9 697.8 813.3 902.2 1013.3 1106.7 1200.0 995.6 : 88.9 204.4 293.3 395.6 497.8 586.7 702.2 791.1 902.2 995.6 1088.9 1200.0 1084.4: 115.6 204.4 306.7 408.9 497.8 613.3 702.2 813.3 906.7 1000.0 1111.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8889 .. 115.5556 cents 26.66667 cents 88.88889 cents 2: 186.6667 .. 204.4444 cents 17.77778 cents 71.11111 cents 3: 293.3333 .. 315.5556 cents 22.22222 cents 88.88889 cents 4: 382.2222 .. 408.8889 cents 26.66667 cents 66.66667 cents 5: 497.7778 .. 506.6667 cents 8.88889 cents 88.88889 cents 6: 586.6667 .. 613.3333 cents 26.66667 cents 80.00000 cents 7: 693.3333 .. 702.2222 cents 8.88889 cents 80.00000 cents 8: 791.1111 .. 817.7778 cents 26.66667 cents 88.88889 cents 9: 884.4444 .. 906.6667 cents 22.22222 cents 66.66667 cents 10: 995.5556 .. 1013.3333 cents 17.77778 cents 88.88889 cents 11: 1084.4444 .. 1111.1111 cents 26.66667 cents 71.11111 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 88.88889 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 115.55556 cents Average / Smallest step : 1.125000 Largest / Average step : 1.155556 Largest / Smallest step : 1.300000 Median interval of one step : 97.77778 cents, amount: 0 Most common interval of one step : 88.88889 cents, amount: 4 Least squares average step : 98.99487 cents, oct.: 1187.93846 cents Scale is strictly proper Scale is a mode of a 270-tone equal temperament with octave 1200.000 cents degrees: 20 43 66 86 112 132 157 178 199 224 244 270 Least number of segments generator : 139 of 617.778 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 163 of 724.444 cents and inv. generated superset size: 169 = 157 more = 1408.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBACADEEDAC Step pattern size order : ACCAEADBBDAE Scale is a Constant Structure, by a margin of 66.66667 cents Scale diversity : 1.158823 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.807407 Rothenberg efficiency : 0.310227 redundancy: 0.689773 Efficiency x scale size : 3.722727 Number of different interval sizes : 47 = 4.27273 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.27273 = 47/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 4.44444 cents Most common intervals : 497.77778 cents & inv., amount: 8 Most common triad is 0.0 497.778 702.222 cents, amount: 7 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 26.6667 cents: 2 5 7 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 8 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.5409 c. M:-17.7778 c. Twelve-tone Chromatic (1/11-comma) 29: 2 2 3 2 3 2 3 2 2 3 2 3 SP M ME SD: 10.1384 c. M: 25.5939 c. 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 8.8277 c. M: 16.9176 c. Meantone Chromatic (53/220-comma) 37: 3 3 3 3 3 3 3 3 3 4 2 4 SP D3 SD: 9.5087 c. M: 16.6967 c. 38: 3 3 3 3 4 3 3 3 3 4 2 4 SP D3 SD: 7.7273 c. M:-14.9708 c. 39: 3 3 4 2 4 3 4 3 3 3 3 4 SP D3 SD: 8.5556 c. M:-14.3590 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 4.6704 c. M:-13.7669 c. Schismic-12 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 7.0111 c. M:-13.6434 c. Meantone Chromatic (1/5-comma) 50: 4 4 4 4 5 3 5 4 4 4 4 5 SP D3 SD: 5.8119 c. M: 11.5556 c. 51: 4 4 4 4 5 4 5 4 4 4 4 5 SP D3 SD: 6.4637 c. M: 10.9804 c. 53: 4 4 5 4 5 4 5 4 4 5 4 5 SP M ME SD: 3.4333 c. M: 9.9790 c. 54: 4 5 4 4 5 4 5 5 4 5 4 5 SP D3 SD: 6.4150 c. M: 8.8889 c. 56: 4 5 5 4 5 4 6 4 4 5 5 5 SP D3 SD: 6.1399 c. M: 9.8413 c. 57: 4 5 5 4 6 4 5 5 4 5 5 5 SP D3 SD: 5.2632 c. M:-10.2924 c. 62: 5 5 5 5 6 4 6 5 5 5 5 6 SP D3 SD: 4.8327 c. M: 8.4588 c. 65: 5 5 6 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.5897 c. M: 6.4957 c. 81: 6 7 7 6 8 6 7 6 7 7 6 8 SP SD: 3.7037 c. M: 5.9259 c. 82: 6 7 7 6 8 6 8 6 6 8 6 8 SP D3 S SD: 2.4660 c. M: 6.3957 c. 94: 7 8 8 7 9 7 9 7 7 9 7 9 SP D3 S SD: 1.6783 c. M:-4.3499 c. 106: 8 9 9 8 10 8 10 8 8 10 8 10 SP D3 S SD: 1.9076 c. M:-4.1090 c. 131: 10 11 11 10 12 10 12 10 11 12 9 13 SP SD: 2.5267 c. M:-4.1052 c. 132: 10 11 11 10 13 10 12 10 10 13 9 13 SP SD: 2.4431 c. M:-4.4444 c. 135: 10 11 12 10 13 10 12 11 10 13 10 13 SP SD: 2.2222 c. M: 4.4444 c. 139: 10 12 12 10 14 10 13 11 10 13 11 13 SP SD: 2.3812 c. M: 3.8689 c. 143: 11 12 12 11 13 11 13 11 11 14 10 14 SP SD: 2.3886 c. M:-3.7918 c. 144: 11 12 12 11 14 10 14 11 11 13 11 14 SP SD: 2.0601 c. M: 3.8889 c. 147: 11 12 13 11 14 11 13 12 11 14 11 14 SP SD: 1.8505 c. M: 3.9002 c. 148: 11 13 12 11 14 11 14 12 11 14 11 14 SP SD: 2.1224 c. M:-3.4835 c. 151: 11 13 13 11 15 11 14 12 11 14 11 15 SP SD: 2.0919 c. M: 3.6497 c. 152: 11 13 13 11 15 11 14 12 12 14 11 15 SP S SD: 1.9615 c. M: 3.2749 c. 156: 12 13 13 12 15 11 15 12 12 14 12 15 SP SD: 1.9584 c. M:-3.4188 c. 163: 12 14 14 12 16 12 15 12 13 15 12 16 SP SD: 1.7851 c. M: 3.3810 c. 164: 12 14 14 12 16 12 15 13 13 15 12 16 SP S SD: 1.2330 c. M: 2.6558 c. 176: 13 15 15 13 17 13 16 14 14 16 13 17 SP S SD: 0.8964 c. M: 2.3232 c. 217: 16 19 18 16 21 16 20 17 17 20 16 21 SP SD: 0.8385 c. M:-2.4373 c. 225: 17 19 19 17 21 17 21 17 18 21 16 22 SP SD: 1.3333 c. M:-1.7778 c. 229: 17 19 20 17 22 17 21 18 18 21 17 22 SP SD: 0.8362 c. M: 2.4648 c. 246: 18 21 21 18 24 18 23 19 19 23 18 24 SP S SD: 1.0284 c. M: 1.7344 c. 258: 19 22 22 19 25 19 24 20 20 24 19 25 SP S SD: 0.4903 c. M: 0.8269 c. 270: 20 23 23 20 26 20 25 21 21 25 20 26 SP S 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: 2.0886 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0935 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.8404 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.7726 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.3570 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.7425 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.0091 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.6539 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.7411 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.9753 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.7019 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.2194 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 7.7258 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.6750 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.2583 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.5359 cents 22:23:25:26:27:29:31:33:35:37:39:41:44 SD: 4.3731 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.4637 cents 32:34:36:38:40:43:45:48:51:53:57:60:64 SD: 2.7313 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.3069 cents 36:38:40:43:45:48:51:54:57:60:64:67:72 SD: 2.2123 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 2.1429 cents 42:44:47:50:52:56:59:63:66:70:75:79:84 SD: 1.9728 cents 45:47:50:53:56:60:63:67:71:75:80:84:90 SD: 1.8373 cents 52:55:58:62:65:69:73:78:82:87:92:97:104 SD: 1.7337 cents 53:56:59:63:66:71:74:79:84:88:94:99:106 SD: 1.6834 cents 54:57:60:64:67:72:76:81:85:90:96:101:108 SD: 1.3207 cents 60:63:67:71:75:80:84:90:95:100:107:112:120 SD: 1.0029 cents 76:80:85:90:95:101:107:114:120:127:135:142:152 SD: 0.9437 cents 77:81:86:91:96:103:108:115:122:128:137:144:154 SD: 0.9214 cents 93:98:104:110:116:124:131:139:147:155:165:174:186 SD: 0.7134 cents 109:115:122:129:136:145:153:163:172:182:194:204:218 SD: 0.6860 cents 114:120:127:135:142:152:160:171:180:190:203:213:228 SD: 0.6229 cents 129:136:144:153:161:172:181:193:204:215:229:241:258 SD: 0.4489 cents 153:161:171:181:191:204:215:229:242:255:272:286:306 SD: 0.4295 cents 171:180:191:203:213:228:240:256:270:285:304:320:342 SD: 0.3612 cents 207:218:231:245:258:276:290:310:327:345:368:387:414 SD: 0.3535 cents 223:235:249:264:278:297:313:334:352:372:396:417:446 SD: 0.3343 cents 231:243:258:274:288:308:324:346:365:385:411:432:462 SD: 0.3268 cents 243:256:271:288:303:324:341:364:384:405:432:455:486 SD: 0.3189 cents 248:261:277:294:309:331:348:371:392:413:441:464:496 SD: 0.3098 cents 250:263:279:296:312:333:351:374:395:417:444:468:500 SD: 0.2996 cents 264:278:295:313:329:352:370:395:417:440:469:494:528 SD: 0.2751 cents 282:297:315:334:352:376:396:422:445:470:501:528:564 SD: 0.2522 cents 288:303:322:341:359:384:404:431:455:480:512:539:576 SD: 0.2405 cents 300:316:335:355:374:400:421:449:474:500:533:561:600 SD: 0.2176 cents 324:341:362:384:404:432:455:485:512:540:576:606:648 SD: 0.1876 cents 385:405:430:456:480:513:540:576:608:642:684:720:770 SD: 0.1867 cents 417:439:466:494:520:556:585:624:659:695:741:780:834 SD: 0.1558 cents 454:478:507:538:566:605:637:679:717:757:807:849:908 SD: 0.1489 cents 471:496:526:558:587:628:661:705:744:785:837:881:942 SD: 0.1231 cents