Scala analysis: well270d
270 et ordinaire 3*156+9*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: 195.556 cents 195.555556 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: 702.222 cents 702.222222 8: 791.111 cents 791.111111 9: 888.889 cents 888.888889 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: 106.6667 cents 106.6667 3: 97.7778 cents 97.7778 4: 88.8889 cents 88.8889 5: 115.5556 cents 115.5556 6: 88.8889 cents 88.8889 7: 115.5556 cents 115.5556 8: 88.8889 cents 88.8889 9: 97.7778 cents 97.7778 10: 106.6667 cents 106.6667 11: 88.8889 cents 88.8889 12: 115.5556 cents 115.5556
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 88.88889 cents 1: 2 97.77778 cents 1: 2 106.66667 cents 1: 3 115.55556 cents 2: 2 186.66667 cents 2: 2 195.55556 cents 2: 8 204.44444 cents 3: 7 293.33333 cents 3: 2 302.22222 cents 3: 2 311.11111 cents 3: 1 320.00000 cents 4: 2 382.22222 cents 4: 2 391.11111 cents 4: 2 400.00000 cents 4: 6 408.88889 cents 5: 9 497.77778 cents 5: 3 506.66667 cents 6: 4 586.66667 cents 6: 2 595.55556 cents 6: 2 604.44444 cents 6: 4 613.33333 cents 7: 3 693.33333 cents 7: 9 702.22222 cents 8: 6 791.11111 cents 8: 2 800.00000 cents 8: 2 808.88889 cents 8: 2 817.77778 cents 9: 1 880.00000 cents 9: 2 888.88889 cents 9: 2 897.77778 cents 9: 7 906.66667 cents 10: 8 995.55556 cents 10: 2 1004.44444 cents 10: 2 1013.33333 cents 11: 3 1084.44444 cents 11: 2 1093.33333 cents 11: 2 1102.22222 cents 11: 5 1111.11111 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 88.9 195.6 293.3 382.2 497.8 586.7 702.2 791.1 888.9 995.6 1084.4 1200.0 88.9 : 106.7 204.4 293.3 408.9 497.8 613.3 702.2 800.0 906.7 995.6 1111.1 1200.0 195.6 : 97.8 186.7 302.2 391.1 506.7 595.6 693.3 800.0 888.9 1004.4 1093.3 1200.0 293.3 : 88.9 204.4 293.3 408.9 497.8 595.6 702.2 791.1 906.7 995.6 1102.2 1200.0 382.2 : 115.6 204.4 320.0 408.9 506.7 613.3 702.2 817.8 906.7 1013.3 1111.1 1200.0 497.8 : 88.9 204.4 293.3 391.1 497.8 586.7 702.2 791.1 897.8 995.6 1084.4 1200.0 586.7 : 115.6 204.4 302.2 408.9 497.8 613.3 702.2 808.9 906.7 995.6 1111.1 1200.0 702.2 : 88.9 186.7 293.3 382.2 497.8 586.7 693.3 791.1 880.0 995.6 1084.4 1200.0 791.1 : 97.8 204.4 293.3 408.9 497.8 604.4 702.2 791.1 906.7 995.6 1111.1 1200.0 888.9 : 106.7 195.6 311.1 400.0 506.7 604.4 693.3 808.9 897.8 1013.3 1102.2 1200.0 995.6 : 88.9 204.4 293.3 400.0 497.8 586.7 702.2 791.1 906.7 995.6 1093.3 1200.0 1084.4: 115.6 204.4 311.1 408.9 497.8 613.3 702.2 817.8 906.7 1004.4 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 .. 320.0000 cents 26.66667 cents 88.88889 cents 4: 382.2222 .. 408.8889 cents 26.66667 cents 62.22222 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: 880.0000 .. 906.6667 cents 26.66667 cents 62.22222 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: 2 Most common interval of one step : 88.88889 cents, amount: 5 Least squares average step : 99.11795 cents, oct.: 1189.41538 cents Scale is strictly proper Scale is a mode of a 135-tone equal temperament with octave 1200.000 cents degrees: 10 22 33 43 56 66 79 89 100 112 122 135 Least number of segments generator : 68 of 604.444 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 112 of 995.556 cents and inv. generated superset size: 72 = 60 more = 600.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCADADACBAD Step pattern size order : ACBADADABCAD Interval vector is [ 0 0 0 0 0 0 0 0 0 5 2 2 3 0 0 0 0 0 0 0 2 2 8 0 0 0 0 0 0 0 0 0 7 2 2 1 0 0 0 0 0 0 2 2 2 6 0 0 0 0 0 0 0 0 0 9 3 0 0 0 0 0 0 0 0 4 2 ] Scale is a Constant Structure, by a margin of 62.22222 cents Scale diversity : 1.162179 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.800000 Rothenberg efficiency : 0.366162 redundancy: 0.633838 Efficiency x scale size : 4.393939 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 8.88889 cents Most common intervals : 497.77778 cents & inv., amount: 9 Most common triad is 0.0 497.778 702.222 cents, amount: 8 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 26.6667 cents: 2 5 7 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.8131 c. M:-17.7778 c. Twelve-tone Chromatic (1/11-comma) 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 8.3352 c. M: 19.9234 c. Schismic-12 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 8.8006 c. M: 16.9176 c. Meantone Chromatic (53/220-comma) 37: 3 3 3 3 3 3 4 2 3 4 2 4 SP D3 SD: 9.2203 c. M: 14.1742 c. 39: 3 3 3 3 4 3 4 3 3 3 3 4 SP D3 SD: 8.6625 c. M: 16.4103 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 4.2235 c. M: 10.8401 c. Schismic-12 49: 4 4 4 4 4 4 5 3 4 5 3 5 SP D3 SD: 6.6579 c. M:-9.6145 c. 50: 4 4 4 4 5 3 5 4 4 4 4 5 SP D3 SD: 6.0614 c. M: 11.5556 c. 51: 4 4 4 4 5 4 5 4 4 4 4 5 SP D3 SD: 5.9732 c. M: 10.9804 c. 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 3.2282 c. M:-8.2180 c. Schismic-12 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.6503 c. M:-7.5214 c. 70: 5 6 6 5 7 5 7 5 6 6 5 7 SP D3 SD: 3.3895 c. M: 6.9841 c. 81: 6 7 7 6 8 6 7 6 7 7 6 8 SP SD: 3.9196 c. M: 5.9259 c. 82: 6 7 7 6 8 6 8 6 7 7 6 8 SP D3 SD: 2.0865 c. M: 5.3117 c. 90: 7 8 7 7 8 7 9 6 8 8 6 9 SP S SD: 3.8490 c. M:-4.4444 c. 91: 7 8 7 7 9 6 9 7 7 8 7 9 SP SD: 3.7888 c. M: 6.5446 c. 92: 7 8 7 7 9 7 9 7 7 8 7 9 SP SD: 3.1241 c. M: 6.3768 c. 94: 7 8 8 7 9 7 9 7 8 8 7 9 SP D3 SD: 1.8422 c. M:-4.7281 c. 111: 8 10 9 8 11 8 11 8 9 10 8 11 SP SD: 2.1217 c. M: 3.8438 c. 123: 9 11 10 9 12 9 12 9 10 11 9 12 SP SD: 0.9574 c. M: 1.7344 c. 135: 10 12 11 10 13 10 13 10 11 12 10 13 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: 0.1336 cents 3 x x x x 4 x x x 5 x x 6 S SD: 1.5127 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.7606 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: 7.3629 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.1276 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.2954 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.7482 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.7089 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 11.2863 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.7038 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 9.2281 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 7.6658 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.6961 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.0686 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 4.8434 cents 22:23:25:26:27:29:31:33:35:37:39:41:44 SD: 4.0561 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.3713 cents 32:34:36:38:40:43:45:48:51:53:57:60:64 SD: 2.7385 cents 33:35:37:39:41:44:46:50:52:55:59:62:66 SD: 2.4420 cents 36:38:40:43:45:48:51:54:57:60:64:67:72 SD: 2.3645 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.8515 cents 52:55:58:62:65:69:73:78:82:87:92:97:104 SD: 1.6975 cents 54:57:60:64:67:72:76:81:85:90:96:101:108 SD: 1.5623 cents 60:63:67:71:75:80:84:90:95:100:107:112:120 SD: 1.0813 cents 76:80:85:90:95:101:107:114:120:127:135:142:152 SD: 0.7781 cents 109:115:122:129:136:145:153:164:172:182:194:204:218 SD: 0.6903 cents 114:120:128:135:142:152:160:171:180:190:203:213:228 SD: 0.6795 cents 126:133:141:149:157:168:177:189:199:211:224:236:252 SD: 0.6199 cents 134:141:150:159:167:179:188:201:212:224:238:251:268 SD: 0.5120 cents 166:175:186:197:207:221:233:249:262:277:295:311:332 SD: 0.5030 cents 174:183:195:206:217:232:244:261:275:291:309:326:348 SD: 0.3744 cents 210:221:235:249:262:280:295:315:332:351:373:393:420 SD: 0.2889 cents 228:240:255:270:284:304:320:342:360:381:405:427:456 SD: 0.2879 cents 243:256:272:288:303:324:341:365:384:406:432:455:486 SD: 0.2727 cents 283:298:317:335:353:377:397:425:447:473:503:529:566 SD: 0.2698 cents 292:307:327:346:364:389:410:438:461:488:519:546:584 SD: 0.2516 cents 300:316:336:355:374:400:421:450:474:501:533:561:600 SD: 0.2405 cents 324:341:363:384:404:432:455:486:512:541:576:606:648 SD: 0.2238 cents 340:358:381:403:424:453:477:510:537:568:604:636:680 SD: 0.1992 cents 396:417:443:469:494:528:556:594:625:662:704:741:792 SD: 0.1987 cents 400:421:448:474:499:533:561:600:632:668:711:748:800 SD: 0.1962 cents 402:423:450:476:501:536:564:603:635:672:714:752:804 SD: 0.1778 cents 417:439:467:494:520:556:585:626:659:697:741:780:834 SD: 0.1596 cents 454:478:508:538:566:605:637:681:717:759:807:849:908 SD: 0.1580 cents 493:519:552:584:615:657:692:740:779:824:876:922:986 SD: 0.1492 cents 510:537:571:604:636:680:716:765:805:852:906:954:1020 SD: 0.1367 cents 526:554:589:623:656:701:738:789:831:879:935:984:1052 SD: 0.1204 cents