Scala analysis: well270b
270 et ordinaire 156+4*157+7*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: 386.667 cents 386.666667 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: 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: 93.3333 cents 93.3333 5: 111.1111 cents 111.1111 6: 88.8889 cents 88.8889 7: 111.1111 cents 111.1111 8: 93.3333 cents 93.3333 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: 3 88.88889 cents 1: 2 93.33333 cents 1: 2 97.77778 cents 1: 2 106.66667 cents 1: 2 111.11111 cents 1: 1 115.55556 cents 2: 2 191.11111 cents 2: 2 195.55556 cents 2: 2 200.00000 cents 2: 6 204.44444 cents 3: 5 293.33333 cents 3: 2 297.77778 cents 3: 2 302.22222 cents 3: 3 311.11111 cents 4: 2 386.66667 cents 4: 2 391.11111 cents 4: 2 400.00000 cents 4: 2 404.44445 cents 4: 4 408.88889 cents 5: 7 497.77778 cents 5: 4 502.22222 cents 5: 1 506.66667 cents 6: 2 586.66667 cents 6: 2 591.11111 cents 6: 2 595.55556 cents 6: 2 604.44444 cents 6: 2 608.88889 cents 6: 2 613.33333 cents 7: 1 693.33333 cents 7: 4 697.77778 cents 7: 7 702.22222 cents 8: 4 791.11111 cents 8: 2 795.55555 cents 8: 2 800.00000 cents 8: 2 808.88889 cents 8: 2 813.33333 cents 9: 3 888.88889 cents 9: 2 897.77778 cents 9: 2 902.22222 cents 9: 5 906.66667 cents 10: 6 995.55556 cents 10: 2 1000.00000 cents 10: 2 1004.44444 cents 10: 2 1008.88889 cents 11: 1 1084.44444 cents 11: 2 1088.88889 cents 11: 2 1093.33333 cents 11: 2 1102.22222 cents 11: 2 1106.66667 cents 11: 3 1111.11111 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.54545 = 50/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 88.9 195.6 293.3 386.7 497.8 586.7 697.8 791.1 888.9 995.6 1084.4 1200.0 88.9 : 106.7 204.4 297.8 408.9 497.8 608.9 702.2 800.0 906.7 995.6 1111.1 1200.0 195.6 : 97.8 191.1 302.2 391.1 502.2 595.6 693.3 800.0 888.9 1004.4 1093.3 1200.0 293.3 : 93.3 204.4 293.3 404.4 497.8 595.6 702.2 791.1 906.7 995.6 1102.2 1200.0 386.7 : 111.1 200.0 311.1 404.4 502.2 608.9 697.8 813.3 902.2 1008.9 1106.7 1200.0 497.8 : 88.9 200.0 293.3 391.1 497.8 586.7 702.2 791.1 897.8 995.6 1088.9 1200.0 586.7 : 111.1 204.4 302.2 408.9 497.8 613.3 702.2 808.9 906.7 1000.0 1111.1 1200.0 697.8 : 93.3 191.1 297.8 386.7 502.2 591.1 697.8 795.6 888.9 1000.0 1088.9 1200.0 791.1 : 97.8 204.4 293.3 408.9 497.8 604.4 702.2 795.6 906.7 995.6 1106.7 1200.0 888.9 : 106.7 195.6 311.1 400.0 506.7 604.4 697.8 808.9 897.8 1008.9 1102.2 1200.0 995.6 : 88.9 204.4 293.3 400.0 497.8 591.1 702.2 791.1 902.2 995.6 1093.3 1200.0 1084.4: 115.6 204.4 311.1 408.9 502.2 613.3 702.2 813.3 906.7 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: 191.1111 .. 204.4444 cents 13.33333 cents 75.55556 cents 3: 293.3333 .. 311.1111 cents 17.77778 cents 88.88889 cents 4: 386.6667 .. 408.8889 cents 22.22222 cents 75.55556 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 .. 813.3333 cents 22.22222 cents 88.88889 cents 9: 888.8889 .. 906.6667 cents 17.77778 cents 75.55556 cents 10: 995.5556 .. 1008.8889 cents 13.33333 cents 88.88889 cents 11: 1084.4444 .. 1111.1111 cents 26.66667 cents 75.55556 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: 3 Least squares average step : 99.09744 cents, oct.: 1189.16923 cents Scale is strictly proper Scale is a mode of a 270-tone equal temperament with octave 1200.000 cents degrees: 20 44 66 87 112 132 157 178 200 224 244 270 Least number of segments generator : 139 of 617.778 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 263 of 1168.889 cents and inv. generated superset size: 133 = 121 more = 1108.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEAEDCBAF Step pattern size order : ADCBEAEBCDAF Scale is a Constant Structure, by a margin of 75.55555 cents Scale diversity : 1.142450 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.829630 Rothenberg efficiency : 0.284969 redundancy: 0.715031 Efficiency x scale size : 3.419625 Number of different interval sizes : 50 = 4.54545 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.54545 = 50/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 4.44444 cents Most common intervals : 497.77778 cents & inv., amount: 7 Most common triad is 0.0 497.778 702.222 cents, amount: 6 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 10 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: 9.2073 c. M:-15.5556 c. Twelve-tone Chromatic (1/11-comma) 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 8.9968 c. M: 19.9234 c. Schismic-12 31: 2 3 3 2 3 2 3 2 3 3 2 3 SP M ME SD: 8.5496 c. M: 16.9176 c. Meantone Chromatic (53/220-comma) 39: 3 3 4 3 3 3 4 3 3 3 3 4 SP D3 SD: 8.7308 c. M:-14.3590 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 4.7513 c. M: 10.8401 c. Schismic-12 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 3.3878 c. M:-8.2180 c. Schismic-12 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.4725 c. M:-7.5214 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 3.9832 c. M:-7.0418 c. 81: 6 7 7 6 8 6 7 6 7 7 6 8 SP SD: 3.4744 c. M: 5.9259 c. 82: 6 7 7 6 8 6 8 6 7 7 6 8 SP D3 SD: 3.0152 c. M: 6.1789 c. 86: 6 8 7 7 8 6 8 7 7 7 7 8 SP D3 S SD: 3.3942 c. M: 5.1680 c. 90: 7 8 7 7 8 7 8 7 8 8 6 9 SP SD: 3.6289 c. M: 4.4444 c. 93: 7 8 8 7 9 6 9 7 8 8 7 9 SP SD: 2.9942 c. M: 6.0215 c. 94: 7 8 8 7 9 7 9 7 8 8 7 9 SP D3 SD: 2.4607 c. M:-4.7281 c. 106: 8 9 9 8 10 8 10 8 9 9 8 10 SP D3 SD: 2.5012 c. M:-5.4507 c. 111: 8 10 9 9 10 8 10 9 9 10 8 11 SP SD: 2.5823 c. M: 5.8859 c. 112: 8 10 9 9 10 9 10 9 9 10 8 11 SP SD: 2.5299 c. M: 4.9206 c. 121: 9 11 10 9 11 9 11 10 10 10 9 12 SP SD: 2.7293 c. M:-4.1873 c. 123: 9 11 10 10 11 9 12 9 10 11 9 12 SP SD: 1.8812 c. M:-4.6612 c. 127: 9 12 10 10 12 9 12 10 10 11 10 12 SP SD: 2.2222 c. M: 3.8495 c. 135: 10 12 11 11 12 10 13 10 11 12 10 13 SP SD: 1.8144 c. M:-4.4444 c. 139: 10 13 11 11 13 10 13 11 11 12 11 13 SP SD: 2.2086 c. M:-3.3253 c. 143: 11 12 12 11 13 11 13 11 12 13 10 14 SP SD: 1.9736 c. M:-3.4188 c. 146: 11 13 12 11 14 10 14 11 12 13 11 14 SP SD: 1.8762 c. M:-3.5921 c. 147: 11 13 12 11 14 11 13 12 12 13 11 14 SP SD: 1.5741 c. M: 3.9002 c. 159: 12 14 13 12 15 12 15 12 13 14 12 15 SP SD: 1.8028 c. M:-4.1090 c. 164: 12 15 13 13 15 12 15 13 13 15 12 16 SP SD: 1.6167 c. M: 3.5230 c. 165: 12 15 13 13 15 13 15 13 13 15 12 16 SP SD: 1.6740 c. M: 3.2323 c. 168: 12 15 14 13 16 12 16 13 13 15 13 16 SP SD: 2.0676 c. M: 3.1746 c. 170: 13 15 14 13 16 12 16 13 14 15 13 16 SP SD: 1.9506 c. M:-3.3987 c. 171: 13 15 14 13 16 13 16 13 14 15 13 16 SP SD: 2.1074 c. M:-3.9766 c. 174: 13 15 14 14 16 13 16 14 14 15 13 17 SP SD: 1.7552 c. M: 3.6782 c. 176: 13 16 14 14 16 13 16 14 14 16 13 17 SP SD: 1.3143 c. M: 2.5253 c. 180: 13 16 15 14 17 13 17 14 14 16 14 17 SP SD: 1.8144 c. M: 2.2222 c. 186: 14 16 15 15 17 14 17 15 15 16 14 18 SP SD: 1.5781 c. M: 3.0108 c. 188: 14 17 15 15 17 14 17 15 15 17 14 18 SP SD: 1.3151 c. M:-2.6950 c. 205: 15 18 17 16 19 15 19 16 17 18 15 20 SP SD: 1.1010 c. M: 2.3848 c. 216: 16 19 18 17 20 16 20 16 18 19 16 21 SP SD: 1.5713 c. M: 2.2222 c. 217: 16 19 18 17 20 16 20 17 18 19 16 21 SP SD: 0.8274 c. M: 2.0072 c. 229: 17 20 19 18 21 17 21 18 19 20 17 22 SP SD: 0.8507 c. M:-1.9408 c. 246: 18 22 20 19 23 18 23 19 20 22 18 24 SP SD: 0.8983 c. M: 1.5176 c. 258: 19 23 21 20 24 19 24 20 21 23 19 25 SP SD: 0.4282 c. M: 0.7235 c. 270: 20 24 22 21 25 20 25 21 22 24 20 26 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: 2.0886 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: 6.7641 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: 7.3956 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.7428 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.2961 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0062 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.7201 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.1509 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.7043 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.2228 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.1104 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.4200 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.0692 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.8144 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2260 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.3721 cents 32:34:36:38:40:43:45:48:51:53:57:60:64 SD: 2.7394 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.3887 cents 36:38:40:43:45:48:51:54:57:60:64:67:72 SD: 2.3656 cents 39:41:44:46:49:52:55:58:62:65:69:73:78 SD: 2.2207 cents 40:42:45:47:50:53:56:60:63:67:71:75:80 SD: 1.8529 cents 52:55:58:62:65:69:73:78:82:87:92:97:104 SD: 1.6991 cents 55:58:62:65:69:73:77:82:87:92:98:103:110 SD: 1.5619 cents 57:60:64:68:71:76:80:85:90:95:101:107:114 SD: 1.5169 cents 59:62:66:70:74:79:83:88:93:99:105:110:118 SD: 1.3415 cents 60:63:67:71:75:80:84:90:95:100:107:112:120 SD: 1.0838 cents 75:79:84:89:94:100:105:112:118:125:133:140:150 SD: 1.0236 cents 76:80:85:90:95:101:107:114:120:127:135:142:152 SD: 0.7815 cents 109:115:122:129:136:145:153:163:172:182:194:204:218 SD: 0.6255 cents 131:138:147:155:164:175:184:196:207:219:233:245:262 SD: 0.5615 cents 151:159:169:179:189:201:212:226:238:252:268:283:302 SD: 0.5567 cents 152:160:170:180:190:203:213:227:240:254:270:284:304 SD: 0.5113 cents 167:176:187:198:209:223:234:250:264:279:297:312:334 SD: 0.4943 cents 168:177:188:199:210:224:236:251:265:281:299:314:336 SD: 0.4505 cents 183:193:205:217:229:244:257:274:289:306:325:342:366 SD: 0.4208 cents 201:212:225:238:251:268:282:301:317:336:357:376:402 SD: 0.4208 cents 207:218:232:245:259:276:290:310:327:346:368:387:414 SD: 0.3822 cents 211:222:236:250:264:281:296:316:333:353:375:395:422 SD: 0.3515 cents 216:227:242:256:270:288:303:323:341:361:384:404:432 SD: 0.3068 cents 228:240:255:270:285:304:320:341:360:381:405:427:456 SD: 0.2473 cents 292:307:327:346:365:389:410:437:461:488:519:546:584 SD: 0.2470 cents 300:316:336:355:375:400:421:449:474:501:533:561:600 SD: 0.2387 cents 319:336:357:378:399:425:448:477:504:533:567:597:638 SD: 0.2290 cents 340:358:381:403:425:453:477:509:537:568:604:636:680 SD: 0.2104 cents 359:378:402:425:449:479:504:537:567:600:638:672:718 SD: 0.2033 cents 395:416:442:468:494:527:554:591:624:660:702:739:790 SD: 0.1875 cents 399:420:447:473:499:532:560:597:630:667:709:746:798 SD: 0.1855 cents 411:433:460:487:514:548:577:615:649:687:730:769:822 SD: 0.1782 cents 417:439:467:494:521:556:585:624:659:697:741:780:834 SD: 0.1629 cents 435:458:487:515:544:580:610:651:687:727:773:814:870 SD: 0.1561 cents 459:483:514:544:574:612:644:687:725:767:816:859:918 SD: 0.1296 cents 471:496:527:558:589:628:661:705:744:787:837:881:942 SD: 0.1273 cents 535:563:599:634:669:713:751:801:845:894:951:1001:1070 SD: 0.1273 cents 552:581:618:654:690:736:775:826:872:922:981:1033:1104 SD: 0.1162 cents 568:598:636:673:710:757:797:850:897:949:1009:1063:1136 SD: 0.1078 cents