Scala analysis: zest12-100-tET
100-tET/EDO version of Zest-12 circle (two in Zest-24)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 72.000 cents 72.000000 2: 192.000 cents 192.000000 3: 288.000 cents 288.000000 4: 384.000 cents 384.000000 5: 504.000 cents 504.000000 6: 576.000 cents 576.000000 7: 696.000 cents 696.000000 8: 780.000 cents 780.000000 9: 888.000 cents 888.000000 10: 996.000 cents 996.000000 11: 1080.000 cents 1080.000000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 120.0000 cents 120.0000 1: 72.0000 cents 72.0000 2: 120.0000 cents 120.0000 3: 96.0000 cents 96.0000 4: 96.0000 cents 96.0000 5: 120.0000 cents 120.0000 6: 72.0000 cents 72.0000 7: 120.0000 cents 120.0000 8: 84.0000 cents 84.0000 9: 108.0000 cents 108.0000 10: 108.0000 cents 108.0000 11: 84.0000 cents 84.0000 12: 120.0000 cents 120.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 72.00000 cents 1: 2 84.00000 cents 1: 2 96.00000 cents 1: 2 108.00000 cents 1: 4 120.00000 cents 2: 7 192.00000 cents 2: 2 204.00000 cents 2: 3 216.00000 cents 3: 2 276.00000 cents 3: 2 288.00000 cents 3: 2 300.00000 cents 3: 6 312.00000 cents 4: 5 384.00000 cents 4: 2 396.00000 cents 4: 2 408.00000 cents 4: 2 420.00000 cents 4: 1 432.00000 cents 5: 4 492.00000 cents 5: 8 504.00000 cents 6: 3 576.00000 cents 6: 2 588.00000 cents 6: 2 600.00000 cents 6: 2 612.00000 cents 6: 3 624.00000 cents 7: 8 696.00000 cents 7: 4 708.00000 cents 8: 1 768.00000 cents 8: 2 780.00000 cents 8: 2 792.00000 cents 8: 2 804.00000 cents 8: 5 816.00000 cents 9: 6 888.00000 cents 9: 2 900.00000 cents 9: 2 912.00000 cents 9: 2 924.00000 cents 10: 3 984.00000 cents 10: 2 996.00000 cents 10: 7 1008.00000 cents 11: 4 1080.00000 cents 11: 2 1092.00000 cents 11: 2 1104.00000 cents 11: 2 1116.00000 cents 11: 2 1128.00000 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.90909 = 43/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 72.0 192.0 288.0 384.0 504.0 576.0 696.0 780.0 888.0 996.0 1080.0 1200.0 72.0 : 120.0 216.0 312.0 432.0 504.0 624.0 708.0 816.0 924.0 1008.0 1128.0 1200.0 192.0 : 96.0 192.0 312.0 384.0 504.0 588.0 696.0 804.0 888.0 1008.0 1080.0 1200.0 288.0 : 96.0 216.0 288.0 408.0 492.0 600.0 708.0 792.0 912.0 984.0 1104.0 1200.0 384.0 : 120.0 192.0 312.0 396.0 504.0 612.0 696.0 816.0 888.0 1008.0 1104.0 1200.0 504.0 : 72.0 192.0 276.0 384.0 492.0 576.0 696.0 768.0 888.0 984.0 1080.0 1200.0 576.0 : 120.0 204.0 312.0 420.0 504.0 624.0 696.0 816.0 912.0 1008.0 1128.0 1200.0 696.0 : 84.0 192.0 300.0 384.0 504.0 576.0 696.0 792.0 888.0 1008.0 1080.0 1200.0 780.0 : 108.0 216.0 300.0 420.0 492.0 612.0 708.0 804.0 924.0 996.0 1116.0 1200.0 888.0 : 108.0 192.0 312.0 384.0 504.0 600.0 696.0 816.0 888.0 1008.0 1092.0 1200.0 996.0 : 84.0 204.0 276.0 396.0 492.0 588.0 708.0 780.0 900.0 984.0 1092.0 1200.0 1080.0: 120.0 192.0 312.0 408.0 504.0 624.0 696.0 816.0 900.0 1008.0 1116.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 72.0000 .. 120.0000 cents 48.00000 cents 72.00000 cents 2: 192.0000 .. 216.0000 cents 24.00000 cents 72.00000 cents 3: 276.0000 .. 312.0000 cents 36.00000 cents 60.00000 cents 4: 384.0000 .. 432.0000 cents 48.00000 cents 72.00000 cents 5: 492.0000 .. 504.0000 cents 12.00000 cents 60.00000 cents 6: 576.0000 .. 624.0000 cents 48.00000 cents 72.00000 cents 7: 696.0000 .. 708.0000 cents 12.00000 cents 72.00000 cents 8: 768.0000 .. 816.0000 cents 48.00000 cents 60.00000 cents 9: 888.0000 .. 924.0000 cents 36.00000 cents 72.00000 cents 10: 984.0000 .. 1008.0000 cents 24.00000 cents 60.00000 cents 11: 1080.0000 .. 1128.0000 cents 48.00000 cents 72.00000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 72.00000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 120.00000 cents Average / Smallest step : 1.388889 Largest / Average step : 1.200000 Largest / Smallest step : 1.666667 Median interval of one step : 102.00000 cents, amount: 0 Most common interval of one step : 120.00000 cents, amount: 4 Least squares average step : 98.73231 cents, oct.: 1184.78769 cents Scale is strictly proper Scale is a mode of a 100-tone equal temperament with octave 2/1 degrees: 6 16 24 32 42 48 58 65 74 83 90 100 Least number of segments generator : 63 of 756.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 63 of 756.000 cents and inv. generated superset size: 71 = 59 more = 591.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCCBABDEEDB Step pattern size order : AECCEAEBDDBE Interval vector is [ 0 0 0 0 0 2 2 2 2 4 0 0 0 0 0 7 2 3 0 0 0 0 2 2 2 6 0 0 0 0 0 5 2 2 2 1 0 0 0 0 4 8 0 0 0 0 0 3 2 1 ] Scale is a Constant Structure, by a margin of 60.00000 cents Scale diversity : 1.275736 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.680000 Rothenberg efficiency : 0.314478 redundancy: 0.685522 Efficiency x scale size : 3.773737 Number of different interval sizes : 43 = 3.90909 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 3.90909 = 43/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 12.00000 cents Most common intervals : 504.00000 cents & inv., amount: 8 Most common triad is 0.0 504.000 696.000 cents, amount: 7 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 48.0000 cents: 5 7 10 Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 9 -- 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: 15.3188 c. M:-28.0000 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 1 2 2 1 2 1 2 2 1 2 P M ME SD: 13.4646 c. M: 35.3684 c. 20: 1 2 2 1 2 2 2 1 2 2 1 2 P D3 SD: 16.9706 c. M:-24.0000 c. 21: 1 2 2 2 2 1 2 2 2 1 2 2 P D3 SD: 15.4515 c. M:-26.2857 c. 23: 1 3 2 1 3 1 2 2 2 2 2 2 P D3 SD: 14.6071 c. M:-25.0435 c. 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 9.2326 c. M: 19.0345 c. Schismic-12 31: 2 3 2 3 3 2 3 2 3 3 2 3 SP M ME SD: 6.5673 c. M: 17.0323 c. 38: 2 4 3 3 4 2 4 3 3 3 3 4 SP D3 S SD: 7.1872 c. M: 17.0526 c. 40: 2 4 4 3 4 2 4 3 4 3 3 4 SP SD: 7.9373 c. M:-12.0000 c. 43: 3 4 3 4 4 3 4 3 4 4 3 4 SP M ME SD: 6.7815 c. M:-11.7209 c. 46: 3 4 4 4 4 3 5 3 4 4 3 5 SP D3 S SD: 6.2209 c. M: 10.4348 c. 50: 3 5 4 4 5 3 5 4 4 5 3 5 SP D3 SD: 4.8990 c. M:-12.0000 c. 54: 3 6 4 4 6 3 5 4 5 5 4 5 SP S SD: 5.2993 c. M:-8.8889 c. 57: 3 6 4 5 6 3 6 4 5 5 4 6 SP SD: 6.2824 c. M: 14.3158 c. 58: 3 6 5 5 5 4 6 4 5 5 4 6 SP SD: 5.8201 c. M: 9.9310 c. 60: 4 6 4 5 6 4 6 4 5 6 4 6 SP T3 SD: 5.2915 c. M: 8.0000 c. 62: 4 6 5 5 6 4 6 4 6 5 5 6 SP D3 SD: 4.1119 c. M: 8.9032 c. 66: 4 7 5 5 7 4 6 5 6 6 4 7 SP SD: 4.5102 c. M:-8.0000 c. 69: 4 7 6 5 7 4 7 5 6 6 5 7 SP SD: 2.9505 c. M:-7.6522 c. 79: 5 8 6 6 8 5 8 5 7 8 5 8 SP SD: 4.1074 c. M: 6.9873 c. 81: 5 8 6 7 8 5 8 6 7 7 6 8 SP SD: 2.7894 c. M: 6.5185 c. 82: 5 8 7 6 8 5 9 5 8 7 6 8 SP SD: 4.0819 c. M:-6.4390 c. 83: 5 8 7 7 8 5 8 6 7 8 6 8 SP SD: 3.2985 c. M:-6.3614 c. 84: 5 8 7 7 8 5 9 6 7 8 6 8 SP SD: 3.9521 c. M: 6.2857 c. 88: 5 9 7 7 9 5 9 6 8 8 6 9 SP S SD: 2.0889 c. M: 3.8182 c. 100: 6 10 8 8 10 6 10 7 9 9 7 10 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: 2.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.3267 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.9787 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.8135 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.3885 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.7593 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 7.7584 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 8.3714 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.6964 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.5767 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.0644 cents 13:14 x 15:16:17:18:19:20:22:23:24:26 S SD: 9.4223 cents 14:15:16 x 17:19:20:21:22:23:25:26:28 SD: 8.8113 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 6.6498 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.4341 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.3520 cents 18:19:20:21:22:24:25:27:28:30:32:34:36 SD: 4.6785 cents 21:22:23:25:26:28:29:31:33:35:37:39:42 SD: 4.4012 cents 23:24:26:27:29:31:32:34:36:38:41:43:46 SD: 3.5154 cents 27:28:30:32:34:36:38:40:42:45:48:50:54 SD: 3.0927 cents 28:29:31:33:35:37:39:42:44:47:50:52:56 SD: 2.7733 cents 33:34:37:39:41:44:46:49:52:55:59:62:66 SD: 2.6250 cents 40:42:45:47:50:54:56:60:63:67:71:75:80 SD: 2.4171 cents 43:45:48:51:54:58:60:64:67:72:76:80:86 SD: 2.2965 cents 44:46:49:52:55:59:61:66:69:73:78:82:88 SD: 1.6356 cents 45:47:50:53:56:60:63:67:71:75:80:84:90 SD: 1.6315 cents 51:53:57:60:64:68:71:76:80:85:91:95:102 SD: 1.4333 cents 67:70:75:79:84:90:93:100:105:112:119:125:134 SD: 1.2439 cents 68:71:76:80:85:91:95:102:107:114:121:127:136 SD: 1.0917 cents 76:79:85:90:95:102:106:114:119:127:135:142:152 SD: 0.9905 cents 77:80:86:91:96:103:107:115:121:129:137:144:154 SD: 0.9681 cents 89:93:99:105:111:119:124:133:140:149:158:166:178 SD: 0.9405 cents 93:97:104:110:116:124:130:139:146:155:165:174:186 SD: 0.8685 cents 109:114:122:129:136:146:152:163:171:182:194:203:218 SD: 0.7270 cents 112:117:125:132:140:150:156:167:176:187:199:209:224 SD: 0.6953 cents 121:126:135:143:151:162:169:181:190:202:215:226:242 SD: 0.4186 cents 172:179:192:203:215:230:240:257:270:287:306:321:344 SD: 0.4137 cents 188:196:210:222:235:252:262:281:295:314:334:351:376 SD: 0.3720 cents 210:219:235:248:262:281:293:314:330:351:373:392:420 SD: 0.3706 cents 216:225:241:255:270:289:301:323:339:361:384:403:432 SD: 0.3486 cents 230:240:257:272:287:308:321:344:361:384:409:429:460 SD: 0.3230 cents 237:247:265:280:296:317:331:354:372:396:421:442:474 SD: 0.3129 cents 255:266:285:301:318:341:356:381:400:426:453:476:510 SD: 0.2876 cents 281:293:314:332:351:376:392:420:441:469:500:524:562 SD: 0.2309 cents 350:365:391:413:437:468:488:523:549:585:622:653:700 SD: 0.2203 cents 358:373:400:423:447:479:499:535:562:598:636:668:716 SD: 0.1876 cents 382:398:427:451:477:511:533:571:599:638:679:713:764 SD: 0.1736 cents 418:436:467:494:522:559:583:625:656:698:743:780:836 SD: 0.1640 cents 471:491:526:556:588:630:657:704:739:787:837:879:942 SD: 0.1323 cents 536:559:599:633:669:717:748:801:841:895:953:1000:1072 SD: 0.1313 cents 580:605:648:685:724:776:809:867:910:969:1031:1082:1160 SD: 0.1102 cents