Scala analysis: xen18-erlich-dimisept-12
8L 4s MOS for Dimisept, L=101.45, s=95.63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 101.450 cents 101.450000 2: 197.080 cents 197.080000 3: 298.530 cents 298.530000 4: 399.980 cents 399.980000 5: 495.610 cents 495.610000 6: 597.060 cents 597.060000 7: 698.510 cents 698.510000 8: 794.140 cents 794.140000 9: 895.590 cents 895.590000 10: 997.040 cents 997.040000 11: 1092.670 cents 1092.670000 12: 1194.120 cents 1194.120000
SHOW/INTERVAL
0: 101.4500 cents 101.4500 1: 101.4500 cents 101.4500 2: 95.6300 cents 95.6300 3: 101.4500 cents 101.4500 4: 101.4500 cents 101.4500 5: 95.6300 cents 95.6300 6: 101.4500 cents 101.4500 7: 101.4500 cents 101.4500 8: 95.6300 cents 95.6300 9: 101.4500 cents 101.4500 10: 101.4500 cents 101.4500 11: 95.6300 cents 95.6300 12: 101.4500 cents 101.4500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 95.63000 cents 1: 8 101.45000 cents 2: 8 197.08000 cents 2: 4 202.90000 cents 3: 12 298.53000 cents 4: 4 394.16000 cents 4: 8 399.98000 cents 5: 8 495.61000 cents 5: 4 501.43000 cents 6: 12 597.06000 cents 7: 4 692.69000 cents 7: 8 698.51000 cents 8: 8 794.14000 cents 8: 4 799.96000 cents 9: 12 895.59000 cents 10: 4 991.22000 cents 10: 8 997.04000 cents 11: 8 1092.67000 cents 11: 4 1098.49000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.72727 = 19/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 101.5 197.1 298.5 400.0 495.6 597.1 698.5 794.1 895.6 997.0 1092.7 1194.1 101.5 : 95.6 197.1 298.5 394.2 495.6 597.1 692.7 794.1 895.6 991.2 1092.7 1194.1 197.1 : 101.4 202.9 298.5 400.0 501.4 597.1 698.5 800.0 895.6 997.0 1098.5 1194.1 298.5 : 101.5 197.1 298.5 400.0 495.6 597.1 698.5 794.1 895.6 997.0 1092.7 1194.1 400.0 : 95.6 197.1 298.5 394.2 495.6 597.1 692.7 794.1 895.6 991.2 1092.7 1194.1 495.6 : 101.4 202.9 298.5 400.0 501.4 597.1 698.5 800.0 895.6 997.0 1098.5 1194.1 597.1 : 101.5 197.1 298.5 400.0 495.6 597.1 698.5 794.1 895.6 997.0 1092.7 1194.1 698.5 : 95.6 197.1 298.5 394.2 495.6 597.1 692.7 794.1 895.6 991.2 1092.7 1194.1 794.1 : 101.5 202.9 298.5 400.0 501.4 597.1 698.5 800.0 895.6 997.0 1098.5 1194.1 895.6 : 101.4 197.1 298.5 400.0 495.6 597.1 698.5 794.1 895.6 997.0 1092.7 1194.1 997.0 : 95.6 197.1 298.5 394.2 495.6 597.1 692.7 794.1 895.6 991.2 1092.7 1194.1 1092.7: 101.5 202.9 298.5 400.0 501.4 597.1 698.5 800.0 895.6 997.0 1098.5 1194.1 1194.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 95.6300 .. 101.4500 cents 5.82000 cents 95.63000 cents 2: 197.0800 .. 202.9000 cents 5.82000 cents 95.63000 cents 3: 298.5300 .. 298.5300 cents 1/1, 0.0000 cents 95.63000 cents 4: 394.1600 .. 399.9800 cents 5.82000 cents 95.63000 cents 5: 495.6100 .. 501.4300 cents 5.82000 cents 95.63000 cents 6: 597.0600 .. 597.0600 cents 1/1, 0.0000 cents 95.63000 cents 7: 692.6900 .. 698.5100 cents 5.82000 cents 95.63000 cents 8: 794.1400 .. 799.9600 cents 5.82000 cents 95.63000 cents 9: 895.5900 .. 895.5900 cents 1/1, 0.0000 cents 95.63000 cents 10: 991.2200 .. 997.0400 cents 5.82000 cents 95.63000 cents 11: 1092.6700 .. 1098.4900 cents 5.82000 cents 95.63000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 95.63000 cents, class 1 Average step (divided formal octave): 99.5100 cents Largest one step interval : 101.45000 cents Average / Smallest step : 1.040573 Largest / Average step : 1.019496 Largest / Smallest step : 1.060860 Median interval of one step : 101.45000 cents, amount: 8 Most common interval of one step : 101.45000 cents, amount: 8 Least squares average step : 99.49806 cents, oct.: 1193.97674 cents Scale is strictly proper Scale has 4 repeating blocks of 3 notes Blocks have Myhill's property chromas: 5.82000 cents and 89.81000 cents, ratio: 15.431271 generators: 1 of 101.45000 cents and 2 of 197.08000 cents ET pair of linear temperament : 200&412 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1024-tone equal temperament with octave 1194.120 cents degrees: 87 169 256 343 425 512 599 681 768 855 937 1024 Least number of segments generator : 513 of 598.226 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 599 of 698.514 cents and inv. generated superset size: 771 = 759 more = 6425.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABAABA Step pattern size order : LSLLSLLSLLSL Scale is a Constant Structure, by a margin of 95.63000 cents Scale diversity : 1.035006 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.961009 Rothenberg efficiency (ambiguous key): 0.312963 redundancy: 0.687037 Efficiency x scale size : 3.755556 Number of different interval sizes : 19 = 1.72727 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.72727 = 19/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 5.82000 cents Most common triad is 0.0 298.530 597.060 cents, amount: 12 Number of recognisable fifths : 12, average 696.5700 cents Number of recognisable fourths : 12, average 497.5500 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 12 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 3 6 9 Limited inverse transpositions : 3 6 9 Inversional symmetry on degrees : 0 3 6 9 Inversional symmetry on intervals : 1-2 4-5 7-8 10-11 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 1.5840 c. M: 1.9400 c. Twelve-tone Chromatic (1/11-comma) 104: 9 8 9 9 8 9 9 8 9 9 8 9 SP B ME I SD: 1.5410 c. M: 1.8873 c. 116: 10 9 10 10 9 10 10 9 10 10 9 10 SP B ME I SD: 1.2177 c. M: 1.4914 c. 128: 11 10 11 11 10 11 11 10 11 11 10 11 SP B ME I SD: 0.9550 c. M: 1.1697 c. 140: 12 11 12 12 11 12 12 11 12 12 11 12 SP B ME I SD: 0.7374 c. M: 0.9031 c. 152: 13 12 13 13 12 13 13 12 13 13 12 13 SP B ME I SD: 0.5541 c. M: 0.6787 c. 164: 14 13 14 14 13 14 14 13 14 14 13 14 SP B ME I SD: 0.3977 c. M: 0.4871 c. 176: 15 14 15 15 14 15 15 14 15 15 14 15 SP B ME I SD: 0.2626 c. M: 0.3216 c. 188: 16 15 16 16 15 16 16 15 16 16 15 16 SP B ME I SD: 0.1447 c. M: 0.1772 c. 200: 17 16 17 17 16 17 17 16 17 17 16 17 SP B ME I SD: 0.0410 c. M: 0.0502 c. 412: 35 33 35 35 33 35 35 33 35 35 33 35 SP B DE I SD: 0.0063 c. M: 0.0078 c. 1024: 87 82 87 87 82 87 87 82 87 87 82 87 SP B DE I SD: 0.0029 c. M: 0.0036 c. 1436: 122 115 122 122 115 122 122 115 122 122 115 122 SP B DE I SD: 0.0003 c. M: 0.0003 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 5.8800 cents 2 x x x x x x 3 x x x x 4 S SD: 3.4074 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.3030 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.0205 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.3311 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2140 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.9294 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.1339 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.0592 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0517 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.1469 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2399 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.7027 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.2731 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.8989 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.7637 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0056 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.6794 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.1807 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.4406 cents 34:36:38:40:43:45:48:51:54:57:60:64:68 SD: 2.2963 cents 43:46:48:51:54:57:61:64:68:72:76:81:86 SD: 2.2495 cents 46:49:52:55:58:61:65:69:73:77:82:86:92 SD: 2.1334 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.9022 cents 49:52:55:58:62:65:69:73:78:82:87:92:98 SD: 1.7095 cents 58:62:65:69:73:77:82:87:92:97:103:109:116 SD: 1.5328 cents 64:68:72:76:81:85:90:96:101:107:114:120:128 SD: 1.4698 cents 65:69:73:77:82:87:92:97:103:109:116:122:130 SD: 1.3557 cents 66:70:74:78:83:88:93:99:104:111:117:124:132 SD: 1.3547 cents 69:73:77:82:87:92:97:103:109:116:123:130:138 SD: 1.2858 cents 81:86:91:96:102:108:114:121:128:136:144:152:161 SD: 0.9620 cents 84:89:94:100:106:112:119:126:133:141:149:158:167 SD: 0.9370 cents 99:105:111:118:125:132:140:148:157:166:176:186:197 SD: 0.8006 cents 100:106:112:119:126:133:141:150:158:168:178:188:199 SD: 0.5852 cents 117:124:131:139:147:156:165:175:185:196:208:220:233 SD: 0.5759 cents 139:147:156:165:175:185:196:208:220:233:247:261:277 SD: 0.5713 cents 148:157:166:176:186:197:209:222:234:248:263:278:295 SD: 0.5623 cents 149:158:167:177:188:198:210:223:236:250:265:280:297 SD: 0.4692 cents 165:175:185:196:208:220:233:247:261:277:293:310:329 SD: 0.3716 cents 199:211:223:236:251:265:281:298:315:334:354:374:397 SD: 0.3662 cents 235:249:263:279:296:313:332:352:372:394:418:442:468 SD: 0.3386 cents 250:265:280:297:315:333:353:374:396:419:445:470:498 SD: 0.2985 cents 265:281:297:315:334:353:374:397:419:445:471:498:528 SD: 0.2674 cents 266:282:298:316:335:354:376:398:421:446:473:500:530 SD: 0.2468 cents 308:327:345:366:388:410:435:461:487:517:548:579:614 SD: 0.2404 cents 316:335:354:375:398:421:446:473:500:530:562:594:630 SD: 0.2243 cents 347:368:389:412:437:462:490:519:549:582:617:652:692 SD: 0.2230 cents 350:371:392:416:441:466:494:524:554:587:623:658:698 SD: 0.1861 cents 366:388:410:435:461:487:517:548:579:614:651:688:730 SD: 0.1750 cents 416:441:466:494:524:554:587:623:658:698:740:782:829 SD: 0.1570 cents 447:474:501:531:563:595:631:669:707:750:795:840:891 SD: 0.1085 cents