Scala analysis: xen18-erlich-dimipent-12
8L 4s MOS for Dimipent, L=101.67, s=95.82
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 101.670 cents 101.670000 2: 197.490 cents 197.490000 3: 299.160 cents 299.160000 4: 400.830 cents 400.830000 5: 496.650 cents 496.650000 6: 598.320 cents 598.320000 7: 699.990 cents 699.990000 8: 795.810 cents 795.810000 9: 897.480 cents 897.480000 10: 999.150 cents 999.150000 11: 1094.970 cents 1094.970000 12: 1196.640 cents 1196.640000
SHOW/INTERVAL
0: 101.6700 cents 101.6700 1: 101.6700 cents 101.6700 2: 95.8200 cents 95.8200 3: 101.6700 cents 101.6700 4: 101.6700 cents 101.6700 5: 95.8200 cents 95.8200 6: 101.6700 cents 101.6700 7: 101.6700 cents 101.6700 8: 95.8200 cents 95.8200 9: 101.6700 cents 101.6700 10: 101.6700 cents 101.6700 11: 95.8200 cents 95.8200 12: 101.6700 cents 101.6700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 95.82000 cents 1: 8 101.67000 cents 2: 8 197.49000 cents 2: 4 203.34000 cents 3: 12 299.16000 cents 4: 4 394.98000 cents 4: 8 400.83000 cents 5: 8 496.65000 cents 5: 4 502.50000 cents 6: 12 598.32000 cents 7: 4 694.14000 cents 7: 8 699.99000 cents 8: 8 795.81000 cents 8: 4 801.66000 cents 9: 12 897.48000 cents 10: 4 993.30000 cents 10: 8 999.15000 cents 11: 8 1094.97000 cents 11: 4 1100.82000 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 : 101.7 197.5 299.2 400.8 496.6 598.3 700.0 795.8 897.5 999.1 1095.0 1196.6 101.7 : 95.8 197.5 299.2 395.0 496.7 598.3 694.1 795.8 897.5 993.3 1095.0 1196.6 197.5 : 101.7 203.3 299.2 400.8 502.5 598.3 700.0 801.7 897.5 999.1 1100.8 1196.6 299.2 : 101.7 197.5 299.2 400.8 496.6 598.3 700.0 795.8 897.5 999.1 1095.0 1196.6 400.8 : 95.8 197.5 299.2 395.0 496.7 598.3 694.1 795.8 897.5 993.3 1095.0 1196.6 496.6 : 101.7 203.3 299.2 400.8 502.5 598.3 700.0 801.7 897.5 999.2 1100.8 1196.6 598.3 : 101.7 197.5 299.2 400.8 496.6 598.3 700.0 795.8 897.5 999.1 1095.0 1196.6 700.0 : 95.8 197.5 299.2 395.0 496.6 598.3 694.1 795.8 897.5 993.3 1095.0 1196.6 795.8 : 101.7 203.3 299.2 400.8 502.5 598.3 700.0 801.7 897.5 999.2 1100.8 1196.6 897.5 : 101.7 197.5 299.2 400.8 496.6 598.3 700.0 795.8 897.5 999.1 1095.0 1196.6 999.1 : 95.8 197.5 299.2 395.0 496.7 598.3 694.1 795.8 897.5 993.3 1095.0 1196.6 1095.0: 101.7 203.3 299.2 400.8 502.5 598.3 700.0 801.7 897.5 999.2 1100.8 1196.6 1196.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 95.8200 .. 101.6700 cents 5.85000 cents 95.82000 cents 2: 197.4900 .. 203.3400 cents 5.85000 cents 95.82000 cents 3: 299.1600 .. 299.1600 cents 1/1, 0.0000 cents 95.82000 cents 4: 394.9800 .. 400.8300 cents 5.85000 cents 95.82000 cents 5: 496.6500 .. 502.5000 cents 5.85000 cents 95.82000 cents 6: 598.3200 .. 598.3200 cents 1/1, 0.0000 cents 95.82000 cents 7: 694.1400 .. 699.9900 cents 5.85000 cents 95.82000 cents 8: 795.8100 .. 801.6600 cents 5.85000 cents 95.82000 cents 9: 897.4800 .. 897.4800 cents 1/1, 0.0000 cents 95.82000 cents 10: 993.3000 .. 999.1500 cents 5.85000 cents 95.82000 cents 11: 1094.9700 .. 1100.8200 cents 5.85000 cents 95.82000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 95.82000 cents, class 1 Average step (divided formal octave): 99.7200 cents Largest one step interval : 101.67000 cents Average / Smallest step : 1.040701 Largest / Average step : 1.019555 Largest / Smallest step : 1.061052 Median interval of one step : 101.67000 cents, amount: 8 Most common interval of one step : 101.67000 cents, amount: 8 Least squares average step : 99.70800 cents, oct.: 1196.49600 cents Scale is strictly proper Scale has 4 repeating blocks of 3 notes Blocks have Myhill's property chromas: 5.85000 cents and 89.97000 cents, ratio: 15.379487 generators: 1 of 101.67000 cents and 2 of 197.49000 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 612-tone equal temperament with octave 1196.640 cents degrees: 52 101 153 205 254 306 358 407 459 511 560 612 Least number of segments generator : 307 of 600.275 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 407 of 795.805 cents and inv. generated superset size: 462 = 450 more = 3850.000% 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 95.82000 cents Scale diversity : 1.033416 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.960890 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 : 5.85000 cents Most common triad is 0.0 299.160 598.320 cents, amount: 12 Number of recognisable fifths : 12, average 698.0400 cents Number of recognisable fourths : 12, average 498.6000 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: 1.5922 c. M:-1.9500 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: 1.5394 c. M: 1.8854 c. 116: 10 9 10 10 9 10 10 9 10 10 9 10 SP B ME I SD: 1.2155 c. M:-1.4886 c. 128: 11 10 11 11 10 11 11 10 11 11 10 11 SP B ME I SD: 0.9522 c. M:-1.1663 c. 140: 12 11 12 12 11 12 12 11 12 12 11 12 SP B ME I SD: 0.7341 c. M: 0.8991 c. 152: 13 12 13 13 12 13 13 12 13 13 12 13 SP B ME I SD: 0.5505 c. M: 0.6742 c. 164: 14 13 14 14 13 14 14 13 14 14 13 14 SP B ME I SD: 0.3937 c. M:-0.4822 c. 176: 15 14 15 15 14 15 15 14 15 15 14 15 SP B ME I SD: 0.2583 c. M:-0.3164 c. 188: 16 15 16 16 15 16 16 15 16 16 15 16 SP B ME I SD: 0.1402 c. M: 0.1717 c. 200: 17 16 17 17 16 17 17 16 17 17 16 17 SP B ME I SD: 0.0363 c. M:-0.0444 c. 412: 35 33 35 35 33 35 35 33 35 35 33 35 SP B DE I SD: 0.0112 c. M:-0.0137 c. 612: 52 49 52 52 49 52 52 49 52 52 49 52 SP B DE I SD: 0.0043 c. M:-0.0053 c. 1024: 87 82 87 87 82 87 87 82 87 87 82 87 SP B DE I SD: 0.0019 c. M:-0.0023 c. 1636: 139 131 139 139 131 139 139 131 139 139 131 139 SP B DE I SD: 0.0004 c. M: 0.0005 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 3.3600 cents 2 x x x x x x 3 x x x x 4 S SD: 1.9462 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.5388 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.4610 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.9069 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.5915 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.7691 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.2199 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.0187 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9021 cents 11 x 12:13:14:15:16 x 17:18:20:21:22 S SD: 11.1456 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.2514 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.8261 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.1738 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.9157 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.8729 cents 19:20:21:23:24:25:27:28:30:32:34:36:38 SD: 4.8677 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.0492 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.5449 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2239 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.5621 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.3654 cents 34:36:38:40:43:45:48:51:54:57:61:64:68 SD: 2.2454 cents 43:46:48:51:54:57:61:64:68:72:77:81:86 SD: 2.2449 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 2.0035 cents 48:51:54:57:61:64:68:72:76:81:85:90:96 SD: 1.8719 cents 49:52:55:58:62:65:69:73:78:82:87:92:98 SD: 1.7966 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.6140 cents 58:62:65:69:73:77:82:87:92:97:103:109:116 SD: 1.5458 cents 60:64:67:71:76:80:85:90:95:101:107:113:120 SD: 1.5271 cents 65:69:73:77:82:87:92:97:103:109:116:122:130 SD: 1.2627 cents 68:72:76:81:86:91:96:102:108:114:121:128:136 SD: 1.1553 cents 81:86:91:96:102:108:114:121:128:136:144:152:162 SD: 1.1297 cents 82:87:92:97:103:109:116:123:130:138:146:154:164 SD: 1.1116 cents 84:89:94:100:106:112:119:126:133:141:150:158:168 SD: 0.7625 cents 100:106:112:119:126:133:141:150:158:168:178:188:200 SD: 0.6644 cents 133:141:149:158:168:177:188:199:211:223:237:250:265 SD: 0.6399 cents 147:156:165:175:185:196:208:220:233:247:262:277:293 SD: 0.5927 cents 150:159:168:178:189:200:212:225:238:252:267:282:299 SD: 0.5281 cents 165:175:185:196:208:220:233:247:261:277:294:311:329 SD: 0.3783 cents 196:208:220:233:247:261:277:294:310:329:349:369:391 SD: 0.3645 cents 233:247:261:277:294:310:329:349:369:391:415:439:465 SD: 0.3336 cents 247:262:277:294:311:329:349:370:391:415:440:465:493 SD: 0.2927 cents 249:264:279:296:314:332:352:373:394:418:443:469:497 SD: 0.2733 cents 265:281:297:315:334:353:374:397:420:445:472:499:529 SD: 0.2101 cents 346:367:388:411:436:461:489:518:548:581:616:651:691 SD: 0.2088 cents 349:370:391:415:440:465:493:523:553:586:622:657:697 SD: 0.1911 cents 365:387:409:434:460:486:516:547:578:613:650:687:729 SD: 0.1667 cents 446:473:500:530:562:594:630:668:706:749:794:839:890 SD: 0.1591 cents 461:489:517:548:581:614:651:691:730:774:821:868:920 SD: 0.1522 cents 499:529:559:593:629:665:705:748:790:838:889:939:996 SD: 0.1462 cents 514:545:576:611:648:685:726:770:814:863:915:967:1026 SD: 0.1275 cents 530:562:594:630:668:706:749:794:839:890:944:998:1058 SD: 0.0944 cents