Scala analysis: xen18-erlich-august-12
9L 3s MOS for August, L=107.31, s=78.06
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 107.310 cents 107.310000 2: 185.370 cents 185.370000 3: 292.680 cents 292.680000 4: 399.990 cents 399.990000 5: 507.300 cents 507.300000 6: 585.360 cents 585.360000 7: 692.670 cents 692.670000 8: 799.980 cents 799.980000 9: 907.290 cents 907.290000 10: 985.350 cents 985.350000 11: 1092.660 cents 1092.660000 12: 1199.970 cents 1199.970000
SHOW/INTERVAL
0: 107.3100 cents 107.3100 1: 107.3100 cents 107.3100 2: 78.0600 cents 78.0600 3: 107.3100 cents 107.3100 4: 107.3100 cents 107.3100 5: 107.3100 cents 107.3100 6: 78.0600 cents 78.0600 7: 107.3100 cents 107.3100 8: 107.3100 cents 107.3100 9: 107.3100 cents 107.3100 10: 78.0600 cents 78.0600 11: 107.3100 cents 107.3100 12: 107.3100 cents 107.3100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 78.06000 cents 1: 9 107.31000 cents 2: 6 185.37000 cents 2: 6 214.62000 cents 3: 9 292.68000 cents 3: 3 321.93000 cents 4: 12 399.99000 cents 5: 3 478.05000 cents 5: 9 507.30000 cents 6: 6 585.36000 cents 6: 6 614.61000 cents 7: 9 692.67000 cents 7: 3 721.92000 cents 8: 12 799.98000 cents 9: 3 878.04000 cents 9: 9 907.29000 cents 10: 6 985.35000 cents 10: 6 1014.60000 cents 11: 9 1092.66000 cents 11: 3 1121.91000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.81818 = 20/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 107.3 185.4 292.7 400.0 507.3 585.4 692.7 800.0 907.3 985.4 1092.7 1200.0 107.3 : 78.1 185.4 292.7 400.0 478.1 585.4 692.7 800.0 878.0 985.4 1092.7 1200.0 185.4 : 107.3 214.6 321.9 400.0 507.3 614.6 721.9 800.0 907.3 1014.6 1121.9 1200.0 292.7 : 107.3 214.6 292.7 400.0 507.3 614.6 692.7 800.0 907.3 1014.6 1092.7 1200.0 400.0 : 107.3 185.4 292.7 400.0 507.3 585.4 692.7 800.0 907.3 985.4 1092.7 1200.0 507.3 : 78.1 185.4 292.7 400.0 478.1 585.4 692.7 800.0 878.0 985.4 1092.7 1200.0 585.4 : 107.3 214.6 321.9 400.0 507.3 614.6 721.9 800.0 907.3 1014.6 1121.9 1200.0 692.7 : 107.3 214.6 292.7 400.0 507.3 614.6 692.7 800.0 907.3 1014.6 1092.7 1200.0 800.0 : 107.3 185.4 292.7 400.0 507.3 585.4 692.7 800.0 907.3 985.4 1092.7 1200.0 907.3 : 78.1 185.4 292.7 400.0 478.1 585.4 692.7 800.0 878.0 985.4 1092.7 1200.0 985.4 : 107.3 214.6 321.9 400.0 507.3 614.6 721.9 800.0 907.3 1014.6 1121.9 1200.0 1092.7: 107.3 214.6 292.7 400.0 507.3 614.6 692.7 800.0 907.3 1014.6 1092.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.0600 .. 107.3100 cents 29.25000 cents 78.06000 cents 2: 185.3700 .. 214.6200 cents 29.25000 cents 78.06000 cents 3: 292.6800 .. 321.9300 cents 29.25000 cents 78.06000 cents 4: 399.9900 .. 399.9900 cents 1/1, 0.0000 cents 78.06000 cents 5: 478.0500 .. 507.3000 cents 29.25000 cents 78.06000 cents 6: 585.3600 .. 614.6100 cents 29.25000 cents 78.06000 cents 7: 692.6700 .. 721.9200 cents 29.25000 cents 78.06000 cents 8: 799.9800 .. 799.9800 cents 1/1, 0.0000 cents 78.06000 cents 9: 878.0400 .. 907.2900 cents 29.25000 cents 78.06000 cents 10: 985.3500 .. 1014.6000 cents 29.25000 cents 78.06000 cents 11: 1092.6600 .. 1121.9100 cents 29.25000 cents 78.06000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 78.06000 cents, class 1 Average step (divided formal octave): 99.9975 cents Largest one step interval : 107.31000 cents Average / Smallest step : 1.281034 Largest / Average step : 1.073127 Largest / Smallest step : 1.374712 Median interval of one step : 107.31000 cents, amount: 9 Most common interval of one step : 107.31000 cents, amount: 9 Least squares average step : 99.52500 cents, oct.: 1194.30000 cents Scale is strictly proper Scale has 3 repeating blocks of 4 notes Blocks have Myhill's property chromas: 29.25000 cents and 48.81000 cents, ratio: 1.668718 generators: 1 of 107.31000 cents and 3 of 292.68000 cents ET pair of linear temperament : 33&45 Scale is maximally even for L / S <= 2 Scale is distributional even Step pattern alph. order: ABAAABAAABAA Step pattern size order : LSLLLSLLLSLL Scale is a Constant Structure, by a margin of 78.06000 cents Scale diversity : 1.159068 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.780620 Rothenberg efficiency (ambiguous key): 0.386905 redundancy: 0.613095 Efficiency x scale size : 4.642857 Number of different interval sizes : 20 = 1.81818 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.81818 = 20/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 29.25000 cents Most common intervals : 399.99000 cents & inv., amount: 12 Most common triad is 0.0 399.990 799.980 cents, amount: 12 Number of recognisable fifths : 9, average 692.6700 cents Number of recognisable fourths : 9, average 507.3000 cents Best fifths form a closed circle Formal octave complements present : 9 = 75.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 4 8 Limited inverse transpositions : 3 7 11 Inversional symmetry on intervals : 1-2 3-4 5-6 7-8 9-10 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.9559 c. M:-14.6250 c. Twelve-tone Chromatic (1/11-comma) 21: 2 1 2 2 2 1 2 2 2 1 2 2 SP B ME SD: 8.5400 c. M: 13.9457 c. Twelve-tone Chromatic 33: 3 2 3 3 3 2 3 3 3 2 3 3 SP B ME SD: 2.1778 c. M: 3.5564 c. 45: 4 3 4 4 4 3 4 4 4 3 4 4 SP B ME SD: 0.7912 c. M:-1.2920 c. 78: 7 5 7 7 7 5 7 7 7 5 7 7 SP B DE SD: 0.4649 c. M: 0.7592 c. 123: 11 8 11 11 11 8 11 11 11 8 11 11 SP B DE SD: 0.0054 c. M: 0.0088 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0300 cents 2 x x x x x x 3 x x x x 4 S SD: 4.6425 cents 3 x x x x 4 x x x 5 x x 6 S SD: 8.2428 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 5.8433 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.3977 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.4846 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.8558 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.6161 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 9.5760 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4530 cents 11 x 12:13:14:15 x 16:17:19 x 21:22 SD: 10.3751 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.9370 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 8.9101 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.7700 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.5804 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.3883 cents 17:18:19:20:21:23:24:25:27:29:30:32:34 SD: 4.3660 cents 26:28:29:31:33:35:36:39:41:44:46:49:52 SD: 3.2790 cents 27:29:30:32:34:36:38:40:43:46:48:51:54 SD: 2.6375 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.5766 cents 34:36:38:40:43:46:48:51:54:57:60:64:68 SD: 2.5619 cents 35:37:39:41:44:47:49:52:56:59:62:66:70 SD: 2.3764 cents 42:45:47:50:53:56:59:63:67:71:74:79:84 SD: 2.0532 cents 43:46:48:51:54:58:60:64:68:73:76:81:86 SD: 1.8609 cents 47:50:52:56:59:63:66:70:75:79:83:88:94 SD: 1.8141 cents 53:56:59:63:67:71:74:79:84:90:94:100:106 SD: 1.7936 cents 55:59:61:65:69:74:77:82:87:93:97:103:110 SD: 1.7683 cents 59:63:66:70:74:79:83:88:94:100:104:111:118 SD: 1.4866 cents 61:65:68:72:77:82:86:91:97:103:108:115:122 SD: 1.2211 cents 65:69:72:77:82:87:91:97:103:110:115:122:130 SD: 0.9814 cents 77:82:86:91:97:103:108:115:122:130:136:145:154 SD: 0.7815 cents 97:103:108:115:122:130:136:145:154:164:171:182:194 SD: 0.6705 cents 124:132:138:147:156:166:174:185:197:209:219:233:248 SD: 0.4760 cents 141:150:157:167:178:189:198:210:224:238:249:265:282 SD: 0.4641 cents 142:151:158:168:179:190:199:212:225:240:251:267:284 SD: 0.4520 cents 158:168:176:187:199:212:222:236:251:267:279:297:316 SD: 0.4270 cents 185:197:206:219:233:248:259:276:294:312:327:348:370 SD: 0.4058 cents 189:201:210:224:238:253:265:282:300:319:334:355:378 SD: 0.3840 cents 218:232:243:258:275:292:306:325:346:368:385:410:436 SD: 0.3815 cents 223:237:248:264:281:299:313:333:354:377:394:419:446 SD: 0.3168 cents 238:253:265:282:300:319:334:355:378:402:420:447:476 SD: 0.3065 cents 250:266:278:296:315:335:351:373:397:422:442:470:500 SD: 0.2650 cents 266:283:296:315:335:357:373:397:422:449:470:500:532 SD: 0.2251 cents 293:312:326:347:369:393:411:437:465:495:518:551:586 SD: 0.2205 cents 343:365:382:406:432:460:481:512:544:579:606:645:686 SD: 0.2202 cents 347:369:386:411:437:465:487:518:551:586:613:652:694 SD: 0.2137 cents 373:397:415:442:470:500:523:557:592:630:659:701:746 SD: 0.1835 cents 390:415:434:462:491:523:547:582:619:659:689:733:780 SD: 0.1635 cents 408:434:454:483:514:547:572:609:648:689:721:767:816 SD: 0.1322 cents 531:565:591:629:669:712:745:792:843:897:938:998:1062 SD: 0.1163 cents