Scala analysis: xen18-erlich-augene-12
3L 9s MOS for Augene, L=121.64, s=92.46
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92.460 cents 92.460000 2: 214.100 cents 214.100000 3: 306.560 cents 306.560000 4: 399.020 cents 399.020000 5: 491.480 cents 491.480000 6: 613.120 cents 613.120000 7: 705.580 cents 705.580000 8: 798.040 cents 798.040000 9: 890.500 cents 890.500000 10: 1012.140 cents 1012.140000 11: 1104.600 cents 1104.600000 12: 1197.060 cents 1197.060000
SHOW/INTERVAL
0: 92.4600 cents 92.4600 1: 92.4600 cents 92.4600 2: 121.6400 cents 121.6400 3: 92.4600 cents 92.4600 4: 92.4600 cents 92.4600 5: 92.4600 cents 92.4600 6: 121.6400 cents 121.6400 7: 92.4600 cents 92.4600 8: 92.4600 cents 92.4600 9: 92.4600 cents 92.4600 10: 121.6400 cents 121.6400 11: 92.4600 cents 92.4600 12: 92.4600 cents 92.4600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 92.46000 cents 1: 3 121.64000 cents 2: 6 184.92000 cents 2: 6 214.10000 cents 3: 3 277.38000 cents 3: 9 306.56000 cents 4: 12 399.02000 cents 5: 9 491.48000 cents 5: 3 520.66000 cents 6: 6 583.94000 cents 6: 6 613.12000 cents 7: 3 676.40000 cents 7: 9 705.58000 cents 8: 12 798.04000 cents 9: 9 890.50000 cents 9: 3 919.68000 cents 10: 6 982.96000 cents 10: 6 1012.14000 cents 11: 3 1075.42000 cents 11: 9 1104.60000 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 : 92.5 214.1 306.6 399.0 491.5 613.1 705.6 798.0 890.5 1012.1 1104.6 1197.1 92.5 : 121.6 214.1 306.6 399.0 520.7 613.1 705.6 798.0 919.7 1012.1 1104.6 1197.1 214.1 : 92.5 184.9 277.4 399.0 491.5 583.9 676.4 798.0 890.5 983.0 1075.4 1197.1 306.6 : 92.5 184.9 306.6 399.0 491.5 583.9 705.6 798.0 890.5 983.0 1104.6 1197.1 399.0 : 92.5 214.1 306.6 399.0 491.5 613.1 705.6 798.0 890.5 1012.1 1104.6 1197.1 491.5 : 121.6 214.1 306.6 399.0 520.7 613.1 705.6 798.0 919.7 1012.1 1104.6 1197.1 613.1 : 92.5 184.9 277.4 399.0 491.5 583.9 676.4 798.0 890.5 983.0 1075.4 1197.1 705.6 : 92.5 184.9 306.6 399.0 491.5 583.9 705.6 798.0 890.5 983.0 1104.6 1197.1 798.0 : 92.5 214.1 306.6 399.0 491.5 613.1 705.6 798.0 890.5 1012.1 1104.6 1197.1 890.5 : 121.6 214.1 306.6 399.0 520.7 613.1 705.6 798.0 919.7 1012.1 1104.6 1197.1 1012.1: 92.5 184.9 277.4 399.0 491.5 583.9 676.4 798.0 890.5 983.0 1075.4 1197.1 1104.6: 92.5 184.9 306.6 399.0 491.5 583.9 705.6 798.0 890.5 983.0 1104.6 1197.1 1197.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.4600 .. 121.6400 cents 29.18000 cents 92.46000 cents 2: 184.9200 .. 214.1000 cents 29.18000 cents 63.28000 cents 3: 277.3800 .. 306.5600 cents 29.18000 cents 63.28000 cents 4: 399.0200 .. 399.0200 cents 1/1, 0.0000 cents 92.46000 cents 5: 491.4800 .. 520.6600 cents 29.18000 cents 92.46000 cents 6: 583.9400 .. 613.1200 cents 29.18000 cents 63.28000 cents 7: 676.4000 .. 705.5800 cents 29.18000 cents 63.28000 cents 8: 798.0400 .. 798.0400 cents 1/1, 0.0000 cents 92.46000 cents 9: 890.5000 .. 919.6800 cents 29.18000 cents 92.46000 cents 10: 982.9600 .. 1012.1400 cents 29.18000 cents 63.28000 cents 11: 1075.4200 .. 1104.6000 cents 29.18000 cents 63.28000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 92.46000 cents, class 1 Average step (divided formal octave): 99.7550 cents Largest one step interval : 121.64000 cents Average / Smallest step : 1.078899 Largest / Average step : 1.219387 Largest / Smallest step : 1.315596 Median interval of one step : 92.46000 cents, amount: 9 Most common interval of one step : 92.46000 cents, amount: 9 Least squares average step : 100.22637 cents, oct.: 1202.71643 cents Scale is strictly proper Scale has 3 repeating blocks of 4 notes Blocks have Myhill's property chromas: 29.18000 cents and 63.28000 cents, ratio: 2.168609 generators: 1 of 92.46000 cents and 3 of 306.56000 cents ET pair of linear temperament : 39&207 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 2175-tone equal temperament with octave 1197.060 cents degrees: 168 389 557 725 893 1114 1282 1450 1618 1839 2007 2175 Least number of segments generator : 1088 of 598.805 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1282 of 705.577 cents and inv. generated superset size: 1454 = 1442 more = 12116.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAAABAA Step pattern size order : SLSSSLSSSLSS Scale is a Constant Structure, by a margin of 63.28000 cents Scale diversity : 1.149063 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.780613 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 : 29.18000 cents Most common intervals : 399.02000 cents & inv., amount: 12 Most common triad is 0.0 399.020 798.040 cents, amount: 12 Number of recognisable fifths : 9, average 705.5800 cents Number of recognisable fourths : 9, average 491.4800 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: 8.9345 c. M: 14.5900 c. Twelve-tone Chromatic (1/11-comma) 27: 2 3 2 2 2 3 2 2 2 3 2 2 SP B ME SD: 4.6404 c. M:-7.5778 c. Starling-12 39: 3 4 3 3 3 4 3 3 3 4 3 3 SP B ME SD: 0.4635 c. M:-0.7569 c. 129: 10 13 10 10 10 13 10 10 10 13 10 10 SP B DE SD: 0.4107 c. M: 0.6707 c. 168: 13 17 13 13 13 17 13 13 13 17 13 13 SP B DE SD: 0.2078 c. M: 0.3393 c. 207: 16 21 16 16 16 21 16 16 16 21 16 16 SP B DE SD: 0.0813 c. M: 0.1328 c. 246: 19 25 19 19 19 25 19 19 19 25 19 19 SP B DE SD: 0.0051 c. M:-0.0083 c. 1929: 149 196 149 149 149 196 149 149 149 196 149 149 SP B DE SD: 0.0042 c. M: 0.0068 c. 2175: 168 221 168 168 168 221 168 168 168 221 168 168 SP B DE SD: 0.0031 c. M: 0.0051 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 2.9400 cents 2 x x x x x x 3 x x x x 4 S SD: 2.3337 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.1527 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.3450 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.2181 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.2246 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.8573 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 11.0508 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.6030 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.7138 cents 11:12 x 13:14:15:16 x 17:18:20:21:22 S SD: 10.7332 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 7.0015 cents 13:14:15 x 16:17:19:20:21:22:23:25:26 SD: 9.5614 cents 14:15:16:17:18:19:20:21:22:23:25:27:28 SD: 6.9460 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.0202 cents 16:17:18:19:20:21:23:24:25:27:29:30:32 SD: 4.2783 cents 21:22:24:25:26:28:30:32:33:35:38:40:42 SD: 4.2117 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.9907 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.4036 cents 30:32:34:36:38:40:43:45:48:50:54:57:60 SD: 2.7492 cents 31:33:35:37:39:41:44:47:49:52:56:59:62 SD: 2.4736 cents 36:38:41:43:45:48:51:54:57:60:65:68:72 SD: 2.0854 cents 46:49:52:55:58:61:66:69:73:77:83:87:92 SD: 1.9938 cents 51:54:58:61:64:68:73:77:81:85:92:97:102 SD: 1.9262 cents 52:55:59:62:65:69:74:78:82:87:93:98:104 SD: 1.7014 cents 54:57:61:64:68:72:77:81:86:90:97:102:108 SD: 1.5440 cents 58:61:66:69:73:77:83:87:92:97:104:110:116 SD: 1.3034 cents 68:72:77:81:86:90:97:102:108:114:122:129:136 SD: 1.2285 cents 73:77:83:87:92:97:104:110:116:122:131:138:146 SD: 0.9306 cents 77:81:87:92:97:102:110:116:122:129:138:146:154 SD: 0.9175 cents 89:94:101:106:112:118:127:134:141:149:160:168:178 SD: 0.8958 cents 92:97:104:110:116:122:131:138:146:154:165:174:184 SD: 0.6201 cents 113:119:128:135:142:150:161:170:179:189:203:214:226 SD: 0.5634 cents 159:168:180:190:200:211:227:239:252:266:285:301:317 SD: 0.5213 cents 165:174:187:197:208:219:235:248:262:276:296:312:329 SD: 0.4400 cents 181:191:205:216:228:240:258:272:287:303:325:343:361 SD: 0.4099 cents 205:216:232:245:258:272:292:308:325:343:368:388:409 SD: 0.3365 cents 243:256:275:290:306:323:346:365:385:406:436:460:485 SD: 0.3316 cents 258:272:292:308:325:343:368:388:409:432:463:488:515 SD: 0.2966 cents 259:273:293:309:326:344:369:389:411:433:465:490:517 SD: 0.2629 cents 289:305:327:345:364:384:412:434:458:483:519:547:577 SD: 0.2538 cents 290:306:328:346:365:385:413:436:460:485:520:549:579 SD: 0.2131 cents 366:386:414:437:461:486:522:550:580:612:657:693:731 SD: 0.2102 cents 381:402:431:455:480:506:543:573:604:637:684:721:761 SD: 0.1831 cents 439:463:497:524:553:583:626:660:696:734:788:831:877 SD: 0.1777 cents 471:497:533:562:593:626:671:708:747:788:845:891:940 SD: 0.1695 cents 485:512:549:579:611:644:691:729:769:811:870:918:968 SD: 0.1656 cents 494:521:559:590:622:656:704:743:783:826:886:935:986 SD: 0.1643 cents 509:537:576:608:641:676:725:765:807:851:913:963:1016 SD: 0.1603 cents 525:554:594:627:661:697:748:789:832:878:942:994:1048 SD: 0.1544 cents 531:560:601:634:669:705:757:798:842:888:953:1005:1060 SD: 0.1432 cents 548:578:620:654:690:728:781:824:869:917:983:1037:1094 SD: 0.1173 cents 598:631:677:714:753:794:852:899:948:1000:1073:1132:1194 SD: 0.1125 cents