Scala analysis: xen18-erlich-injera-12
2L 10s MOS for Injera, L=132.84, s=93.61
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93.610 cents 93.610000 2: 187.220 cents 187.220000 3: 280.830 cents 280.830000 4: 413.670 cents 413.670000 5: 507.280 cents 507.280000 6: 600.890 cents 600.890000 7: 694.500 cents 694.500000 8: 788.110 cents 788.110000 9: 881.720 cents 881.720000 10: 1014.560 cents 1014.560000 11: 1108.170 cents 1108.170000 12: 1201.780 cents 1201.780000
SHOW/INTERVAL
0: 93.6100 cents 93.6100 1: 93.6100 cents 93.6100 2: 93.6100 cents 93.6100 3: 93.6100 cents 93.6100 4: 132.8400 cents 132.8400 5: 93.6100 cents 93.6100 6: 93.6100 cents 93.6100 7: 93.6100 cents 93.6100 8: 93.6100 cents 93.6100 9: 93.6100 cents 93.6100 10: 132.8400 cents 132.8400 11: 93.6100 cents 93.6100 12: 93.6100 cents 93.6100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 93.61000 cents 1: 2 132.84000 cents 2: 8 187.22000 cents 2: 4 226.45000 cents 3: 6 280.83000 cents 3: 6 320.06000 cents 4: 4 374.44000 cents 4: 8 413.67000 cents 5: 2 468.05000 cents 5: 10 507.28000 cents 6: 12 600.89000 cents 7: 10 694.50000 cents 7: 2 733.73000 cents 8: 8 788.11000 cents 8: 4 827.34000 cents 9: 6 881.72000 cents 9: 6 920.95000 cents 10: 4 975.33000 cents 10: 8 1014.56000 cents 11: 2 1068.94000 cents 11: 10 1108.17000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.90909 = 21/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 93.6 187.2 280.8 413.7 507.3 600.9 694.5 788.1 881.7 1014.6 1108.2 1201.8 93.6 : 93.6 187.2 320.1 413.7 507.3 600.9 694.5 788.1 921.0 1014.6 1108.2 1201.8 187.2 : 93.6 226.5 320.1 413.7 507.3 600.9 694.5 827.3 921.0 1014.6 1108.2 1201.8 280.8 : 132.8 226.5 320.1 413.7 507.3 600.9 733.7 827.3 921.0 1014.6 1108.2 1201.8 413.7 : 93.6 187.2 280.8 374.4 468.0 600.9 694.5 788.1 881.7 975.3 1068.9 1201.8 507.3 : 93.6 187.2 280.8 374.4 507.3 600.9 694.5 788.1 881.7 975.3 1108.2 1201.8 600.9 : 93.6 187.2 280.8 413.7 507.3 600.9 694.5 788.1 881.7 1014.6 1108.2 1201.8 694.5 : 93.6 187.2 320.1 413.7 507.3 600.9 694.5 788.1 921.0 1014.6 1108.2 1201.8 788.1 : 93.6 226.5 320.1 413.7 507.3 600.9 694.5 827.3 921.0 1014.6 1108.2 1201.8 881.7 : 132.8 226.5 320.1 413.7 507.3 600.9 733.7 827.3 921.0 1014.6 1108.2 1201.8 1014.6: 93.6 187.2 280.8 374.4 468.0 600.9 694.5 788.1 881.7 975.3 1068.9 1201.8 1108.2: 93.6 187.2 280.8 374.4 507.3 600.9 694.5 788.1 881.7 975.3 1108.2 1201.8 1201.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6100 .. 132.8400 cents 39.23000 cents 93.61000 cents 2: 187.2200 .. 226.4500 cents 39.23000 cents 54.38000 cents 3: 280.8300 .. 320.0600 cents 39.23000 cents 54.38000 cents 4: 374.4400 .. 413.6700 cents 39.23000 cents 54.38000 cents 5: 468.0500 .. 507.2800 cents 39.23000 cents 54.38000 cents 6: 600.8900 .. 600.8900 cents 1/1, 0.0000 cents 93.61000 cents 7: 694.5000 .. 733.7300 cents 39.23000 cents 93.61000 cents 8: 788.1100 .. 827.3400 cents 39.23000 cents 54.38000 cents 9: 881.7200 .. 920.9500 cents 39.23000 cents 54.38000 cents 10: 975.3300 .. 1014.5600 cents 39.23000 cents 54.38000 cents 11: 1068.9400 .. 1108.1700 cents 39.23000 cents 54.38000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 93.61000 cents, class 1 Average step (divided formal octave): 100.1483 cents Largest one step interval : 132.84000 cents Average / Smallest step : 1.069847 Largest / Average step : 1.326432 Largest / Smallest step : 1.419079 Median interval of one step : 93.61000 cents, amount: 10 Most common interval of one step : 93.61000 cents, amount: 10 Least squares average step : 99.94715 cents, oct.: 1199.36585 cents Scale is strictly proper Scale has 2 repeating blocks of 6 notes Blocks have Myhill's property chromas: 39.23000 cents and 54.38000 cents, ratio: 1.386184 generators: 1 of 93.61000 cents and 5 of 507.28000 cents ET pair of linear temperament : 26&64 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1348-tone equal temperament with octave 1201.780 cents degrees: 105 210 315 464 569 674 779 884 989 1138 1243 1348 Least number of segments generator : 675 of 601.782 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 779 of 694.500 cents and inv. generated superset size: 680 = 668 more = 5666.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAABAA Step pattern size order : SSSLSSSSSLSS Scale is a Constant Structure, by a margin of 54.38000 cents Scale diversity : 1.193376 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.673568 Rothenberg efficiency (ambiguous key): 0.505556 redundancy: 0.494444 Efficiency x scale size : 6.066667 Number of different interval sizes : 21 = 1.90909 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.90909 = 21/11 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 39.23000 cents Most common intervals : 600.89000 cents & inv., amount: 12 Number of recognisable fifths : 10, average 694.5000 cents Number of recognisable fourths : 10, average 507.2800 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 10 = 83.3333% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 6 Limited inverse transpositions : 1 7 Inversional symmetry on intervals : 0-1 3-4 6-7 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.6350 c. M:-19.6150 c. Twelve-tone Chromatic (1/11-comma) 26: 2 2 2 3 2 2 2 2 2 3 2 2 SP B ME SD: 2.0738 c. M: 3.4962 c. 64: 5 5 5 7 5 5 5 5 5 7 5 5 SP B DE SD: 0.4966 c. M:-0.8372 c. 90: 7 7 7 10 7 7 7 7 7 10 7 7 SP B DE SD: 0.2460 c. M: 0.4147 c. 154: 12 12 12 17 12 12 12 12 12 17 12 12 SP B DE SD: 0.0626 c. M:-0.1056 c. 244: 19 19 19 27 19 19 19 19 19 27 19 19 SP B DE SD: 0.0512 c. M: 0.0863 c. 398: 31 31 31 44 31 31 31 31 31 44 31 31 SP B DE SD: 0.0072 c. M: 0.0121 c. 950: 74 74 74 105 74 74 74 74 74 105 74 74 SP B DE SD: 0.0042 c. M:-0.0070 c. 1348: 105 105 105 149 105 105 105 105 105 149 105 105 SP B DE SD: 0.0008 c. M:-0.0014 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 1.7800 cents 2 x x x x x x 3 x x x x 4 S SD: 3.8323 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.2560 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 13.4599 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.4151 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 6.5767 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.6703 cents 8 x 9 x 10:11 x 12 x 13:14:15:16 S SD: 10.6136 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 9.1054 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 7.6036 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 8.3594 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 6.2433 cents 13:14 x 15 x 17:18:19:21:22:23:25:26 SD: 10.4233 cents 14:15:16 x 18:19:20:21:22:23:25:27:28 SD: 6.6352 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 6.0531 cents 16:17:18:19:20:21:23:24:25:27:29:30:32 SD: 5.9038 cents 17:18:19:20:22:23:24:25:27:28:31:32:34 SD: 4.8787 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.1234 cents 24:25:27:28:30:32:34:36:38:40:43:46:48 SD: 4.0080 cents 26:27:29:31:33:35:37:39:41:43:47:49:52 SD: 3.6525 cents 29:31:32:34:37:39:41:43:46:48:52:55:58 SD: 2.9601 cents 33:35:37:39:42:44:47:49:52:55:59:63:66 SD: 2.3580 cents 36:38:40:42:46:48:51:54:57:60:65:68:72 SD: 2.1476 cents 41:43:46:48:52:55:58:61:65:68:74:78:82 SD: 2.0417 cents 50:53:56:59:63:67:71:75:79:83:90:95:100 SD: 1.8608 cents 51:54:57:60:65:68:72:76:80:85:92:97:102 SD: 1.5977 cents 53:56:59:62:67:71:75:79:84:88:95:101:106 SD: 1.5685 cents 56:59:62:66:71:75:79:84:88:93:101:106:112 SD: 1.5341 cents 59:62:66:69:75:79:83:88:93:98:106:112:118 SD: 1.5170 cents 67:71:75:79:85:90:95:100:106:111:120:127:134 SD: 1.4272 cents 68:72:76:80:86:91:96:102:107:113:122:129:136 SD: 1.2192 cents 73:77:81:86:93:98:103:109:115:121:131:138:146 SD: 1.2160 cents 77:81:86:91:98:103:109:115:121:128:138:146:154 SD: 1.2067 cents 79:83:88:93:100:106:112:118:125:131:142:150:158 SD: 1.1740 cents 85:90:95:100:108:114:120:127:134:141:153:161:170 SD: 0.9243 cents 89:94:99:105:113:119:126:133:140:148:160:169:178 SD: 0.7627 cents 108:114:120:127:137:145:153:161:170:180:194:205:216 SD: 0.6925 cents 123:130:137:145:156:165:174:184:194:205:221:233:246 SD: 0.5968 cents 142:150:158:167:180:190:201:212:224:236:255:269:284 SD: 0.5452 cents 158:167:176:186:201:212:224:236:249:263:284:300:316 SD: 0.5239 cents 164:173:183:193:208:220:232:245:259:273:295:311:328 SD: 0.4694 cents 182:192:203:214:231:244:258:272:287:303:327:345:364 SD: 0.3906 cents 193:204:215:227:245:259:273:288:304:321:347:366:386 SD: 0.3738 cents 217:229:242:255:276:291:307:324:342:361:390:412:434 SD: 0.3720 cents 253:267:282:298:321:339:358:378:399:421:455:480:507 SD: 0.3340 cents 255:269:284:300:324:342:361:381:402:424:458:484:511 SD: 0.2853 cents 289:305:322:340:367:387:409:432:456:481:519:548:579 SD: 0.2697 cents 290:306:323:341:368:389:410:433:457:483:521:550:581 SD: 0.2690 cents 306:323:341:360:389:410:433:457:482:509:550:580:613 SD: 0.2608 cents 323:341:360:380:410:433:457:482:509:538:580:613:647 SD: 0.2599 cents 330:348:368:388:419:442:467:493:520:549:593:626:661 SD: 0.2534 cents 340:359:379:400:432:456:481:508:536:566:611:645:681 SD: 0.1764 cents 359:379:400:422:456:481:508:536:566:597:645:681:719 SD: 0.1685 cents 437:461:487:514:555:586:618:653:689:727:785:829:875 SD: 0.1645 cents 470:496:524:553:597:630:665:702:741:782:845:891:941 SD: 0.1623 cents 482:509:537:567:612:646:682:720:760:802:866:914:965 SD: 0.0916 cents