Scala analysis: mothra11br4
Mothra[11] with a brat of 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 194.557 cents 194.556810 2: 232.426 cents 232.426135 3: 426.983 cents 426.982945 4: 464.852 cents 464.852270 5: 659.409 cents 659.409080 6: 697.278 cents 697.278405 7: 891.835 cents 891.835215 8: 929.705 cents 929.704540 9: 1124.261 cents 1124.261350 10: 1162.131 cents 1162.130675 11: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 37.8693 cents 37.8693 1: 194.5568 cents 194.5568 2: 37.8693 cents 37.8693 3: 194.5568 cents 194.5568 4: 37.8693 cents 37.8693 5: 194.5568 cents 194.5568 6: 37.8693 cents 37.8693 7: 194.5568 cents 194.5568 8: 37.8693 cents 37.8693 9: 194.5568 cents 194.5568 10: 37.8693 cents 37.8693 11: 37.8693 cents 37.8693
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 37.86933 cents 1: 5 194.55681 cents 2: 1 75.73865 cents 2: 10 232.42613 cents 3: 7 270.29546 cents 3: 4 426.98294 cents 4: 2 308.16479 cents 4: 9 464.85227 cents 5: 8 502.72160 cents 5: 3 659.40908 cents 6: 3 540.59092 cents 6: 8 697.27840 cents 7: 9 735.14773 cents 7: 2 891.83521 cents 8: 4 773.01706 cents 8: 7 929.70454 cents 9: 10 967.57387 cents 9: 1 1124.26135 cents 10: 5 1005.44319 cents 10: 6 1162.13067 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 194.6 232.4 427.0 464.9 659.4 697.3 891.8 929.7 1124.3 1162.1 1200.0 194.6 : 37.9 232.4 270.3 464.9 502.7 697.3 735.1 929.7 967.6 1005.4 1200.0 232.4 : 194.6 232.4 427.0 464.9 659.4 697.3 891.8 929.7 967.6 1162.1 1200.0 427.0 : 37.9 232.4 270.3 464.9 502.7 697.3 735.1 773.0 967.6 1005.4 1200.0 464.9 : 194.6 232.4 427.0 464.9 659.4 697.3 735.1 929.7 967.6 1162.1 1200.0 659.4 : 37.9 232.4 270.3 464.9 502.7 540.6 735.1 773.0 967.6 1005.4 1200.0 697.3 : 194.6 232.4 427.0 464.9 502.7 697.3 735.1 929.7 967.6 1162.1 1200.0 891.8 : 37.9 232.4 270.3 308.2 502.7 540.6 735.1 773.0 967.6 1005.4 1200.0 929.7 : 194.6 232.4 270.3 464.9 502.7 697.3 735.1 929.7 967.6 1162.1 1200.0 1124.3: 37.9 75.7 270.3 308.2 502.7 540.6 735.1 773.0 967.6 1005.4 1200.0 1162.1: 37.9 232.4 270.3 464.9 502.7 697.3 735.1 929.7 967.6 1162.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 37.8693 .. 194.5568 cents 156.68748 cents 37.86933 cents 2: 75.7387 .. 232.4261 cents 156.68748 cents -118.81816 cents 3: 270.2955 .. 426.9829 cents 156.68748 cents 37.86933 cents 4: 308.1648 .. 464.8523 cents 156.68748 cents -118.81816 cents 5: 502.7216 .. 659.4091 cents 156.68748 cents 37.86933 cents 6: 540.5909 .. 697.2784 cents 156.68748 cents -118.81816 cents 7: 735.1477 .. 891.8352 cents 156.68748 cents 37.86933 cents 8: 773.0171 .. 929.7045 cents 156.68748 cents -118.81816 cents 9: 967.5739 .. 1124.2613 cents 156.68748 cents 37.86933 cents 10: 1005.4432 .. 1162.1307 cents 156.68748 cents -118.81816 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 37.86933 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 194.55681 cents Average / Smallest step : 2.880720 Largest / Average step : 1.783437 Largest / Smallest step : 5.137583 Median interval of one step : 37.86933 cents, amount: 6 Most common interval of one step : 37.86933 cents, amount: 6 Least squares average step : 118.38068 cents, oct.: 1302.18749 cents Scale is not proper Scale has Myhill's property chromas: 156.68748 cents and 118.81816 cents, ratio: 1.318717 generators: 2 of 232.42613 cents and 967.57387 cents ET pair of linear temperament : 31&222 Scale is distributional even Scale is a mode of a 919-tone equal temperament with octave 1200.000 cents degrees: 149 178 327 356 505 534 683 712 861 890 919 generators: 178 and 741 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABB Step pattern size order : LSLSLSLSLSS Scale is a Constant Structure, by a margin of 37.86933 cents Scale diversity : 1.140197 Lumma stability : 0.189347 Lumma impropriety factor : 0.495076 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 37.86933 cents Most common intervals : 232.42613 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 232.426 464.852 cents Most common triad is 0.0 232.426 967.574 cents, amount: 9 Number of recognisable fifths : 8, average 697.2784 cents Scale contains two identical disjunct pentachords Formal octave complements present : 1 = 9.0909% Limited inverse transpositions : 9 Inversional symmetry on degrees : 10 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
11: 2 0 2 0 2 0 2 0 2 0 1 N T3 SD: 34.7809 c. M: 71.2216 c. 12: 2 0 2 1 2 0 2 0 2 1 0 N SD: 26.4081 c. M:-40.5909 c. 14: 2 1 2 0 3 0 2 1 2 1 0 N SD: 23.7420 c. M:-37.8693 c. 15: 2 1 2 1 2 1 2 1 2 1 0 N T3 SD: 22.5876 c. M:-37.8693 c. 16: 3 0 3 0 3 0 3 0 3 0 1 N T3 SD: 20.8893 c. M: 37.1307 c. 17: 3 0 3 1 2 1 3 0 3 0 1 N SD: 19.4367 c. M: 32.7189 c. 18: 3 0 3 1 3 0 3 1 3 0 1 N T3 SD: 19.9098 c. M: 32.4261 c. 19: 3 1 3 0 3 1 3 1 3 0 1 N SD: 16.8661 c. M: 27.8301 c. 20: 3 1 3 1 3 1 3 0 4 0 1 N SD: 15.8131 c. M: 29.7045 c. 23: 4 0 4 1 4 0 4 1 4 0 1 N T3 SD: 14.9754 c. M: 23.7305 c. 26: 4 1 4 1 4 1 4 1 4 1 1 N M DE S SD: 9.8024 c. M: 16.5690 c. Mothra-11 31: 5 1 5 1 5 1 5 1 5 1 1 N M DE S SD: 0.9943 c. M: 1.6807 c. de Vries 11-tone, Mothra-11 129: 21 4 21 4 21 4 21 4 21 4 4 N M DE S SD: 0.7809 c. M:-1.3200 c. 160: 26 5 26 5 26 5 26 5 26 5 5 N M DE S SD: 0.4370 c. M:-0.7387 c. 191: 31 6 31 6 31 6 31 6 31 6 6 N M DE S SD: 0.2047 c. M:-0.3460 c. 222: 36 7 36 7 36 7 36 7 36 7 7 N M DE S SD: 0.0373 c. M:-0.0630 c. 475: 77 15 77 15 77 15 77 15 77 15 15 N M DE S SD: 0.0301 c. M: 0.0508 c. 697: 113 22 113 22 113 22 113 22 113 22 22 N M DE S SD: 0.0086 c. M: 0.0146 c. 919: 149 29 149 29 149 29 149 29 149 29 29 N M DE S SD: 0.0025 c. M:-0.0042 c. 1616: 262 51 262 51 262 51 262 51 262 51 51 N M DE S SD: 0.0023 c. M: 0.0039 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x x 4 S SD: 2.3383 cents 3 x x x 4 x x 5 x x x 6 S SD: 11.3414 cents 4 x x 5 x x 6 x 7 x x 8 S SD: 14.1561 cents 5 x 6 x x 7 x 8:9 x x 10 S SD: 32.6620 cents 6 x 7 x 8 x 9:10 x 11 x 12 S SD: 14.8845 cents 7 x 8:9 x 10 x x 12:13 x 14 S SD: 11.3024 cents 8:9 x 10 x x 12:13:14:15 x 16 S SD: 12.1401 cents 9:10 x x 12:13 x 15 x 17 x 18 SD: 8.1031 cents 10:11 x x 13 x 15 x 17:19 x 20 SD: 6.0125 cents 11:12:13:14 x 16 x 18:19:21 x 22 SD: 10.6016 cents 12:13:14:15:16 x 18:20:21:23 x 24 SD: 10.3571 cents 13 x 15 x 17:19 x x 22:25 x 26 SD: 4.2811 cents 14 x 16:18 x 20:21:23:24:27 x 28 SD: 6.9264 cents 15 x 17:19:20:22 x 25:26:29 x 30 SD: 6.2906 cents 16:18 x 20:21:23:24:27 x x 31:32 SD: 7.1337 cents 17:19 x x 22:25 x 28:29 x 33:34 SD: 5.3696 cents 19:21:22:24:25:28 x 32:33:36:37:38 SD: 5.3345 cents 20:22:23 x 26:29:30:33:34:38:39:40 SD: 4.8035 cents 21 x 24:27 x 31 x 35:36:40:41:42 SD: 2.6405 cents 22 x 25:28:29:32:33:37:38:42:43:44 SD: 2.9930 cents 23:26 x 29:30:34 x x 39:44:45:46 SD: 4.8993 cents 24:27 x 31 x 35:36:40:41:46:47:48 SD: 2.4245 cents 25:28:29:32:33 x 37:42:43:48:49:50 SD: 3.6832 cents 26:29:30:33:34:38:39 x 44:50:51:52 SD: 3.0541 cents 27:30:31 x 35 x 40:45:46:52:53:54 SD: 3.4547 cents 28:31:32:36:37:41:42:47:48:54:55:56 SD: 2.8481 cents 30 x 34:38:39:44:45:50:51:57:59:60 SD: 3.3713 cents 31:35 x 40:41:45:46:52:53:59:61:62 SD: 3.7749 cents 32:36:37:41:42:47:48:54:55:61:63:64 SD: 2.8320 cents 34:38:39 x 44:50:51:57:58:65:67:68 SD: 2.5496 cents 35:39:40:45:46:51:52:59:60:67:68:70 SD: 2.4047 cents 36:40:41:46:47:53:54:60:62:69:70:72 SD: 2.3232 cents 38 x 43:49:50:56:57:64:65:73:74:76 SD: 3.1622 cents 39:44:45:50:51:57:58:65:67:75:76:78 SD: 2.5335 cents 41:46:47:52:54:60:61:69:70:78:80:82 SD: 2.4937 cents 42:47:48:54:55:61:63:70:72:80:82:84 SD: 1.8824 cents 43:48:49:55:56:63:64:72:74:82:84:86 SD: 1.7031 cents 49:55:56:63:64:72:73:82:84:94:96:98 SD: 1.3797 cents 58:65:66:74:76:85:87:97:99:111:113:116 SD: 1.3561 cents 65:73:74:83:85:95:97:109:111:124:127:130 SD: 1.3033 cents 68:76:78:87:89:100:102:114:116:130:133:136 SD: 1.1524 cents 69:77:79:88:90:101:103:115:118:132:135:138 SD: 1.1326 cents 75:84:86:96:98:110:112:126:128:144:147:150 SD: 1.0801 cents 82:92:94:105:107:120:123:137:140:157:160:164 SD: 1.0193 cents 90:101:103:115:118:132:135:151:154:172:176:180 SD: 0.9619 cents 91:102:104:116:119:133:136:152:156:174:178:182 SD: 0.8864 cents 93:104:106:119:122:136:139:156:159:178:182:186 SD: 0.8182 cents 104:116:119:133:136:152:156:174:178:199:204:208 SD: 0.8142 cents 107:120:122:137:140:157:160:179:183:205:209:214 SD: 0.7982 cents 110:123:126:141:144:161:165:184:188:211:215:220 SD: 0.7088 cents 117:131:134:150:153:171:175:196:200:224:229:234 SD: 0.4790 cents 153:171:175:196:200:224:229:256:262:293:299:306 SD: 0.3812 cents 201:225:230:257:263:294:301:336:344:385:393:402 SD: 0.3704 cents 208:233:238:266:272:304:311:348:356:398:407:416 SD: 0.3457 cents 211:236:241:270:276:309:316:353:361:404:413:422 SD: 0.3116 cents 236:264:270:302:309:345:353:395:404:452:462:472 SD: 0.2871 cents 276:309:316:353:361:404:413:462:472:528:540:552 SD: 0.2544 cents 279:312:319:357:365:408:417:467:477:534:546:558 SD: 0.2502 cents 304:340:348:389:398:445:455:509:520:582:595:608 SD: 0.2427 cents 319:357:365:408:417:467:477:534:546:611:624:638 SD: 0.2053 cents 328:367:375:420:429:480:491:549:561:628:642:656 SD: 0.1692 cents 419:469:479:536:548:613:627:701:717:802:820:838 SD: 0.1613 cents 464:519:531:594:607:679:694:777:794:888:908:928 SD: 0.1595 cents 487:545:557:623:637:713:729:815:833:932:953:974 SD: 0.1490 cents 494:553:565:632:646:723:739:827:845:946:967:988 SD: 0.1265 cents 522:584:597:668:683:764:781:874:893:999:1021:1044 SD: 0.1096 cents