Scala analysis: mothra11rat
Mothra[11] with exact 8/7 as generator
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16807/16384 44.129532 cloudy 2: 8/7 231.174094 septimal whole tone 3: 2401/2048 275.303626 4: 64/49 462.348187 2 septatones or septatonic major third 5: 343/256 506.477719 6: 512/343 693.522281 3 septatones or septatonic fifth 7: 49/32 737.651813 8: 4096/2401 924.696374 4 septatones or septatonic major sixth 9: 7/4 968.825906 harmonic seventh 10: 32768/16807 1155.870468 5 septatones or septatonic diminished octave 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16807/16384 44.1295 cloudy 1: 16807/16384 44.1295 cloudy 2: 131072/117649 187.0446 3: 16807/16384 44.1295 cloudy 4: 131072/117649 187.0446 5: 16807/16384 44.1295 cloudy 6: 131072/117649 187.0446 7: 16807/16384 44.1295 cloudy 8: 131072/117649 187.0446 9: 16807/16384 44.1295 cloudy 10: 131072/117649 187.0446 11: 16807/16384 44.1295 cloudy
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 16807/16384 44.130 cents cloudy 1: 5 131072/117649 187.045 cents 2: 1 282475249/268435456 88.259 cents two (cloudy) 2: 10 8/7 231.174 cents septimal whole tone 3: 7 2401/2048 275.304 cents 3: 4 1048576/823543 418.219 cents 4: 2 40353607/33554432 319.433 cents 4: 9 64/49 462.348 cents 2 septatones or septatonic major third 5: 8 343/256 506.478 cents 5: 3 8388608/5764801 649.393 cents 6: 3 5764801/4194304 550.607 cents 6: 8 512/343 693.522 cents 3 septatones or septatonic fifth 7: 9 49/32 737.652 cents 7: 2 67108864/40353607 880.567 cents 8: 4 823543/524288 781.781 cents 8: 7 4096/2401 924.696 cents 4 septatones or septatonic major sixth 9: 10 7/4 968.826 cents harmonic seventh 9: 1 536870912/282475249 1111.741 cents 10: 5 117649/65536 1012.955 cents 10: 6 32768/16807 1155.870 cents 5 septatones or septatonic diminished octave 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 : 44.1 231.2 275.3 462.3 506.5 693.5 737.7 924.7 968.8 1155.9 1200.0 44.1 : 187.0 231.2 418.2 462.3 649.4 693.5 880.6 924.7 1111.7 1155.9 1200.0 231.2 : 44.1 231.2 275.3 462.3 506.5 693.5 737.7 924.7 968.8 1013.0 1200.0 275.3 : 187.0 231.2 418.2 462.3 649.4 693.5 880.6 924.7 968.8 1155.9 1200.0 462.3 : 44.1 231.2 275.3 462.3 506.5 693.5 737.7 781.8 968.8 1013.0 1200.0 506.5 : 187.0 231.2 418.2 462.3 649.4 693.5 737.7 924.7 968.8 1155.9 1200.0 693.5 : 44.1 231.2 275.3 462.3 506.5 550.6 737.7 781.8 968.8 1013.0 1200.0 737.7 : 187.0 231.2 418.2 462.3 506.5 693.5 737.7 924.7 968.8 1155.9 1200.0 924.7 : 44.1 231.2 275.3 319.4 506.5 550.6 737.7 781.8 968.8 1013.0 1200.0 968.8 : 187.0 231.2 275.3 462.3 506.5 693.5 737.7 924.7 968.8 1155.9 1200.0 1155.9: 44.1 88.3 275.3 319.4 506.5 550.6 737.7 781.8 968.8 1013.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.1295 .. 187.0446 cents 142.91503 cents 16807/16384, 44.1295 cents 2: 88.2591 .. 231.1741 cents 142.91503 cents -98.78550 cents 3: 275.3036 .. 418.2187 cents 142.91503 cents 16807/16384, 44.1295 cents 4: 319.4332 .. 462.3482 cents 142.91503 cents -98.78550 cents 5: 506.4777 .. 649.3927 cents 142.91503 cents 16807/16384, 44.1295 cents 6: 550.6073 .. 693.5223 cents 142.91503 cents -98.78550 cents 7: 737.6518 .. 880.5668 cents 142.91503 cents 16807/16384, 44.1295 cents 8: 781.7813 .. 924.6964 cents 142.91503 cents -98.78550 cents 9: 968.8259 .. 1111.7409 cents 142.91503 cents 16807/16384, 44.1295 cents 10: 1012.9554 .. 1155.8705 cents 142.91503 cents -98.78550 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 16807/16384, 44.1295 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 131072/117649, 187.0446 cents Average / Smallest step : 2.472061 Largest / Average step : 1.714575 Largest / Smallest step : 4.238535 Median interval of one step : 16807/16384, 44.1295 cents, amount: 6 Most common interval of one step : 16807/16384, 44.1295 cents, amount: 6 Least squares average step : 110.50311 cents, oct.: 1215.53424 cents Scale is not proper Scale has Myhill's property chromas: 142.91503 cents and 98.78550 cents, ratio: 1.446721 generators: 2 of 231.17409 cents and 9 of 968.82591 cents ET pair of linear temperament : 26&109 Scale is distributional even Scale is a mode of a 571-tone equal temperament with octave 2/1 degrees: 21 110 131 220 241 330 351 440 461 550 571 generators: 110 and 461 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABA Step pattern size order : SLSLSLSLSLS Scale is a Constant Structure, by a margin of 44.12953 cents Scale diversity : 1.205631 Lumma stability : 0.220648 Lumma impropriety factor : 0.411606 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 : 16807/16384, 44.1295 cents Most common intervals : 8/7, 231.1741 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 231.174 462.348 cents Most common triad is 0.0 231.174 968.826 cents, amount: 9 Number of recognisable fifths : 8, average 693.5223 cents Scale contains two identical disjunct hexachords Scale is a complete genus musicum : 2^m 7^10 Scale is a complete diamond : 1 7 49 343 2401 16807 Formal octave complements present : 11 = 100.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 7 Odd number limit : 282475249 (O: 282475249 U: 282475249) Highest odd numerator or denominator: 16807 Scale harmonicity : 0.007584 Average absolute harmonicity : 0.122960 Specific harmonicity : 0.043803 Fundamental : 1/275365888, -28.0368 octaves, 0.0000 Hz. Guide tone : 550731776, 29.0368 octaves, 144085512225.224 Hz. Exponens Consonantiae : 1.516527E+17, 57.07355 octaves Euler's gradus suavitatis : 90 Sum of Mann's harmonic distance : 47694.5, average 4335.86364 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 25.35294, average 2.30481 Sum of Tenney's harmonic distance : 51.24152, average 4.65832 Vogel's harmonic complexity : 49.54545 Wille's k value : 141237624 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 10 Triangular lattice diameter : 10 Lattice compactness : 758.53802, average 11.49300 Lattice compactness (without 2's) : 250.00000, average 3.78788 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -14 .. 15 0.54545 86 1 7: -5 .. 5 0.00000 30 10 Average exponent except 2's : 0 / 11 = 0.00000 Average absolute exponent except 2's: 30 / 11 = 2.72727 Scale is weakly epimorphic with val: <11 28| Scale is weakly epimorphic with val: <11 29| Scale is weakly epimorphic with val: <11 30| Scale is JI-epimorphic with val: <11 31| = patent Scale is weakly epimorphic with val: <11 32| Scale is weakly epimorphic with val: <11 34|
FIT/MODE
11: 0 2 0 2 0 2 0 2 0 2 1 N T3 SD: 56.8506 c. M: 96.0986 c. 12: 0 2 1 2 0 2 0 2 1 2 0 N I SD: 30.1173 c. M: 44.1295 c. 14: 0 2 1 2 1 2 0 3 0 2 1 N SD: 33.7646 c. M: 59.7455 c. 16: 1 2 1 2 1 2 1 2 1 2 1 P M ME I SD: 19.5242 c. M:-30.8705 c. Gorgo-11 21: 1 3 1 3 1 3 1 3 1 3 1 N M DE I SD: 8.2303 c. M: 13.0133 c. Gorgo-11 26: 1 4 1 4 1 4 1 4 1 4 1 N M DE I SD: 1.2803 c. M:-2.0243 c. 57: 2 9 2 9 2 9 2 9 2 9 2 N M DE I SD: 1.2803 c. M: 2.0243 c. 83: 3 13 3 13 3 13 3 13 3 13 3 N M DE I SD: 0.4782 c. M: 0.7560 c. 109: 4 17 4 17 4 17 4 17 4 17 4 N M DE I SD: 0.0587 c. M: 0.0928 c. 353: 13 55 13 55 13 55 13 55 13 55 13 N M DE I SD: 0.0399 c. M:-0.0631 c. 462: 17 72 17 72 17 72 17 72 17 72 17 N M DE I SD: 0.0166 c. M: 0.0263 c. 571: 21 89 21 89 21 89 21 89 21 89 21 N M DE I SD: 0.0023 c. M: 0.0036 c. 1822: 67 284 67 284 67 284 67 284 67 284 67 N M DE I SD: 0.0014 c. M:-0.0022 c. 2393: 88 373 88 373 88 373 88 373 88 373 88 N M DE I SD: 0.0005 c. M:-0.0008 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: 4.2164 cents 3 x x x x 4 x x 5 x x 6 S SD: 13.7366 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 19.1252 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 24.9545 cents 6 x x 7 x 8:9 x 10:11 x 12 S SD: 15.2084 cents 7 x 8 x 9 x 10:11:12 x x 14 S SD: 15.4617 cents 8 x 9 x 10:11:12 x x 14 x 16 S SD: 15.4617 cents 9 x 10:11 x 12:13:14:15:16 x 18 S SD: 14.7905 cents 10 x 11:12:13 x 15 x 17:18 x 20 SD: 13.2157 cents 11 x x 13:14:15:16:17:19 x 21:22 SD: 10.5967 cents 12 x x 14 x 16:18 x 20:21:23:24 SD: 7.4419 cents 13:14:15 x 17 x 19:20:22:23:25:26 SD: 11.0446 cents 14:15:16 x 18:19:21 x 24:25:27:28 SD: 10.3213 cents 15:16:17:18 x 20:22:23 x 26:29:30 SD: 9.8750 cents 16:17:18:19:21 x 24:25:27:28:31:32 SD: 8.2304 cents 17:18:19:20:22:23:25:26:29:30:33:34 SD: 7.0490 cents 18:19 x 21 x 24:27:28:31:32:35:36 SD: 7.4029 cents 19:20 x 22:25 x 28:29:32:33:37:38 SD: 6.8613 cents 20:21:23 x 26:27:30:31:34:35:39:40 SD: 5.0323 cents 22:23:25:26:29 x 33:34:38:39:43:44 SD: 5.4112 cents 23:24:26:27:30:31:34:35:39:40:45:46 SD: 4.0768 cents 25:26 x 29:33 x 37:38:43:44:49:50 SD: 4.9709 cents 26:27:30 x 34:35:39:40:44:46:51:52 SD: 3.9923 cents 27:28:31:32:35:36:40:41:46:47:53:54 SD: 3.6626 cents 28:29:32:33:37:38:42:43:48:49:55:56 SD: 3.6306 cents 29:30:33:34:38:39:43:44:49:51:57:58 SD: 3.2436 cents 30:31:34:35:39:40:45:46:51:53:58:60 SD: 3.1131 cents 33:34:38:39:43:44:49:51:56:58:64:66 SD: 2.9756 cents 34:35:39:40:44:46:51:52:58:60:66:68 SD: 2.8679 cents 35:36:40:41:46:47:52:54:60:61:68:70 SD: 2.1318 cents 36:37:41:42:47:48:54:55:61:63:70:72 SD: 1.8971 cents 41:42:47:48:54:55:61:63:70:72:80:82 SD: 1.7285 cents 62:64:71:73:81:83:93:95:106:109:121:124 SD: 1.6772 cents 64:66:73:75:84:86:96:98:109:112:125:128 SD: 1.5236 cents 65:67:74:76:85:87:97:100:111:114:127:130 SD: 1.4103 cents 68:70:78:80:89:91:102:104:116:119:133:136 SD: 1.3984 cents 69:71:79:81:90:92:103:106:118:121:135:138 SD: 1.3472 cents 71:73:81:83:93:95:106:109:121:124:138:142 SD: 1.0884 cents 75:77:86:88:98:100:112:115:128:131:146:150 SD: 1.0504 cents 77:79:88:90:101:103:115:118:131:135:150:154 SD: 1.0245 cents 79:81:90:93:103:106:118:121:135:138:154:158 SD: 0.9861 cents 85:87:97:100:111:114:127:130:145:149:166:170 SD: 0.8384 cents 105:108:120:123:137:141:157:161:179:184:205:210 SD: 0.7538 cents 111:114:127:130:145:149:166:170:189:194:216:222 SD: 0.6973 cents 120:123:137:141:157:161:179:184:205:210:234:240 SD: 0.6253 cents 147:151:168:172:192:197:219:225:251:257:287:294 SD: 0.5764 cents 153:157:175:179:200:205:228:234:261:268:298:306 SD: 0.5429 cents 156:160:178:183:204:209:233:239:266:273:304:312 SD: 0.3695 cents 197:202:225:231:257:264:294:302:336:345:384:394 SD: 0.3164 cents 203:208:232:238:265:272:303:311:346:355:396:406 SD: 0.2940 cents 232:238:265:272:303:311:346:355:396:406:452:464 SD: 0.2564 cents 307:315:351:360:401:411:458:470:524:537:599:614 SD: 0.2416 cents 320:328:366:375:418:429:478:490:546:560:624:640 SD: 0.2393 cents 343:352:392:402:448:460:512:525:585:600:669:686 SD: 0.2059 cents 392:402:448:460:512:525:585:600:669:686:764:784 SD: 0.2032 cents 412:423:471:483:538:552:615:631:703:721:803:824 SD: 0.1629 cents 435:446:497:510:568:583:649:666:742:761:848:870 SD: 0.1520 cents 497:510:568:583:649:666:742:761:848:870:969:994 SD: 0.1268 cents 574:589:656:673:750:769:857:879:979:1005:1119:1148 SD: 0.1233 cents