Scala analysis: unimajor
A 2.3.11/7 subgroup scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 9/8 203.910002 major whole tone 3: 32/27 294.134997 Pythagorean minor third 4: 14/11 417.507964 undecimal diminished fourth or major third 5: 4/3 498.044999 perfect fourth 6: 63/44 621.417966 7: 3/2 701.955001 perfect fifth 8: 11/7 782.492036 undecimal augmented fifth 9: 27/16 905.865003 Pythagorean major sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 21/11 1119.462965 undecimal major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 22/21 80.5370 undecimal minor semitone 2: 189/176 123.3730 3: 256/243 90.2250 limma, Pythagorean minor second 4: 189/176 123.3730 5: 22/21 80.5370 undecimal minor semitone 6: 189/176 123.3730 7: 22/21 80.5370 undecimal minor semitone 8: 22/21 80.5370 undecimal minor semitone 9: 189/176 123.3730 10: 256/243 90.2250 limma, Pythagorean minor second 11: 189/176 123.3730 12: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 22/21 80.537 cents undecimal minor semitone 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 189/176 123.373 cents 2: 2 484/441 161.074 cents two (undecimal minor semitone) 2: 6 9/8 203.910 cents major whole tone 2: 4 112/99 213.598 cents 3: 5 33/28 284.447 cents undecimal minor third 3: 4 32/27 294.135 cents Pythagorean minor third 3: 1 1701/1408 327.283 cents 3: 2 147/121 336.971 cents 4: 1 121/98 364.984 cents 4: 3 704/567 374.672 cents 4: 3 81/64 407.820 cents Pythagorean major third 4: 5 14/11 417.508 cents undecimal diminished fourth or major third 5: 2 297/224 488.357 cents 5: 9 4/3 498.045 cents perfect fourth 5: 1 1323/968 540.881 cents 6: 5 88/63 578.582 cents 6: 1 1024/729 588.270 cents Pythagorean diminished fifth 6: 1 729/512 611.730 cents Pythagorean tritone 6: 5 63/44 621.418 cents 7: 1 1936/1323 659.119 cents 7: 9 3/2 701.955 cents perfect fifth 7: 2 448/297 711.643 cents 8: 5 11/7 782.492 cents undecimal augmented fifth 8: 3 128/81 792.180 cents Pythagorean minor sixth 8: 3 567/352 825.328 cents 8: 1 196/121 835.016 cents two (undecimal diminished fourth or major third) 9: 2 242/147 863.029 cents 9: 1 2816/1701 872.717 cents 9: 4 27/16 905.865 cents Pythagorean major sixth 9: 5 56/33 915.553 cents 10: 4 99/56 986.402 cents 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 2 441/242 1038.926 cents 11: 5 352/189 1076.627 cents 11: 2 243/128 1109.775 cents Pythagorean major seventh 11: 5 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 80.5 203.9 294.1 417.5 498.0 621.4 702.0 782.5 905.9 996.1 1119.5 1200.0 80.5 : 123.4 213.6 337.0 417.5 540.9 621.4 702.0 825.3 915.6 1038.9 1119.5 1200.0 203.9 : 90.2 213.6 294.1 417.5 498.0 578.6 702.0 792.2 915.6 996.1 1076.6 1200.0 294.1 : 123.4 203.9 327.3 407.8 488.4 611.7 702.0 825.3 905.9 986.4 1109.8 1200.0 417.5 : 80.5 203.9 284.4 365.0 488.4 578.6 702.0 782.5 863.0 986.4 1076.6 1200.0 498.0 : 123.4 203.9 284.4 407.8 498.0 621.4 702.0 782.5 905.9 996.1 1119.5 1200.0 621.4 : 80.5 161.1 284.4 374.7 498.0 578.6 659.1 782.5 872.7 996.1 1076.6 1200.0 702.0 : 80.5 203.9 294.1 417.5 498.0 578.6 702.0 792.2 915.6 996.1 1119.5 1200.0 782.5 : 123.4 213.6 337.0 417.5 498.0 621.4 711.6 835.0 915.6 1038.9 1119.5 1200.0 905.9 : 90.2 213.6 294.1 374.7 498.0 588.3 711.6 792.2 915.6 996.1 1076.6 1200.0 996.1 : 123.4 203.9 284.4 407.8 498.0 621.4 702.0 825.3 905.9 986.4 1109.8 1200.0 1119.5: 80.5 161.1 284.4 374.7 498.0 578.6 702.0 782.5 863.0 986.4 1076.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 123.3730 cents 3969/3872, 42.8359 cents 22/21, 80.5370 cents 2: 161.0741 .. 213.5980 cents 1372/1331, 52.5239 cents 85184/83349, 37.7011 cents 3: 284.4470 .. 336.9709 cents 1372/1331, 52.5239 cents 3267/3136, 70.8491 cents 4: 364.9841 .. 417.5080 cents 1372/1331, 52.5239 cents 14641/14406, 28.0131 cents 5: 488.3570 .. 540.8809 cents 1372/1331, 52.5239 cents 3267/3136, 70.8491 cents 6: 578.5820 .. 621.4180 cents 3969/3872, 42.8359 cents 85184/83349, 37.7011 cents 7: 659.1191 .. 711.6430 cents 1372/1331, 52.5239 cents 85184/83349, 37.7011 cents 8: 782.4920 .. 835.0159 cents 1372/1331, 52.5239 cents 3267/3136, 70.8491 cents 9: 863.0291 .. 915.5530 cents 1372/1331, 52.5239 cents 14641/14406, 28.0131 cents 10: 986.4020 .. 1038.9259 cents 1372/1331, 52.5239 cents 3267/3136, 70.8491 cents 11: 1076.6270 .. 1119.4630 cents 3969/3872, 42.8359 cents 85184/83349, 37.7011 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 189/176, 123.3730 cents Average / Smallest step : 1.241665 Largest / Average step : 1.233730 Largest / Smallest step : 1.531879 Median interval of one step : 256/243, 90.2250 cents, amount: 2 Least squares average step : 100.40142 cents, oct.: 1204.81709 cents Scale is strictly proper Step pattern alph. order: ABCBABAABCBA Step pattern size order : SLMLSLSSLMLS Scale is a Constant Structure, by a margin of 28.01314 cents Scale diversity : 1.304627 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.542751 Rothenberg efficiency : 0.406055 redundancy: 0.593945 Efficiency x scale size : 4.872655 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 896/891, 9.6880 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 11, average 703.7164 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Scale contains a complete diamond : 1 3 9 27 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 11 = 91.6667% Limited inverse transpositions with margin 52.5239 cents: 7 -- Rational properties -- Prime limit : 11 Odd number limit : 1701 (O: 1701 U: 1701) Highest odd numerator or denominator: 63 Scale harmonicity : 0.012205 Average absolute harmonicity : 0.169553 Specific harmonicity : 0.079956 Fundamental : 1/33264, -15.0217 octaves, 0.0079 Hz. Guide tone : 66528, 16.0217 octaves, 17405425.608 Hz. Exponens Consonantiae : 2.212987E+09, 31.04335 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 192.0, average 16.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.25202, average 1.02100 Sum of Tenney's harmonic distance : 24.29111, average 2.02426 Vogel's harmonic complexity : 31.50000 Wille's k value : 28066 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 305.28825, average 3.91395 Lattice compactness (without 2's) : 189.19919, average 2.42563 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.33333 24 1 3: -3 .. 3 0.16667 16 6 7: -1 .. 1 0.08333 5 11: -1 .. 1 -0.08333 5 5 Average exponent except 2's : 2 / 12 = 0.16667 Average absolute exponent except 2's: 26 / 12 = 2.16667 Scale is weakly epimorphic with val: <12 17 35 39| Scale is weakly epimorphic with val: <12 17 36 40| Scale is weakly epimorphic with val: <12 17 37 41| Scale is JI-epimorphic with val: <12 19 31 39| Scale is JI-epimorphic with val: <12 19 32 40| Scale is JI-epimorphic with val: <12 19 33 41| Scale is JI-epimorphic with val: <12 19 34 42| = patent Scale is JI-epimorphic with val: <12 19 35 43| Scale is JI-epimorphic with val: <12 19 36 44| Scale is JI-epimorphic with val: <12 19 37 45|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.7031 c. M: 21.4180 c. Twelve-tone Chromatic (1/11-comma) 17: 1 2 1 2 1 2 1 1 2 1 2 1 P M ME SD: 8.6357 c. M:-13.8762 c. 29: 2 3 2 3 2 3 2 2 3 2 3 2 SP M ME SD: 2.8931 c. M: 4.4798 c. 77: 5 8 6 8 5 8 5 5 8 6 8 5 SP SD: 2.0610 c. M:-3.2713 c. 89: 6 9 7 9 6 9 6 6 9 7 9 6 SP SD: 1.3379 c. M:-2.4942 c. 106: 7 11 8 11 7 11 7 7 11 8 11 7 SP SD: 0.8497 c. M:-1.3600 c. 118: 8 12 9 12 8 12 8 8 12 9 12 8 SP SD: 0.6470 c. M: 1.0790 c. 135: 9 14 10 14 9 14 9 9 14 10 14 9 SP SD: 0.5298 c. M:-0.8043 c. 224: 15 23 17 23 15 23 15 15 23 17 23 15 SP SD: 0.3043 c. M:-0.5079 c. 253: 17 26 19 26 17 26 17 17 26 19 26 17 SP SD: 0.0728 c. M:-0.1167 c. 730: 49 75 55 75 49 75 49 49 75 55 75 49 SP SD: 0.0596 c. M:-0.1116 c. 865: 58 89 65 89 58 89 58 58 89 65 89 58 SP SD: 0.0497 c. M:-0.0849 c. 983: 66 101 74 101 66 101 66 66 101 74 101 66 SP SD: 0.0399 c. M:-0.0664 c. 1118: 75 115 84 115 75 115 75 75 115 84 115 75 SP SD: 0.0298 c. M:-0.0489 c. 1371: 92 141 103 141 92 141 92 92 141 103 141 92 SP SD: 0.0237 c. M:-0.0431 c. 1848: 124 190 139 190 124 190 124 124 190 139 190 124 SP SD: 0.0165 c. M:-0.0245 c. 2101: 141 216 158 216 141 216 141 141 216 158 216 141 SP SD: 0.0064 c. M:-0.0106 c. 2354: 158 242 177 242 158 242 158 158 242 177 242 158 SP SD: 0.0045 c. M: 0.0076 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.3574 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.6821 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.5986 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.1386 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 11.7896 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.5704 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 8.0649 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 9.5352 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 7.5226 cents 13:14:15 x x 17:19 x 20:22:23:25:26 SD: 10.0605 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.6643 cents 16:17:18:19:20:21:23:24:25:27:28:31:32 SD: 5.1812 cents 18:19:20:21:23:24:26:27:28:30:32:34:36 SD: 4.3821 cents 21:22:24:25:27:28:30:32:33:35:37:40:42 SD: 4.2406 cents 22:23:25:26:28:29:32:33:35:37:39:42:44 SD: 3.7155 cents 23:24:26:27:29:31:33:35:36:39:41:44:46 SD: 3.5238 cents 26:27:29:31:33:35:37:39:41:44:46:50:52 SD: 2.9570 cents 32:34:36:38:41:43:46:48:50:54:57:61:64 SD: 2.7450 cents 37:39:42:44:47:49:53:56:58:62:66:71:74 SD: 2.7101 cents 38:40:43:45:48:51:54:57:60:64:68:73:76 SD: 2.5928 cents 39:41:44:46:50:52:56:59:61:66:69:74:78 SD: 2.3616 cents 40:42:45:47:51:53:57:60:63:68:71:76:80 SD: 2.1869 cents 42:44:47:50:53:56:60:63:66:71:75:80:84 SD: 1.7913 cents 48:50:54:57:61:64:69:72:75:81:85:92:96 SD: 1.5648 cents 54:57:61:64:69:72:77:81:85:91:96:103:108 SD: 1.5269 cents 58:61:65:69:74:77:83:87:91:98:103:111:116 SD: 1.2945 cents 63:66:71:75:80:84:90:95:99:106:112:120:126 SD: 1.2487 cents 70:73:79:83:89:93:100:105:110:118:124:134:140 SD: 1.2182 cents 80:84:90:95:102:107:115:120:126:135:142:153:160 SD: 1.0031 cents 81:85:91:96:103:108:116:122:127:137:144:155:162 SD: 0.8914 cents 102:107:115:121:130:136:146:153:160:172:181:195:204 SD: 0.6201 cents 128:134:144:152:163:171:183:192:201:216:228:244:256 SD: 0.5979 cents 144:151:162:171:183:192:206:216:226:243:256:275:288 SD: 0.4424 cents 190:199:214:225:242:253:272:285:299:321:338:363:380 SD: 0.4291 cents 194:203:218:230:247:259:278:291:305:327:345:370:388 SD: 0.4044 cents 206:216:232:244:262:275:295:309:324:348:366:393:412 SD: 0.3838 cents 210:220:236:249:267:280:301:315:330:354:373:401:420 SD: 0.3368 cents 231:242:260:274:294:308:331:347:363:390:411:441:462 SD: 0.3036 cents 234:245:263:277:298:312:335:351:368:395:416:447:468 SD: 0.2941 cents 294:308:331:348:374:392:421:441:462:496:523:561:588 SD: 0.2562 cents 296:310:333:351:377:395:424:444:465:500:526:565:592 SD: 0.2537 cents 297:311:334:352:378:396:425:446:467:501:528:567:594 SD: 0.2267 cents 320:335:360:379:407:427:458:480:503:540:569:611:640 SD: 0.2202 cents 336:352:378:398:428:448:481:504:528:567:597:641:672 SD: 0.1980 cents 352:369:396:417:448:469:504:528:553:594:626:672:704 SD: 0.1652 cents 378:396:425:448:481:504:541:567:594:638:672:722:756 SD: 0.1330 cents 480:503:540:569:611:640:687:720:754:810:853:916:960 SD: 0.1251 cents 528:553:594:626:672:704:756:792:830:891:939:1008:1056 SD: 0.0954 cents