Scala analysis: mistyschism3
Mistyschism scale 2048/2025 67108864/66430125
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 9/8 203.910002 major whole tone 3: 1215/1024 296.088718 wide augmented second 4: 512/405 405.866283 narrow diminished fourth 5: 4/3 498.044999 perfect fourth 6: 1476225/1048576 592.177436 two (wide augmented second) 7: 3/2 701.955001 perfect fifth 8: 405/256 794.133717 wide augmented fifth 9: 2048/1215 903.911282 narrow diminished seventh 10: 3645/2048 998.043719 wide augmented sixth 11: 256/135 1107.821284 octave - major chroma 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 135/128 92.1787 major chroma, major limma 2: 16/15 111.7313 minor diatonic semitone 3: 135/128 92.1787 major chroma, major limma 4: 524288/492075 109.7776 5: 135/128 92.1787 major chroma, major limma 6: 4428675/4194304 94.1324 7: 524288/492075 109.7776 8: 135/128 92.1787 major chroma, major limma 9: 524288/492075 109.7776 10: 4428675/4194304 94.1324 11: 524288/492075 109.7776 12: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 135/128 92.179 cents major chroma, major limma 1: 2 4428675/4194304 94.132 cents 1: 4 524288/492075 109.778 cents 1: 1 16/15 111.731 cents minor diatonic semitone 2: 1 18225/16384 184.357 cents two (major chroma, major limma) 2: 1 597871125/536870912 186.311 cents 2: 5 4096/3645 201.956 cents narrow diminished third 2: 5 9/8 203.910 cents major whole tone 3: 2 32/27 294.135 cents Pythagorean minor third 3: 7 1215/1024 296.089 cents wide augmented second 3: 1 311.73385 cents 3: 2 65536/54675 313.688 cents 4: 4 164025/131072 388.267 cents 4: 8 512/405 405.866 cents narrow diminished fourth 5: 8 4/3 498.045 cents perfect fourth 5: 3 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 5: 1 268435456/199290375 515.644 cents 6: 3 45/32 590.224 cents diatonic tritone 6: 3 1476225/1048576 592.177 cents two (wide augmented second) 6: 3 2097152/1476225 607.823 cents 6: 3 64/45 609.776 cents 2nd tritone 7: 1 199290375/134217728 684.356 cents 7: 3 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 7: 8 3/2 701.955 cents perfect fifth 8: 8 405/256 794.134 cents wide augmented fifth 8: 4 262144/164025 811.733 cents two (narrow diminished fourth) 9: 2 54675/32768 886.312 cents 9: 1 1793613375/10737418 888.266 cents 9: 7 2048/1215 903.911 cents narrow diminished seventh 9: 2 27/16 905.865 cents Pythagorean major sixth 10: 5 16/9 996.090 cents Pythagorean minor seventh 10: 5 3645/2048 998.044 cents wide augmented sixth 10: 1 1073741824/59787112 1013.689 cents 10: 1 32768/18225 1015.643 cents 11: 1 15/8 1088.269 cents classic major seventh 11: 4 492075/262144 1090.222 cents 11: 2 8388608/4428675 1105.868 cents 11: 5 256/135 1107.821 cents octave - major chroma 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 : 92.2 203.9 296.1 405.9 498.0 592.2 702.0 794.1 903.9 998.0 1107.8 1200.0 92.2 : 111.7 203.9 313.7 405.9 500.0 609.8 702.0 811.7 905.9 1015.6 1107.8 1200.0 203.9 : 92.2 202.0 294.1 388.3 498.0 590.2 700.0 794.1 903.9 996.1 1088.3 1200.0 296.1 : 109.8 202.0 296.1 405.9 498.0 607.8 702.0 811.7 903.9 996.1 1107.8 1200.0 405.9 : 92.2 186.3 296.1 388.3 498.0 592.2 702.0 794.1 886.3 998.0 1090.2 1200.0 498.0 : 94.1 203.9 296.1 405.9 500.0 609.8 702.0 794.1 905.9 998.0 1107.8 1200.0 592.2 : 109.8 202.0 311.7 405.9 515.6 607.8 700.0 811.7 903.9 1013.7 1105.9 1200.0 702.0 : 92.2 202.0 296.1 405.9 498.0 590.2 702.0 794.1 903.9 996.1 1090.2 1200.0 794.1 : 109.8 203.9 313.7 405.9 498.0 609.8 702.0 811.7 903.9 998.0 1107.8 1200.0 903.9 : 94.1 203.9 296.1 388.3 500.0 592.2 702.0 794.1 888.3 998.0 1090.2 1200.0 998.0 : 109.8 202.0 294.1 405.9 498.0 607.8 700.0 794.1 903.9 996.1 1105.9 1200.0 1107.8: 92.2 184.4 296.1 388.3 498.0 590.2 684.4 794.1 886.3 996.1 1090.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 111.7313 cents 2048/2025, 19.5526 cents 135/128, 92.1787 cents 2: 184.3574 .. 203.9100 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 3: 294.1350 .. 313.6876 cents 2048/2025, 19.5526 cents 256/243, 90.2250 cents 4: 388.2674 .. 405.8663 cents 67108864/66430125, 17.5988 cents 74.57987 cents 5: 498.0450 .. 515.6438 cents 67108864/66430125, 17.5988 cents 135/128, 92.1787 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 74.57987 cents 7: 684.3562 .. 701.9550 cents 67108864/66430125, 17.5988 cents 74.57987 cents 8: 794.1337 .. 811.7326 cents 67108864/66430125, 17.5988 cents 135/128, 92.1787 cents 9: 886.3124 .. 905.8650 cents 2048/2025, 19.5526 cents 74.57987 cents 10: 996.0900 .. 1015.6426 cents 2048/2025, 19.5526 cents 256/243, 90.2250 cents 11: 1088.2687 .. 1107.8213 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.084849 Largest / Average step : 1.117313 Largest / Smallest step : 1.212116 Median interval of one step : 4428675/4194304, 94.1324 cents, amount: 2 Most common interval of one step : 135/128, 92.1787 cents, amount: 5 Least squares average step : 100.03607 cents, oct.: 1200.43287 cents Scale is strictly proper Step pattern alph. order: ABACADCACDCA Step pattern size order : ADACABCACBCA Scale is a Constant Structure, by a margin of 72.62615 cents Scale diversity : 1.134301 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.827281 Rothenberg efficiency : 0.387296 redundancy: 0.612704 Efficiency x scale size : 4.647547 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 32805/32768, 1.9537 cents Number of recognisable fifths : 11, average 701.4222 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 405 1215 Formal octave complements present : 9 = 75.0000% Limited inverse transpositions with margin 19.5526 cents: 5 -- Rational properties -- Prime limit : 5 Odd number limit : too high to compute Highest odd numerator or denominator: 1476225 Scale harmonicity : 0.011086 Average absolute harmonicity : 0.157464 Fundamental : 1/1274019840, -30.2467 octaves, 0.0000 Hz. Guide tone : too high to compute Exponens Consonantiae : 3.851755E+18, 61.74022 octaves Euler's gradus suavitatis : 74 Sum of Mann's harmonic distance : 1269130.0, average 105760.83333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 27.28407, average 2.27367 Sum of Tenney's harmonic distance : 54.67779, average 4.55648 Vogel's harmonic complexity : too high to compute Wille's k value : 896806687 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 18 Triangular lattice diameter : 18 Lattice compactness : 908.02808, average 11.64139 Lattice compactness (without 2's) : 399.94755, average 5.12753 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -20 .. 11 -2.41667 91 1 3: -5 .. 10 1.50000 44 3 5: -1 .. 2 0.25000 9 8 Average exponent except 2's : 21 / 12 = 1.75000 Average absolute exponent except 2's: 53 / 12 = 4.41667 Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 21 28|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.0803 c. M:-7.8226 c. Twelve-tone Chromatic (1/11-comma) 41: 3 4 3 4 3 3 4 3 4 3 4 3 SP M ME SD: 3.5126 c. M: 6.8116 c. 53: 4 5 4 5 4 4 5 4 5 4 5 4 SP M ME SD: 1.6467 c. M: 3.4982 c. 65: 5 6 5 6 5 5 6 5 6 5 6 5 SP M ME SD: 0.6752 c. M: 1.4082 c. 77: 6 7 6 7 6 6 7 6 7 6 7 6 SP M ME SD: 0.7866 c. M:-1.3278 c. 142: 11 13 11 13 11 11 13 11 13 11 13 11 SP M DE SD: 0.6087 c. M: 1.0931 c. 207: 16 19 16 19 16 16 19 16 19 16 19 16 SP M DE SD: 0.5942 c. M: 1.0115 c. 272: 21 25 21 25 21 21 25 21 25 21 25 21 SP M DE SD: 0.6000 c. M: 1.0010 c. 328: 25 31 25 30 25 26 30 25 30 26 30 25 SP SD: 0.5371 c. M:-0.9680 c. 340: 26 32 26 31 26 27 31 26 31 27 31 26 SP SD: 0.4810 c. M:-0.7959 c. 393: 30 37 30 36 30 31 36 30 36 31 36 30 SP SD: 0.3753 c. M:-0.6702 c. 405: 31 38 31 37 31 32 37 31 37 32 37 31 SP SD: 0.3073 c. M:-0.5344 c. 417: 32 39 32 38 32 33 38 32 38 33 38 32 SP SD: 0.3095 c. M:-0.6283 c. 458: 35 43 35 42 35 36 42 35 42 36 42 35 SP SD: 0.2790 c. M: 0.4757 c. 470: 36 44 36 43 36 37 43 36 43 37 43 36 SP SD: 0.1913 c. M:-0.3453 c. 482: 37 45 37 44 37 38 44 37 44 38 44 37 SP SD: 0.1770 c. M:-0.3537 c. 535: 41 50 41 49 41 42 49 41 49 42 49 41 SP SD: 0.1258 c. M:-0.2161 c. 547: 42 51 42 50 42 43 50 42 50 43 50 42 SP SD: 0.0765 c. M:-0.1443 c. 612: 47 57 47 56 47 48 56 47 56 48 56 47 SP SD: 0.0139 c. M:-0.0219 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: 6.5175 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.7891 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.0437 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.3677 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.6166 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 9.2197 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.8589 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0025 cents 11 x 12:13:14:15 x x 17:19:20:21:22 SD: 10.8089 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4831 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.6663 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 7.1682 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.5093 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.4621 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.9276 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.1213 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 3.0648 cents 32:34:36:38:40:43:45:48:51:54:57:61:64 SD: 2.6143 cents 38:40:43:45:48:51:54:57:60:64:68:72:76 SD: 2.0767 cents 42:44:47:50:53:56:59:63:66:71:75:80:84 SD: 1.9193 cents 48:51:54:57:61:64:68:72:76:81:85:91:96 SD: 1.7614 cents 54:57:61:64:68:72:76:81:85:91:96:102:108 SD: 1.2602 cents 72:76:81:85:91:96:101:108:114:121:128:137:144 SD: 1.1332 cents 86:91:97:102:109:115:121:129:136:145:153:163:172 SD: 0.8352 cents 96:101:108:114:121:128:135:144:152:162:171:182:192 SD: 0.6407 cents 128:135:144:152:162:171:180:192:203:216:228:243:256 SD: 0.5831 cents 144:152:162:171:182:192:203:216:228:243:256:273:288 SD: 0.3674 cents 182:192:205:216:230:243:256:273:288:307:324:345:364 SD: 0.3284 cents 216:228:243:256:273:288:304:324:342:364:384:410:432 SD: 0.3247 cents 240:253:270:285:303:320:338:360:380:405:427:455:480 SD: 0.3220 cents 242:255:272:287:306:323:341:363:383:408:431:459:484 SD: 0.3067 cents 258:272:290:306:326:344:363:387:408:435:459:489:516 SD: 0.2204 cents 328:346:369:389:415:437:462:492:519:553:584:622:656 SD: 0.2039 cents 366:386:412:434:463:488:515:549:579:617:651:694:732 SD: 0.1963 cents 402:424:452:477:508:536:566:603:636:678:715:762:804 SD: 0.1719 cents 424:447:477:503:536:565:597:636:671:715:755:804:848 SD: 0.1516 cents 510:538:574:605:645:680:718:765:807:860:908:967:1020 SD: 0.1265 cents 586:618:659:695:741:781:825:879:927:988:1043:1111:1172 SD: 0.1199 cents