Scala analysis: mistyschism2
Mistyschism scale 2048/2025 67108864/66430125 = duoden12.scl
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: 64/45 609.776284 2nd tritone 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: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma 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: 6 135/128 92.179 cents major chroma, major limma 1: 1 4428675/4194304 94.132 cents 1: 3 524288/492075 109.778 cents 1: 2 16/15 111.731 cents minor diatonic semitone 2: 2 18225/16384 184.357 cents two (major chroma, major limma) 2: 4 4096/3645 201.956 cents narrow diminished third 2: 6 9/8 203.910 cents major whole tone 3: 3 32/27 294.135 cents Pythagorean minor third 3: 6 1215/1024 296.089 cents wide augmented second 3: 3 65536/54675 313.688 cents 4: 4 164025/131072 388.267 cents 4: 8 512/405 405.866 cents narrow diminished fourth 5: 9 4/3 498.045 cents perfect fourth 5: 2 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 5: 1 8192/6075 517.598 cents 6: 4 45/32 590.224 cents diatonic tritone 6: 2 1476225/1048576 592.177 cents two (wide augmented second) 6: 2 2097152/1476225 607.823 cents 6: 4 64/45 609.776 cents 2nd tritone 7: 1 6075/4096 682.402 cents 7: 2 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 7: 9 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: 3 54675/32768 886.312 cents 9: 6 2048/1215 903.911 cents narrow diminished seventh 9: 3 27/16 905.865 cents Pythagorean major sixth 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 4 3645/2048 998.044 cents wide augmented sixth 10: 2 32768/18225 1015.643 cents 11: 2 15/8 1088.269 cents classic major seventh 11: 3 492075/262144 1090.222 cents 11: 1 8388608/4428675 1105.868 cents 11: 6 256/135 1107.821 cents octave - major chroma Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 203.9 296.1 405.9 498.0 609.8 702.0 794.1 903.9 998.0 1107.8 1200.0 92.2 : 111.7 203.9 313.7 405.9 517.6 609.8 702.0 811.7 905.9 1015.6 1107.8 1200.0 203.9 : 92.2 202.0 294.1 405.9 498.0 590.2 700.0 794.1 903.9 996.1 1088.3 1200.0 296.1 : 109.8 202.0 313.7 405.9 498.0 607.8 702.0 811.7 903.9 996.1 1107.8 1200.0 405.9 : 92.2 203.9 296.1 388.3 498.0 592.2 702.0 794.1 886.3 998.0 1090.2 1200.0 498.0 : 111.7 203.9 296.1 405.9 500.0 609.8 702.0 794.1 905.9 998.0 1107.8 1200.0 609.8 : 92.2 184.4 294.1 388.3 498.0 590.2 682.4 794.1 886.3 996.1 1088.3 1200.0 702.0 : 92.2 202.0 296.1 405.9 498.0 590.2 702.0 794.1 903.9 996.1 1107.8 1200.0 794.1 : 109.8 203.9 313.7 405.9 498.0 609.8 702.0 811.7 903.9 1015.6 1107.8 1200.0 903.9 : 94.1 203.9 296.1 388.3 500.0 592.2 702.0 794.1 905.9 998.0 1090.2 1200.0 998.0 : 109.8 202.0 294.1 405.9 498.0 607.8 700.0 811.7 903.9 996.1 1105.9 1200.0 1107.8: 92.2 184.4 296.1 388.3 498.0 590.2 702.0 794.1 886.3 996.1 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 .. 517.5976 cents 2048/2025, 19.5526 cents 135/128, 92.1787 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 7: 682.4024 .. 701.9550 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 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 : 93.15558 cents, amount: 0 Most common interval of one step : 135/128, 92.1787 cents, amount: 6 Least squares average step : 100.19852 cents, oct.: 1202.38228 cents Scale is strictly proper Step pattern alph. order: ABACABAACDCA Step pattern size order : ADACADAACBCA Scale is a Constant Structure, by a margin of 72.62615 cents Scale diversity : 1.135243 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.824024 Rothenberg efficiency : 0.439743 redundancy: 0.560257 Efficiency x scale size : 5.276912 Number of different interval sizes : 34 = 3.09091 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 32805/32768, 1.9537 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 701.5998 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 : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties -- Prime limit : 5 Odd number limit : 4428675 (O: 4428675 U: 4428675) Highest odd numerator or denominator: 3645 Scale harmonicity : 0.015593 Average absolute harmonicity : 0.160761 Specific harmonicity : 0.084353 Fundamental : 1/2488320, -21.2467 octaves, 0.0001 Hz. Guide tone : 7464960, 22.8317 octaves, 1953024379.949 Hz. Exponens Consonantiae : 1.857521E+13, 44.07844 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 6784.0, average 565.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 22.76813, average 1.89734 Sum of Tenney's harmonic distance : 45.94743, average 3.82895 Vogel's harmonic complexity : 32.25000 Wille's k value : 2214337 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 13 Triangular lattice diameter : 13 Lattice compactness : 761.52084, average 9.76309 Lattice compactness (without 2's) : 331.98065, average 4.25616 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -11 .. 11 -0.25000 77 1 3: -5 .. 6 0.50000 36 3 5: -1 .. 1 0.00000 8 8 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 44 / 12 = 3.66667 Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 21 25| Scale is weakly epimorphic with val: <12 21 26| Scale is weakly epimorphic with val: <12 21 28| Scale is weakly epimorphic with val: <12 21 29| Scale is weakly epimorphic with val: <12 21 31|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.3549 c. M: 9.7763 c. Twelve-tone Chromatic (1/11-comma) 41: 3 4 3 4 3 4 3 3 4 3 4 3 SP M ME SD: 3.2309 c. M:-4.8579 c. 53: 4 5 4 5 4 5 4 4 5 4 5 4 SP M ME SD: 1.3750 c. M: 1.8173 c. 65: 5 6 5 6 5 6 5 5 6 5 6 5 SP M ME SD: 0.5616 c. M: 1.1206 c. 207: 16 19 16 19 16 19 16 16 19 16 19 16 SP M DE SD: 0.6220 c. M: 1.0806 c. 272: 21 25 21 25 21 25 21 21 25 21 25 21 SP M DE SD: 0.5934 c. M: 0.9849 c. 337: 26 31 26 31 26 31 26 26 31 26 31 26 SP M DE SD: 0.5799 c. M: 1.0111 c. 340: 26 32 26 31 26 32 26 26 31 27 31 26 SP SD: 0.4876 c. M:-0.8120 c. 352: 27 33 27 32 27 33 27 27 32 28 32 27 SP SD: 0.4173 c. M:-0.8199 c. 405: 31 38 31 37 31 38 31 31 37 32 37 31 SP SD: 0.3309 c. M:-0.5941 c. 417: 32 39 32 38 32 39 32 32 38 33 38 32 SP SD: 0.2649 c. M:-0.5174 c. 470: 36 44 36 43 36 44 36 36 43 37 43 36 SP SD: 0.2242 c. M:-0.4365 c. 482: 37 45 37 44 37 45 37 37 44 38 44 37 SP SD: 0.1538 c. M:-0.2965 c. 547: 42 51 42 50 42 51 42 42 50 43 50 42 SP SD: 0.0698 c. M:-0.1281 c. 612: 47 57 47 56 47 57 47 47 56 48 56 47 SP SD: 0.0149 c. M:-0.0276 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: 8.6954 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: 8.9788 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.1617 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.9368 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4522 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 10.4771 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4375 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 10.2164 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.8810 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.9047 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.8127 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.3937 cents 26:27:29:31:33:35:37:39:41:44:46:49:52 SD: 3.3687 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.8454 cents 33:35:37:39:42:44:47:50:52:56:59:63:66 SD: 2.6348 cents 38:40:43:45:48:51:54:57:60:64:68:72:76 SD: 1.5843 cents 54:57:61:64:68:72:77:81:85:91:96:102:108 SD: 1.3142 cents 69:73:78:82:87:92:98:104:109:116:123:131:138 SD: 1.2940 cents 72:76:81:85:91:96:102:108:114:121:128:137:144 SD: 1.1546 cents 76:80:86:90:96:101:108:114:120:128:135:144:152 SD: 1.1432 cents 80:84:90:95:101:107:114:120:127:135:142:152:160 SD: 1.1185 cents 86:91:97:102:109:115:122:129:136:145:153:163:172 SD: 0.9082 cents 90:95:101:107:114:120:128:135:142:152:160:171:180 SD: 0.7993 cents 96:101:108:114:121:128:137:144:152:162:171:182:192 SD: 0.7914 cents 106:112:119:126:134:141:151:159:168:179:189:201:212 SD: 0.7786 cents 112:118:126:133:142:149:159:168:177:189:199:212:224 SD: 0.7493 cents 114:120:128:135:144:152:162:171:180:192:203:216:228 SD: 0.6155 cents 128:135:144:152:162:171:182:192:203:216:228:243:256 SD: 0.5610 cents 144:152:162:171:182:192:205:216:228:243:256:273:288 SD: 0.3429 cents 182:192:205:216:230:243:259:273:288:307:324:345:364 SD: 0.3147 cents 242:255:272:287:306:323:344:363:383:408:431:459:484 SD: 0.2884 cents 258:272:290:306:326:344:367:387:408:435:459:489:516 SD: 0.2037 cents 344:363:387:408:435:459:489:516:544:580:612:652:688 SD: 0.2000 cents 386:407:434:458:488:515:549:579:611:651:687:732:772 SD: 0.1729 cents 424:447:477:503:536:565:603:636:671:715:755:804:848 SD: 0.1506 cents 462:487:520:548:584:616:657:693:731:779:822:876:924 SD: 0.1358 cents 552:582:621:655:698:736:785:828:873:930:982:1047:1104 SD: 0.1260 cents 568:599:639:674:718:757:808:852:899:957:1011:1077:1136 SD: 0.1188 cents