Scala analysis: schisdia5
Schisdia 32805/32768 2048/2025 scale
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: 27/16 905.865003 Pythagorean major sixth 10: 16/9 996.089998 Pythagorean minor seventh 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: 16/15 111.7313 minor diatonic semitone 10: 256/243 90.2250 limma, Pythagorean minor second 11: 16/15 111.7313 minor diatonic semitone 12: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 6 135/128 92.179 cents major chroma, major limma 1: 1 524288/492075 109.778 cents 1: 4 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: 2 5/4 386.314 cents major third 4: 2 164025/131072 388.267 cents 4: 6 512/405 405.866 cents narrow diminished fourth 4: 2 81/64 407.820 cents Pythagorean major third 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: 6 45/32 590.224 cents diatonic tritone 6: 6 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: 2 128/81 792.180 cents Pythagorean minor sixth 8: 6 405/256 794.134 cents wide augmented fifth 8: 2 262144/164025 811.733 cents two (narrow diminished fourth) 8: 2 8/5 813.686 cents minor sixth 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: 4 15/8 1088.269 cents classic major seventh 11: 1 492075/262144 1090.222 cents 11: 6 256/135 1107.821 cents octave - major chroma 11: 1 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 203.9 296.1 405.9 498.0 609.8 702.0 794.1 905.9 996.1 1107.8 1200.0 92.2 : 111.7 203.9 313.7 405.9 517.6 609.8 702.0 813.7 903.9 1015.6 1107.8 1200.0 203.9 : 92.2 202.0 294.1 405.9 498.0 590.2 702.0 792.2 903.9 996.1 1088.3 1200.0 296.1 : 109.8 202.0 313.7 405.9 498.0 609.8 700.0 811.7 903.9 996.1 1107.8 1200.0 405.9 : 92.2 203.9 296.1 388.3 500.0 590.2 702.0 794.1 886.3 998.0 1090.2 1200.0 498.0 : 111.7 203.9 296.1 407.8 498.0 609.8 702.0 794.1 905.9 998.0 1107.8 1200.0 609.8 : 92.2 184.4 296.1 386.3 498.0 590.2 682.4 794.1 886.3 996.1 1088.3 1200.0 702.0 : 92.2 203.9 294.1 405.9 498.0 590.2 702.0 794.1 903.9 996.1 1107.8 1200.0 794.1 : 111.7 202.0 313.7 405.9 498.0 609.8 702.0 811.7 903.9 1015.6 1107.8 1200.0 905.9 : 90.2 202.0 294.1 386.3 498.0 590.2 700.0 792.2 903.9 996.1 1088.3 1200.0 996.1 : 111.7 203.9 296.1 407.8 500.0 609.8 702.0 813.7 905.9 998.0 1109.8 1200.0 1107.8: 92.2 184.4 296.1 388.3 498.0 590.2 702.0 794.1 886.3 998.0 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 111.7313 cents 81/80, 21.5063 cents 256/243, 90.2250 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: 386.3137 .. 407.8200 cents 81/80, 21.5063 cents 273375/262144, 72.6261 cents 5: 498.0450 .. 517.5976 cents 2048/2025, 19.5526 cents 256/243, 90.2250 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: 792.1800 .. 813.6863 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 9: 886.3124 .. 905.8650 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 10: 996.0900 .. 1015.6426 cents 2048/2025, 19.5526 cents 256/243, 90.2250 cents 11: 1088.2687 .. 1109.7750 cents 81/80, 21.5063 cents 273375/262144, 72.6261 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.108340 Largest / Average step : 1.117313 Largest / Smallest step : 1.238363 Median interval of one step : 135/128, 92.1787 cents, amount: 6 Most common interval of one step : 135/128, 92.1787 cents, amount: 6 Least squares average step : 100.19552 cents, oct.: 1202.34621 cents Scale is strictly proper Step pattern alph. order: ABACABAABDBA Step pattern size order : BDBCBDBBDADB Scale is a Constant Structure, by a margin of 72.62615 cents Scale diversity : 1.143424 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.814256 Rothenberg efficiency : 0.415278 redundancy: 0.584722 Efficiency x scale size : 4.983333 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 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 9 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 : 492075 (O: 492075 U: 492075) Highest odd numerator or denominator: 1215 Scale harmonicity : 0.017921 Average absolute harmonicity : 0.171428 Specific harmonicity : 0.102631 Fundamental : 1/414720, -18.6618 octaves, 0.0006 Hz. Guide tone : 622080, 19.2467 octaves, 162752031.662 Hz. Exponens Consonantiae : 2.579890E+11, 37.90852 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 2340.0, average 195.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 18.50746, average 1.54229 Sum of Tenney's harmonic distance : 37.47235, average 3.12270 Vogel's harmonic complexity : 28.25000 Wille's k value : 246037 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 11 Triangular lattice diameter : 11 Lattice compactness : 628.19701, average 8.05381 Lattice compactness (without 2's) : 273.34529, average 3.50443 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -10 .. 9 -0.25000 63 1 3: -4 .. 5 0.50000 30 5 5: -1 .. 1 0.00000 6 6 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 36 / 12 = 3.00000 Scale is weakly epimorphic with val: <12 17 29| Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 19 31|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.5877 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: 3.0024 c. M:-4.8579 c. 53: 4 5 4 5 4 5 4 4 5 4 5 4 SP M ME SD: 1.1685 c. M: 1.7491 c. 65: 5 6 5 6 5 6 5 5 6 5 6 5 SP M ME SD: 0.5978 c. M: 1.2496 c. 118: 9 11 9 11 9 11 9 9 11 9 11 9 SP M DE SD: 0.6670 c. M: 1.1735 c. 183: 14 17 14 17 14 17 14 14 17 14 17 14 SP M DE SD: 0.5879 c. M: 1.0068 c. 248: 19 23 19 23 19 23 19 19 23 19 23 19 SP M DE SD: 0.5699 c. M: 1.0263 c. 313: 24 29 24 29 24 29 24 24 29 24 29 24 SP M DE SD: 0.5661 c. M: 1.0727 c. 352: 27 33 27 32 27 33 27 27 33 26 33 27 SP SD: 0.4544 c. M:-0.9532 c. 364: 28 34 28 33 28 34 28 28 34 27 34 28 SP SD: 0.3895 c. M:-0.7284 c. 376: 29 35 29 34 29 35 29 29 35 28 35 29 SP SD: 0.4087 c. M:-0.7198 c. 405: 31 38 31 37 31 38 31 31 38 30 38 31 SP SD: 0.4055 c. M:-0.8017 c. 417: 32 39 32 38 32 39 32 32 39 31 39 32 SP SD: 0.2905 c. M:-0.6098 c. 429: 33 40 33 39 33 40 33 33 40 32 40 33 SP SD: 0.2486 c. M:-0.4287 c. 482: 37 45 37 44 37 45 37 37 45 36 45 37 SP SD: 0.1710 c. M:-0.3591 c. 494: 38 46 38 45 38 46 38 38 46 37 46 38 SP SD: 0.1523 c. M:-0.2676 c. 547: 42 51 42 50 42 51 42 42 51 41 51 42 SP SD: 0.0804 c. M:-0.1679 c. 559: 43 52 43 51 43 52 43 43 52 42 52 43 SP SD: 0.0975 c. M:-0.1546 c. 612: 47 57 47 56 47 57 47 47 57 46 57 47 SP SD: 0.0158 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: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.3876 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.8780 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.7422 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.8525 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.0765 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.9960 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4699 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 10.4708 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4182 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 10.1923 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.8384 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.9983 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.7297 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 3.3895 cents 26:27:29:31:33:35:37:39:41:44:46:49:52 SD: 3.3069 cents 31:33:35:37:39:41:44:47:49:52:55:59:62 SD: 2.8688 cents 33:35:37:39:42:44:47:50:52:56:59:63:66 SD: 2.6253 cents 38:40:43:45:48:51:54:57:60:64:68:72:76 SD: 1.6902 cents 48:51:54:57:61:64:68:72:76:81:85:91:96 SD: 1.5399 cents 54:57:61:64:68:72:77:81:85:91:96:102:108 SD: 1.3185 cents 71:75:80:84:90:95:101:107:112:120:126:135:142 SD: 1.2576 cents 72:76:81:85:91:96:102:108:114:122:128:137:144 SD: 1.2128 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: 1.0604 cents 86:91:97:102:109:115:122:129:136:145:153:163:172 SD: 0.9200 cents 90:95:101:107:114:120:128:135:142:152:160:171:180 SD: 0.7398 cents 112:118:126:133:142:149:159:168:177:189:199:212:224 SD: 0.6944 cents 128:135:144:152:162:171:182:192:203:216:228:243:256 SD: 0.5945 cents 144:152:162:171:182:192:205:216:228:243:256:273:288 SD: 0.2541 cents 258:272:290:306:326:344:367:387:408:435:459:489:516 SD: 0.2511 cents 294:310:331:349:372:392:418:441:465:496:523:558:588 SD: 0.2508 cents 306:323:344:363:387:408:435:459:484:516:544:580:612 SD: 0.2237 cents 368:388:414:437:465:491:523:552:582:621:654:698:736 SD: 0.2174 cents 386:407:434:458:488:515:549:579:611:651:686:732:772 SD: 0.1806 cents 402:424:452:477:508:536:572:603:636:678:715:762:804 SD: 0.1697 cents 424:447:477:503:536:565:603:636:671:716:754:804:848 SD: 0.1605 cents 462:487:520:548:584:616:657:693:731:780:821:876:924 SD: 0.1496 cents 510:538:574:605:645:680:725:765:807:861:907:967:1020 SD: 0.1462 cents 514:542:578:610:650:685:731:771:813:867:914:975:1028 SD: 0.1435 cents 552:582:621:655:698:736:785:828:873:932:981:1047:1104 SD: 0.1233 cents