Scala analysis: schisdia2
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: 256/243 90.224996 limma, Pythagorean minor second 2: 10/9 182.403712 minor whole tone 3: 32/27 294.134997 Pythagorean minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 45/32 590.223716 diatonic tritone 7: 16384/10935 700.001280 fifth - schisma, 5-limit approximation to ET fifth 8: 128/81 792.179997 Pythagorean minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 256/243 90.2250 limma, Pythagorean minor second 2: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 135/128 92.1787 major chroma, major limma 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 524288/492075 109.7776 8: 135/128 92.1787 major chroma, major limma 9: 135/128 92.1787 major chroma, major limma 10: 16/15 111.7313 minor diatonic semitone 11: 135/128 92.1787 major chroma, major limma 12: 16/15 111.7313 minor diatonic semitone
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: 1 10/9 182.404 cents minor whole tone 2: 1 18225/16384 184.357 cents two (major chroma, major limma) 2: 3 4096/3645 201.956 cents narrow diminished third 2: 7 9/8 203.910 cents major whole tone 3: 5 32/27 294.135 cents Pythagorean minor third 3: 4 1215/1024 296.089 cents wide augmented second 3: 1 65536/54675 313.688 cents 3: 2 6/5 315.641 cents minor third 4: 3 5/4 386.314 cents major third 4: 1 164025/131072 388.267 cents 4: 5 512/405 405.866 cents narrow diminished fourth 4: 3 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: 3 128/81 792.180 cents Pythagorean minor sixth 8: 5 405/256 794.134 cents wide augmented fifth 8: 1 262144/164025 811.733 cents two (narrow diminished fourth) 8: 3 8/5 813.686 cents minor sixth 9: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 54675/32768 886.312 cents 9: 4 2048/1215 903.911 cents narrow diminished seventh 9: 5 27/16 905.865 cents Pythagorean major sixth 10: 7 16/9 996.090 cents Pythagorean minor seventh 10: 3 3645/2048 998.044 cents wide augmented sixth 10: 1 32768/18225 1015.643 cents 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 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: 3.63636 = 40/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 90.2 182.4 294.1 386.3 498.0 590.2 700.0 792.2 884.4 996.1 1088.3 1200.0 90.2 : 92.2 203.9 296.1 407.8 500.0 609.8 702.0 794.1 905.9 998.0 1109.8 1200.0 182.4 : 111.7 203.9 315.6 407.8 517.6 609.8 702.0 813.7 905.9 1017.6 1107.8 1200.0 294.1 : 92.2 203.9 296.1 405.9 498.0 590.2 702.0 794.1 905.9 996.1 1088.3 1200.0 386.3 : 111.7 203.9 313.7 405.9 498.0 609.8 702.0 813.7 903.9 996.1 1107.8 1200.0 498.0 : 92.2 202.0 294.1 386.3 498.0 590.2 702.0 792.2 884.4 996.1 1088.3 1200.0 590.2 : 109.8 202.0 294.1 405.9 498.0 609.8 700.0 792.2 903.9 996.1 1107.8 1200.0 700.0 : 92.2 184.4 296.1 388.3 500.0 590.2 682.4 794.1 886.3 998.0 1090.2 1200.0 792.2 : 92.2 203.9 296.1 407.8 498.0 590.2 702.0 794.1 905.9 998.0 1107.8 1200.0 884.4 : 111.7 203.9 315.6 405.9 498.0 609.8 702.0 813.7 905.9 1015.6 1107.8 1200.0 996.1 : 92.2 203.9 294.1 386.3 498.0 590.2 702.0 794.1 903.9 996.1 1088.3 1200.0 1088.3: 111.7 202.0 294.1 405.9 498.0 609.8 702.0 811.7 903.9 996.1 1107.8 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: 182.4037 .. 203.9100 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 3: 294.1350 .. 315.6413 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 4: 386.3137 .. 407.8200 cents 81/80, 21.5063 cents 25/24, 70.6724 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: 884.3587 .. 905.8650 cents 81/80, 21.5063 cents 25/24, 70.6724 cents 10: 996.0900 .. 1017.5963 cents 81/80, 21.5063 cents 256/243, 90.2250 cents 11: 1088.2687 .. 1109.7750 cents 81/80, 21.5063 cents 25/24, 70.6724 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 : 99.14276 cents, oct.: 1189.71310 cents Scale is strictly proper Step pattern alph. order: ABCBCBDBBCBC Step pattern size order : ABDBDBCBBDBD Scale is a Constant Structure, by a margin of 70.67243 cents Scale diversity : 1.148749 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.807743 Rothenberg efficiency : 0.393353 redundancy: 0.606647 Efficiency x scale size : 4.720238 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.63636 = 40/11 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: 7 Number of recognisable fifths : 11, average 701.5998 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited inverse transpositions with margin 21.5063 cents: 9 -- Rational properties -- Prime limit : 5 Odd number limit : 492075 (O: 492075 U: 492075) Highest odd numerator or denominator: 10935 Scale harmonicity : 0.017921 Average absolute harmonicity : 0.164828 Specific harmonicity : 0.120817 Fundamental : 1/349920, -18.4167 octaves, 0.0007 Hz. Guide tone : 737280, 19.4919 octaves, 192891296.785 Hz. Exponens Consonantiae : 2.579890E+11, 37.90852 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 14128.5, average 1177.37500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 16.37712, average 1.36476 Sum of Tenney's harmonic distance : 33.20677, average 2.76723 Vogel's harmonic complexity : 29.83333 Wille's k value : 246037 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 11 Triangular lattice diameter : 11 Lattice compactness : 522.34813, average 6.69677 Lattice compactness (without 2's) : 241.34067, average 3.09411 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 14 2.66667 52 1 3: -7 .. 2 -1.83333 28 5 5: -1 .. 1 0.33333 6 6 Average exponent except 2's :-18 / 12 =-1.50000 Average absolute exponent except 2's: 34 / 12 = 2.83333 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.9373 c. M:-17.5963 c. Twelve-tone Chromatic (1/11-comma) 29: 2 2 3 2 3 2 3 2 2 3 2 3 SP M ME SD: 9.6733 c. M: 16.8865 c. 32: 2 3 3 2 3 3 3 2 3 3 2 3 SP D3 SD: 10.4865 c. M:-16.4100 c. 33: 2 3 3 3 3 2 3 3 2 3 3 3 SP D3 SD: 9.9443 c. M: 17.4977 c. 34: 3 2 3 3 3 3 3 2 3 3 3 3 SP B ME SD: 8.7329 c. M: 15.7094 c. 38: 3 3 3 3 4 3 3 3 3 4 2 4 SP D3 SD: 8.3014 c. M: 14.5845 c. 39: 3 3 4 3 3 3 4 3 3 3 3 4 SP D3 SD: 8.6052 c. M:-13.6863 c. 41: 3 3 4 3 4 3 4 3 3 4 3 4 SP M ME SD: 3.9883 c. M: 6.7940 c. 53: 4 4 5 4 5 4 5 4 4 5 4 5 SP M ME SD: 1.0712 c. M:-1.8855 c. 118: 9 9 11 9 11 9 11 9 9 11 9 11 SP M DE SD: 0.7824 c. M:-1.6936 c. 171: 13 13 16 13 16 13 16 13 13 16 13 16 SP M DE SD: 0.7244 c. M:-1.7531 c. 183: 14 14 17 14 17 14 17 14 14 17 14 17 SP M DE SD: 0.9484 c. M:-1.6381 c. 224: 17 17 21 17 21 17 21 17 17 21 17 21 SP M DE SD: 0.7552 c. M:-1.7844 c. 289: 22 22 27 22 27 22 27 22 22 27 22 27 SP M DE SD: 0.7301 c. M:-1.7288 c. 305: 23 23 29 23 29 23 28 23 24 28 24 28 SP SD: 0.9936 c. M:-1.6271 c. 307: 23 24 28 24 28 24 28 24 23 29 23 29 SP SD: 0.9861 c. M: 1.6281 c. 311: 23 24 29 24 29 24 28 24 24 29 24 29 SP SD: 0.8823 c. M: 1.6090 c. 322: 24 25 30 25 30 24 30 25 24 30 25 30 SP SD: 0.9769 c. M:-1.6088 c. 323: 24 25 30 25 30 25 29 25 25 30 25 30 SP SD: 0.6675 c. M: 1.5493 c. 333: 25 26 31 25 31 26 30 26 25 31 26 31 SP SD: 0.9599 c. M: 1.4954 c. 335: 25 26 31 26 31 26 30 26 26 31 26 31 SP SD: 0.6411 c. M: 1.4938 c. 346: 26 27 32 26 33 26 32 26 27 32 27 32 SP SD: 0.9116 c. M: 1.4286 c. 347: 26 27 32 27 32 27 31 27 27 32 27 32 SP SD: 0.7850 c. M: 1.4422 c. 355: 27 27 33 27 33 28 32 27 28 33 27 33 SP SD: 0.8877 c. M:-1.3256 c. 358: 27 27 34 27 34 27 33 27 28 33 28 33 SP SD: 0.8610 c. M: 1.3981 c. 364: 27 28 34 28 34 28 33 28 28 34 28 34 SP SD: 0.7549 c. M: 1.2140 c. 376: 28 29 35 29 35 29 34 29 29 35 29 35 SP SD: 0.5144 c. M: 1.0651 c. 388: 29 30 36 30 36 30 35 30 30 36 30 36 SP SD: 0.4293 c. M: 1.0322 c. 400: 30 31 37 31 37 31 36 31 31 37 31 37 SP SD: 0.5392 c. M: 1.0013 c. 429: 32 33 40 33 40 33 39 33 33 40 33 40 SP SD: 0.4347 c. M: 0.7145 c. 441: 33 34 41 34 41 34 40 34 34 41 34 41 SP SD: 0.2852 c. M: 0.6816 c. 453: 34 35 42 35 42 35 41 35 35 42 35 42 SP SD: 0.3511 c. M: 0.6635 c. 482: 36 37 45 37 45 37 44 37 37 45 37 45 SP SD: 0.4075 c. M: 0.6610 c. 494: 37 38 46 38 46 38 45 38 38 46 38 46 SP SD: 0.2058 c. M: 0.4061 c. 506: 38 39 47 39 47 39 46 39 39 47 39 47 SP SD: 0.2027 c. M: 0.3965 c. 547: 41 42 51 42 51 42 50 42 42 51 42 51 SP SD: 0.1943 c. M: 0.3196 c. 559: 42 43 52 43 52 43 51 43 43 52 43 52 SP SD: 0.0837 c. M: 0.1802 c. 612: 46 47 57 47 57 47 56 47 47 57 47 57 SP SD: 0.0287 c. M: 0.0508 c. 1783: 134 137 166 137 166 137 163 137 137 166 137 166 SP SD: 0.0249 c. M: 0.0574 c. 2395: 180 184 223 184 223 184 219 184 184 223 184 223 SP SD: 0.0220 c. M: 0.0430 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: 0.9769 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.8335 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.6080 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.9247 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.9735 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.5188 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.5135 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3320 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.5523 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 6.4502 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.5180 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.3785 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.9135 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.5740 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.7121 cents 20:21:22:24:25:27:28:30:32:33:36:38:40 SD: 4.6232 cents 21:22:23:25:26:28:30:31:33:35:37:39:42 SD: 4.6127 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.6781 cents 27:28:30:32:34:36:38:40:43:45:48:51:54 SD: 3.3703 cents 32:34:36:38:40:43:45:48:51:53:57:60:64 SD: 2.9136 cents 33:35:37:39:41:44:46:49:52:55:59:62:66 SD: 2.7944 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 1.9269 cents 52:55:58:62:65:69:73:78:82:87:92:98:104 SD: 1.8386 cents 54:57:60:64:68:72:76:81:85:90:96:101:108 SD: 1.3037 cents 64:67:71:76:80:85:90:96:101:107:114:120:128 SD: 1.2739 cents 71:75:79:84:89:95:100:106:112:118:126:133:142 SD: 1.1441 cents 72:76:80:85:90:96:101:108:114:120:128:135:144 SD: 0.7944 cents 96:101:107:114:120:128:135:144:152:160:171:180:192 SD: 0.7102 cents 108:114:120:128:135:144:152:162:171:180:192:203:216 SD: 0.5707 cents 135:142:150:160:169:180:190:202:213:225:240:253:270 SD: 0.4518 cents 153:161:170:181:191:204:215:229:242:255:272:287:306 SD: 0.4349 cents 189:199:210:224:236:252:266:283:299:315:336:354:378 SD: 0.3187 cents 207:218:230:245:259:276:291:310:327:345:368:388:414 SD: 0.2681 cents 243:256:270:288:304:324:342:364:384:405:432:456:486 SD: 0.2086 cents 297:313:330:352:371:396:418:445:469:495:528:557:594 SD: 0.1942 cents 351:370:390:416:439:468:494:526:555:585:624:658:702 SD: 0.1931 cents 369:389:410:437:461:492:519:553:583:615:656:692:738 SD: 0.1750 cents 431:454:479:511:539:575:606:646:681:718:766:808:862 SD: 0.1608 cents 432:455:480:512:540:576:608:647:683:720:768:810:864 SD: 0.1546 cents 465:490:517:551:581:620:654:697:735:775:827:872:930 SD: 0.1541 cents 504:531:560:597:630:672:709:755:796:840:896:945:1008 SD: 0.1283 cents 540:569:600:640:675:720:759:809:853:900:960:1013:1080 SD: 0.1198 cents 576:607:640:683:720:768:810:863:910:960:1024:1080:1152 SD: 0.0903 cents