Scala analysis: schisdia3
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: 4096/3645 201.956281 narrow diminished third 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: 3/2 701.955001 perfect fifth 8: 128/81 792.179997 Pythagorean minor sixth 9: 2048/1215 903.911282 narrow diminished seventh 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: 135/128 92.1787 major chroma, major limma 2: 524288/492075 109.7776 3: 135/128 92.1787 major chroma, major limma 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: 16/15 111.7313 minor diatonic semitone 8: 256/243 90.2250 limma, Pythagorean minor second 9: 16/15 111.7313 minor diatonic semitone 10: 135/128 92.1787 major chroma, major limma 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: 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: 4 32/27 294.135 cents Pythagorean minor third 3: 5 1215/1024 296.089 cents wide augmented second 3: 2 65536/54675 313.688 cents 3: 1 6/5 315.641 cents minor third 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: 1 5/3 884.359 cents major sixth, BP sixth 9: 2 54675/32768 886.312 cents 9: 5 2048/1215 903.911 cents narrow diminished seventh 9: 4 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: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 202.0 294.1 386.3 498.0 590.2 702.0 792.2 903.9 996.1 1088.3 1200.0 92.2 : 109.8 202.0 294.1 405.9 498.0 609.8 700.0 811.7 903.9 996.1 1107.8 1200.0 202.0 : 92.2 184.4 296.1 388.3 500.0 590.2 702.0 794.1 886.3 998.0 1090.2 1200.0 294.1 : 92.2 203.9 296.1 407.8 498.0 609.8 702.0 794.1 905.9 998.0 1107.8 1200.0 386.3 : 111.7 203.9 315.6 405.9 517.6 609.8 702.0 813.7 905.9 1015.6 1107.8 1200.0 498.0 : 92.2 203.9 294.1 405.9 498.0 590.2 702.0 794.1 903.9 996.1 1088.3 1200.0 590.2 : 111.7 202.0 313.7 405.9 498.0 609.8 702.0 811.7 903.9 996.1 1107.8 1200.0 702.0 : 90.2 202.0 294.1 386.3 498.0 590.2 700.0 792.2 884.4 996.1 1088.3 1200.0 792.2 : 111.7 203.9 296.1 407.8 500.0 609.8 702.0 794.1 905.9 998.0 1109.8 1200.0 903.9 : 92.2 184.4 296.1 388.3 498.0 590.2 682.4 794.1 886.3 998.0 1088.3 1200.0 996.1 : 92.2 203.9 296.1 405.9 498.0 590.2 702.0 794.1 905.9 996.1 1107.8 1200.0 1088.3: 111.7 203.9 313.7 405.9 498.0 609.8 702.0 813.7 903.9 1015.6 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: 184.3574 .. 203.9100 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 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 .. 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 : 99.49769 cents, oct.: 1193.97232 cents Scale is strictly proper Step pattern alph. order: ABAACACDCAAC Step pattern size order : BCBBDBDADBBD Scale is a Constant Structure, by a margin of 70.67243 cents Scale diversity : 1.146078 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.811000 Rothenberg efficiency : 0.409689 redundancy: 0.590311 Efficiency x scale size : 4.916270 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 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 Formal octave complements present : 3 = 25.0000% Limited inverse transpositions with margin 21.5063 cents: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 492075 (O: 492075 U: 492075) Highest odd numerator or denominator: 3645 Scale harmonicity : 0.017921 Average absolute harmonicity : 0.174808 Specific harmonicity : 0.107151 Fundamental : 1/466560, -18.8317 octaves, 0.0006 Hz. Guide tone : 552960, 19.0768 octaves, 144668472.589 Hz. Exponens Consonantiae : 2.579890E+11, 37.90852 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 5842.0, average 486.83333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.55322, average 1.46277 Sum of Tenney's harmonic distance : 35.61501, average 2.96792 Vogel's harmonic complexity : 29.33333 Wille's k value : 246037 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 11 Triangular lattice diameter : 11 Lattice compactness : 597.56240, average 7.66106 Lattice compactness (without 2's) : 264.46886, average 3.39063 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 12 2.00000 60 1 3: -6 .. 3 -1.16667 28 5 5: -1 .. 1 0.16667 6 6 Average exponent except 2's :-12 / 12 =-1.00000 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: 7.1839 c. M:-13.6863 c. Twelve-tone Chromatic (1/11-comma) 40: 3 4 3 3 4 3 3 3 4 3 3 4 SP D3 SD: 7.9998 c. M: 12.1800 c. 41: 3 4 3 3 4 3 4 3 4 3 3 4 SP M ME SD: 3.3242 c. M: 5.8259 c. 53: 4 5 4 4 5 4 5 4 5 4 4 5 SP M ME SD: 1.1422 c. M:-1.8173 c. 65: 5 6 5 5 6 5 6 5 6 5 5 6 SP M ME SD: 0.9251 c. M:-1.6662 c. 118: 9 11 9 9 11 9 11 9 11 9 9 11 SP M DE SD: 0.7156 c. M:-1.4335 c. 183: 14 17 14 14 17 14 17 14 17 14 14 17 SP M DE SD: 0.7296 c. M:-1.3224 c. 248: 19 23 19 19 23 19 23 19 23 19 19 23 SP M DE SD: 0.7625 c. M:-1.3684 c. 289: 22 27 22 22 27 22 27 22 27 22 22 27 SP M DE SD: 0.7465 c. M:-1.5039 c. 301: 23 28 23 23 28 23 28 23 28 23 23 28 SP M DE SD: 0.7148 c. M:-1.3660 c. 311: 24 28 24 24 29 24 29 23 29 24 24 29 SP SD: 0.7018 c. M: 1.3132 c. 313: 24 29 24 24 29 24 29 24 29 24 24 29 SP M DE SD: 0.7885 c. M:-1.4302 c. 323: 25 29 25 25 30 25 30 24 30 25 25 30 SP SD: 0.6620 c. M: 1.3371 c. 352: 27 32 27 27 33 27 33 26 33 27 27 33 SP SD: 0.7098 c. M: 1.2709 c. 364: 28 33 28 28 34 28 34 27 34 28 28 34 SP SD: 0.5367 c. M: 0.9712 c. 376: 29 34 29 29 35 29 35 28 35 29 29 35 SP SD: 0.4510 c. M: 0.8925 c. 417: 32 38 32 32 39 32 39 31 39 32 32 39 SP SD: 0.4551 c. M: 0.8131 c. 429: 33 39 33 33 40 33 40 32 40 33 33 40 SP SD: 0.3224 c. M: 0.5716 c. 441: 34 40 34 34 41 34 41 33 41 34 34 41 SP SD: 0.2966 c. M: 0.5957 c. 482: 37 44 37 37 45 37 45 36 45 37 37 45 SP SD: 0.2691 c. M: 0.4788 c. 494: 38 45 38 38 46 38 46 37 46 38 38 46 SP SD: 0.1733 c. M: 0.3368 c. 547: 42 50 42 42 51 42 51 41 51 42 42 51 SP SD: 0.1277 c. M: 0.2239 c. 559: 43 51 43 43 52 43 52 42 52 43 43 52 SP SD: 0.0940 c. M: 0.1674 c. 612: 47 56 47 47 57 47 57 46 57 47 47 57 SP SD: 0.0205 c. M: 0.0392 c. 2395: 184 219 184 184 223 184 223 180 223 184 184 223 SP SD: 0.0184 c. M: 0.0356 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: 6.8160 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: 8.5623 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.2992 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.4763 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.1174 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4003 cents 11 x 12:13:14:15 x x 17:19:20:21:22 SD: 11.6029 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.8296 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 9.1724 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.7741 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.5664 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.9294 cents 17:18:19:20:21:23:24:26:27:29:30:32:34 SD: 4.7481 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 3.9904 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.6781 cents 31:33:35:37:39:41:44:47:49:52:55:58:62 SD: 3.2176 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.0279 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.6726 cents 54:57:61:64:68:72:76:81:85:91:96:101:108 SD: 1.4763 cents 64:68:72:76:80:85:90:96:101:108:114:120:128 SD: 1.3044 cents 71:75:80:84:89:95:100:107:112:120:126:133:142 SD: 1.2224 cents 72:76:81:85:90:96:101:108:114:121:128:135:144 SD: 0.8675 cents 96:101:108:114:120:128:135:144:152:162:171:180:192 SD: 0.6465 cents 128:135:144:152:160:171:180:192:202:216:228:240:256 SD: 0.5730 cents 145:153:163:172:181:193:204:218:229:244:258:272:290 SD: 0.5698 cents 152:160:171:180:190:203:214:228:240:256:270:285:304 SD: 0.4967 cents 162:171:182:192:203:216:228:243:256:273:288:304:324 SD: 0.4139 cents 184:194:207:218:230:245:259:276:291:310:327:345:368 SD: 0.3313 cents 216:228:243:256:270:288:304:324:341:364:384:405:432 SD: 0.2753 cents 276:291:310:327:345:368:388:414:436:465:491:518:552 SD: 0.2187 cents 324:342:364:384:405:432:456:486:512:546:576:608:648 SD: 0.2115 cents 372:392:418:441:465:496:523:558:588:627:661:698:744 SD: 0.1897 cents 404:426:454:479:505:539:568:606:638:681:718:758:808 SD: 0.1822 cents 420:443:472:498:525:560:591:630:664:708:747:788:840 SD: 0.1718 cents 436:460:490:517:545:581:613:654:689:735:775:818:872 SD: 0.1551 cents 492:519:553:583:615:656:692:738:777:829:875:923:984 SD: 0.1525 cents 512:540:575:607:640:683:720:768:809:863:910:960:1024 SD: 0.1270 cents 584:616:656:692:730:779:821:876:923:984:1038:1095:1168 SD: 0.1217 cents 588:620:661:697:735:784:827:882:929:991:1045:1103:1176 SD: 0.1131 cents 600:633:674:711:750:800:844:900:948:1011:1067:1125:1200 SD: 0.1092 cents