Scala analysis: schisdia4
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: 16/15 111.731285 minor diatonic semitone 2: 9/8 203.910002 major whole tone 3: 1215/1024 296.088718 wide augmented second 4: 81/64 407.820003 Pythagorean major third 5: 4/3 498.044999 perfect fourth 6: 64/45 609.776284 2nd tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 27/16 905.865003 Pythagorean major sixth 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: 16/15 111.7313 minor diatonic semitone 2: 135/128 92.1787 major chroma, major limma 3: 135/128 92.1787 major chroma, major limma 4: 16/15 111.7313 minor diatonic semitone 5: 256/243 90.2250 limma, Pythagorean minor second 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma 8: 16/15 111.7313 minor diatonic semitone 9: 135/128 92.1787 major chroma, major limma 10: 135/128 92.1787 major chroma, major limma 11: 524288/492075 109.7776 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: 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 : 111.7 203.9 296.1 407.8 498.0 609.8 702.0 813.7 905.9 998.0 1107.8 1200.0 111.7 : 92.2 184.4 296.1 386.3 498.0 590.2 702.0 794.1 886.3 996.1 1088.3 1200.0 203.9 : 92.2 203.9 294.1 405.9 498.0 609.8 702.0 794.1 903.9 996.1 1107.8 1200.0 296.1 : 111.7 202.0 313.7 405.9 517.6 609.8 702.0 811.7 903.9 1015.6 1107.8 1200.0 407.8 : 90.2 202.0 294.1 405.9 498.0 590.2 700.0 792.2 903.9 996.1 1088.3 1200.0 498.0 : 111.7 203.9 315.6 407.8 500.0 609.8 702.0 813.7 905.9 998.0 1109.8 1200.0 609.8 : 92.2 203.9 296.1 388.3 498.0 590.2 702.0 794.1 886.3 998.0 1088.3 1200.0 702.0 : 111.7 203.9 296.1 405.9 498.0 609.8 702.0 794.1 905.9 996.1 1107.8 1200.0 813.7 : 92.2 184.4 294.1 386.3 498.0 590.2 682.4 794.1 884.4 996.1 1088.3 1200.0 905.9 : 92.2 202.0 294.1 405.9 498.0 590.2 702.0 792.2 903.9 996.1 1107.8 1200.0 998.0 : 109.8 202.0 313.7 405.9 498.0 609.8 700.0 811.7 903.9 1015.6 1107.8 1200.0 1107.8: 92.2 203.9 296.1 388.3 500.0 590.2 702.0 794.1 905.9 998.0 1090.2 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 : 100.50833 cents, oct.: 1206.09991 cents Scale is strictly proper Step pattern alph. order: ABBACABABBDB Step pattern size order : DBBDADBDBBCB 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 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% Limited inverse transpositions with margin 21.5063 cents: 11 -- 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 : 0.174822 Specific harmonicity : 0.107151 Fundamental : 1/276480, -18.0768 octaves, 0.0009 Hz. Guide tone : 933120, 19.8317 octaves, 244128047.494 Hz. Exponens Consonantiae : 2.579890E+11, 37.90852 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 4348.0, average 362.33333 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 : 35.31398, average 2.94283 Vogel's harmonic complexity : 26.75000 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: -11 .. 8 -0.91667 59 1 3: -3 .. 6 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: 4 3 3 4 3 3 3 4 3 3 4 3 SP D3 SD: 7.9998 c. M:-12.1800 c. 41: 4 3 3 4 3 4 3 4 3 3 4 3 SP M ME SD: 3.3242 c. M:-5.8259 c. Twelve-tone Chromatic (1/44-comma positive) 53: 5 4 4 5 4 5 4 5 4 4 5 4 SP M ME SD: 1.1422 c. M: 1.8173 c. Meantone Chromatic (1/315-comma) 65: 6 5 5 6 5 6 5 6 5 5 6 5 SP M ME SD: 0.9251 c. M: 1.6662 c. Meantone Chromatic (1/52-comma) 118: 11 9 9 11 9 11 9 11 9 9 11 9 SP M DE SD: 0.7156 c. M: 1.4335 c. Meantone Chromatic (1/83-comma), Helmholtz-12 183: 17 14 14 17 14 17 14 17 14 14 17 14 SP M DE SD: 0.7296 c. M: 1.3224 c. Meantone Chromatic (1/68-comma), Countermeantone-12 248: 23 19 19 23 19 23 19 23 19 19 23 19 SP M DE SD: 0.7625 c. M: 1.3684 c. 289: 27 22 22 27 22 27 22 27 22 22 27 22 SP M DE SD: 0.7465 c. M: 1.5039 c. 301: 28 23 23 28 23 28 23 28 23 23 28 23 SP M DE SD: 0.7148 c. M: 1.3660 c. 311: 29 24 24 29 23 29 24 29 24 24 28 24 SP SD: 0.7018 c. M:-1.3132 c. 313: 29 24 24 29 24 29 24 29 24 24 29 24 SP M DE SD: 0.7885 c. M: 1.4302 c. 323: 30 25 25 30 24 30 25 30 25 25 29 25 SP SD: 0.6620 c. M:-1.3371 c. 352: 33 27 27 33 26 33 27 33 27 27 32 27 SP SD: 0.7098 c. M:-1.2709 c. 364: 34 28 28 34 27 34 28 34 28 28 33 28 SP SD: 0.5367 c. M:-0.9712 c. 376: 35 29 29 35 28 35 29 35 29 29 34 29 SP SD: 0.4510 c. M:-0.8925 c. 417: 39 32 32 39 31 39 32 39 32 32 38 32 SP SD: 0.4551 c. M:-0.8131 c. 429: 40 33 33 40 32 40 33 40 33 33 39 33 SP SD: 0.3224 c. M:-0.5716 c. 441: 41 34 34 41 33 41 34 41 34 34 40 34 SP SD: 0.2966 c. M:-0.5957 c. 482: 45 37 37 45 36 45 37 45 37 37 44 37 SP SD: 0.2691 c. M:-0.4788 c. 494: 46 38 38 46 37 46 38 46 38 38 45 38 SP SD: 0.1733 c. M:-0.3368 c. 547: 51 42 42 51 41 51 42 51 42 42 50 42 SP SD: 0.1277 c. M:-0.2239 c. 559: 52 43 43 52 42 52 43 52 43 43 51 43 SP SD: 0.0940 c. M:-0.1674 c. 612: 57 47 47 57 46 57 47 57 47 47 56 47 SP SD: 0.0205 c. M:-0.0392 c. 2395: 223 184 184 223 180 223 184 223 184 184 219 184 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: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.0699 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.7664 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.4747 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.6544 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.0631 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.0999 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1536 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 9.9563 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.7994 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 9.4173 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 6.8471 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.4816 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 4.9668 cents 18:19:20:21:23:24:26:27:29:30:32:34:36 SD: 4.7834 cents 22:23:25:26:28:29:31:33:35:37:39:42:44 SD: 4.2629 cents 26:28:29:31:33:35:37:39:42:44:46:49:52 SD: 3.1015 cents 30:32:34:36:38:40:43:45:48:51:53:57:60 SD: 2.7231 cents 33:35:37:39:42:44:47:50:53:56:59:63:66 SD: 2.5211 cents 38:41:43:45:48:51:54:57:61:64:68:72:76 SD: 2.3311 cents 42:45:47:50:53:56:60:63:67:71:75:80:84 SD: 1.6477 cents 48:51:54:57:61:64:68:72:77:81:85:91:96 SD: 1.2938 cents 64:68:72:76:81:85:91:96:102:108:114:121:128 SD: 1.0829 cents 80:85:90:95:101:107:114:120:128:135:142:152:160 SD: 0.9860 cents 86:92:97:102:109:115:122:129:138:145:153:163:172 SD: 0.9327 cents 87:93:98:103:110:116:124:131:139:147:155:165:174 SD: 0.8673 cents 90:96:101:107:114:120:128:135:144:152:160:171:180 SD: 0.5863 cents 135:144:152:160:171:180:192:203:216:228:240:256:270 SD: 0.4710 cents 150:160:169:178:190:200:213:225:240:253:267:284:300 SD: 0.4089 cents 182:194:205:216:230:243:259:273:291:307:324:345:364 SD: 0.3905 cents 192:205:216:228:243:256:273:288:307:324:342:364:384 SD: 0.2435 cents 240:256:270:285:304:320:341:360:384:405:427:455:480 SD: 0.2276 cents 327:349:368:388:414:436:465:491:523:552:582:620:654 SD: 0.1989 cents 358:382:403:425:453:477:509:537:573:604:637:679:716 SD: 0.1867 cents 422:450:475:501:534:563:600:633:675:712:751:800:844 SD: 0.1693 cents 450:480:506:534:570:600:640:675:720:759:801:853:900 SD: 0.1674 cents 462:493:520:548:585:616:657:693:739:780:822:876:924 SD: 0.1549 cents 528:563:594:626:668:704:751:792:845:891:940:1001:1056 SD: 0.1494 cents 542:578:610:643:686:723:771:813:867:915:965:1028:1084 SD: 0.1367 cents 558:595:628:662:706:744:794:837:893:942:993:1058:1116 SD: 0.1350 cents 568:606:639:674:719:757:808:852:909:959:1011:1077:1136 SD: 0.1174 cents