Scala analysis: diadiaschis2
Diadiaschisma scale 2048/2025 67108864/66430125
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: 54675/32768 886.312434 10: 32768/18225 1015.642567 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: 135/128 92.1787 major chroma, major limma 10: 1073741824/996451875 129.3301 11: 135/128 92.1787 major chroma, major limma 12: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 135/128 92.179 cents major chroma, major limma 1: 1 524288/492075 109.778 cents 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 1073741824/99645187 129.330 cents 2: 4 18225/16384 184.357 cents two (major chroma, major limma) 2: 2 4096/3645 201.956 cents narrow diminished third 2: 4 9/8 203.910 cents major whole tone 2: 2 8388608/7381125 221.509 cents 3: 2 2460375/2097152 276.536 cents 3: 1 32/27 294.135 cents Pythagorean minor third 3: 4 1215/1024 296.089 cents wide augmented second 3: 5 65536/54675 313.688 cents 4: 4 164025/131072 388.267 cents 4: 8 512/405 405.866 cents narrow diminished fourth 5: 2 22143375/16777216 480.446 cents 5: 7 4/3 498.045 cents perfect fourth 5: 3 8192/6075 517.598 cents 6: 6 45/32 590.224 cents diatonic tritone 6: 6 64/45 609.776 cents 2nd tritone 7: 3 6075/4096 682.402 cents 7: 7 3/2 701.955 cents perfect fifth 7: 2 33554432/22143375 719.554 cents 8: 8 405/256 794.134 cents wide augmented fifth 8: 4 262144/164025 811.733 cents two (narrow diminished fourth) 9: 5 54675/32768 886.312 cents 9: 4 2048/1215 903.911 cents narrow diminished seventh 9: 1 27/16 905.865 cents Pythagorean major sixth 9: 2 4194304/2460375 923.464 cents 10: 2 7381125/4194304 978.491 cents 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 3645/2048 998.044 cents wide augmented sixth 10: 4 32768/18225 1015.643 cents 11: 1 996451875/536870912 1070.670 cents 11: 2 15/8 1088.269 cents classic major seventh 11: 1 492075/262144 1090.222 cents 11: 8 256/135 1107.821 cents octave - major chroma Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 203.9 296.1 405.9 498.0 609.8 702.0 794.1 886.3 1015.6 1107.8 1200.0 92.2 : 111.7 203.9 313.7 405.9 517.6 609.8 702.0 794.1 923.5 1015.6 1107.8 1200.0 203.9 : 92.2 202.0 294.1 405.9 498.0 590.2 682.4 811.7 903.9 996.1 1088.3 1200.0 296.1 : 109.8 202.0 313.7 405.9 498.0 590.2 719.6 811.7 903.9 996.1 1107.8 1200.0 405.9 : 92.2 203.9 296.1 388.3 480.4 609.8 702.0 794.1 886.3 998.0 1090.2 1200.0 498.0 : 111.7 203.9 296.1 388.3 517.6 609.8 702.0 794.1 905.9 998.0 1107.8 1200.0 609.8 : 92.2 184.4 276.5 405.9 498.0 590.2 682.4 794.1 886.3 996.1 1088.3 1200.0 702.0 : 92.2 184.4 313.7 405.9 498.0 590.2 702.0 794.1 903.9 996.1 1107.8 1200.0 794.1 : 92.2 221.5 313.7 405.9 498.0 609.8 702.0 811.7 903.9 1015.6 1107.8 1200.0 886.3 : 129.3 221.5 313.7 405.9 517.6 609.8 719.6 811.7 923.5 1015.6 1107.8 1200.0 1015.6: 92.2 184.4 276.5 388.3 480.4 590.2 682.4 794.1 886.3 978.5 1070.7 1200.0 1107.8: 92.2 184.4 296.1 388.3 498.0 590.2 702.0 794.1 886.3 978.5 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 129.3301 cents 37.15142 cents 135/128, 92.1787 cents 2: 184.3574 .. 221.5088 cents 37.15142 cents 55.02730 cents 3: 276.5361 .. 313.6876 cents 37.15142 cents 55.02730 cents 4: 388.2674 .. 405.8663 cents 67108864/66430125, 17.5988 cents 74.57987 cents 5: 480.4462 .. 517.5976 cents 37.15142 cents 74.57987 cents 6: 590.2237 .. 609.7763 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 cents 7: 682.4024 .. 719.5538 cents 37.15142 cents 273375/262144, 72.6261 cents 8: 794.1337 .. 811.7326 cents 67108864/66430125, 17.5988 cents 74.57987 cents 9: 886.3124 .. 923.4639 cents 37.15142 cents 74.57987 cents 10: 978.4912 .. 1015.6426 cents 37.15142 cents 55.02730 cents 11: 1070.6699 .. 1107.8213 cents 37.15142 cents 55.02730 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 : 1073741824/996451875, 129.3301 cents Average / Smallest step : 1.084849 Largest / Average step : 1.293301 Largest / Smallest step : 1.403037 Median interval of one step : 135/128, 92.1787 cents, amount: 8 Most common interval of one step : 135/128, 92.1787 cents, amount: 8 Least squares average step : 100.22560 cents, oct.: 1202.70718 cents Scale is strictly proper Step pattern alph. order: ABACABAAADAA Step pattern size order : ACABACAAADAA Scale is a Constant Structure, by a margin of 55.02730 cents Scale diversity : 1.228403 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.706699 Rothenberg efficiency : 0.395893 redundancy: 0.604107 Efficiency x scale size : 4.750722 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 triad is 0.0 92.179 794.134 cents, amount: 6 Number of recognisable fifths : 9, average 705.8659 cents Number of appreciable fifths : 7, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 405 Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties -- Prime limit : 5 Odd number limit : 996451875 (O: 996451875 U: 996451875) Highest odd numerator or denominator: 54675 Scale harmonicity : 0.011078 Average absolute harmonicity : 0.159251 Specific harmonicity : 0.072937 Fundamental : 1/597196800, -29.1536 octaves, 0.0000 Hz. Guide tone : 1791590400, 30.7386 octaves, 468725851187.845 Hz. Exponens Consonantiae : 1.069932E+18, 59.89222 octaves Euler's gradus suavitatis : 73 Sum of Mann's harmonic distance : 71524.0, average 5960.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 25.12031, average 2.09336 Sum of Tenney's harmonic distance : 50.70786, average 4.22565 Vogel's harmonic complexity : 44.25000 Wille's k value : 498225937 Wilson's harmonic complexity : 59 Rectangular lattice diameter : 17 Triangular lattice diameter : 17 Lattice compactness : 860.39027, average 11.03064 Lattice compactness (without 2's) : 360.91794, average 4.62715 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -15 .. 15 -0.25000 85 1 3: -6 .. 7 0.50000 38 3 5: -2 .. 2 0.00000 10 8 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 48 / 12 = 4.00000 Scale is JI-epimorphic with val: <12 19 28| = patent Scale is weakly epimorphic with val: <12 21 28|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.9426 c. M: 15.6426 c. Twelve-tone Chromatic (1/11-comma) 38: 3 3 3 4 3 3 3 3 3 4 3 3 SP B ME SD: 7.2824 c. M: 14.4363 c. 39: 3 4 3 3 3 4 3 3 3 4 3 3 SP B ME SD: 6.2481 c. M:-11.6036 c. 41: 3 4 3 4 3 4 3 3 3 5 3 3 SP D3 SD: 4.5638 c. M:-8.7477 c. 53: 4 5 4 5 4 5 4 4 4 6 4 4 SP D3 SD: 1.7695 c. M: 3.2936 c. 65: 5 6 5 6 5 6 5 5 5 7 5 5 SP D3 SD: 0.4208 c. M: 0.8331 c. 340: 26 32 26 31 26 32 26 26 26 37 26 26 SP SD: 0.4974 c. M:-0.8280 c. 352: 27 33 27 32 27 33 27 27 27 38 27 27 SP SD: 0.3213 c. M:-0.6355 c. 364: 28 34 28 33 28 34 28 28 28 39 28 28 SP SD: 0.3381 c. M:-0.6146 c. 417: 32 39 32 38 32 39 32 32 32 45 32 32 SP SD: 0.2062 c. M:-0.4065 c. 482: 37 45 37 44 37 45 37 37 37 52 37 37 SP SD: 0.1226 c. M:-0.2394 c. 547: 42 51 42 50 42 51 42 42 42 59 42 42 SP SD: 0.0604 c. M:-0.1119 c. 612: 47 57 47 56 47 57 47 47 47 66 47 47 SP SD: 0.0222 c. M:-0.0437 c. 1901: 146 177 146 174 146 177 146 146 146 205 146 146 SP SD: 0.0231 c. M: 0.0420 c. 2395: 184 223 184 219 184 223 184 184 184 258 184 184 SP SD: 0.0188 c. M:-0.0341 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: 0.6512 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 12.6839 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.7763 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 7.4434 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.3888 cents 8 x 9 x 10:11 x 12 x 13:14:15:16 S SD: 11.1037 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: 7.7480 cents 11 x 12:13:14:15:16 x 17:18:20:21:22 S SD: 9.6619 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 6.3762 cents 13:14:15 x 16:17:18:20:21:22:23:25:26 SD: 10.7000 cents 14:15:16:17:18:19:20:21:22:23:25:27:28 SD: 6.8684 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.4414 cents 16:17:18:19:20:21:23:24:25:27:29:30:32 SD: 4.6055 cents 21:22:24:25:27:28:30:32:33:35:38:40:42 SD: 4.4801 cents 22:23:25:26:28:29:31:33:35:37:40:42:44 SD: 3.8718 cents 24:25:27:28:30:32:34:36:38:40:43:46:48 SD: 3.8455 cents 26:27:29:31:33:35:37:39:41:43:47:49:52 SD: 3.5382 cents 30:32:34:36:38:40:43:45:47:50:54:57:60 SD: 3.1461 cents 31:33:35:37:39:41:44:47:49:52:56:59:62 SD: 2.9059 cents 33:35:37:39:42:44:47:50:52:55:59:63:66 SD: 2.5017 cents 38:40:43:45:48:51:54:57:60:63:68:72:76 SD: 1.7899 cents 48:51:54:57:61:64:68:72:76:80:86:91:96 SD: 1.5283 cents 54:57:61:64:68:72:77:81:85:90:97:102:108 SD: 1.3206 cents 69:73:78:82:87:92:98:104:109:115:124:131:138 SD: 1.2284 cents 72:76:81:85:91:96:102:108:114:120:129:137:144 SD: 1.1845 cents 76:80:86:90:96:101:108:114:120:127:137:144:152 SD: 1.1832 cents 80:84:90:95:101:107:114:120:127:133:144:152:160 SD: 1.1724 cents 86:91:97:102:109:115:122:129:136:143:155:163:172 SD: 1.0911 cents 87:92:98:103:110:116:124:131:138:145:156:165:174 SD: 1.0027 cents 88:93:99:104:111:117:125:132:139:147:158:167:176 SD: 0.9220 cents 90:95:101:107:114:120:128:135:142:150:162:171:180 SD: 0.7656 cents 106:112:119:126:134:141:151:159:168:177:191:201:212 SD: 0.7607 cents 112:118:126:133:142:149:159:168:177:187:201:212:224 SD: 0.7457 cents 114:120:128:135:144:152:162:171:180:190:205:216:228 SD: 0.6215 cents 128:135:144:152:162:171:182:192:203:214:230:243:256 SD: 0.6037 cents 144:152:162:171:182:192:205:216:228:240:259:273:288 SD: 0.3062 cents 242:255:272:287:306:323:344:363:383:404:435:459:484 SD: 0.2823 cents 258:272:290:306:326:344:367:387:408:430:464:489:516 SD: 0.2542 cents 272:287:306:323:344:363:387:408:430:454:489:516:544 SD: 0.2435 cents 296:312:333:351:374:395:421:444:468:494:532:561:592 SD: 0.2314 cents 344:363:387:408:435:459:489:516:544:574:619:652:688 SD: 0.2206 cents 360:380:405:427:455:480:512:540:570:601:647:683:720 SD: 0.2156 cents 386:407:434:458:488:515:549:579:611:644:694:732:772 SD: 0.1540 cents 402:424:452:477:508:536:572:603:636:671:723:762:804 SD: 0.1500 cents 440:464:495:522:556:587:626:660:696:734:791:834:880 SD: 0.1416 cents 462:487:520:548:584:616:657:693:731:771:831:876:924 SD: 0.1348 cents 510:538:574:605:645:680:725:765:807:851:917:967:1020 SD: 0.1212 cents 552:582:621:655:698:736:785:828:873:921:992:1047:1104 SD: 0.1082 cents