Scala analysis: diadiaschis1
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: 18225/16384 184.357433 two (major chroma, major limma) 3: 1215/1024 296.088718 wide augmented second 4: 512/405 405.866283 narrow diminished fourth 5: 4/3 498.044999 perfect fourth 6: 45/32 590.223716 diatonic tritone 7: 3/2 701.955001 perfect fifth 8: 405/256 794.133717 wide augmented fifth 9: 54675/32768 886.312434 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: 135/128 92.1787 major chroma, major limma 3: 16/15 111.7313 minor diatonic semitone 4: 524288/492075 109.7776 5: 135/128 92.1787 major chroma, major limma 6: 135/128 92.1787 major chroma, major limma 7: 16/15 111.7313 minor diatonic semitone 8: 135/128 92.1787 major chroma, major limma 9: 135/128 92.1787 major chroma, major limma 10: 524288/492075 109.7776 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: 7 135/128 92.179 cents major chroma, major limma 1: 2 524288/492075 109.778 cents 1: 3 16/15 111.731 cents minor diatonic semitone 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: 1 2460375/2097152 276.536 cents 3: 2 32/27 294.135 cents Pythagorean minor third 3: 5 1215/1024 296.089 cents wide augmented second 3: 4 65536/54675 313.688 cents 4: 4 164025/131072 388.267 cents 4: 8 512/405 405.866 cents narrow diminished fourth 5: 1 22143375/16777216 480.446 cents 5: 8 4/3 498.045 cents perfect fourth 5: 1 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 5: 2 8192/6075 517.598 cents 6: 6 45/32 590.224 cents diatonic tritone 6: 6 64/45 609.776 cents 2nd tritone 7: 2 6075/4096 682.402 cents 7: 1 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 7: 8 3/2 701.955 cents perfect fifth 7: 1 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: 4 54675/32768 886.312 cents 9: 5 2048/1215 903.911 cents narrow diminished seventh 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 1 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: 3 15/8 1088.269 cents classic major seventh 11: 2 492075/262144 1090.222 cents 11: 7 256/135 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 : 92.2 184.4 296.1 405.9 498.0 590.2 702.0 794.1 886.3 996.1 1107.8 1200.0 92.2 : 92.2 203.9 313.7 405.9 498.0 609.8 702.0 794.1 903.9 1015.6 1107.8 1200.0 184.4 : 111.7 221.5 313.7 405.9 517.6 609.8 702.0 811.7 923.5 1015.6 1107.8 1200.0 296.1 : 109.8 202.0 294.1 405.9 498.0 590.2 700.0 811.7 903.9 996.1 1088.3 1200.0 405.9 : 92.2 184.4 296.1 388.3 480.4 590.2 702.0 794.1 886.3 978.5 1090.2 1200.0 498.0 : 92.2 203.9 296.1 388.3 498.0 609.8 702.0 794.1 886.3 998.0 1107.8 1200.0 590.2 : 111.7 203.9 296.1 405.9 517.6 609.8 702.0 794.1 905.9 1015.6 1107.8 1200.0 702.0 : 92.2 184.4 294.1 405.9 498.0 590.2 682.4 794.1 903.9 996.1 1088.3 1200.0 794.1 : 92.2 202.0 313.7 405.9 498.0 590.2 702.0 811.7 903.9 996.1 1107.8 1200.0 886.3 : 109.8 221.5 313.7 405.9 498.0 609.8 719.6 811.7 903.9 1015.6 1107.8 1200.0 996.1 : 111.7 203.9 296.1 388.3 500.0 609.8 702.0 794.1 905.9 998.0 1090.2 1200.0 1107.8: 92.2 184.4 276.5 388.3 498.0 590.2 682.4 794.1 886.3 978.5 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 111.7313 cents 2048/2025, 19.5526 cents 135/128, 92.1787 cents 2: 184.3574 .. 221.5088 cents 37.15142 cents 273375/262144, 72.6261 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: 1088.2687 .. 1107.8213 cents 2048/2025, 19.5526 cents 273375/262144, 72.6261 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 : 16/15, 111.7313 cents Average / Smallest step : 1.084849 Largest / Average step : 1.117313 Largest / Smallest step : 1.212116 Median interval of one step : 135/128, 92.1787 cents, amount: 7 Most common interval of one step : 135/128, 92.1787 cents, amount: 7 Least squares average step : 99.68414 cents, oct.: 1196.20972 cents Scale is strictly proper Step pattern alph. order: AABCAABAACBA Step pattern size order : SSLMSSLSSMLS Scale is a Constant Structure, by a margin of 55.02730 cents Scale diversity : 1.206887 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.736030 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 : 3 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 Number of recognisable fifths : 10, average 703.5195 cents Number of appreciable fifths : 9, average 701.7379 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 : 1 Inversional symmetry on intervals : 0-1 6-7 -- Rational properties -- Prime limit : 5 Odd number limit : 22143375 (O: 22143375 U: 22143375) Highest odd numerator or denominator: 54675 Scale harmonicity : 0.013787 Average absolute harmonicity : 0.158505 Specific harmonicity : 0.079105 Fundamental : 1/13271040, -23.6618 octaves, 0.0000 Hz. Guide tone : 27993600, 24.7386 octaves, 7323841424.810 Hz. Exponens Consonantiae : 3.715042E+14, 48.40037 octaves Euler's gradus suavitatis : 59 Sum of Mann's harmonic distance : 63320.0, average 5276.66667 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 : 50.40683, average 4.20057 Vogel's harmonic complexity : 36.00000 Wille's k value : 11071687 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 14 Triangular lattice diameter : 14 Lattice compactness : 798.03362, average 10.23120 Lattice compactness (without 2's) : 337.40417, average 4.32569 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -15 .. 9 -3.00000 84 1 3: -4 .. 7 1.50000 38 3 5: -1 .. 2 0.50000 10 8 Average exponent except 2's : 24 / 12 = 2.00000 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 3 4 3 3 3 4 3 3 3 4 3 SP B ME SD: 6.2481 c. M:-11.6036 c. Augmented-12 41: 3 3 4 4 3 3 4 3 3 4 4 3 SP D3 SD: 4.5638 c. M: 8.7477 c. 53: 4 4 5 5 4 4 5 4 4 5 5 4 SP D3 SD: 1.7695 c. M: 3.2936 c. 65: 5 5 6 6 5 5 6 5 5 6 6 5 SP D3 SD: 0.4208 c. M:-0.8331 c. 340: 26 26 32 31 26 26 32 26 26 31 32 26 SP SD: 0.4974 c. M: 0.8280 c. 352: 27 27 33 32 27 27 33 27 27 32 33 27 SP SD: 0.3213 c. M: 0.6355 c. 364: 28 28 34 33 28 28 34 28 28 33 34 28 SP SD: 0.3381 c. M:-0.6146 c. 417: 32 32 39 38 32 32 39 32 32 38 39 32 SP SD: 0.2062 c. M: 0.4065 c. 482: 37 37 45 44 37 37 45 37 37 44 45 37 SP SD: 0.1226 c. M: 0.2394 c. 547: 42 42 51 50 42 42 51 42 42 50 51 42 SP SD: 0.0604 c. M: 0.1119 c. 612: 47 47 57 56 47 47 57 47 47 56 57 47 SP SD: 0.0222 c. M: 0.0437 c. 1901: 146 146 177 174 146 146 177 146 146 174 177 146 SP SD: 0.0231 c. M: 0.0420 c. 2395: 184 184 223 219 184 184 223 184 184 219 223 184 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: 8.3876 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.1738 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.1318 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.3063 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 9.2704 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.3838 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.8109 cents 11 x 12:13:14:15 x x 17:18:20:21:22 SD: 9.4671 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 6.1569 cents 13:14 x 15:16:17:18:20:21:22:23:25:26 SD: 10.0120 cents 14:15:16:17:18:19:20:21:22:23:25:27:28 SD: 7.8372 cents 15:16:17:18:19:20:21:23:24:25:27:28:30 SD: 5.8455 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 5.6668 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.2227 cents 22:23:24:26:28:29:31:33:35:37:39:42:44 SD: 4.0800 cents 26:27:29:31:33:35:37:39:41:43:46:49:52 SD: 3.7355 cents 27:28:30:32:34:36:38:41:43:45:48:51:54 SD: 3.2733 cents 32:34:36:38:40:43:45:48:51:53:57:61:64 SD: 3.2620 cents 33:35:37:39:42:44:46:50:52:55:59:63:66 SD: 2.9839 cents 34:36:38:40:43:45:48:51:54:57:60:64:68 SD: 2.6080 cents 36:38:40:43:46:48:51:54:57:60:64:68:72 SD: 2.1980 cents 42:44:47:50:53:56:59:63:66:70:75:80:84 SD: 1.9502 cents 52:55:58:62:66:69:73:78:82:87:92:99:104 SD: 1.6939 cents 54:57:60:64:68:72:76:81:85:90:96:102:108 SD: 1.1290 cents 72:76:80:85:91:96:101:108:114:120:128:137:144 SD: 0.9905 cents 90:95:100:107:114:120:127:135:142:150:160:171:180 SD: 0.8408 cents 96:101:107:114:121:128:135:144:152:160:171:182:192 SD: 0.7291 cents 106:112:118:126:134:141:149:159:168:177:188:201:212 SD: 0.6822 cents 108:114:120:128:137:144:152:162:171:180:192:205:216 SD: 0.6196 cents 144:152:160:171:182:192:203:216:228:240:256:273:288 SD: 0.4736 cents 162:171:180:192:205:216:228:243:256:270:288:307:324 SD: 0.4036 cents 204:215:227:242:258:272:287:306:323:340:363:387:408 SD: 0.2884 cents 258:272:287:306:326:344:363:387:408:430:459:489:516 SD: 0.2521 cents 310:327:345:368:392:413:436:465:490:517:551:588:620 SD: 0.2201 cents 328:346:365:389:415:437:461:492:519:547:583:622:656 SD: 0.2188 cents 348:367:387:413:440:464:489:522:551:581:619:660:696 SD: 0.2076 cents 364:384:405:432:460:485:512:546:576:607:647:690:728 SD: 0.1708 cents 402:424:447:477:508:536:565:603:636:671:715:762:804 SD: 0.1539 cents 462:487:514:548:584:616:650:693:731:771:821:876:924 SD: 0.1362 cents 492:519:547:584:622:656:692:738:778:821:875:933:984 SD: 0.1336 cents 510:538:567:605:645:680:717:765:807:851:907:967:1020 SD: 0.1290 cents 552:582:614:655:698:736:776:828:873:921:981:1047:1104 SD: 0.1063 cents