Scala analysis: xen12-wilson-40-5C2-dekany-05
3-5-7-9-11 5C2 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 11/10 165.004228 Ptolemy's second, 4/5-tone 3: 7/6 266.870906 septimal minor third 4: 77/60 431.875134 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 3/2 701.955001 perfect fifth 7: 33/20 866.959229 8: 9/5 1017.596288 just minor seventh, BP seventh 9: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 21/20 84.4672 minor semitone 2: 22/21 80.5370 undecimal minor semitone 3: 35/33 101.8667 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 15/14 119.4428 major diatonic semitone 7: 11/10 165.0042 Ptolemy's second, 4/5-tone 8: 12/11 150.6371 undecimal neutral second, 3/4-tone 9: 55/54 31.7667 telepathma 10: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 21/20 84.467 cents minor semitone 1: 1 35/33 101.867 cents 1: 1 15/14 119.443 cents major diatonic semitone 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 3 10/9 182.404 cents minor whole tone 2: 1 63/55 235.104 cents 2: 1 7/6 266.871 cents septimal minor third 2: 1 90/77 270.080 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 2 6/5 315.641 cents minor third 3: 2 7/6 266.871 cents septimal minor third 3: 1 6/5 315.641 cents minor third 3: 1 40/33 333.041 cents 3: 2 11/9 347.408 cents undecimal neutral third 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 3 9/7 435.084 cents septimal major third, BP third 4: 1 11/9 347.408 cents undecimal neutral third 4: 2 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 77/60 431.875 cents 4: 1 55/42 466.851 cents 4: 2 4/3 498.045 cents perfect fourth 4: 1 15/11 536.951 cents undecimal augmented fourth 4: 1 108/77 585.721 cents 4: 1 99/70 600.088 cents 2nd quasi-equal tritone 5: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 5: 1 4/3 498.045 cents perfect fourth 5: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 3 10/7 617.488 cents Euler's tritone 5: 1 3/2 701.955 cents perfect fifth 5: 1 54/35 750.725 cents septimal semi-augmented fifth 6: 1 140/99 599.912 cents quasi-equal tritone 6: 1 77/54 614.279 cents 6: 1 22/15 663.049 cents undecimal diminished fifth 6: 2 3/2 701.955 cents perfect fifth 6: 1 84/55 733.149 cents 6: 1 120/77 768.125 cents 6: 2 11/7 782.492 cents undecimal augmented fifth 6: 1 18/11 852.592 cents undecimal neutral sixth 7: 3 14/9 764.916 cents septimal minor sixth 7: 1 11/7 782.492 cents undecimal augmented fifth 7: 2 18/11 852.592 cents undecimal neutral sixth 7: 1 33/20 866.959 cents 7: 1 5/3 884.359 cents major sixth, BP sixth 7: 2 12/7 933.129 cents septimal major sixth 8: 2 5/3 884.359 cents major sixth, BP sixth 8: 1 56/33 915.553 cents 8: 1 77/45 929.920 cents 8: 1 12/7 933.129 cents septimal major sixth 8: 1 110/63 964.896 cents 8: 3 9/5 1017.596 cents just minor seventh, BP seventh 8: 1 20/11 1034.996 cents large minor seventh 9: 2 20/11 1034.996 cents large minor seventh 9: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 1 28/15 1080.557 cents grave major seventh 9: 1 66/35 1098.133 cents 9: 1 40/21 1115.533 cents acute major seventh 9: 1 21/11 1119.463 cents undecimal major seventh 9: 1 108/55 1168.233 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.88889 = 62/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 84.5 165.0 266.9 431.9 582.5 702.0 867.0 1017.6 1049.4 1200.0 84.5 : 80.5 182.4 347.4 498.0 617.5 782.5 933.1 964.9 1115.5 1200.0 165.0 : 101.9 266.9 417.5 537.0 702.0 852.6 884.4 1035.0 1119.5 1200.0 266.9 : 165.0 315.6 435.1 600.1 750.7 782.5 933.1 1017.6 1098.1 1200.0 431.9 : 150.6 270.1 435.1 585.7 617.5 768.1 852.6 933.1 1035.0 1200.0 582.5 : 119.4 284.4 435.1 466.9 617.5 702.0 782.5 884.4 1049.4 1200.0 702.0 : 165.0 315.6 347.4 498.0 582.5 663.0 764.9 929.9 1080.6 1200.0 867.0 : 150.6 182.4 333.0 417.5 498.0 599.9 764.9 915.6 1035.0 1200.0 1017.6: 31.8 182.4 266.9 347.4 449.3 614.3 764.9 884.4 1049.4 1200.0 1049.4: 150.6 235.1 315.6 417.5 582.5 733.1 852.6 1017.6 1168.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 165.0042 cents 27/25, 133.2376 cents 55/54, 31.7667 cents 2: 165.0042 .. 315.6413 cents 12/11, 150.6371 cents 1/1, 0.0000 cents 3: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 35/36,-48.7704 cents 4: 347.4079 .. 600.0883 cents 81/70, 252.6804 cents 77/81,-87.6762 cents 5: 449.2746 .. 750.7254 cents 1458/1225, 301.4508 cents 2450/2673,-150.8137 cents 6: 599.9117 .. 852.5921 cents 81/70, 252.6804 cents 2450/2673,-150.8137 cents 7: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 77/81,-87.6762 cents 8: 884.3587 .. 1034.9958 cents 12/11, 150.6371 cents 35/36,-48.7704 cents 9: 1034.9958 .. 1168.2333 cents 27/25, 133.2376 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 11/10, 165.0042 cents Average / Smallest step : 3.777546 Largest / Average step : 1.375035 Largest / Smallest step : 5.194259 Median interval of one step : 135.03993 cents, amount: 0 Most common interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 118.75489 cents, oct.: 1187.54886 cents Scale is not proper Step pattern alph. order: ABCDEFDEGE Step pattern size order : CBDGFEGFAF Scale is not a Constant Structure Scale diversity : 1.526965 Lumma stability : 0.052944 Lumma impropriety factor : 0.478620 Rothenberg efficiency : 0.283333 redundancy: 0.716667 Efficiency x scale size : 2.833333 Number of different interval sizes : 50 = 5.55556 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.88889 = 62/9 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 9801/9800, 0.1766 cents Number of recognisable fifths : 3, average 701.9550 cents Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 77 Scale harmonicity : 0.021802 Average absolute harmonicity : 0.168073 Specific harmonicity : 0.099471 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 1386, 10.4367 octaves, 362613.034 Hz. Exponens Consonantiae : 8.316000E+04, 16.34360 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 158.0, average 15.80000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.93157, average 0.99316 Sum of Tenney's harmonic distance : 18.86808, average 1.88681 Vogel's harmonic complexity : 13.90000 Wille's k value : 49 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 123.20735, average 2.24013 Lattice compactness (without 2's) : 97.21691, average 1.76758 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.90000 11 1 3: -1 .. 2 0.20000 8 1 5: -1 .. 0 -0.60000 6 1 7: 0 .. 1 0.40000 4 3 11: 0 .. 1 0.40000 4 4 Average exponent except 2's : 4 / 10 = 0.40000 Average absolute exponent except 2's: 22 / 10 = 2.20000
FIT/MODE
10: 1 0 1 2 1 1 1 2 0 1 N SD: 35.3795 c. M:-62.4037 c. 11: 1 0 1 2 1 1 2 1 0 2 N SD: 39.5221 c. M: 67.5448 c. 12: 1 1 1 1 2 1 2 1 1 1 N D3 SD: 28.0261 c. M:-50.6371 c. 13: 1 1 1 2 1 2 1 2 0 2 N SD: 24.5980 c. M:-36.5065 c. 14: 1 1 1 2 2 1 2 2 0 2 N SD: 11.6921 c. M: 20.7915 c. 22: 2 1 2 3 3 2 3 3 0 3 N SD: 12.5453 c. M:-24.6237 c. 25: 2 1 3 3 3 3 3 3 1 3 N SD: 12.3837 c. M:-21.1291 c. 26: 2 2 2 3 4 2 4 3 1 3 N SD: 12.1258 c. M:-19.6112 c. 27: 2 2 2 4 3 3 4 3 1 3 N SD: 11.1746 c. M:-21.9297 c. 31: 2 2 3 4 4 3 4 4 1 4 N SD: 7.8378 c. M: 15.3463 c. 39: 3 2 4 5 5 4 5 5 1 5 N SD: 6.0841 c. M: 11.1581 c. 41: 3 3 3 6 5 4 6 5 1 5 N SD: 6.1858 c. M:-11.0896 c. 48: 3 4 4 6 6 5 7 6 1 6 N SD: 6.9500 c. M:-9.9958 c. 50: 3 4 4 7 6 5 7 6 2 6 N SD: 6.2883 c. M: 12.4672 c. 51: 4 3 4 7 7 5 7 6 2 6 N SD: 6.4225 c. M:-9.6505 c. 53: 4 3 5 7 7 5 7 7 1 7 N SD: 5.0042 c. M: 7.8535 c. 58: 4 4 5 8 7 6 8 7 2 7 N SD: 2.8123 c. M:-5.8095 c. 72: 5 5 6 10 9 7 10 9 2 9 N SD: 1.0986 c. M: 1.9550 c. 183: 13 12 16 25 23 18 25 23 5 23 N SD: 1.0586 c. M:-1.9816 c. 198: 14 13 17 27 25 20 27 25 5 25 N SD: 0.8583 c. M: 1.5721 c. 255: 18 17 22 35 32 25 35 32 7 32 N SD: 0.8494 c. M:-1.3644 c. 256: 18 17 22 35 32 26 35 32 7 32 N SD: 0.7052 c. M: 1.2622 c. 270: 19 18 23 37 34 27 37 34 7 34 N SD: 0.3792 c. M: 0.7640 c. 342: 24 23 29 47 43 34 47 43 9 43 N SD: 0.1983 c. M: 0.2962 c. 764: 54 51 65 105 96 76 105 96 20 96 N SD: 0.1687 c. M:-0.3496 c. 822: 58 55 70 113 103 82 113 103 22 103 N SD: 0.1885 c. M:-0.2824 c. 836: 59 56 71 115 105 83 115 105 22 105 N SD: 0.1377 c. M:-0.2629 c. 1034: 73 69 88 142 130 103 142 130 27 130 N SD: 0.1626 c. M:-0.2523 c. 1092: 77 73 93 150 137 109 150 137 29 137 N SD: 0.1257 c. M:-0.2428 c. 1106: 78 74 94 152 139 110 152 139 29 139 N SD: 0.1022 c. M: 0.1767 c. 1164: 82 78 99 160 146 116 160 146 31 146 N SD: 0.0834 c. M:-0.1394 c. 1434: 101 96 122 197 180 143 197 180 38 180 N SD: 0.0798 c. M: 0.1507 c. 1506: 106 101 128 207 189 150 207 189 40 189 N SD: 0.0421 c. M: 0.0664 c. 1848: 130 124 157 254 232 184 254 232 49 232 N SD: 0.0479 c. M: 0.0761 c. 2342: 165 157 199 322 294 233 322 294 62 294 N SD: 0.0460 c. M:-0.0804 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 22.8064 cents 4 x x x 5 x 6 x 7 x 8 S SD: 16.6853 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 14.4451 cents 6 x x 7:8 x 9:10 x 11:12 S SD: 11.4032 cents 7 x x 8:9:10:11:12 x 13:14 S SD: 16.8254 cents 8 x 9 x 10:11:12:13:14:15:16 S SD: 11.9592 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 16.2903 cents 10 x 11:12:13:14:15:17:18 x 20 SD: 9.3112 cents 11 x 12:13:14:15:17:18 x 20:22 SD: 9.7401 cents 12 x 13:14:15:17:18:20 x 22:24 SD: 7.3919 cents 13 x 14:15:17:18:20:21:23:24:26 SD: 9.5865 cents 14:15 x 16:18:20:21:23:25:26:28 SD: 7.4344 cents 15:16 x 18:19:21:23:25:27:28:30 SD: 8.8595 cents 16:17:18:19:21:22:24:26:29 x 32 SD: 8.7498 cents 17:18:19:20:22:24:26:28 x 31:34 SD: 5.9052 cents 18:19:20:21:23:25:27:30:32:33:36 SD: 3.7392 cents 20:21:22:23:26:28:30:33:36:37:40 SD: 3.6946 cents 22:23:24:26:28:31:33:36 x 40:44 SD: 4.3129 cents 24:25:26:28:31:34:36:40:43:44:48 SD: 4.2444 cents 28:29:31:33:36:39:42:46:50:51:56 SD: 3.8204 cents 31:33:34:36:40:43:47:51:56:57:62 SD: 3.7854 cents 32:34:35:37:41:45:48:53:58:59:64 SD: 3.3289 cents 35:37:39:41:45:49:53:58:63:64:70 SD: 3.2285 cents 36:38:40:42:46:50:54:59:65:66:72 SD: 2.8253 cents 38:40:42:44:49:53:57:63:68:70:76 SD: 2.4663 cents 40:42:44:47:51:56:60:66:72:73:80 SD: 1.8473 cents 42:44:46:49:54:59:63:69:76:77:84 SD: 1.6018 cents 60:63:66:70:77:84:90:99:108:110:120 SD: 0.0000 cents