Scala analysis: xen12-wilson-40-5C2-dekany-02
1-3-5-9-11 5C2 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 2: 9/8 203.910002 major whole tone 3: 55/48 235.676655 undecimal semi-augmented whole tone 4: 5/4 386.313714 major third 5: 11/8 551.317942 undecimal semi-augmented fourth 6: 3/2 701.955001 perfect fifth 7: 5/3 884.358713 major sixth, BP sixth 8: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 9: 15/8 1088.268715 classic major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 55/54 31.7667 telepathma 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 10/9 182.4037 minor whole tone 8: 11/10 165.0042 Ptolemy's second, 4/5-tone 9: 45/44 38.9058 1/5-tone 10: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 1 45/44 38.906 cents 1/5-tone 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 16/15 111.731 cents minor 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 1: 1 10/9 182.404 cents minor whole tone 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 2 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 2 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 2: 1 11/9 347.408 cents undecimal neutral third 3: 1 9/8 203.910 cents major whole tone 3: 1 55/48 235.677 cents undecimal semi-augmented whole tone 3: 2 6/5 315.641 cents minor third 3: 1 40/33 333.041 cents 3: 1 11/9 347.408 cents undecimal neutral third 3: 1 5/4 386.314 cents major third 3: 1 72/55 466.278 cents undecimal semi-diminished fourth 3: 2 4/3 498.045 cents perfect fourth 4: 1 11/9 347.408 cents undecimal neutral third 4: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 1 99/80 368.914 cents 4: 1 5/4 386.314 cents major third 4: 3 4/3 498.045 cents perfect fourth 4: 1 15/11 536.951 cents undecimal augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 5: 1 5/4 386.314 cents major third 5: 1 4/3 498.045 cents perfect fourth 5: 1 27/20 519.551 cents acute fourth 5: 2 11/8 551.318 cents undecimal semi-augmented fourth 5: 2 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 40/27 680.449 cents grave fifth 5: 1 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 6: 1 15/11 536.951 cents undecimal augmented fourth 6: 1 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 22/15 663.049 cents undecimal diminished fifth 6: 3 3/2 701.955 cents perfect fifth 6: 1 8/5 813.686 cents minor sixth 6: 1 160/99 831.086 cents 6: 1 44/27 845.453 cents neutral sixth 6: 1 18/11 852.592 cents undecimal neutral sixth 7: 2 3/2 701.955 cents perfect fifth 7: 1 55/36 733.722 cents undecimal semi-augmented fifth 7: 1 8/5 813.686 cents minor sixth 7: 1 18/11 852.592 cents undecimal neutral sixth 7: 1 33/20 866.959 cents 7: 2 5/3 884.359 cents major sixth, BP sixth 7: 1 96/55 964.323 cents 7: 1 16/9 996.090 cents Pythagorean minor seventh 8: 1 18/11 852.592 cents undecimal neutral sixth 8: 1 33/20 866.959 cents 8: 2 5/3 884.359 cents major sixth, BP sixth 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 2 9/5 1017.596 cents just minor seventh, BP seventh 8: 1 20/11 1034.996 cents large minor seventh 8: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 1 9/5 1017.596 cents just minor seventh, BP 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 15/8 1088.269 cents classic major seventh 9: 1 64/33 1146.727 cents 33rd subharmonic 9: 1 88/45 1161.094 cents 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: 7.55556 = 68/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 53.3 203.9 235.7 386.3 551.3 702.0 884.4 1049.4 1088.3 1200.0 53.3 : 150.6 182.4 333.0 498.0 648.7 831.1 996.1 1035.0 1146.7 1200.0 203.9 : 31.8 182.4 347.4 498.0 680.4 845.5 884.4 996.1 1049.4 1200.0 235.7 : 150.6 315.6 466.3 648.7 813.7 852.6 964.3 1017.6 1168.2 1200.0 386.3 : 165.0 315.6 498.0 663.0 702.0 813.7 867.0 1017.6 1049.4 1200.0 551.3 : 150.6 333.0 498.0 537.0 648.7 702.0 852.6 884.4 1035.0 1200.0 702.0 : 182.4 347.4 386.3 498.0 551.3 702.0 733.7 884.4 1049.4 1200.0 884.4 : 165.0 203.9 315.6 368.9 519.6 551.3 702.0 867.0 1017.6 1200.0 1049.4: 38.9 150.6 203.9 354.5 386.3 537.0 702.0 852.6 1035.0 1200.0 1088.3: 111.7 165.0 315.6 347.4 498.0 663.0 813.7 996.1 1161.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 182.4037 cents 12/11, 150.6371 cents 55/54, 31.7667 cents 2: 150.6371 .. 347.4079 cents 121/108, 196.7709 cents 54/55,-31.7667 cents 3: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 81/88,-143.4979 cents 4: 347.4079 .. 663.0492 cents 6/5, 315.6413 cents 11/12,-150.6371 cents 5: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 75/88,-276.7355 cents 6: 536.9508 .. 852.5921 cents 6/5, 315.6413 cents 75/88,-276.7355 cents 7: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 11/12,-150.6371 cents 8: 852.5921 .. 1049.3629 cents 121/108, 196.7709 cents 81/88,-143.4979 cents 9: 1017.5963 .. 1168.2333 cents 12/11, 150.6371 cents 54/55,-31.7667 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 : 10/9, 182.4037 cents Average / Smallest step : 3.777546 Largest / Average step : 1.520031 Largest / Smallest step : 5.741987 Median interval of one step : 12/11, 150.6371 cents, amount: 3 Most common interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 119.64034 cents, oct.: 1196.40339 cents Scale is not proper Step pattern alph. order: ABCBDBEDFG Step pattern size order : CEAEFEGFBD Scale is not a Constant Structure Scale diversity : 1.398589 Lumma stability : 0.052944 Lumma impropriety factor : 0.713094 Rothenberg efficiency : 0.343571 redundancy: 0.656429 Efficiency x scale size : 3.435714 Number of different interval sizes : 40 = 4.44444 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 7.55556 = 68/9 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 6, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 10.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Scale is n-1 differentially coherent in interval classes 7 and 8 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 55 Scale harmonicity : 0.025919 Average absolute harmonicity : 0.186861 Specific harmonicity : 0.124023 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 990, 9.9513 octaves, 259009.310 Hz. Exponens Consonantiae : 9.504000E+04, 16.53625 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 134.5, average 13.45000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.34706, average 0.93471 Sum of Tenney's harmonic distance : 17.70211, average 1.77021 Vogel's harmonic complexity : 12.90000 Wille's k value : 49 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 160.62887, average 2.92052 Lattice compactness (without 2's) : 87.83999, average 1.59709 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.10000 23 1 3: -1 .. 2 0.20000 8 2 5: 0 .. 1 0.40000 4 3 11: 0 .. 1 0.40000 4 4 Average exponent except 2's : 10 / 10 = 1.00000 Average absolute exponent except 2's: 16 / 10 = 1.60000
FIT/MODE
10: 0 2 0 1 2 1 1 2 0 1 N SD: 32.4374 c. M: 53.2729 c. 11: 0 2 0 1 2 1 2 1 1 1 N SD: 37.1755 c. M: 67.5448 c. 12: 1 1 1 1 2 1 2 2 0 1 N SD: 34.4146 c. M:-64.3233 c. 14: 1 1 1 1 2 2 2 2 1 1 N S SD: 28.1812 c. M: 43.4566 c. 15: 1 2 0 2 2 2 2 2 1 1 N SD: 19.3323 c. M:-36.0900 c. 19: 1 2 1 2 3 2 3 3 0 2 N SD: 13.4042 c. M:-24.3213 c. 22: 1 3 0 3 3 3 3 3 1 2 N SD: 9.6339 c. M: 17.4948 c. 24: 1 3 1 3 3 3 4 3 1 2 N SD: 8.9817 c. M:-15.6413 c. 31: 1 4 1 4 4 4 5 4 1 3 N SD: 7.2054 c. M: 14.5633 c. 40: 2 5 1 5 5 5 6 6 1 4 N SD: 8.1277 c. M: 14.3587 c. 41: 2 5 1 5 6 5 6 6 1 4 N SD: 4.1810 c. M: 6.3099 c. 46: 2 6 1 6 6 6 7 6 2 4 N SD: 4.0451 c. M:-7.3835 c. 65: 3 8 2 8 9 8 10 9 2 6 N SD: 2.1244 c. M:-4.3233 c. 87: 4 11 2 11 12 11 13 12 3 8 N SD: 1.4840 c. M:-2.9865 c. 118: 5 15 3 15 16 15 18 16 4 11 N SD: 1.3374 c. M: 2.4255 c. 137: 6 17 4 17 19 17 21 19 4 13 N SD: 1.3209 c. M: 2.4501 c. 152: 7 19 4 19 21 19 23 21 5 14 N SD: 1.0720 c. M:-1.9902 c. 159: 7 20 4 20 22 20 24 22 5 15 N SD: 0.9669 c. M: 1.7144 c. 183: 8 23 5 23 25 23 28 25 6 17 N SD: 0.5266 c. M:-0.8872 c. 224: 10 28 6 28 31 28 34 31 7 21 N SD: 0.4465 c. M: 0.7687 c. 270: 12 34 7 34 37 34 41 37 9 25 N SD: 0.3405 c. M:-0.6202 c. 342: 15 43 9 43 47 43 52 47 11 32 N SD: 0.4070 c. M: 0.6414 c. 407: 18 51 11 51 56 51 62 56 13 38 N SD: 0.2356 c. M: 0.4702 c. 494: 22 62 13 62 68 62 75 68 16 46 N SD: 0.0968 c. M:-0.1684 c. 677: 30 85 18 85 93 85 103 93 22 63 N SD: 0.0745 c. M:-0.1317 c. 1171: 52 147 31 147 161 147 178 161 38 109 N SD: 0.0167 c. M:-0.0319 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 x 4 x 5 x x 6 S SD: 17.7576 cents 4 x x x 5 x 6 x 7 x 8 S SD: 20.1343 cents 5 x x x 6:7 x 8:9 x 10 S SD: 21.8828 cents 6 x x 7 x 8:9:10:11 x 12 S SD: 10.2890 cents 7 x x 8:9:10:11:12 x 13:14 S SD: 18.0229 cents 8 x 9 x 10:11:12:13 x 15:16 SD: 6.2616 cents 9 x 10 x 11:12:14:15 x 17:18 SD: 13.5085 cents 10 x 11 x 13:14:15:17:18:19:20 SD: 12.3791 cents 11 x 12:13:14:15:17:18:20:21:22 SD: 12.0406 cents 12 x x 14:15:17:18:20:22:23:24 SD: 8.9198 cents 13:14 x 15:16:18:20:22:24 x 26 S SD: 12.1229 cents 14:15 x 16:18:19:21:23 x 26:28 SD: 11.3085 cents 15:16:17 x 19:21:23:25 x 28:30 SD: 10.1449 cents 16:17:18 x 20:22:24:27:29:30:32 SD: 6.5969 cents 17:18:19 x 21:23:26:28:31:32:34 SD: 7.9360 cents 18:19:20:21:23:25:27:30:33:34:36 SD: 7.0540 cents 19:20:21:22:24:26:29:32:35:36:38 SD: 6.7524 cents 20:21 x 23:25:28:30:33:37:38:40 SD: 6.1460 cents 21:22 x 24:26:29:32:35 x 39:42 SD: 5.7443 cents 22:23 x 25:28:30:33:37:40:41:44 SD: 5.5661 cents 23:24:26 x 29:32:35:38:42:43:46 SD: 5.0291 cents 24:25:27:28:30:33:36:40:44:45:48 SD: 3.5719 cents 28:29 x 32:35:39:42:47:51:53:56 SD: 3.7244 cents 29:30 x 33:36:40:44:48:53:54:58 SD: 3.6071 cents 30:31:34 x 38:41:45:50:55:56:60 SD: 3.2801 cents 32:33:36:37:40:44:48:53:59:60:64 SD: 2.1436 cents 36:37 x 41:45:50:54:60:66:68:72 SD: 2.7461 cents 37:38:42 x 46:51:56:62:68:69:74 SD: 3.2048 cents 39:40:44:45:49:54:59:65:72:73:78 SD: 2.9229 cents 40:41:45:46:50:55:60:67:73:75:80 SD: 1.6941 cents 44:45 x 50:55:61:66:73:81:83:88 SD: 3.2174 cents 45:46:51:52:56:62:68:75:83:84:90 SD: 3.1823 cents 46:47:52:53:58:63:69:77:84:86:92 SD: 2.8610 cents 47:48:53:54:59:65:71:78:86:88:94 SD: 2.6411 cents 48:50:54:55:60:66:72:80:88:90:96 SD: 1.7399 cents 56:58:63:64:70:77:84:93:103:105:112 SD: 1.2085 cents 64:66:72:73:80:88:96:107:117:120:128 SD: 1.0754 cents 88:91:99:101:110:121:132:147:161:165:176 SD: 0.7689 cents 96:99:108:110:120:132:144:160:176:180:192 S SD: 0.0000 cents