Scala analysis: xen12-wilson-40-5C3-dekany-02
1-3-5-9-11 5C3 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: 11/10 165.004228 Ptolemy's second, 4/5-tone 3: 9/8 203.910002 major whole tone 4: 99/80 368.914230 5: 11/8 551.317942 undecimal semi-augmented 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: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 16/15 111.7313 minor diatonic semitone 3: 45/44 38.9058 1/5-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 10/9 182.4037 minor whole tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 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 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 : 53.3 165.0 203.9 368.9 551.3 702.0 867.0 1017.6 1049.4 1200.0 53.3 : 111.7 150.6 315.6 498.0 648.7 813.7 964.3 996.1 1146.7 1200.0 165.0 : 38.9 203.9 386.3 537.0 702.0 852.6 884.4 1035.0 1088.3 1200.0 203.9 : 165.0 347.4 498.0 663.0 813.7 845.5 996.1 1049.4 1161.1 1200.0 368.9 : 182.4 333.0 498.0 648.7 680.4 831.1 884.4 996.1 1035.0 1200.0 551.3 : 150.6 315.6 466.3 498.0 648.7 702.0 813.7 852.6 1017.6 1200.0 702.0 : 165.0 315.6 347.4 498.0 551.3 663.0 702.0 867.0 1049.4 1200.0 867.0 : 150.6 182.4 333.0 386.3 498.0 537.0 702.0 884.4 1035.0 1200.0 1017.6: 31.8 182.4 235.7 347.4 386.3 551.3 733.7 884.4 1049.4 1200.0 1049.4: 150.6 203.9 315.6 354.5 519.6 702.0 852.6 1017.6 1168.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 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 : 117.12400 cents, oct.: 1171.23999 cents Scale is not proper Step pattern alph. order: ABCDEFDFGF Step pattern size order : CDBFGEFEAE 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 6 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 n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.025919 Average absolute harmonicity : 0.171238 Specific harmonicity : 0.119174 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 9.504000E+04, 16.53625 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 196.5, average 19.65000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.54245, average 1.05424 Sum of Tenney's harmonic distance : 20.13708, average 2.01371 Vogel's harmonic complexity : 18.10000 Wille's k value : 247 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 160.60735, average 2.92013 Lattice compactness (without 2's) : 90.11134, average 1.63839 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.90000 21 1 3: -1 .. 2 0.80000 10 2 5: -1 .. 0 -0.40000 4 1 11: 0 .. 1 0.60000 6 6 Average exponent except 2's : 10 / 10 = 1.00000 Average absolute exponent except 2's: 20 / 10 = 2.00000
FIT/MODE
10: 0 1 1 1 2 1 1 1 1 1 N T3 SD: 37.3144 c. M: 57.5963 c. 11: 0 1 1 1 2 1 2 1 0 2 N SD: 40.0745 c. M: 67.5448 c. 12: 0 1 1 1 2 2 1 2 0 2 N SD: 46.5781 c. M: 68.9142 c. 13: 1 1 0 2 2 2 1 2 0 2 N SD: 24.6758 c. M:-39.0347 c. 14: 0 2 0 2 2 2 2 2 0 2 N SD: 26.2632 c. M: 53.2729 c. 15: 1 1 1 2 2 2 2 2 0 2 N SD: 20.4177 c. M:-36.0900 c. 16: 1 1 1 2 2 2 3 2 0 2 N SD: 21.7723 c. M:-33.0408 c. 17: 1 1 1 2 3 2 2 2 1 2 N SD: 16.5126 c. M: 29.3610 c. 19: 1 2 0 3 3 2 3 2 1 2 N SD: 15.1303 c. M:-24.4695 c. 22: 1 2 1 3 3 3 3 3 0 3 N SD: 10.0670 c. M:-18.7673 c. 24: 1 2 1 3 4 3 3 3 1 3 N SD: 11.0095 c. M: 18.9142 c. 26: 1 3 0 4 4 3 4 3 1 3 N SD: 10.7682 c. M:-19.6112 c. 29: 1 3 1 4 4 4 4 4 0 4 N SD: 9.2462 c. M:-16.8865 c. 32: 1 3 1 5 5 4 4 4 1 4 N SD: 10.3089 c. M: 16.4100 c. 33: 1 4 1 4 5 4 5 4 1 4 N SD: 10.0848 c. M: 16.9093 c. 36: 2 3 1 5 6 4 5 5 1 4 N SD: 9.9451 c. M:-17.3037 c. 39: 2 3 2 5 6 5 5 5 1 5 N SD: 6.3912 c. M:-11.4746 c. 41: 2 4 1 6 6 5 6 5 1 5 N SD: 6.9695 c. M:-11.5736 c. 43: 2 4 1 6 7 5 6 5 2 5 N SD: 6.9446 c. M: 12.9451 c. 46: 2 4 2 6 7 6 6 6 1 6 N SD: 4.4655 c. M: 8.4825 c. 53: 2 5 2 7 8 7 7 7 1 7 N SD: 5.6558 c. M: 7.9899 c. 58: 3 5 2 8 9 7 8 7 2 7 N SD: 4.5453 c. M:-8.7960 c. 61: 3 5 2 9 9 8 8 8 1 8 N SD: 5.3070 c. M: 7.6272 c. 64: 3 6 2 9 9 8 9 8 2 8 N SD: 4.8607 c. M: 8.2050 c. 65: 3 6 2 9 10 8 9 8 2 8 N SD: 1.6505 c. M:-2.9448 c. 111: 5 10 4 15 17 14 15 14 3 14 N SD: 1.4177 c. M: 2.8421 c. 118: 5 11 4 16 18 15 16 15 3 15 N SD: 1.8612 c. M: 2.8125 c. 137: 6 13 4 19 21 17 19 17 4 17 N SD: 1.2945 c. M: 2.4501 c. 152: 7 14 5 21 23 19 21 19 4 19 N SD: 1.2801 c. M:-2.1384 c. 159: 7 15 5 22 24 20 22 20 4 20 N SD: 0.6982 c. M:-1.2716 c. 224: 10 21 7 31 34 28 31 28 6 28 N SD: 0.5832 c. M:-1.0672 c. 270: 12 25 9 37 41 34 37 34 7 34 N SD: 0.3257 c. M: 0.5598 c. 335: 15 31 11 46 51 42 46 42 9 42 N SD: 0.2416 c. M:-0.4584 c. 494: 22 46 16 68 75 62 68 62 13 62 N SD: 0.1742 c. M:-0.3165 c. 677: 30 63 22 93 103 85 93 85 18 85 N SD: 0.1278 c. M: 0.2289 c. 836: 37 78 27 115 127 105 115 105 22 105 N SD: 0.0856 c. M: 0.1629 c. 901: 40 84 29 124 137 113 124 113 24 113 N SD: 0.0883 c. M:-0.1456 c. 1171: 52 109 38 161 178 147 161 147 31 147 N SD: 0.0103 c. M:-0.0183 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: 18.6808 cents 4 x x x 5 x 6 x 7 x 8 S SD: 12.9453 cents 5 x x x 6:7 x 8:9 x 10 S SD: 16.3084 cents 6 x x 7 x 8:9:10 x 11:12 S SD: 14.0484 cents 7 x x 8:9:10:11:12 x 13:14 S SD: 20.6348 cents 8 x x 9:10:11:12:13:14:15:16 S SD: 8.7443 cents 9 x 10 x 11:12:14:15:16:17:18 S SD: 13.1123 cents 10 x 11 x 12:14:15:17:18 x 20 SD: 11.5017 cents 11 x 12 x 14:15:17:18 x 20:22 SD: 10.9340 cents 12 x 13:14:15:17:18:20 x 22:24 SD: 11.1378 cents 13 x 14:15:16:18:20:21:23:24:26 SD: 9.8182 cents 14 x 15:16:17:19:21:23:25:26:28 SD: 7.9752 cents 15 x x 17:19:21:23:25:27:28:30 SD: 9.2589 cents 16:17 x 18:20:22:24:26:29 x 32 SD: 7.7217 cents 17:18 x 19:21:23:26:28 x 31:34 SD: 8.1346 cents 18:19:20 x 22:25:27:30:32:33:36 SD: 6.5355 cents 19:20:21 x 24:26:29:31:34:35:38 SD: 7.1297 cents 20:21:22:23:25:28:30:33:36:37:40 SD: 6.2787 cents 21:22:23:24:26:29:32:35:38:39:42 SD: 5.6818 cents 22:23:24:25:27:30:33:36 x 40:44 SD: 4.8378 cents 24:25:26:27:30:33:36:40:43:44:48 SD: 4.0883 cents 25:26 x 28:31:34:38:41:45:46:50 SD: 4.0404 cents 26:27 x 29:32:36:39:43:47:48:52 SD: 3.1767 cents 27:28:30 x 33:37:41:45:49:50:54 SD: 5.1536 cents 28:29:31:32:35:39:42:46:50:51:56 SD: 4.5831 cents 29:30:32:33:36:40:44:48:52:53:58 SD: 3.1678 cents 30:31:33:34:37:41:45:50:54:55:60 SD: 2.4961 cents 35:36 x 39:43:48:53:58:63:64:70 SD: 3.1772 cents 37:38:41:42:46:51:56:61:67:68:74 SD: 3.0069 cents 38:39:42:43:47:52:57:63:68:70:76 SD: 2.3422 cents 40:41:44:45:50:55:60:66:72:73:80 SD: 2.1811 cents 50:52:55:56:62:69:75:83:90:92:100 SD: 2.1772 cents 54:56:59:61:67:74:81:89:97:99:108 SD: 1.8770 cents 56:58:62:63:69:77:84:92:101:103:112 SD: 1.8373 cents 58:60:64:65:72:80:87:96:104:106:116 SD: 1.6269 cents 62:64:68:70:77:85:93:102:112:114:124 SD: 1.4873 cents 64:66:70:72:79:88:96:106:115:117:128 SD: 1.3879 cents 71:73:78:80:88:98:107:117:128:130:142 SD: 1.3168 cents 72:74:79:81:89:99:108:119:130:132:144 SD: 0.9694 cents 88:91:97:99:109:121:132:145:158:161:176 SD: 0.8698 cents 96:99:106:108:119:132:144:158:173:176:192 SD: 0.8631 cents 118:122:130:133:146:162:177:195:212:216:236 SD: 0.8338 cents 120:124:132:135:149:165:180:198:216:220:240 SD: 0.6788 cents 126:130:139:142:156:173:189:208:227:231:252 SD: 0.6697 cents 128:132:141:144:158:176:192:211:230:235:256 SD: 0.6556 cents 130:134:143:146:161:179:195:215:234:238:260 SD: 0.6261 cents 152:157:167:171:188:209:228:251:274:279:304 SD: 0.5034 cents 160:165:176:180:198:220:240:264:288:293:320 SD: 0.1968 cents 320:330:352:360:396:440:480:528:576:587:640 SD: 0.0983 cents 480:495:528:540:594:660:720:792:864:880:960 S SD: 0.0000 cents