Scala analysis: xen12-wilson-33-dekany
5C3 1.5.7.11.15 Dekany, Figure 33
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: 15/14 119.442808 major diatonic semitone 3: 11/10 165.004228 Ptolemy's second, 4/5-tone 4: 33/28 284.447037 undecimal minor third 5: 11/8 551.317942 undecimal semi-augmented fourth 6: 165/112 670.760751 7: 3/2 701.955001 perfect fifth 8: 11/7 782.492036 undecimal augmented fifth 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: 80/77 66.1699 3: 77/75 45.5614 4: 15/14 119.4428 major diatonic semitone 5: 7/6 266.8709 septimal minor third 6: 15/14 119.4428 major diatonic semitone 7: 56/55 31.1943 undecimal diesis, konbini comma 8: 22/21 80.5370 undecimal minor semitone 9: 105/88 305.7767 10: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 77/75 45.561 cents 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 80/77 66.170 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 7/6 266.871 cents septimal minor third 1: 1 105/88 305.777 cents 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 3 5/4 386.314 cents major third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 3: 3 8/7 231.174 cents septimal whole tone 3: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 77/60 431.875 cents 3: 1 21/16 470.781 cents narrow fourth 3: 1 4/3 498.045 cents perfect fourth 3: 1 75/56 505.757 cents marvelous fourth 4: 1 88/75 276.736 cents 4: 1 33/28 284.447 cents undecimal minor third 4: 2 4/3 498.045 cents perfect fourth 4: 1 224/165 529.239 cents 4: 3 15/11 536.951 cents undecimal augmented fourth 4: 2 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 44/35 396.178 cents 5: 1 11/8 551.318 cents undecimal semi-augmented 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 16/11 648.682 cents undecimal semi-diminished fifth 5: 1 35/22 803.822 cents 6: 2 16/11 648.682 cents undecimal semi-diminished fifth 6: 3 22/15 663.049 cents undecimal diminished fifth 6: 1 165/112 670.761 cents 6: 2 3/2 701.955 cents perfect fifth 6: 1 56/33 915.553 cents 6: 1 75/44 923.264 cents 7: 1 112/75 694.243 cents marvelous fifth 7: 1 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 7: 1 120/77 768.125 cents 7: 2 11/7 782.492 cents undecimal augmented fifth 7: 3 7/4 968.826 cents harmonic seventh 7: 1 20/11 1034.996 cents large minor seventh 8: 1 11/7 782.492 cents undecimal augmented fifth 8: 3 8/5 813.686 cents minor sixth 8: 2 20/11 1034.996 cents large minor seventh 8: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 8: 1 28/15 1080.557 cents grave major seventh 8: 2 15/8 1088.269 cents classic major seventh 9: 1 176/105 894.223 cents 9: 1 12/7 933.129 cents septimal major sixth 9: 2 28/15 1080.557 cents grave major seventh 9: 1 15/8 1088.269 cents classic major seventh 9: 1 21/11 1119.463 cents undecimal major seventh 9: 1 77/40 1133.830 cents 9: 1 64/33 1146.727 cents 33rd subharmonic 9: 1 150/77 1154.439 cents 9: 1 55/28 1168.806 cents Highest number of different intervals for one interval class: 9 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 : 53.3 119.4 165.0 284.4 551.3 670.8 702.0 782.5 1088.3 1200.0 53.3 : 66.2 111.7 231.2 498.0 617.5 648.7 729.2 1035.0 1146.7 1200.0 119.4 : 45.6 165.0 431.9 551.3 582.5 663.0 968.8 1080.6 1133.8 1200.0 165.0 : 119.4 386.3 505.8 537.0 617.5 923.3 1035.0 1088.3 1154.4 1200.0 284.4 : 266.9 386.3 417.5 498.0 803.8 915.6 968.8 1035.0 1080.6 1200.0 551.3 : 119.4 150.6 231.2 537.0 648.7 702.0 768.1 813.7 933.1 1200.0 670.8 : 31.2 111.7 417.5 529.2 582.5 648.7 694.2 813.7 1080.6 1200.0 702.0 : 80.5 386.3 498.0 551.3 617.5 663.0 782.5 1049.4 1168.8 1200.0 782.5 : 305.8 417.5 470.8 537.0 582.5 702.0 968.8 1088.3 1119.5 1200.0 1088.3: 111.7 165.0 231.2 276.7 396.2 663.0 782.5 813.7 894.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 305.7767 cents 75/64, 274.5824 cents 56/55, 31.1943 cents 2: 111.7313 .. 417.5080 cents 105/88, 305.7767 cents 1408/1575,-194.0454 cents 3: 165.0042 .. 505.7565 cents 375/308, 340.7523 cents 121/140,-252.5037 cents 4: 276.7355 .. 551.3179 cents 75/64, 274.5824 cents 4928/5625,-229.0210 cents 5: 396.1783 .. 803.8217 cents 1225/968, 407.6434 cents 32/35,-155.1396 cents 6: 648.6821 .. 923.2645 cents 75/64, 274.5824 cents 32/35,-155.1396 cents 7: 694.2435 .. 1034.9958 cents 375/308, 340.7523 cents 4928/5625,-229.0210 cents 8: 782.4920 .. 1088.2687 cents 105/88, 305.7767 cents 121/140,-252.5037 cents 9: 894.2233 .. 1168.8057 cents 75/64, 274.5824 cents 1408/1575,-194.0454 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 105/88, 305.7767 cents Average / Smallest step : 3.846863 Largest / Average step : 2.548139 Largest / Smallest step : 9.802341 Median interval of one step : 96.13416 cents, amount: 0 Most common interval of one step : 15/14, 119.4428 cents, amount: 2 Least squares average step : 108.24455 cents, oct.: 1082.44554 cents Scale is not proper Step pattern alph. order: ABCDEDFGHI Step pattern size order : CDBGHGAEIF Scale is not a Constant Structure Scale diversity : 1.513892 Lumma stability : 0.051990 Lumma impropriety factor : 0.732644 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 : 9 Highest interval variety : 9 Mean interval variety : 6.88889 = 62/9 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 225/224, 7.7115 cents Number of recognisable fifths : 4, average 700.0271 cents Length of longest harmonic part : 1 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 classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 11 Odd number limit : 165 (O: 165 U: 165) Highest odd numerator or denominator: 165 Scale harmonicity : 0.020026 Average absolute harmonicity : 0.161910 Specific harmonicity : 0.096718 Fundamental : 1/1120, -10.1293 octaves, 0.2336 Hz. Guide tone : 330, 8.3663 octaves, 86336.437 Hz. Exponens Consonantiae : 3.696000E+05, 18.49561 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 260.5, average 26.05000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.20799, average 1.12080 Sum of Tenney's harmonic distance : 21.60899, average 2.16090 Vogel's harmonic complexity : 21.70000 Wille's k value : 577 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 153.61158, average 2.79294 Lattice compactness (without 2's) : 80.34566, average 1.46083 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.90000 21 1 3: 0 .. 1 0.60000 6 1 5: -1 .. 1 0.20000 4 1 7: -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 0 1 2 1 0 1 3 1 N SD: 55.9473 c. M: 101.9550 c. 11: 0 1 0 1 3 1 0 1 3 1 N SD: 36.5651 c. M: 66.2652 c. 12: 1 0 1 1 3 1 0 1 3 1 N T3 SD: 27.7505 c. M:-48.6821 c. 13: 1 0 1 1 3 1 1 0 4 1 N SD: 26.3852 c. M: 44.0305 c. 14: 1 0 1 1 3 2 0 1 4 1 N SD: 23.7379 c. M: 37.0322 c. 17: 1 1 0 2 4 2 0 1 4 2 N G SD: 19.1723 c. M:-35.1216 c. 18: 1 1 0 2 4 2 0 2 4 2 N SD: 20.1251 c. M: 35.2883 c. 20: 1 1 1 2 4 2 1 1 5 2 N SD: 10.7537 c. M:-18.0450 c. 22: 1 1 1 2 5 2 1 1 6 2 N SD: 9.7916 c. M: 18.8557 c. 28: 1 2 1 3 6 3 0 2 7 3 N SD: 11.8418 c. M: 16.8401 c. 29: 1 2 1 3 6 3 1 2 7 3 N SD: 7.8460 c. M: 13.3869 c. 31: 1 2 1 3 7 3 1 2 8 3 N SD: 9.3401 c. M: 14.5633 c. 37: 2 2 1 4 8 4 1 2 10 3 N SD: 8.7697 c. M:-14.4340 c. 39: 2 2 1 4 9 4 1 2 10 4 N SD: 8.0281 c. M: 13.2613 c. 41: 2 2 2 4 9 4 1 3 10 4 N SD: 5.7545 c. M:-10.6055 c. 43: 2 2 2 4 10 4 1 3 11 4 N SD: 4.1164 c. M: 7.8149 c. 63: 3 3 3 6 14 6 2 4 16 6 N SD: 3.4513 c. M:-6.4243 c. 68: 3 4 2 7 15 7 2 4 18 6 N SD: 4.0430 c. M: 6.1807 c. 72: 3 4 3 7 16 7 2 5 18 7 N SD: 2.6421 c. M: 4.9354 c. 87: 4 5 3 9 19 9 2 6 22 8 N SD: 3.1174 c. M:-5.2081 c. 89: 4 5 3 9 20 9 2 6 23 8 N SD: 2.1368 c. M:-3.8661 c. 109: 5 6 4 11 24 11 3 7 28 10 N SD: 1.4429 c. M:-2.6322 c. 118: 5 7 4 12 26 12 3 8 30 11 N SD: 1.5234 c. M:-2.5911 c. 130: 6 7 5 13 29 13 3 9 33 12 N SD: 1.7471 c. M:-3.0854 c. 140: 6 8 5 14 31 14 4 9 36 13 N SD: 1.7408 c. M: 2.7465 c. 152: 7 8 6 15 34 15 4 10 39 14 N SD: 1.0115 c. M:-1.9902 c. 161: 7 9 6 16 36 16 4 11 41 15 N SD: 0.7509 c. M: 1.3339 c. 181: 8 10 7 18 40 18 5 12 46 17 N SD: 0.7111 c. M: 1.1475 c. 270: 12 15 10 27 60 27 7 18 69 25 N SD: 0.3636 c. M:-0.6202 c. 342: 15 19 13 34 76 34 9 23 87 32 N SD: 0.3711 c. M: 0.6414 c. 431: 19 24 16 43 96 43 11 29 110 40 N SD: 0.3577 c. M: 0.7351 c. 451: 20 25 17 45 100 45 12 30 115 42 N SD: 0.2825 c. M: 0.5419 c. 494: 22 27 19 49 110 49 13 33 126 46 N SD: 0.2226 c. M: 0.4145 c. 612: 27 34 23 61 136 61 16 41 156 57 N SD: 0.2021 c. M: 0.3376 c. 742: 33 41 28 74 165 74 19 50 189 69 N SD: 0.1944 c. M:-0.3983 c. 764: 34 42 29 76 170 76 20 51 195 71 N SD: 0.1448 c. M: 0.2931 c. 923: 41 51 35 92 205 92 24 62 235 86 N SD: 0.1336 c. M:-0.2767 c. 966: 43 53 37 96 215 96 25 65 246 90 N SD: 0.1365 c. M:-0.2349 c. 1075: 48 59 41 107 239 107 28 72 274 100 N SD: 0.1595 c. M:-0.3085 c. 1084: 48 60 41 108 241 108 28 73 276 101 N SD: 0.0958 c. M:-0.1648 c. 1236: 55 68 47 123 275 123 32 83 315 115 N SD: 0.0763 c. M:-0.1384 c. 1417: 63 78 54 141 315 141 37 95 361 132 N SD: 0.0698 c. M:-0.1334 c. 1578: 70 87 60 157 351 157 41 106 402 147 N SD: 0.0371 c. M: 0.0558 c. 1848: 82 102 70 184 411 184 48 124 471 172 N SD: 0.0333 c. M: 0.0692 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 x 3 x x 4 S SD: 0.0000 cents 3 x x x x 4 x x 5 x 6 S SD: 38.3186 cents 4 x x x 5 x x 6 x x 8 S SD: 33.9556 cents 5 x x x 6:7 x x 8:9:10 S SD: 17.7919 cents 6 x x x 7:8 x 9 x 11:12 SD: 13.6537 cents 7 x x x 8 x 10 x 11:13:14 SD: 15.4279 cents 8 x x 9 x 11 x 12:13:15:16 SD: 11.6450 cents 9 x x 10:11:12:13 x 14:17:18 SD: 13.3575 cents 10 x x 11:12:14 x 15:16:19:20 SD: 8.3849 cents 11 x x 12:13:15:16 x 17:21:22 SD: 7.4624 cents 12 x 13 x 14:17 x 18:19:23:24 SD: 10.0656 cents 13 x 14 x 15:18:19 x 20:24:26 S SD: 8.8397 cents 14 x 15 x 17:19 x 21:22:26:28 SD: 8.4003 cents 15 x 16:17:18:21:22:23:24:28:30 S SD: 9.4389 cents 16 x 17:18:19:22 x 24:25:30:32 SD: 5.5784 cents 17 x 18:19:20:23:25:26:27:32:34 SD: 6.5708 cents 18 x 19:20:21:25 x 27:28:34:36 SD: 5.6655 cents 19 x 20:21:22:26:28:29:30:36:38 SD: 6.4011 cents 20:21 x 22:24:28:29:30:31:38:40 SD: 7.6708 cents 21:22 x 23:25:29:31:32:33:39:42 SD: 5.1978 cents 22:23 x 24:26:30:32:33:35:41:44 SD: 5.0303 cents 23:24 x 25:27:32:34:35:36:43:46 SD: 5.0114 cents 24:25:26 x 28:33:35:36:38:45:48 SD: 4.2416 cents 26:27:28:29:31:36:38:39:41:49:52 SD: 4.0680 cents 27:28:29:30:32:37:40:41:42:51:54 SD: 3.9497 cents 28:29:30:31:33:39:41:42:44:53:56 SD: 3.2566 cents 30:31:32:33:35:41:44:45:47:56:60 SD: 2.5257 cents 32:33:34:35:38:44:47:48:50:60:64 SD: 2.4553 cents 35:36 x 39:41:48:52:53:55:66:70 SD: 3.8982 cents 37:38:40:41:44:51:55:56:58:69:74 SD: 3.6065 cents 38:39:41:42:45:52:56:57:60:71:76 SD: 2.2949 cents 40:41:43:44:47:55:59:60:63:75:80 SD: 1.3835 cents 70:72:75:77:83:96:103:105:110:131:140 SD: 1.2856 cents 72:74:77:79:85:99:106:108:113:135:144 SD: 0.8842 cents 112:116:120:123:132:154:165:168:176:210:224 SD: 0.7990 cents 122:126:131:134:144:168:180:183:192:229:244 SD: 0.7600 cents 128:132:137:141:151:176:189:192:201:240:256 SD: 0.5379 cents 152:157:163:167:179:209:224:228:239:285:304 SD: 0.4183 cents 192:198:206:211:226:264:283:288:302:360:384 SD: 0.4086 cents 222:229:238:244:262:305:327:333:349:416:444 SD: 0.3545 cents 224:231:240:246:264:308:330:336:352:420:448 SD: 0.2813 cents 280:289:300:308:330:385:413:420:440:525:560 SD: 0.2577 cents 320:330:343:352:377:440:471:480:503:600:640 SD: 0.1916 cents 408:421:437:449:481:561:601:612:641:765:816 SD: 0.1558 cents 448:462:480:493:528:616:660:672:704:840:896 SD: 0.0702 cents