Scala analysis: xen12-wilson-32-dekany
5C2 1.5.7.11.15 Dekany, Figure 32
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: 21/16 470.780907 narrow fourth 4: 11/8 551.317942 undecimal semi-augmented fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 3/2 701.955001 perfect fifth 7: 7/4 968.825906 harmonic seventh 8: 15/8 1088.268715 classic major seventh 9: 77/40 1133.830135 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 80/77 66.1699 1: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 16/15 111.7313 minor diatonic semitone 3: 105/88 305.7767 4: 22/21 80.5370 undecimal minor semitone 5: 56/55 31.1943 undecimal diesis, konbini comma 6: 15/14 119.4428 major diatonic semitone 7: 7/6 266.8709 septimal minor third 8: 15/14 119.4428 major diatonic semitone 9: 77/75 45.5614 10: 80/77 66.1699
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 : 53.3 165.0 470.8 551.3 582.5 702.0 968.8 1088.3 1133.8 1200.0 53.3 : 111.7 417.5 498.0 529.2 648.7 915.6 1035.0 1080.6 1146.7 1200.0 165.0 : 305.8 386.3 417.5 537.0 803.8 923.3 968.8 1035.0 1088.3 1200.0 470.8 : 80.5 111.7 231.2 498.0 617.5 663.0 729.2 782.5 894.2 1200.0 551.3 : 31.2 150.6 417.5 537.0 582.5 648.7 702.0 813.7 1119.5 1200.0 582.5 : 119.4 386.3 505.8 551.3 617.5 670.8 782.5 1088.3 1168.8 1200.0 702.0 : 266.9 386.3 431.9 498.0 551.3 663.0 968.8 1049.4 1080.6 1200.0 968.8 : 119.4 165.0 231.2 284.4 396.2 702.0 782.5 813.7 933.1 1200.0 1088.3: 45.6 111.7 165.0 276.7 582.5 663.0 694.2 813.7 1080.6 1200.0 1133.8: 66.2 119.4 231.2 537.0 617.5 648.7 768.1 1035.0 1154.4 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 : 126.79893 cents, oct.: 1267.98933 cents Scale is not proper Step pattern alph. order: ABCDEFGFHI Step pattern size order : CFIEAGHGBD 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 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: 77 Scale harmonicity : 0.020026 Average absolute harmonicity : 0.170731 Specific harmonicity : 0.099887 Fundamental : 1/160, -7.3219 octaves, 1.6352 Hz. Guide tone : 2310, 11.1737 octaves, 604355.056 Hz. Exponens Consonantiae : 3.696000E+05, 18.49561 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 156.5, average 15.65000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.15342, average 1.01534 Sum of Tenney's harmonic distance : 19.17402, average 1.91740 Vogel's harmonic complexity : 15.30000 Wille's k value : 82 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 154.43650, average 2.80794 Lattice compactness (without 2's) : 79.02783, average 1.43687 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -2.10000 23 1 3: 0 .. 1 0.40000 4 1 5: -1 .. 1 -0.20000 4 1 7: 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 1 3 0 1 1 2 1 0 1 N SD: 37.0271 c. M: 71.3179 c. 11: 0 1 3 1 0 1 3 1 0 1 N SD: 35.8080 c. M: 55.9133 c. 13: 1 1 3 1 0 2 3 1 0 1 N SD: 27.1712 c. M:-46.5587 c. 14: 1 1 3 1 1 1 3 2 0 1 N SD: 25.5921 c. M: 42.2095 c. 15: 1 1 4 1 0 2 3 2 0 1 N SD: 17.3442 c. M:-31.7313 c. 17: 1 1 5 1 0 2 4 1 1 1 N SD: 17.8527 c. M: 29.4452 c. 19: 1 2 4 2 0 2 4 2 1 1 N SD: 16.5654 c. M: 28.6756 c. 20: 1 2 5 1 1 2 4 2 1 1 N SD: 11.3973 c. M:-18.0450 c. 21: 1 2 5 2 0 2 5 2 1 1 N SD: 10.6211 c. M:-20.1106 c. 22: 1 2 6 1 1 2 5 2 1 1 N SD: 10.5388 c. M:-20.1282 c. 29: 1 3 7 2 1 3 6 3 1 2 N SD: 11.3957 c. M: 17.1018 c. 31: 1 3 8 2 1 3 7 3 1 2 N SD: 7.8746 c. M: 14.5633 c. 41: 2 4 10 3 1 4 9 4 2 2 N SD: 5.2272 c. M:-10.6055 c. 43: 2 4 11 3 1 4 10 4 2 2 N SD: 5.2243 c. M:-10.3559 c. 51: 2 5 13 3 2 5 11 5 2 3 N SD: 5.1114 c. M: 10.1415 c. 52: 2 5 13 4 1 5 12 5 2 3 N SD: 5.4927 c. M: 9.6473 c. 53: 2 5 14 3 2 5 12 5 2 3 N SD: 5.0692 c. M: 7.9899 c. 58: 3 5 15 4 1 6 13 6 2 3 N SD: 5.1726 c. M:-8.7960 c. 61: 3 5 16 4 2 6 13 6 3 3 N SD: 5.5276 c. M:-7.6517 c. 63: 3 6 16 4 2 6 14 6 3 3 N SD: 5.0272 c. M:-9.0270 c. 66: 3 6 17 4 2 7 14 7 2 4 N SD: 4.1227 c. M:-7.1359 c. 68: 3 6 18 4 2 7 15 7 2 4 N SD: 4.0139 c. M: 6.1807 c. 72: 3 7 18 5 2 7 16 7 3 4 N SD: 2.5672 c. M: 4.9354 c. 74: 3 7 19 5 2 7 17 7 3 4 N SD: 2.7407 c. M: 4.6577 c. 87: 4 8 22 6 2 9 19 9 3 5 N SD: 2.0124 c. M: 3.3087 c. 109: 5 10 28 7 3 11 24 11 4 6 N SD: 1.4598 c. M:-2.6322 c. 130: 6 12 33 9 3 13 29 13 5 7 N SD: 1.2962 c. M:-2.5282 c. 161: 7 15 41 11 4 16 36 16 6 9 N SD: 0.8798 c. M: 1.3339 c. 181: 8 17 46 12 5 18 40 18 7 10 N SD: 0.7004 c. M: 1.0417 c. 270: 12 25 69 18 7 27 60 27 10 15 N SD: 0.3549 c. M:-0.6202 c. 342: 15 32 87 23 9 34 76 34 13 19 N SD: 0.4167 c. M: 0.6414 c. 451: 20 42 115 30 12 45 100 45 17 25 N SD: 0.2862 c. M: 0.5419 c. 472: 21 44 120 32 12 47 105 47 18 26 N SD: 0.2514 c. M: 0.4419 c. 581: 26 54 148 39 15 58 129 58 22 32 N SD: 0.2064 c. M:-0.4276 c. 653: 29 61 166 44 17 65 145 65 25 36 N SD: 0.2322 c. M:-0.3863 c. 655: 29 61 167 44 17 65 146 65 25 36 N SD: 0.1725 c. M:-0.3344 c. 742: 33 69 189 50 19 74 165 74 28 41 N SD: 0.1440 c. M: 0.3020 c. 836: 37 78 213 56 22 83 186 83 32 46 N SD: 0.1401 c. M:-0.2629 c. 923: 41 86 235 62 24 92 205 92 35 51 N SD: 0.1173 c. M: 0.2452 c. 1106: 49 103 282 74 29 110 246 110 42 61 N SD: 0.0859 c. M: 0.1425 c. 1236: 55 115 315 83 32 123 275 123 47 68 N SD: 0.0928 c. M:-0.1504 c. 1417: 63 132 361 95 37 141 315 141 54 78 N SD: 0.0840 c. M:-0.1334 c. 1578: 70 147 402 106 41 157 351 157 60 87 N SD: 0.0341 c. M: 0.0585 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 4 x x x 5 x x 6 S SD: 29.5861 cents 4 x x 5 x x 6:7 x x 8 S SD: 21.1168 cents 5 x 6 x x 7:8:9 x x 10 S SD: 38.7577 cents 6 x 7:8 x x 9 x 11 x 12 SD: 22.4800 cents 7 x 8:9 x 10:11:12:13 x 14 S SD: 17.4443 cents 8 x 9 x 11 x 12:14:15 x 16 SD: 6.4843 cents 9 x 10:12 x 13:14:16:17 x 18 S SD: 13.4347 cents 10 x 11:13 x 14:15:18 x 19:20 SD: 8.0371 cents 11 x 12:14:15 x 17:19 x 21:22 SD: 11.6413 cents 12 x 13:16 x 17:18:21 x 23:24 SD: 6.2566 cents 13 x 14:17:18 x 20:23:24:25:26 SD: 8.4186 cents 14 x 15:18:19:20:21:25:26:27:28 SD: 9.0223 cents 15 x 17:20 x 21:23:26:28:29:30 SD: 9.0589 cents 16:17:18:21:22 x 24:28:30:31:32 S SD: 7.2948 cents 18:19:20:24 x 25:27:32:34:35:36 SD: 7.0904 cents 19:20:21:25:26:27:29:33:36:37:38 SD: 6.2385 cents 20:21:22:26 x 28:30:35 x 39:40 SD: 5.2240 cents 21:22:23:28:29 x 32:37:39:40:42 SD: 6.1758 cents 22:23:24:29:30:31:33:39:41:42:44 SD: 4.4401 cents 23:24:25:30 x 32:35:40:43:44:46 SD: 4.9117 cents 24:25:26:32:33:34:36:42:45:46:48 SD: 4.7126 cents 26:27:29:34:36 x 39:46:49:50:52 SD: 4.0810 cents 28:29:31:37 x 39:42:49:53:54:56 SD: 2.8916 cents 30:31:33:39:41:42:45:53:56:58:60 SD: 2.7966 cents 31:32:34:41:43 x 47:54:58:60:62 SD: 3.4124 cents 32:33:35:42:44:45:48:56:60:62:64 SD: 1.6803 cents 36:37:40:47 x 50:54:63:68:69:72 SD: 3.2033 cents 37:38:41:49:51:52:56:65:69:71:74 SD: 3.0322 cents 38:39:42:50:52:53:57:67:71:73:76 SD: 2.2030 cents 40:41:44:53:55:56:60:70:75:77:80 SD: 1.9495 cents 57:59:63:75:78:80:86:100:107:110:114 SD: 1.8966 cents 58:60:64:76:80:81:87:102:109:112:116 SD: 1.5230 cents 64:66:70:84:88:90:96:112:120:123:128 SD: 1.2833 cents 70:72:77:92:96:98:105:123:131:135:140 SD: 1.0817 cents 80:83:88:105:110:112:120:140:150:154:160 SD: 1.0461 cents 90:93:99:118:124:126:135:158:169:173:180 SD: 0.8409 cents 118:122:130:155:162:165:177:207:221:227:236 SD: 0.7935 cents 120:124:132:158:165:168:180:210:225:231:240 SD: 0.6505 cents 128:132:141:168:176:179:192:224:240:246:256 SD: 0.4206 cents 160:165:176:210:220:224:240:280:300:308:320 SD: 0.0000 cents