Scala analysis: xen12-wilson-40-5C3-dekany-01
1-3-5-7-11 5C3 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 7/6 266.870906 septimal minor third 3: 77/60 431.875134 4: 11/8 551.317942 undecimal semi-augmented fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 77/48 818.188848 7: 7/4 968.825906 harmonic seventh 8: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 9: 77/40 1133.830135 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 80/77 66.1699 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 35/33 101.8667 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 15/14 119.4428 major diatonic semitone 5: 56/55 31.1943 undecimal diesis, konbini comma 6: 55/48 235.6767 undecimal semi-augmented whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone 8: 22/21 80.5370 undecimal minor semitone 9: 21/20 84.4672 minor semitone 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 80/77 66.170 cents 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: 1 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 55/48 235.677 cents undecimal semi-augmented whole tone 2: 2 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 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 33/28 284.447 cents undecimal minor third 2: 1 5/4 386.314 cents major third 3: 1 8/7 231.174 cents septimal whole tone 3: 3 6/5 315.641 cents minor third 3: 1 40/33 333.041 cents 3: 2 5/4 386.314 cents major third 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 77/60 431.875 cents 3: 1 55/42 466.851 cents 4: 1 96/77 381.811 cents 4: 1 44/35 396.178 cents 4: 2 14/11 417.508 cents undecimal diminished fourth or major third 4: 2 4/3 498.045 cents perfect fourth 4: 1 15/11 536.951 cents undecimal augmented fourth 4: 3 11/8 551.318 cents undecimal semi-augmented fourth 5: 1 4/3 498.045 cents perfect fourth 5: 1 48/35 546.815 cents septimal 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 35/24 653.185 cents septimal semi-diminished fifth 5: 1 3/2 701.955 cents perfect fifth 6: 3 16/11 648.682 cents undecimal semi-diminished fifth 6: 1 22/15 663.049 cents undecimal diminished fifth 6: 2 3/2 701.955 cents perfect fifth 6: 2 11/7 782.492 cents undecimal augmented fifth 6: 1 35/22 803.822 cents 6: 1 77/48 818.189 cents 7: 1 84/55 733.149 cents 7: 1 120/77 768.125 cents 7: 1 11/7 782.492 cents undecimal augmented fifth 7: 2 8/5 813.686 cents minor sixth 7: 1 33/20 866.959 cents 7: 3 5/3 884.359 cents major sixth, BP sixth 7: 1 7/4 968.826 cents harmonic seventh 8: 1 8/5 813.686 cents minor sixth 8: 1 56/33 915.553 cents 8: 3 12/7 933.129 cents septimal major sixth 8: 2 7/4 968.826 cents harmonic seventh 8: 1 20/11 1034.996 cents large minor seventh 8: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 9: 1 96/55 964.323 cents 9: 2 20/11 1034.996 cents large minor seventh 9: 1 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 77/40 1133.830 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 : 165.0 266.9 431.9 551.3 582.5 818.2 968.8 1049.4 1133.8 1200.0 165.0 : 101.9 266.9 386.3 417.5 653.2 803.8 884.4 968.8 1035.0 1200.0 266.9 : 165.0 284.4 315.6 551.3 702.0 782.5 867.0 933.1 1098.1 1200.0 431.9 : 119.4 150.6 386.3 537.0 617.5 702.0 768.1 933.1 1035.0 1200.0 551.3 : 31.2 266.9 417.5 498.0 582.5 648.7 813.7 915.6 1080.6 1200.0 582.5 : 235.7 386.3 466.9 551.3 617.5 782.5 884.4 1049.4 1168.8 1200.0 818.2 : 150.6 231.2 315.6 381.8 546.8 648.7 813.7 933.1 964.3 1200.0 968.8 : 80.5 165.0 231.2 396.2 498.0 663.0 782.5 813.7 1049.4 1200.0 1049.4: 84.5 150.6 315.6 417.5 582.5 702.0 733.1 968.8 1119.5 1200.0 1133.8: 66.2 231.2 333.0 498.0 617.5 648.7 884.4 1035.0 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 235.6767 cents 3025/2688, 204.4824 cents 56/55, 31.1943 cents 2: 150.6371 .. 386.3137 cents 55/48, 235.6767 cents 576/605,-85.0396 cents 3: 231.1741 .. 466.8507 cents 55/48, 235.6767 cents 32/35,-155.1396 cents 4: 381.8112 .. 551.3179 cents 847/768, 169.5068 cents 576/605,-85.0396 cents 5: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 32/33,-53.2729 cents 6: 648.6821 .. 818.1888 cents 847/768, 169.5068 cents 32/33,-53.2729 cents 7: 733.1493 .. 968.8259 cents 55/48, 235.6767 cents 576/605,-85.0396 cents 8: 813.6863 .. 1049.3629 cents 55/48, 235.6767 cents 32/35,-155.1396 cents 9: 964.3233 .. 1168.8057 cents 3025/2688, 204.4824 cents 576/605,-85.0396 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 : 55/48, 235.6767 cents Average / Smallest step : 3.846863 Largest / Average step : 1.963972 Largest / Smallest step : 7.555131 Median interval of one step : 110.65474 cents, amount: 0 Most common interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 128.31816 cents, oct.: 1283.18165 cents Scale is not proper Step pattern alph. order: ABACDEFGHI Step pattern size order : HEHFAIGCDB Scale is not a Constant Structure Scale diversity : 1.562078 Lumma stability : 0.051990 Lumma impropriety factor : 0.615811 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 : 441/440, 3.9302 cents Number of recognisable fifths : 3, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 7 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 : 77 (O: 77 U: 77) Highest odd numerator or denominator: 77 Scale harmonicity : 0.023510 Average absolute harmonicity : 0.142523 Specific harmonicity : 0.100340 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 154, 7.2668 octaves, 40290.337 Hz. Exponens Consonantiae : 3.696000E+04, 15.17368 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 237.5, average 23.75000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.31894, average 1.13189 Sum of Tenney's harmonic distance : 21.44185, average 2.14418 Vogel's harmonic complexity : 18.00000 Wille's k value : 192 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 132.70015, average 2.41273 Lattice compactness (without 2's) : 77.36141, average 1.40657 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.60000 18 1 3: -1 .. 0 -0.40000 4 5: -1 .. 0 -0.40000 4 7: 0 .. 1 0.60000 6 3 11: 0 .. 1 0.60000 6 6 Average exponent except 2's : 4 / 10 = 0.40000 Average absolute exponent except 2's: 20 / 10 = 2.00000
FIT/MODE
10: 1 1 1 1 0 2 2 0 1 1 N T3 S SD: 66.4160 c. M: 102.5122 c. 11: 1 1 2 1 0 2 1 1 1 1 N D3 SD: 50.5373 c. M: 96.0986 c. 12: 1 1 2 1 0 3 1 1 1 1 N SD: 52.7296 c. M: 82.5122 c. 13: 2 1 2 1 0 3 1 1 1 1 N SD: 25.0652 c. M: 45.7490 c. 14: 2 1 2 1 1 2 2 1 1 1 N D3 SD: 23.4504 c. M: 46.7603 c. 15: 2 1 2 2 0 3 2 1 1 1 N SD: 17.4154 c. M: 31.8751 c. 16: 2 2 2 1 1 3 2 1 1 1 N SD: 16.7706 c. M:-33.1291 c. 17: 2 2 2 2 0 4 2 1 1 1 N SD: 16.4092 c. M:-28.8700 c. 19: 3 1 3 2 0 4 2 2 1 1 N SD: 15.7050 c. M:-24.4695 c. 21: 3 2 3 2 0 4 3 1 2 1 N SD: 15.5353 c. M:-25.2677 c. 22: 3 2 3 2 1 4 3 1 2 1 N SD: 9.3243 c. M:-17.4878 c. 31: 4 3 4 3 1 6 4 2 2 2 N SD: 6.4945 c. M: 11.2495 c. 37: 5 3 5 4 1 7 5 2 3 2 N SD: 6.1313 c. M: 11.5251 c. 41: 6 3 6 4 1 8 5 3 3 2 N SD: 5.4206 c. M:-10.6055 c. 48: 7 4 6 5 1 10 6 3 3 3 N SD: 6.5903 c. M:-9.9958 c. 50: 7 4 7 5 1 10 6 4 3 3 N SD: 4.6993 c. M: 8.8259 c. 53: 7 5 7 5 2 10 7 3 4 3 N SD: 5.1608 c. M: 7.9217 c. 56: 8 4 8 6 1 11 7 4 4 3 N SD: 4.8589 c. M: 9.7280 c. 57: 8 5 8 5 2 11 7 4 4 3 N SD: 5.0491 c. M:-10.2301 c. 58: 8 5 8 6 1 12 7 4 4 3 N SD: 4.7622 c. M:-9.3974 c. 66: 9 6 9 6 2 13 8 5 4 4 N SD: 4.3355 c. M: 6.5574 c. 68: 9 6 9 7 2 13 9 4 5 4 N SD: 5.1149 c. M: 8.3457 c. 72: 10 6 10 7 2 14 9 5 5 4 N SD: 1.2237 c. M: 2.1592 c. 161: 22 14 22 16 4 32 20 11 11 9 N SD: 1.0423 c. M:-1.6869 c. 167: 23 14 23 17 4 33 21 11 12 9 N SD: 1.0263 c. M:-1.9755 c. 198: 27 17 27 20 5 39 25 13 14 11 N SD: 0.8174 c. M: 1.5721 c. 233: 32 20 32 23 6 46 29 16 16 13 N SD: 0.7003 c. M:-1.2808 c. 239: 33 20 33 24 6 47 30 16 17 13 N SD: 0.5414 c. M:-0.9833 c. 270: 37 23 37 27 7 53 34 18 19 15 N SD: 0.4135 c. M: 0.7640 c. 342: 47 29 47 34 9 67 43 23 24 19 N SD: 0.3492 c. M: 0.6450 c. 472: 65 40 65 47 12 93 59 32 33 26 N SD: 0.3263 c. M:-0.6371 c. 494: 68 42 68 49 13 97 62 33 35 27 N SD: 0.3668 c. M:-0.5828 c. 503: 69 43 69 50 13 99 63 34 35 28 N SD: 0.3250 c. M: 0.6293 c. 509: 70 43 70 51 13 100 64 34 36 28 N SD: 0.2628 c. M: 0.4662 c. 581: 80 49 80 58 15 114 73 39 41 32 N SD: 0.2096 c. M: 0.4337 c. 653: 90 55 90 65 17 128 82 44 46 36 N SD: 0.2529 c. M: 0.4247 c. 670: 92 57 92 67 17 132 84 45 47 37 N SD: 0.2353 c. M: 0.4226 c. 742: 102 63 102 74 19 146 93 50 52 41 N SD: 0.1506 c. M: 0.3020 c. 764: 105 65 105 76 20 150 96 51 54 42 N SD: 0.1541 c. M:-0.2840 c. 814: 112 69 112 81 21 160 102 55 57 45 N SD: 0.1537 c. M: 0.2755 c. 836: 115 71 115 83 22 164 105 56 59 46 N SD: 0.1292 c. M:-0.2629 c. 1034: 142 88 142 103 27 203 130 69 73 57 N SD: 0.1362 c. M: 0.2333 c. 1084: 149 92 149 108 28 213 136 73 76 60 N SD: 0.1411 c. M: 0.2508 c. 1106: 152 94 152 110 29 217 139 74 78 61 N SD: 0.0977 c. M: 0.1767 c. 1345: 185 114 185 134 35 264 169 90 95 74 N SD: 0.0905 c. M:-0.1476 c. 1417: 195 120 195 141 37 278 178 95 100 78 N SD: 0.0928 c. M:-0.1334 c. 1506: 207 128 207 150 39 296 189 101 106 83 N SD: 0.0685 c. M:-0.1378 c. 1578: 217 134 217 157 41 310 198 106 111 87 N SD: 0.0392 c. M:-0.0667 c. 1848: 254 157 254 184 48 363 232 124 130 102 N SD: 0.0385 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 3 x x x 4 S SD: 58.1169 cents 3 x x x 4 x 5 x x x 6 S SD: 28.3166 cents 4 x x 5 x x 6:7 x x 8 S SD: 31.2111 cents 5 x 6 x x 7:8 x 9 x 10 S SD: 11.6755 cents 6 x 7 x 8 x 10 x 11 x 12 S SD: 16.9899 cents 7 x 8:9 x 10:11:12:13 x 14 S SD: 10.6478 cents 8:9 x 10:11 x 13:14:15 x 16 SD: 10.6925 cents 9:10:11 x 12:13:14:16 x 17:18 S SD: 16.3986 cents 10:11:12:13 x 14:16 x 18:19:20 S SD: 8.3096 cents 11:12:13:14:15 x 18:19:20:21:22 S SD: 6.3117 cents 12:13:14:15 x 17:19:21:22:23:24 SD: 6.8157 cents 13:14:15:17:18 x 21:23:24:25:26 SD: 6.6394 cents 15 x 18:19 x 21:24:26:28:29:30 SD: 8.1148 cents 16:18:19:21:22 x 26:28:29:31:32 SD: 7.8428 cents 17:19:20:22:23:24:27:30:31:33:34 SD: 5.4565 cents 18:20:21:23 x 25:29:32:33:35:36 SD: 4.5153 cents 20:22:23:26 x 28:32:35:37:39:40 SD: 4.8232 cents 21:23:25:27:29 x 34:37:39:40:42 SD: 5.6361 cents 22:24:26:28:30:31:35:39:40:42:44 SD: 4.8601 cents 23:25:27:30 x 32:37:40:42:44:46 SD: 4.6507 cents 24:26:28:31:33:34:39:42:44:46:48 SD: 4.2419 cents 25:28:29:32:34:35:40:44:46:48:50 SD: 4.0370 cents 26:29:30:33:36 x 42:46:48:50:52 SD: 5.1011 cents 27:30:32:35:37:38:43:47:50:52:54 SD: 4.4848 cents 28:31:33:36 x 39:45:49:51:54:56 SD: 2.8782 cents 31:34:36:40:43 x 50:54:57:60:62 SD: 2.8860 cents 32:35:37:41:44:45:51:56:59:62:64 SD: 2.7473 cents 36:40:42:46 x 50:58:63:66:69:72 SD: 2.8584 cents 37:41:43:47:51:52:59:65:68:71:74 SD: 2.7977 cents 38:42:44:49:52:53:61:67:70:73:76 SD: 2.5870 cents 40:44:47:51:55:56:64:70:73:77:80 SD: 1.9014 cents 43:47:50:55:59:60:69:75:79:83:86 SD: 1.7414 cents 48:53:56:62:66:67:77:84:88:92:96 SD: 1.5857 cents 53:58:62:68:73:74:85:93:97:102:106 SD: 1.2776 cents 67:74:78:86:92:94:107:117:123:129:134 SD: 1.2707 cents 71:78:83:91:98:99:114:124:130:137:142 SD: 1.2297 cents 77:85:90:99:106:108:124:135:141:148:154 SD: 1.1784 cents 78:86:91:100:107:109:125:137:143:150:156 SD: 0.9576 cents 88:97:103:113:121:123:141:154:161:169:176 SD: 0.9326 cents 91:100:106:117:125:127:146:159:167:175:182 SD: 0.8171 cents 109:120:127:140:150:153:175:191:200:210:218 SD: 0.6583 cents 120:132:140:154:165:168:193:210:220:231:240 SD: 0.4491 cents 187:206:218:240:257:262:300:327:343:360:374 SD: 0.3616 cents 222:244:259:285:305:311:356:389:407:427:444 SD: 0.3602 cents 227:250:265:291:312:318:364:397:416:437:454 SD: 0.3589 cents 229:252:267:294:315:321:367:401:420:441:458 SD: 0.3485 cents 240:264:280:308:330:336:385:420:440:462:480 SD: 0.0000 cents