Scala analysis: xen12-wilson-40-5C3-dekany-05
3-5-7-9-11 5C3 Dekany, Figure 40
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 33/28 284.447037 undecimal minor third 3: 9/7 435.084095 septimal major third, BP third 4: 99/70 600.088324 2nd quasi-equal tritone 5: 3/2 701.955001 perfect fifth 6: 11/7 782.492036 undecimal augmented 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 15/14 119.4428 major diatonic semitone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 35/33 101.8667 6: 22/21 80.5370 undecimal minor semitone 7: 21/20 84.4672 minor semitone 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 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: 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 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 3 10/9 182.404 cents minor whole tone 2: 1 63/55 235.104 cents 2: 1 7/6 266.871 cents septimal minor third 2: 1 90/77 270.080 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 2 6/5 315.641 cents minor third 3: 2 7/6 266.871 cents septimal minor third 3: 1 6/5 315.641 cents minor third 3: 1 40/33 333.041 cents 3: 2 11/9 347.408 cents undecimal neutral third 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 3 9/7 435.084 cents septimal major third, BP third 4: 1 11/9 347.408 cents undecimal neutral third 4: 2 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 77/60 431.875 cents 4: 1 55/42 466.851 cents 4: 2 4/3 498.045 cents perfect fourth 4: 1 15/11 536.951 cents undecimal augmented fourth 4: 1 108/77 585.721 cents 4: 1 99/70 600.088 cents 2nd quasi-equal tritone 5: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 5: 1 4/3 498.045 cents perfect 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 3/2 701.955 cents perfect fifth 5: 1 54/35 750.725 cents septimal semi-augmented fifth 6: 1 140/99 599.912 cents quasi-equal tritone 6: 1 77/54 614.279 cents 6: 1 22/15 663.049 cents undecimal diminished fifth 6: 2 3/2 701.955 cents perfect fifth 6: 1 84/55 733.149 cents 6: 1 120/77 768.125 cents 6: 2 11/7 782.492 cents undecimal augmented fifth 6: 1 18/11 852.592 cents undecimal neutral sixth 7: 3 14/9 764.916 cents septimal minor sixth 7: 1 11/7 782.492 cents undecimal augmented fifth 7: 2 18/11 852.592 cents undecimal neutral sixth 7: 1 33/20 866.959 cents 7: 1 5/3 884.359 cents major sixth, BP sixth 7: 2 12/7 933.129 cents septimal major sixth 8: 2 5/3 884.359 cents major sixth, BP sixth 8: 1 56/33 915.553 cents 8: 1 77/45 929.920 cents 8: 1 12/7 933.129 cents septimal major sixth 8: 1 110/63 964.896 cents 8: 3 9/5 1017.596 cents just minor seventh, BP seventh 8: 1 20/11 1034.996 cents large minor 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 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: 1 108/55 1168.233 cents Highest number of different intervals for one interval class: 8 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 : 165.0 284.4 435.1 600.1 702.0 782.5 867.0 1017.6 1049.4 1200.0 165.0 : 119.4 270.1 435.1 537.0 617.5 702.0 852.6 884.4 1035.0 1200.0 284.4 : 150.6 315.6 417.5 498.0 582.5 733.1 764.9 915.6 1080.6 1200.0 435.1 : 165.0 266.9 347.4 431.9 582.5 614.3 764.9 929.9 1049.4 1200.0 600.1 : 101.9 182.4 266.9 417.5 449.3 599.9 764.9 884.4 1035.0 1200.0 702.0 : 80.5 165.0 315.6 347.4 498.0 663.0 782.5 933.1 1098.1 1200.0 782.5 : 84.5 235.1 266.9 417.5 582.5 702.0 852.6 1017.6 1119.5 1200.0 867.0 : 150.6 182.4 333.0 498.0 617.5 768.1 933.1 1035.0 1115.5 1200.0 1017.6: 31.8 182.4 347.4 466.9 617.5 782.5 884.4 964.9 1049.4 1200.0 1049.4: 150.6 315.6 435.1 585.7 750.7 852.6 933.1 1017.6 1168.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 165.0042 cents 27/25, 133.2376 cents 55/54, 31.7667 cents 2: 165.0042 .. 315.6413 cents 12/11, 150.6371 cents 1/1, 0.0000 cents 3: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 35/36,-48.7704 cents 4: 347.4079 .. 600.0883 cents 81/70, 252.6804 cents 77/81,-87.6762 cents 5: 449.2746 .. 750.7254 cents 1458/1225, 301.4508 cents 2450/2673,-150.8137 cents 6: 599.9117 .. 852.5921 cents 81/70, 252.6804 cents 2450/2673,-150.8137 cents 7: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 77/81,-87.6762 cents 8: 884.3587 .. 1034.9958 cents 12/11, 150.6371 cents 35/36,-48.7704 cents 9: 1034.9958 .. 1168.2333 cents 27/25, 133.2376 cents 1/1, 0.0000 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 : 11/10, 165.0042 cents Average / Smallest step : 3.777546 Largest / Average step : 1.375035 Largest / Smallest step : 5.194259 Median interval of one step : 135.03993 cents, amount: 0 Most common interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 125.44931 cents, oct.: 1254.49305 cents Scale is not proper Step pattern alph. order: ABCADEFCGC Step pattern size order : GEFGDBCFAF Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 1.526965 Lumma stability : 0.052944 Lumma impropriety factor : 0.478620 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 : 7 Highest interval variety : 8 Mean interval variety : 6.88889 = 62/9 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 9801/9800, 0.1766 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 2 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.021802 Average absolute harmonicity : 0.163060 Specific harmonicity : 0.097476 Fundamental : 1/420, -8.7142 octaves, 0.6229 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 8.316000E+04, 16.34360 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 188.5, average 18.85000 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 : 19.90511, average 1.99051 Vogel's harmonic complexity : 20.50000 Wille's k value : 346 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 122.26774, average 2.22305 Lattice compactness (without 2's) : 98.68452, average 1.79426 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.70000 9 1 3: -1 .. 2 0.80000 10 1 5: -1 .. 0 -0.40000 4 1 7: -1 .. 0 -0.40000 4 1 11: 0 .. 1 0.60000 6 6 Average exponent except 2's : 6 / 10 = 0.60000 Average absolute exponent except 2's: 24 / 10 = 2.40000
FIT/MODE
10: 1 1 2 1 1 1 0 1 1 1 N T3 SD: 38.2543 c. M: 57.5963 c. 12: 2 1 1 2 1 1 1 1 0 2 N SD: 26.1646 c. M: 49.3629 c. 14: 2 1 2 2 1 1 1 2 0 2 N SD: 13.6546 c. M: 27.3042 c. 22: 3 2 3 3 2 1 2 3 0 3 N SD: 10.4966 c. M: 18.8557 c. 24: 3 3 3 3 2 2 1 3 1 3 N SD: 12.6393 c. M: 17.5963 c. 26: 4 2 3 4 2 2 2 3 1 3 N SD: 10.8595 c. M: 19.6995 c. 29: 4 3 4 4 2 2 2 4 0 4 N SD: 11.7557 c. M:-20.6013 c. 30: 4 3 4 4 3 2 2 3 1 4 N SD: 11.2628 c. M:-18.0450 c. 31: 4 3 4 4 3 2 2 4 1 4 N SD: 11.0554 c. M: 19.4432 c. 32: 4 4 4 4 3 2 2 4 1 4 N SD: 9.3384 c. M:-15.5530 c. 34: 5 3 4 5 3 2 3 4 1 4 N SD: 8.2628 c. M:-15.3937 c. 38: 5 4 5 5 3 3 2 5 1 5 N SD: 7.1323 c. M: 14.3277 c. 41: 6 4 5 6 3 3 3 5 1 5 N SD: 8.0952 c. M:-14.5458 c. 42: 6 4 5 6 4 2 3 6 1 5 N SD: 7.9818 c. M:-12.3307 c. 44: 6 4 6 6 4 3 3 5 1 6 N SD: 7.3296 c. M: 12.9993 c. 46: 6 5 6 6 4 3 3 6 1 6 N SD: 4.7562 c. M: 8.4825 c. 58: 8 6 7 8 5 4 4 7 2 7 N SD: 3.0988 c. M:-5.8095 c. 72: 10 7 9 10 6 5 5 9 2 9 N SD: 1.1385 c. M: 1.9550 c. 152: 21 15 19 21 13 10 11 19 4 19 N SD: 0.7719 c. M:-1.4618 c. 190: 26 19 24 26 16 13 13 24 5 24 N SD: 0.8235 c. M: 1.6961 c. 198: 27 20 25 27 17 13 14 25 5 25 N SD: 0.8054 c. M: 1.3679 c. 224: 31 22 28 31 19 15 16 28 6 28 N SD: 0.6466 c. M: 1.1555 c. 262: 36 26 33 36 22 18 18 33 7 33 N SD: 0.6928 c. M: 1.3104 c. 270: 37 27 34 37 23 18 19 34 7 34 N SD: 0.3211 c. M: 0.5598 c. 342: 47 34 43 47 29 23 24 43 9 43 N SD: 0.1612 c. M: 0.2926 c. 764: 105 76 96 105 65 51 54 96 20 96 N SD: 0.1452 c. M: 0.2931 c. 822: 113 82 103 113 70 55 58 103 22 103 N SD: 0.1533 c. M:-0.2721 c. 836: 115 83 105 115 71 56 59 105 22 105 N SD: 0.1229 c. M: 0.2365 c. 1012: 139 101 127 139 86 68 71 127 27 127 N SD: 0.1236 c. M: 0.2050 c. 1092: 150 109 137 150 93 73 77 137 29 137 N SD: 0.1221 c. M:-0.2428 c. 1106: 152 110 139 152 94 74 78 139 29 139 N SD: 0.1199 c. M: 0.2136 c. 1164: 160 116 146 160 99 78 82 146 31 146 N SD: 0.0735 c. M:-0.1216 c. 1506: 207 150 189 207 128 101 106 189 40 189 N SD: 0.0461 c. M: 0.0883 c. 1848: 254 184 232 254 157 124 130 232 49 232 N SD: 0.0496 c. M: 0.0883 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x 4 x x x 5 x x 6 S SD: 21.7736 cents 4 x x 5 x 6 x x 7 x 8 S SD: 17.2429 cents 5 x 6 x 7 x 8 x 9 x 10 S SD: 9.4975 cents 6 x 7:8 x 9 x 10 x 11:12 S SD: 11.2740 cents 7 x 8:9:10 x 11:12 x 13:14 S SD: 12.7921 cents 8:9 x 10:11:12 x 13:14:15:16 S SD: 13.0274 cents 9:10:11:12:13 x 14:15:16:17:18 S SD: 12.8190 cents 10:11:12:13:14:15:16:17:18 x 20 S SD: 8.0830 cents 11:12:13:14:16 x 17:18 x 20:22 S SD: 8.0475 cents 12:13:14:15:17:18:19:20 x 22:24 SD: 6.9104 cents 13:14:15:17:18 x 20:21:23:24:26 SD: 10.3245 cents 14:15:17:18:20:21:22:23:25:26:28 SD: 7.6127 cents 16:18:19:21:23:24:25:26:29 x 32 SD: 7.6114 cents 17:19:20:22:24:26:27:28 x 31:34 SD: 5.5227 cents 18:20:21:23:25:27:28:30:32:33:36 SD: 5.2772 cents 20:22:24:26:28:30:31:33:36:37:40 SD: 4.9583 cents 21:23:25:27:30:32:33:35:38:39:42 SD: 4.7859 cents 22:24:26:28:31:33:35:36 x 40:44 SD: 4.2257 cents 24:26:28:31:34:36:38:40:43:44:48 SD: 4.0224 cents 28:31:33:36:40:42:44:46:50:51:56 SD: 2.8323 cents 32:35:38:41:45:48:50:53:58:59:64 SD: 2.7955 cents 38:42:45:49:54:57:60:63:68:70:76 SD: 2.3203 cents 40:44:47:51:57:60:63:66:72:73:80 SD: 2.2042 cents 46:51:54:59:65:69:72:76:83:84:92 SD: 1.9218 cents 49:54:58:63:69:74:77:81:88:90:98 SD: 1.7217 cents 56:62:66:72:79:84:88:92:101:103:112 SD: 1.5633 cents 60:66:71:77:85:90:94:99:108:110:120 SD: 0.9753 cents 80:88:94:103:113:120:126:132:144:147:160 SD: 0.8310 cents 102:112:120:131:144:153:160:168:184:187:204 SD: 0.8091 cents 108:119:127:139:153:162:170:178:194:198:216 SD: 0.7761 cents 112:123:132:144:158:168:176:185:202:205:224 SD: 0.7090 cents 128:141:151:165:181:192:201:211:230:235:256 SD: 0.6954 cents 130:143:153:167:184:195:204:215:234:238:260 SD: 0.6153 cents 140:154:165:180:198:210:220:231:252:257:280 SD: 0.2247 cents 280:308:330:360:396:420:440:462:504:513:560 SD: 0.1125 cents 420:462:495:540:594:630:660:693:756:770:840 SD: 0.0000 cents