Scala analysis: xen15-chalmers-triadic-diamond-14-11
Triadic diamond for M=14/11, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/28 284.447037 undecimal minor third 2: 14/11 417.507964 undecimal diminished fourth or major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 11/7 782.492036 undecimal augmented fifth 6: 56/33 915.552963 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 33/28 284.4470 undecimal minor third 1: 33/28 284.4470 undecimal minor third 2: 392/363 133.0609 3: 22/21 80.5370 undecimal minor semitone 4: 9/8 203.9100 major whole tone 5: 22/21 80.5370 undecimal minor semitone 6: 392/363 133.0609 7: 33/28 284.4470 undecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 392/363 133.061 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 33/28 284.447 cents undecimal minor third 2: 2 112/99 213.598 cents 2: 2 33/28 284.447 cents undecimal minor third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 1089/784 568.894 cents two (undecimal minor third) 3: 1 121/98 364.984 cents 3: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 2 11/7 782.492 cents undecimal augmented fifth 4: 1 196/121 835.016 cents two (undecimal diminished fourth or major third) 5: 1 1568/1089 631.106 cents 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 2 56/33 915.553 cents 5: 2 99/56 986.402 cents 6: 2 56/33 915.553 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 363/196 1066.939 cents 6: 2 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 284.4 417.5 498.0 702.0 782.5 915.6 1200.0 284.4 : 133.1 213.6 417.5 498.0 631.1 915.6 1200.0 417.5 : 80.5 284.4 365.0 498.0 782.5 1066.9 1200.0 498.0 : 203.9 284.4 417.5 702.0 986.4 1119.5 1200.0 702.0 : 80.5 213.6 498.0 782.5 915.6 996.1 1200.0 782.5 : 133.1 417.5 702.0 835.0 915.6 1119.5 1200.0 915.6 : 284.4 568.9 702.0 782.5 986.4 1066.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 284.4470 cents 9/8, 203.9100 cents 22/21, 80.5370 cents 2: 213.5980 .. 568.8941 cents 107811/87808, 355.2961 cents 3136/3267,-70.8491 cents 3: 364.9841 .. 701.9550 cents 147/121, 336.9709 cents 8/9,-203.9100 cents 4: 498.0450 .. 835.0159 cents 147/121, 336.9709 cents 8/9,-203.9100 cents 5: 631.1059 .. 986.4020 cents 107811/87808, 355.2961 cents 8/9,-203.9100 cents 6: 915.5530 .. 1119.4630 cents 9/8, 203.9100 cents 3136/3267,-70.8491 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 33/28, 284.4470 cents Average / Smallest step : 2.128568 Largest / Average step : 1.659274 Largest / Smallest step : 3.531879 Median interval of one step : 392/363, 133.0609 cents, amount: 2 Least squares average step : 165.90854 cents, oct.: 1161.35980 cents Scale is not proper Scale is a mode of a 2354-tone equal temperament with octave 2/1 degrees: 558 819 977 1377 1535 1796 2354 Least number of segments generator : 1179 of 601.020 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2263 of 1153.611 cents and inv. generated superset size: 83 = 76 more = 1185.714% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCBA Step pattern size order : DBACABD Scale is not a Constant Structure Scale diversity : 1.459502 Lumma stability : 0.134228 Lumma impropriety factor : 0.509775 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 896/891, 9.6880 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 7 11 33 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 11 Odd number limit : 1089 (O: 1089 U: 1089) Highest odd numerator or denominator: 33 Scale harmonicity : 0.014866 Average absolute harmonicity : 0.230793 Specific harmonicity : 0.079878 Fundamental : 1/924, -9.8517 octaves, 0.2831 Hz. Guide tone : 1848, 10.8517 octaves, 483484.045 Hz. Exponens Consonantiae : 1.707552E+06, 20.70350 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 104.0, average 14.85714 Mersenne's string divisions : 17101350 Sum of van Prooijen's expressibility: 6.07406, average 0.86772 Sum of Tenney's harmonic distance : 12.46475, average 1.78068 Vogel's harmonic complexity : 23.57143 Wille's k value : 544 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 74.59496, average 2.66411 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 10 1 3: -1 .. 1 0.00000 4 2 7: -1 .. 1 0.00000 4 11: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 18 23| Scale is weakly epimorphic with val: <7 10 18 24| Scale is weakly epimorphic with val: <7 10 19 24| Scale is weakly epimorphic with val: <7 10 19 25| Scale is weakly epimorphic with val: <7 10 20 25| Scale is weakly epimorphic with val: <7 10 20 26| Scale is weakly epimorphic with val: <7 10 21 26| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 20 22| Scale is weakly epimorphic with val: <7 11 21 22| Scale is weakly epimorphic with val: <7 11 21 23| Scale is weakly epimorphic with val: <7 11 22 23| Scale is weakly epimorphic with val: <7 11 22 24| Scale is weakly epimorphic with val: <7 12 18 24| Scale is weakly epimorphic with val: <7 12 19 22| Scale is weakly epimorphic with val: <7 12 19 25| Scale is weakly epimorphic with val: <7 12 20 23| Scale is weakly epimorphic with val: <7 12 20 26| Scale is weakly epimorphic with val: <7 12 21 24| Scale is weakly epimorphic with val: <7 12 22 25|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 51.4039 c. M: 74.6508 c. 8: 2 1 0 2 0 1 2 N I SD: 32.0978 c. M:-48.0450 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 23.1019 c. M:-35.2883 c. 12: 3 1 1 2 1 1 3 N I SD: 12.5612 c. M: 17.5080 c. Mela Yagapriya, Raga Kalahamsa 17: 4 2 1 3 1 2 4 N I SD: 4.0024 c. M:-6.0214 c. 29: 7 3 2 5 2 3 7 N I SD: 3.5114 c. M: 5.2081 c. 46: 11 5 3 8 3 5 11 N I SD: 1.8545 c. M: 2.5095 c. 63: 15 7 4 11 4 7 15 N I SD: 1.8404 c. M: 2.8069 c. 72: 17 8 5 12 5 8 17 N I SD: 1.2840 c. M: 1.9550 c. 89: 21 10 6 15 6 10 21 N I SD: 0.8626 c. M: 1.3010 c. 118: 28 13 8 20 8 13 28 N I SD: 0.3661 c. M:-0.5588 c. 135: 32 15 9 23 9 15 32 N I SD: 0.2030 c. M:-0.2698 c. 253: 60 28 17 43 17 28 60 N I SD: 0.0972 c. M: 0.1379 c. 388: 92 43 26 66 26 43 92 N I SD: 0.0750 c. M:-0.1069 c. 595: 141 66 40 101 40 66 141 N I SD: 0.0719 c. M:-0.1063 c. 730: 173 81 49 124 49 81 173 N I SD: 0.0418 c. M: 0.0635 c. 983: 233 109 66 167 66 109 233 N I SD: 0.0145 c. M:-0.0221 c. 1371: 325 152 92 233 92 152 325 N I SD: 0.0119 c. M:-0.0169 c. 2101: 498 233 141 357 141 233 498 N I SD: 0.0074 c. M: 0.0111 c. 2354: 558 261 158 400 158 261 558 N I SD: 0.0041 c. M:-0.0058 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x 5:6 S SD: 10.3981 cents 4 x 5 x 6 x 7:8 S SD: 15.4335 cents 5:6 x 7 x 8 x 10 S SD: 23.8234 cents 6:7 x 8:9 x 10:12 S SD: 7.1610 cents 7:8:9 x x 11:12:14 SD: 11.7573 cents 9:11 x 12 x 14:15:18 SD: 14.4860 cents 10:12:13 x 15:16:17:20 SD: 9.5787 cents 11:13:14:15 x 17:19:22 SD: 9.5857 cents 12:14:15:16:18:19:20:24 S SD: 7.0361 cents 13:15 x 17 x 20:22:26 SD: 12.4056 cents 14:17:18:19:21:22:24:28 SD: 9.2889 cents 16:19:20:21:24:25:27:32 SD: 6.5126 cents 18:21:23:24:27:28:31:36 SD: 5.1879 cents 22:26:28:29:33:35:37:44 SD: 4.7599 cents 26:31:33:35:39:41:44:52 SD: 3.9351 cents 30:35:38:40:45:47:51:60 SD: 2.9080 cents 33:39:42:44:50:52:56:66 SD: 2.6654 cents 40:47:51:53:60:63:68:80 SD: 1.9163 cents 56:66:71:75:84:88:95:112 SD: 1.4556 cents 66:78:84:88:99:104:112:132 SD: 0.9622 cents 84:99:107:112:126:132:143:168 SD: 0.8150 cents 96:113:122:128:144:151:163:192 SD: 0.5542 cents 162:191:206:216:243:255:275:324 SD: 0.4857 cents 168:198:214:224:252:264:285:336 SD: 0.2245 cents 264:311:336:352:396:415:448:528 SD: 0.1420 cents 432:509:550:576:648:679:733:864 SD: 0.1231 cents 492:580:626:656:738:773:835:984 SD: 0.1081 cents