Scala analysis: xen15-chalmers-triadic-reversed-diamond-14-11
Triadic reversed 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: 22/21 80.537035 undecimal minor semitone 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: 21/11 1119.462965 undecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 22/21 80.5370 undecimal minor semitone 2: 147/121 336.9709 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: 147/121 336.9709 7: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 22/21 80.537 cents undecimal minor semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 147/121 336.971 cents 2: 1 484/441 161.074 cents two (undecimal minor semitone) 2: 2 33/28 284.447 cents undecimal minor third 2: 4 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 121/98 364.984 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 63/44 621.418 cents 4: 2 88/63 578.582 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 196/121 835.016 cents two (undecimal diminished fourth or major third) 5: 4 11/7 782.492 cents undecimal augmented fifth 5: 2 56/33 915.553 cents 5: 1 441/242 1038.926 cents 6: 2 242/147 863.029 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 80.5 417.5 498.0 702.0 782.5 1119.5 1200.0 80.5 : 337.0 417.5 621.4 702.0 1038.9 1119.5 1200.0 417.5 : 80.5 284.4 365.0 702.0 782.5 863.0 1200.0 498.0 : 203.9 284.4 621.4 702.0 782.5 1119.5 1200.0 702.0 : 80.5 417.5 498.0 578.6 915.6 996.1 1200.0 782.5 : 337.0 417.5 498.0 835.0 915.6 1119.5 1200.0 1119.5: 80.5 161.1 498.0 578.6 782.5 863.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 336.9709 cents 3087/2662, 256.4339 cents 22/21, 80.5370 cents 2: 161.0741 .. 417.5080 cents 3087/2662, 256.4339 cents 58564/64827,-175.8969 cents 3: 364.9841 .. 621.4180 cents 3087/2662, 256.4339 cents 1331/1372,-52.5239 cents 4: 578.5820 .. 835.0159 cents 3087/2662, 256.4339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 1038.9259 cents 3087/2662, 256.4339 cents 1331/1372,-52.5239 cents 6: 863.0291 .. 1119.4630 cents 3087/2662, 256.4339 cents 58564/64827,-175.8969 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 : 147/121, 336.9709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.965664 Largest / Smallest step : 4.184049 Median interval of one step : 22/21, 80.5370 cents, amount: 4 Most common interval of one step : 22/21, 80.5370 cents, amount: 4 Least squares average step : 173.19104 cents, oct.: 1212.33730 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 28.01314 cents Scale diversity : 1.466616 Lumma stability : 0.134228 Lumma impropriety factor : 0.416398 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 : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 14641/14406, 28.0131 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale is a complete diamond : 7 11 21 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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 : 441 (O: 441 U: 441) Highest odd numerator or denominator: 21 Scale harmonicity : 0.015321 Average absolute harmonicity : 0.231330 Specific harmonicity : 0.082344 Fundamental : 1/462, -8.8517 octaves, 0.5663 Hz. Guide tone : 924, 9.8517 octaves, 241742.022 Hz. Exponens Consonantiae : 4.268880E+05, 18.70350 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 66.5, average 9.50000 Mersenne's string divisions : 2167200 Sum of van Prooijen's expressibility: 5.68147, average 0.81164 Sum of Tenney's harmonic distance : 11.26063, average 1.60866 Vogel's harmonic complexity : 22.57143 Wille's k value : 346 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 60.17688, average 2.14917 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 6 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 26| Scale is weakly epimorphic with val: <7 10 20 22| Scale is weakly epimorphic with val: <7 10 21 22| Scale is weakly epimorphic with val: <7 10 21 23| Scale is weakly epimorphic with val: <7 10 22 23| Scale is weakly epimorphic with val: <7 10 22 24| Scale is JI-epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 18 24| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 25| Scale is JI-epimorphic with val: <7 11 20 25| Scale is weakly epimorphic with val: <7 11 20 26| Scale is JI-epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 19 23| Scale is weakly epimorphic with val: <7 12 20 24| Scale is weakly epimorphic with val: <7 12 21 22| Scale is weakly epimorphic with val: <7 12 21 25| Scale is weakly epimorphic with val: <7 12 22 23| Scale is weakly epimorphic with val: <7 12 22 26|
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 65.6981 c. M: 96.7778 c. 8: 0 2 1 1 1 2 1 N D3 SD: 74.5255 c. M: 117.5080 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 35.2106 c. M: 52.7963 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 14.0322 c. M: 19.4630 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 14: 1 4 1 2 1 4 1 N T3 I SD: 10.8623 c. M:-16.2407 c. 17: 1 5 1 3 1 5 1 N T3 I SD: 6.5609 c. M: 9.9488 c. 29: 2 8 2 5 2 8 2 N T3 I SD: 2.4475 c. M:-3.7149 c. 46: 3 13 3 8 3 13 3 N T3 I SD: 1.7664 c. M: 2.3928 c. 60: 4 17 4 10 4 17 4 N T3 I SD: 1.7172 c. M:-2.4920 c. 75: 5 21 5 13 5 21 5 N T3 I SD: 1.3882 c. M:-2.0450 c. 89: 6 25 6 15 6 25 6 N T3 I SD: 0.5458 c. M:-0.8314 c. 118: 8 33 8 20 8 33 8 N T3 I SD: 0.5479 c. M: 0.8189 c. 135: 9 38 9 23 9 38 9 N T3 I SD: 0.3516 c. M: 0.5370 c. 164: 11 46 11 28 11 46 11 N T3 I SD: 0.3488 c. M:-0.4840 c. 224: 15 63 15 38 15 63 15 N T3 I SD: 0.2286 c. M:-0.3492 c. 253: 17 71 17 43 17 71 17 N T3 I SD: 0.0813 c. M:-0.1167 c. 477: 32 134 32 81 32 134 32 N T3 I SD: 0.0681 c. M:-0.1021 c. 641: 43 180 43 109 43 180 43 N T3 I SD: 0.0479 c. M:-0.0731 c. 730: 49 205 49 124 49 205 49 N T3 I SD: 0.0250 c. M:-0.0372 c. 983: 66 276 66 167 66 276 66 N T3 I SD: 0.0218 c. M: 0.0326 c. 1371: 92 385 92 233 92 385 92 N T3 I SD: 0.0100 c. M:-0.0144 c. 2101: 141 590 141 357 141 590 141 N T3 I SD: 0.0049 c. M:-0.0075 c. 2354: 158 661 158 400 158 661 158 N T3 I SD: 0.0048 c. M: 0.0067 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 5 x 6 S SD: 33.9556 cents 4 x 5 x 6 x x 8 S SD: 10.3981 cents 5 x 6:7 x 8 x 10 S SD: 33.9895 cents 6 x x 8:9 x 11:12 SD: 17.5250 cents 7:8:9 x x 11:13:14 SD: 31.8004 cents 8:9:10:11:12:13:15:16 SD: 21.8404 cents 9:10:11:12 x 14:17:18 SD: 21.0416 cents 10:11:13 x 15:16:19:20 SD: 16.2647 cents 11:12:14:15 x 17:21:22 SD: 14.2012 cents 12:13:15:16:18:19:23:24 SD: 9.6457 cents 13:14 x 17 x 20:25:26 SD: 14.0261 cents 14:15:18:19:21:22:27:28 SD: 7.9159 cents 16:17:20:21:24:25:31:32 SD: 7.9075 cents 18:19:23:24:27:28:34:36 SD: 4.2036 cents 22:23:28:29:33:35:42:44 SD: 4.1876 cents 26:27:33:35:39:41:50:52 SD: 3.8449 cents 36:38:46:48:54:57:69:72 SD: 2.9811 cents 40:42:51:53:60:63:76:80 SD: 2.1501 cents 44:46:56:59:66:69:84:88 SD: 1.5770 cents 63:66:80:84:95:99:120:126 SD: 1.5277 cents 66:69:84:88:99:104:126:132 SD: 0.8512 cents 84:88:107:112:126:132:160:168 SD: 0.5995 cents 144:151:183:192:216:226:275:288 SD: 0.5429 cents 150:157:191:200:225:236:286:300 SD: 0.5030 cents 168:176:214:224:252:264:321:336 SD: 0.2973 cents 210:220:267:280:315:330:401:420 SD: 0.2586 cents 252:264:321:336:378:396:481:504 SD: 0.2153 cents 294:308:374:392:441:462:561:588 SD: 0.1700 cents 378:396:481:504:567:594:722:756 SD: 0.1331 cents 462:484:588:616:693:726:882:924 SD: 0.0000 cents