Scala analysis: xen12-chalmers-tritriadic-dm-7-13-1
Tritriadic D->M scale built from 7:13:1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 16/13 359.472338 tridecimal neutral third 3: 128/91 590.646432 4: 169/112 712.229417 5: 13/8 840.527662 tridecimal neutral sixth 6: 13/7 1071.701755 16/3-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/13 128.2982 2/3-tone 1: 8/7 231.1741 septimal whole tone 2: 14/13 128.2982 2/3-tone 3: 8/7 231.1741 septimal whole tone 4: 2197/2048 121.5830 5: 14/13 128.2982 2/3-tone 6: 8/7 231.1741 septimal whole tone 7: 14/13 128.2982 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2197/2048 121.583 cents 1: 3 14/13 128.298 cents 2/3-tone 1: 3 8/7 231.174 cents septimal whole tone 2: 1 1183/1024 249.881 cents 2: 1 2197/1792 352.757 cents 2: 5 16/13 359.472 cents tridecimal neutral third 3: 3 169/128 481.055 cents 3: 2 224/169 487.771 cents 3: 2 128/91 590.646 cents 4: 2 91/64 609.354 cents 4: 2 169/112 712.229 cents 4: 3 256/169 718.945 cents two (tridecimal neutral third) 5: 5 13/8 840.528 cents tridecimal neutral sixth 5: 1 3584/2197 847.243 cents 5: 1 2048/1183 950.119 cents 6: 3 7/4 968.826 cents harmonic seventh 6: 3 13/7 1071.702 cents 16/3-tone 6: 1 4096/2197 1078.417 cents 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 : 231.2 359.5 590.6 712.2 840.5 1071.7 1200.0 231.2 : 128.3 359.5 481.1 609.4 840.5 968.8 1200.0 359.5 : 231.2 352.8 481.1 712.2 840.5 1071.7 1200.0 590.6 : 121.6 249.9 481.1 609.4 840.5 968.8 1200.0 712.2 : 128.3 359.5 487.8 718.9 847.2 1078.4 1200.0 840.5 : 231.2 359.5 590.6 718.9 950.1 1071.7 1200.0 1071.7: 128.3 359.5 487.8 718.9 840.5 968.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 121.5830 .. 231.1741 cents 16384/15379, 109.5911 cents 2197/2048, 121.5830 cents 2: 249.8812 .. 359.4723 cents 16384/15379, 109.5911 cents 8281/8192, 18.7071 cents 3: 481.0553 .. 590.6464 cents 16384/15379, 109.5911 cents 2197/2048, 121.5830 cents 4: 609.3536 .. 718.9447 cents 16384/15379, 109.5911 cents 8281/8192, 18.7071 cents 5: 840.5277 .. 950.1188 cents 16384/15379, 109.5911 cents 2197/2048, 121.5830 cents 6: 968.8259 .. 1078.4170 cents 16384/15379, 109.5911 cents 8281/8192, 18.7071 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 2197/2048, 121.5830 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.409972 Largest / Average step : 1.348516 Largest / Smallest step : 1.901369 Median interval of one step : 14/13, 128.2982 cents, amount: 3 Least squares average step : 175.74160 cents, oct.: 1230.19123 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : LMLSMLM Scale is a Constant Structure, by a margin of 18.70714 cents Scale diversity : 1.260343 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.452044 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 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 : 28672/28561, 6.7153 cents Most common intervals : 16/13, 359.4723 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 128.298 359.472 cents Most common triad is 0.0 359.472 840.528 cents, amount: 3 Number of recognisable fifths : 5, average 716.2586 cents Number of appreciable fifths : 2, average 712.2294 cents Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 13 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 109.5911 cents: 1 -- Rational properties -- Prime limit : 13 Odd number limit : 2197 (O: 2197 U: 2197) Highest odd numerator or denominator: 169 Scale harmonicity : 0.011396 Average absolute harmonicity : 0.175215 Specific harmonicity : 0.061550 Fundamental : 1/1456, -10.5078 octaves, 0.1797 Hz. Guide tone : 21632, 14.4009 octaves, 5659484.229 Hz. Exponens Consonantiae : 3.149619E+07, 24.90867 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 294.0, average 42.00000 Mersenne's string divisions : 249848340 Sum of van Prooijen's expressibility: 8.37386, average 1.19627 Sum of Tenney's harmonic distance : 16.68671, average 2.38382 Vogel's harmonic complexity : 24.85714 Wille's k value : 1098 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 131.51652, average 4.69702 Lattice compactness (without 2's) : 42.00604, average 1.50022 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 7 1.14286 22 1 7: -1 .. 0 -0.57143 4 1 13: -1 .. 2 0.28571 6 5 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 18 29| Scale is weakly epimorphic with val: <7 19 24| Scale is JI-epimorphic with val: <7 20 26| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 42.2846 c. M: 76.3607 c. Lebeng 8: 2 0 2 1 1 1 1 P D3 S SD: 44.3943 c. M:-68.8259 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 6.4938 c. M:-9.3536 c. 37: 7 4 7 4 4 7 4 SP M DE S SD: 3.4380 c. M: 6.8626 c. 47: 9 5 9 5 5 9 5 SP M DE S SD: 2.0452 c. M: 3.4124 c. 57: 11 6 11 6 6 11 6 SP M DE S SD: 1.8174 c. M:-3.5601 c. 93: 18 10 18 9 10 18 10 SP T3 SD: 1.8228 c. M:-2.9020 c. 104: 20 11 20 11 11 20 11 SP M DE S SD: 1.8174 c. M:-3.1552 c. 110: 21 12 21 11 12 21 12 SP T3 SD: 1.8510 c. M: 3.1385 c. 120: 23 13 23 12 13 23 13 SP T3 SD: 1.2083 c. M: 2.2294 c. 130: 25 14 25 13 14 25 14 SP T3 SD: 0.7307 c. M: 1.4602 c. 140: 27 15 27 14 15 27 15 SP T3 SD: 0.5277 c. M: 0.8008 c. 177: 34 19 34 18 19 34 19 SP T3 SD: 0.4710 c. M: 0.8159 c. 187: 36 20 36 19 20 36 20 SP T3 SD: 0.1373 c. M: 0.2721 c. 384: 74 41 74 39 41 74 41 SP T3 SD: 0.1354 c. M:-0.2706 c. 514: 99 55 99 52 55 99 55 SP T3 SD: 0.0836 c. M: 0.1672 c. 701: 135 75 135 71 75 135 75 SP T3 SD: 0.0641 c. M: 0.1039 c. 711: 137 76 137 72 76 137 76 SP T3 SD: 0.0363 c. M:-0.0709 c. 898: 173 96 173 91 96 173 96 SP T3 SD: 0.0101 c. M:-0.0200 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: 5.1372 cents 3 x x 4 x 5 x 6 S SD: 34.1503 cents 4 x 5 x 6 x 7:8 S SD: 26.7038 cents 5 x 6:7 x 8:9:10 S SD: 15.0136 cents 6:7 x 8:9:10:11:12 S SD: 18.5405 cents 7:8:9:10 x 11:13:14 SD: 16.5040 cents 8:9:10:11:12:13:15:16 SD: 8.3183 cents 13:15:16:18:20:21:24:26 SD: 6.9326 cents 14:16:17:20:21:23:26:28 SD: 5.9400 cents 21:24:26:30:32:34:39:42 SD: 4.8551 cents 22:25:27:31:33:36:41:44 SD: 2.9229 cents 27:31:33:38:41:44:50:54 SD: 2.7828 cents 34:39:42:48:51:55:63:68 SD: 2.4895 cents 35:40:43:49:53:57:65:70 SD: 1.6152 cents 57:65:70:80:86:93:106:114 SD: 1.4124 cents 61:70:75:86:92:99:113:122 SD: 1.3833 cents 69:79:85:97:104:112:128:138 SD: 0.7060 cents 91:104:112:128:137:148:169:182 SD: 0.6010 cents 118:135:145:166:178:192:219:236 SD: 0.5998 cents 126:144:155:177:190:205:234:252 SD: 0.4862 cents 147:168:181:207:222:239:273:294 SD: 0.3841 cents 216:247:266:304:326:351:401:432 SD: 0.2685 cents 238:272:293:335:359:387:442:476 SD: 0.2573 cents 251:287:309:353:379:408:466:502 SD: 0.2460 cents 273:312:336:384:412:444:507:546 SD: 0.2123 cents 330:377:406:464:498:536:613:660 SD: 0.2090 cents 342:391:421:481:516:556:635:684 SD: 0.1647 cents 477:545:587:671:720:775:886:954 SD: 0.1253 cents 546:624:672:768:824:887:1014:1092 SD: 0.0792 cents 568:649:699:799:857:923:1055:1136 SD: 0.0744 cents