Scala analysis: xen09-chalmers-tritriadic-27-24-22
Tritriadic scale built from 27:24:22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 968/729 490.905880 4: 352/243 641.542938 5: 44/27 845.452940 neutral sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 9/8 203.9100 major whole tone 3: 21296/19683 136.3588 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 9/8 203.9100 major whole tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 21296/19683 136.359 cents 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 3 9/8 203.910 cents major whole tone 2: 1 7744/6561 286.996 cents two (2nd undecimal neutral second) 2: 1 2662/2187 340.269 cents 2: 5 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 3 968/729 490.906 cents 3: 2 162/121 505.184 cents 3: 2 243/176 558.457 cents 4: 2 352/243 641.543 cents 4: 2 121/81 694.816 cents two (undecimal neutral third) 4: 3 729/484 709.094 cents two (neutral third, Zalzal wosta of al-Farabi) 5: 5 44/27 845.453 cents neutral sixth 5: 1 2187/1331 859.731 cents 5: 1 6561/3872 913.004 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 19683/10648 1063.641 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 : 150.6 354.5 490.9 641.5 845.5 996.1 1200.0 150.6 : 203.9 340.3 490.9 694.8 845.5 1049.4 1200.0 354.5 : 136.4 287.0 490.9 641.5 845.5 996.1 1200.0 490.9 : 150.6 354.5 505.2 709.1 859.7 1063.6 1200.0 641.5 : 203.9 354.5 558.5 709.1 913.0 1049.4 1200.0 845.5 : 150.6 354.5 505.2 709.1 845.5 996.1 1200.0 996.1 : 203.9 354.5 558.5 694.8 845.5 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 136.3588 .. 203.9100 cents 177147/170368, 67.5512 cents 21296/19683, 136.3588 cents 2: 286.9959 .. 354.5471 cents 177147/170368, 67.5512 cents 61952/59049, 83.0859 cents 3: 490.9059 .. 558.4571 cents 177147/170368, 67.5512 cents 21296/19683, 136.3588 cents 4: 641.5429 .. 709.0941 cents 177147/170368, 67.5512 cents 61952/59049, 83.0859 cents 5: 845.4529 .. 913.0041 cents 177147/170368, 67.5512 cents 21296/19683, 136.3588 cents 6: 996.0900 .. 1063.6412 cents 177147/170368, 67.5512 cents 61952/59049, 83.0859 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 21296/19683, 136.3588 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.257187 Largest / Average step : 1.189475 Largest / Smallest step : 1.495393 Median interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 167.87447 cents, oct.: 1175.12126 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAB Step pattern size order : MLSMLML Scale is a Constant Structure, by a margin of 83.08588 cents Scale diversity : 1.306351 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.662244 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 : 59049/58564, 14.2782 cents Most common intervals : 27/22, 354.5471 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 150.637 354.547 cents Most common triad is 0.0 354.547 845.453 cents, amount: 3 Number of recognisable fifths : 5, average 703.3828 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 11 27 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 67.5512 cents: 6 -- Rational properties -- Prime limit : 11 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.011828 Average absolute harmonicity : 0.181233 Specific harmonicity : 0.066423 Fundamental : 1/16038, -13.9692 octaves, 0.0163 Hz. Guide tone : 104544, 16.6738 octaves, 27351383.099 Hz. Exponens Consonantiae : 1.676677E+09, 30.64296 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 1231.5, average 175.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.10670, average 1.44381 Sum of Tenney's harmonic distance : 21.20932, average 3.02990 Vogel's harmonic complexity : 30.28571 Wille's k value : 9841 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 12 Triangular lattice diameter : 9 Lattice compactness : 135.48715, average 4.83883 Lattice compactness (without 2's) : 110.68117, average 3.95290 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 2.28571 18 1 3: -6 .. 3 -1.71429 20 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's :-10 / 7 =-1.42857 Average absolute exponent except 2's: 26 / 7 = 3.71429 Scale is weakly epimorphic with val: <7 10 25| Scale is JI-epimorphic with val: <7 11 24| = patent Scale is weakly epimorphic with val: <7 12 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 24.6645 c. M:-44.1713 c. Lebeng 10: 1 2 1 1 2 1 2 P M ME S SD: 24.3350 c. M: 41.5429 c. 13: 2 2 1 2 2 2 2 SP M ME S SD: 20.1485 c. M:-33.9783 c. Oukranian 17: 2 3 2 2 3 2 3 SP M ME S SD: 5.4211 c. M: 9.4606 c. 24: 3 4 3 3 4 3 4 SP M ME S SD: 5.4938 c. M:-9.0941 c. Neutral Mixolydian, Iced Blizzard 41: 5 7 5 5 7 5 7 SP M DE S SD: 3.6133 c. M:-6.6551 c. 47: 6 8 5 6 8 6 8 SP T3 SD: 3.1082 c. M: 5.7995 c. 54: 7 9 6 7 9 7 9 SP T3 SD: 2.7775 c. M:-4.9185 c. 64: 8 11 7 8 11 8 11 SP T3 SD: 2.3793 c. M: 4.0429 c. 71: 9 12 8 9 12 9 12 SP T3 SD: 0.8242 c. M:-1.4756 c. 88: 11 15 10 11 15 11 15 SP T3 SD: 0.4160 c. M: 0.6371 c. 159: 20 27 18 20 27 20 27 SP T3 SD: 0.2024 c. M: 0.3398 c. 247: 31 42 28 31 42 31 42 SP T3 SD: 0.1475 c. M: 0.2474 c. 406: 51 69 46 51 69 51 69 SP T3 SD: 0.1433 c. M: 0.2655 c. 518: 65 88 59 65 88 65 88 SP T3 SD: 0.1187 c. M:-0.2138 c. 589: 74 100 67 74 100 74 100 SP T3 SD: 0.1254 c. M:-0.2228 c. 606: 76 103 69 76 103 76 103 SP T3 SD: 0.1033 c. M:-0.1832 c. 677: 85 115 77 85 115 85 115 SP T3 SD: 0.0639 c. M:-0.1114 c. 765: 96 130 87 96 130 96 130 SP T3 SD: 0.0405 c. M:-0.0745 c. 924: 116 157 105 116 157 116 157 SP T3 SD: 0.0093 c. M:-0.0155 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: 30.2060 cents 3 x x 4 x 5 x 6 S SD: 13.1851 cents 4 x 5 x 6 x 7:8 S SD: 18.3747 cents 5 x 6 x 7:8:9:10 S SD: 16.0872 cents 6 x 7:8:9:10:11:12 S SD: 20.9094 cents 7:8 x 9:10:11:12:14 S SD: 22.4283 cents 8:9:10:11:12:13:14:16 S SD: 15.5930 cents 9:10:11:12:13:15:16:18 SD: 7.3526 cents 13:14:16:17:19:21:23:26 SD: 5.9991 cents 18:20:22:24:26:29:32:36 SD: 5.5820 cents 21:23:26:28:30:34:37:42 SD: 5.1029 cents 22:24:27:29:32:36:39:44 SD: 2.4165 cents 40:44:49:53:58:65:71:80 SD: 2.3258 cents 43:47:53:57:62:70:76:86 SD: 2.2360 cents 45:49:55:60:65:73:80:90 SD: 2.0137 cents 54:59:66:72:78:88:96:108 SD: 1.6495 cents 65:71:80:86:94:106:116:130 SD: 1.5773 cents 67:73:82:89:97:109:119:134 SD: 0.9058 cents 76:83:93:101:110:124:135:152 SD: 0.9001 cents 89:97:109:118:129:145:158:178 SD: 0.7784 cents 122:133:150:162:177:199:217:244 SD: 0.6700 cents 132:144:162:175:191:215:235:264 SD: 0.6041 cents 162:177:199:215:235:264:288:324 SD: 0.5798 cents 167:182:205:222:242:272:297:334 SD: 0.4204 cents 176:192:216:234:255:287:313:352 SD: 0.3687 cents 189:206:232:251:274:308:336:378 SD: 0.3026 cents 265:289:325:352:384:432:471:530 SD: 0.2468 cents 308:336:378:409:446:502:548:616 SD: 0.2221 cents 330:360:405:438:478:538:587:660 SD: 0.2044 cents 397:433:487:527:575:647:706:794 SD: 0.1694 cents 497:542:610:660:720:810:884:994 SD: 0.1556 cents 537:586:659:713:778:875:955:1074 SD: 0.1285 cents