Scala analysis: xen09-chalmers-tritriadic-22-24-27
Tritriadic scale built from 22:24:27
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: 162/121 505.184119 4: 729/484 709.094120 two (neutral third, Zalzal wosta of al-Farabi) 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: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 21296/19683 136.3588 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 : 150.6 354.5 505.2 709.1 845.5 996.1 1200.0 150.6 : 203.9 354.5 558.5 694.8 845.5 1049.4 1200.0 354.5 : 150.6 354.5 490.9 641.5 845.5 996.1 1200.0 505.2 : 203.9 340.3 490.9 694.8 845.5 1049.4 1200.0 709.1 : 136.4 287.0 490.9 641.5 845.5 996.1 1200.0 845.5 : 150.6 354.5 505.2 709.1 859.7 1063.6 1200.0 996.1 : 203.9 354.5 558.5 709.1 913.0 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 : 170.11046 cents, oct.: 1190.77324 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABABCAB Step pattern size order : MLMLSML 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: 3 -- 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 : 0.180342 Specific harmonicity : 0.065706 Fundamental : 1/13068, -13.6738 octaves, 0.0200 Hz. Guide tone : 128304, 16.9692 octaves, 33567606.530 Hz. Exponens Consonantiae : 1.676677E+09, 30.64296 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 833.5, average 119.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.80388, average 1.40055 Sum of Tenney's harmonic distance : 20.26844, average 2.89549 Vogel's harmonic complexity : 30.00000 Wille's k value : 9841 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 12 Triangular lattice diameter : 9 Lattice compactness : 132.81786, average 4.74350 Lattice compactness (without 2's) : 110.05428, average 3.93051 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.00000 13 1 3: -3 .. 6 1.28571 19 1 11: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 4 / 7 = 0.57143 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: 18.4782 c. M:-32.4814 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 20.8866 c. M: 36.0900 c. 16: 2 3 2 2 2 2 3 P D3 S SD: 20.1314 c. M: 34.0941 c. 17: 2 3 2 3 2 2 3 SP M ME S SD: 6.4269 c. M: 11.0665 c. 24: 3 4 3 4 3 3 4 SP M ME S SD: 4.8789 c. M: 9.0941 c. Neutral Hypophrygian, Iced Mixolydian 41: 5 7 5 7 5 5 7 SP M DE S SD: 4.5346 c. M: 7.6231 c. 47: 6 8 6 8 5 6 8 SP T3 SD: 3.5222 c. M:-5.7995 c. 54: 7 9 7 9 6 7 9 SP T3 SD: 3.3956 c. M:-5.9270 c. 64: 8 11 8 11 7 8 11 SP T3 SD: 1.8677 c. M:-3.4059 c. 71: 9 12 9 12 8 9 12 SP T3 SD: 1.0490 c. M:-1.8581 c. 88: 11 15 11 15 10 11 15 SP T3 SD: 0.4171 c. M: 0.6387 c. 159: 20 27 20 27 18 20 27 SP T3 SD: 0.2706 c. M:-0.4763 c. 247: 31 42 31 42 28 31 42 SP T3 SD: 0.1179 c. M:-0.2176 c. 518: 65 88 65 88 59 65 88 SP T3 SD: 0.1204 c. M: 0.2138 c. 582: 73 99 73 99 66 73 99 SP T3 SD: 0.1266 c. M: 0.2137 c. 589: 74 100 74 100 67 74 100 SP T3 SD: 0.0976 c. M:-0.1749 c. 677: 85 115 85 115 77 85 115 SP T3 SD: 0.0483 c. M: 0.0838 c. 765: 96 130 96 130 87 96 130 SP T3 SD: 0.0511 c. M: 0.0861 c. 836: 105 142 105 142 95 105 142 SP T3 SD: 0.0528 c. M:-0.0823 c. 924: 116 157 116 157 105 116 157 SP T3 SD: 0.0082 c. M:-0.0139 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: 3.5696 cents 3 x x 4 x 5 x 6 S SD: 13.1851 cents 4 x 5 x 6 x 7:8 S SD: 10.6167 cents 5 x 6:7 x 8:9:10 S SD: 18.9367 cents 6 x 7:8:9:10:11:12 S SD: 18.3641 cents 7:8 x 9 x 11:12:14 SD: 27.8053 cents 8:9:10:11:12:13:14:16 S SD: 11.7751 cents 9:10:11:12:14:15:16:18 S SD: 10.8240 cents 12:13:15:16:18:20:21:24 SD: 8.4679 cents 14:15:17:19:21:23:25:28 SD: 6.6563 cents 18:20:22:24:27:29:32:36 SD: 5.6306 cents 21:23:26:28:32:34:37:42 SD: 4.7430 cents 22:24:27:29:33:36:39:44 SD: 4.1678 cents 30:33:37:40:45:49:53:60 SD: 3.2399 cents 32:35:39:43:48:52:57:64 SD: 2.4435 cents 35:38:43:47:53:57:62:70 SD: 2.1385 cents 44:48:54:59:66:72:78:88 SD: 1.6495 cents 53:58:65:71:80:86:94:106 SD: 1.5511 cents 65:71:80:87:98:106:116:130 SD: 1.2617 cents 67:73:82:90:101:109:119:134 SD: 1.2274 cents 79:86:97:106:119:129:140:158 SD: 1.2004 cents 89:97:109:119:134:145:158:178 SD: 0.7479 cents 132:144:162:177:199:215:235:264 SD: 0.5798 cents 154:168:189:206:232:251:274:308 SD: 0.3026 cents 221:241:271:296:333:360:393:442 SD: 0.2926 cents 251:274:308:336:378:409:446:502 SD: 0.2159 cents 330:360:405:442:497:538:587:660 SD: 0.2026 cents 383:418:470:513:577:624:681:766 SD: 0.1781 cents 405:442:497:542:610:660:720:810 SD: 0.1484 cents 419:457:514:561:631:683:745:838 SD: 0.1476 cents 440:480:540:589:663:717:782:880 SD: 0.1300 cents 581:634:713:778:875:947:1033:1162 SD: 0.1045 cents