Scala analysis: xen09-chalmers-tritriadic-11-8-6
Tritriadic scale built from 11:8:6
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: 144/121 301.274117 two (undecimal neutral second, 3/4-tone) 3: 4/3 498.044999 perfect fourth 4: 16/11 648.682058 undecimal semi-diminished fifth 5: 192/121 799.319116 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 121/108 196.7709 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 1331/1152 250.0438 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 121/108 196.771 cents 1: 1 1331/1152 250.044 cents 2: 3 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 121/96 400.681 cents 3: 1 1728/1331 451.911 cents 3: 3 4/3 498.045 cents perfect fourth 3: 3 11/8 551.318 cents undecimal semi-augmented fourth 4: 3 16/11 648.682 cents undecimal semi-diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 1331/864 748.089 cents 5: 2 192/121 799.319 cents 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 3 121/72 898.726 cents 6: 1 2304/1331 949.956 cents 6: 1 216/121 1003.229 cents 6: 5 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 150.6 301.3 498.0 648.7 799.3 1049.4 1200.0 150.6 : 150.6 347.4 498.0 648.7 898.7 1049.4 1200.0 301.3 : 196.8 347.4 498.0 748.1 898.7 1049.4 1200.0 498.0 : 150.6 301.3 551.3 702.0 852.6 1003.2 1200.0 648.7 : 150.6 400.7 551.3 702.0 852.6 1049.4 1200.0 799.3 : 250.0 400.7 551.3 702.0 898.7 1049.4 1200.0 1049.4: 150.6 301.3 451.9 648.7 799.3 950.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 250.0438 cents 14641/13824, 99.4068 cents 12/11, 150.6371 cents 2: 301.2741 .. 400.6809 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 3: 451.9112 .. 551.3179 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 4: 648.6821 .. 748.0888 cents 14641/13824, 99.4068 cents 128/121, 97.3641 cents 5: 799.3191 .. 898.7259 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents 6: 949.9562 .. 1049.3629 cents 14641/13824, 99.4068 cents 165888/161051, 51.2303 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1331/1152, 250.0438 cents Average / Smallest step : 1.138024 Largest / Average step : 1.458589 Largest / Smallest step : 1.659909 Median interval of one step : 12/11, 150.6371 cents, amount: 5 Most common interval of one step : 12/11, 150.6371 cents, amount: 5 Least squares average step : 168.10587 cents, oct.: 1176.74109 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABAACA Step pattern size order : SSMSSLS Scale is a Constant Structure, by a margin of 51.23029 cents Scale diversity : 1.396184 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.502966 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 : 1331/1296, 46.1338 cents Most common intervals : 12/11, 150.6371 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 1049.363 cents Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Scale contains a complete diamond : 3 11 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 classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.014379 Average absolute harmonicity : 0.198999 Specific harmonicity : 0.079500 Fundamental : 1/726, -9.5038 octaves, 0.3604 Hz. Guide tone : 6336, 12.6294 octaves, 1657659.582 Hz. Exponens Consonantiae : 4.599936E+06, 22.13318 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 327.5, average 46.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.76687, average 1.10955 Sum of Tenney's harmonic distance : 16.17308, average 2.31044 Vogel's harmonic complexity : 21.57143 Wille's k value : 665 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 97.83317, average 3.49404 Lattice compactness (without 2's) : 51.84729, average 1.85169 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 6 2.57143 20 1 3: -1 .. 2 0.28571 6 1 11: -2 .. 1 -0.71429 7 5 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 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: 32.8904 c. M:-57.8237 c. Lebeng 8: 1 1 1 1 1 2 1 P M ME S SD: 31.8772 c. M: 49.3191 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 21.9274 c. M:-35.2883 c. 15: 2 2 2 2 2 3 2 SP M ME S SD: 11.5106 c. M:-18.7259 c. 17: 2 2 3 2 2 4 2 P T3 SD: 13.3830 c. M: 22.8485 c. 24: 3 3 4 3 3 5 3 SP T3 SD: 1.0992 c. M:-1.9550 c. 111: 14 14 18 14 14 23 14 SP T3 SD: 0.7639 c. M:-1.4286 c. 135: 17 17 22 17 17 28 17 SP T3 SD: 0.5246 c. M:-0.9481 c. 159: 20 20 26 20 20 33 20 SP T3 SD: 0.4091 c. M:-0.6809 c. 183: 23 23 30 23 23 38 23 SP T3 SD: 0.3802 c. M:-0.6809 c. 311: 39 39 51 39 39 65 39 SP T3 SD: 0.3382 c. M: 0.6053 c. 335: 42 42 55 42 42 70 42 SP T3 SD: 0.2931 c. M: 0.5131 c. 359: 45 45 59 45 45 75 45 SP T3 SD: 0.2731 c. M: 0.4385 c. 422: 53 53 69 53 53 88 53 SP T3 SD: 0.2367 c. M: 0.4147 c. 446: 56 56 73 56 56 93 56 SP T3 SD: 0.1690 c. M: 0.2872 c. 470: 59 59 77 59 59 98 59 SP T3 SD: 0.1122 c. M: 0.1727 c. 494: 62 62 81 62 62 103 62 SP T3 SD: 0.0722 c. M: 0.1288 c. 518: 65 65 85 65 65 108 65 SP T3 SD: 0.0657 c. M: 0.1158 c. 653: 82 82 107 82 82 136 82 SP T3 SD: 0.0567 c. M:-0.1041 c. 677: 85 85 111 85 85 141 85 SP T3 SD: 0.0504 c. M:-0.0900 c. 1147: 144 144 188 144 144 239 144 SP T3 SD: 0.0283 c. M: 0.0502 c. 1171: 147 147 192 147 147 244 147 SP T3 SD: 0.0052 c. M: 0.0091 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: 26.6365 cents 3 x x 4 x 5 x 6 S SD: 28.3465 cents 4 x 5 x 6 x 7:8 S SD: 32.1675 cents 5 x 6 x 7:8:9:10 S SD: 15.2321 cents 6 x 7:8:9:10:11:12 S SD: 17.6803 cents 7 x 8:9:10:11:13:14 SD: 17.1864 cents 9:10:11:12:13:14:17:18 SD: 12.0692 cents 10:11:12:13:15:16:18:20 SD: 11.4174 cents 11:12:13:15:16:17:20:22 SD: 8.9812 cents 12:13:14:16:17:19:22:24 SD: 8.3667 cents 15:16:18:20:22:24:28:30 S SD: 7.9616 cents 18:20:21:24:26:29:33:36 SD: 7.8668 cents 19:21:23:25:28:30:35:38 SD: 7.2298 cents 20:22:24:27:29:32:37:40 SD: 5.2617 cents 22:24:26:29:32:35:40:44 SD: 3.9479 cents 31:34:37:41:45:49:57:62 SD: 2.8243 cents 36:39:43:48:52:57:66:72 SD: 2.6548 cents 42:46:50:56:61:67:77:84 SD: 1.6828 cents 53:58:63:71:77:84:97:106 SD: 1.5470 cents 68:74:81:91:99:108:125:136 SD: 1.3353 cents 75:82:89:100:109:119:138:150 SD: 1.2867 cents 78:85:93:104:113:124:143:156 SD: 1.2176 cents 84:92:100:112:122:133:154:168 SD: 1.1792 cents 90:98:107:120:131:143:165:180 SD: 0.6399 cents 121:132:144:161:176:192:222:242 SD: 0.5442 cents 143:156:170:191:208:227:262:286 SD: 0.5395 cents 174:190:207:232:253:276:319:348 SD: 0.2824 cents 264:288:314:352:384:419:484:528 SD: 0.1529 cents 462:504:550:616:672:733:847:924 SD: 0.0873 cents