Scala analysis: xen09-chalmers-tritriadic-7-11-13
Tritriadic scale built from 7:11:13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 143/98 654.193791 3: 11/7 782.492036 undecimal augmented fifth 4: 22/13 910.790281 tridecimal major sixth 5: 169/98 943.403511 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: 14/13 128.2982 2/3-tone 2: 1859/1372 525.8955 3: 14/13 128.2982 2/3-tone 4: 14/13 128.2982 2/3-tone 5: 2197/2156 32.6132 6: 14/13 128.2982 2/3-tone 7: 14/13 128.2982 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2197/2156 32.613 cents 1: 5 14/13 128.298 cents 2/3-tone 1: 1 1859/1372 525.896 cents 2: 2 169/154 160.911 cents 2: 3 196/169 256.596 cents two (2/3-tone) 2: 2 143/98 654.194 cents 3: 3 13/11 289.210 cents tridecimal minor third 3: 1 2744/2197 384.895 cents 3: 3 11/7 782.492 cents undecimal augmented fifth 4: 3 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 2197/1372 815.105 cents 4: 3 22/13 910.790 cents tridecimal major sixth 5: 2 196/143 545.806 cents 5: 3 169/98 943.404 cents 5: 2 308/169 1039.089 cents 6: 1 2744/1859 674.104 cents 6: 5 13/7 1071.702 cents 16/3-tone 6: 1 4312/2197 1167.387 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 : 128.3 654.2 782.5 910.8 943.4 1071.7 1200.0 128.3 : 525.9 654.2 782.5 815.1 943.4 1071.7 1200.0 654.2 : 128.3 256.6 289.2 417.5 545.8 674.1 1200.0 782.5 : 128.3 160.9 289.2 417.5 545.8 1071.7 1200.0 910.8 : 32.6 160.9 289.2 417.5 943.4 1071.7 1200.0 943.4 : 128.3 256.6 384.9 910.8 1039.1 1167.4 1200.0 1071.7: 128.3 256.6 782.5 910.8 1039.1 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 32.6132 .. 525.8955 cents 121/91, 493.2823 cents 2197/2156, 32.6132 cents 2: 160.9115 .. 654.1938 cents 121/91, 493.2823 cents 98/121,-364.9841 cents 3: 289.2097 .. 782.4920 cents 121/91, 493.2823 cents 98/121,-364.9841 cents 4: 417.5080 .. 910.7903 cents 121/91, 493.2823 cents 98/121,-364.9841 cents 5: 545.8062 .. 1039.0885 cents 121/91, 493.2823 cents 98/121,-364.9841 cents 6: 674.1045 .. 1167.3868 cents 121/91, 493.2823 cents 98/121,-364.9841 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 2197/2156, 32.6132 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1859/1372, 525.8955 cents Average / Smallest step : 5.256412 Largest / Average step : 3.067724 Largest / Smallest step : 16.125221 Median interval of one step : 14/13, 128.2982 cents, amount: 5 Most common interval of one step : 14/13, 128.2982 cents, amount: 5 Least squares average step : 192.67537 cents, oct.: 1348.72756 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : MLMMSMM Scale is a Constant Structure, by a margin of 19.91066 cents Scale diversity : 1.373368 Lumma stability : 0.054355 Lumma impropriety factor : 0.731814 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 : 268912/265837, 19.9107 cents Most common intervals : 14/13, 128.2982 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 782.492 1071.702 cents Most common triad is 0.0 128.298 1071.702 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 7 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% -- Rational properties -- Prime limit : 13 Odd number limit : 2197 (O: 2197 U: 2197) Highest odd numerator or denominator: 169 Scale harmonicity : 0.008511 Average absolute harmonicity : 0.164483 Specific harmonicity : 0.045295 Fundamental : 1/1274, -10.3151 octaves, 0.2054 Hz. Guide tone : 26026, 14.6677 octaves, 6809066.963 Hz. Exponens Consonantiae : 3.315712E+07, 24.98282 octaves Euler's gradus suavitatis : 67 Sum of Mann's harmonic distance : 305.5, average 43.64286 Mersenne's string divisions : 81077220 Sum of van Prooijen's expressibility: 8.76645, average 1.25235 Sum of Tenney's harmonic distance : 17.22867, average 2.46124 Vogel's harmonic complexity : 31.57143 Wille's k value : 1098 Wilson's harmonic complexity : 71 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 64.60508, average 2.30732 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.14286 5 1 7: -2 .. 1 -0.71429 7 11: 0 .. 1 0.42857 3 1 13: -1 .. 2 0.28571 6 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 18 22 26| Scale is weakly epimorphic with val: <7 18 23 28| Scale is weakly epimorphic with val: <7 18 26 27| Scale is JI-epimorphic with val: <7 19 22 25| Scale is weakly epimorphic with val: <7 19 23 27| Scale is weakly epimorphic with val: <7 19 24 29| Scale is weakly epimorphic with val: <7 20 22 24| Scale is JI-epimorphic with val: <7 20 23 26| Scale is weakly epimorphic with val: <7 20 24 28| Scale is weakly epimorphic with val: <7 21 23 25| Scale is JI-epimorphic with val: <7 21 24 27| Scale is weakly epimorphic with val: <7 21 25 29| Scale is weakly epimorphic with val: <7 22 23 24| Scale is weakly epimorphic with val: <7 22 24 26| Scale is JI-epimorphic with val: <7 22 25 28|
FIT/MODE
7: 0 3 1 1 0 1 1 N SD: 90.6956 c. M: 139.9081 c. 8: 1 3 1 1 0 1 1 N T3 SD: 31.4754 c. M: 54.1938 c. 9: 1 4 1 1 0 1 1 N T3 SD: 12.6627 c. M:-22.5431 c. 20: 2 9 2 2 1 2 2 N T3 SD: 9.0200 c. M:-16.5965 c. 28: 3 12 3 3 1 3 3 N T3 SD: 7.2486 c. M: 11.3366 c. 29: 3 13 3 3 1 3 3 N T3 SD: 5.0690 c. M:-8.3206 c. 37: 4 16 4 4 1 4 4 N T3 SD: 3.0975 c. M: 5.5451 c. 46: 5 20 5 5 1 5 5 N T3 SD: 2.2853 c. M: 4.2731 c. 66: 7 29 7 7 2 7 7 N T3 SD: 1.1817 c. M:-2.0510 c. 75: 8 33 8 8 2 8 8 N T3 SD: 1.0374 c. M:-1.8062 c. 112: 12 49 12 12 3 12 12 N T3 SD: 0.3709 c. M: 0.6224 c. 187: 20 82 20 20 5 20 20 N T3 SD: 0.2633 c. M:-0.4397 c. 253: 27 111 27 27 7 27 27 N T3 SD: 0.2626 c. M:-0.4700 c. 299: 32 131 32 32 8 32 32 N T3 SD: 0.1584 c. M: 0.2597 c. 365: 39 160 39 39 10 39 39 N T3 SD: 0.0863 c. M:-0.1581 c. 477: 51 209 51 51 13 51 51 N T3 SD: 0.0670 c. M: 0.1057 c. 664: 71 291 71 71 18 71 71 N T3 SD: 0.0296 c. M:-0.0531 c. 1029: 110 451 110 110 28 110 110 N T3 SD: 0.0220 c. M:-0.0367 c. 1141: 122 500 122 122 31 122 122 N T3 SD: 0.0173 c. M: 0.0308 c. 1693: 181 742 181 181 46 181 181 N T3 SD: 0.0168 c. M:-0.0295 c. 1805: 193 791 193 193 49 193 193 N T3 SD: 0.0129 c. M: 0.0240 c. 2170: 232 951 232 232 59 232 232 N T3 SD: 0.0042 c. M: 0.0069 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x 3 x x x x 4 S SD: 23.8806 cents 3 x 4 x 5 x x 6 S SD: 52.7900 cents 4:5:6 x x 7 x 8 S SD: 65.9069 cents 5:6:7:8 x x 9:10 S SD: 42.0172 cents 6:7:9 x 10 x 11:12 SD: 30.1205 cents 7:8:10:11 x 12:13:14 S SD: 18.2850 cents 8:9:12:13 x 14:15:16 S SD: 18.4746 cents 9:10:13:14:15:16:17:18 SD: 12.6820 cents 10:11:15:16:17 x 19:20 SD: 13.1479 cents 11:12:16:17 x 19:20:22 SD: 8.6877 cents 13:14:19:20:22 x 24:26 SD: 6.3698 cents 14:15:20:22 x 24:26:28 S SD: 6.5220 cents 17:18:25:27:29 x 32:34 SD: 7.6705 cents 19:20:28:30:32:33:35:38 SD: 6.9122 cents 20:22:29:31:34 x 37:40 SD: 7.7064 cents 21:23:31:33 x 36:39:42 SD: 6.1472 cents 22:24:32:35:37:38:41:44 SD: 4.8330 cents 24:26:35:38 x 41:45:48 SD: 4.7648 cents 26:28:38:41:44:45:48:52 SD: 1.9664 cents 51:55:74:80:86:88:95:102 SD: 1.9011 cents 52:56:76:82:88:90:97:104 SD: 1.7064 cents 54:58:79:85:91:93:100:108 SD: 1.6442 cents 61:66:89:96:103:105:113:122 SD: 1.5416 cents 63:68:92:99:107:109:117:126 SD: 1.3426 cents 65:70:95:102:110:112:121:130 SD: 0.8135 cents 91:98:133:143:154:157:169:182 SD: 0.4144 cents 168:181:245:264:284:290:312:336 SD: 0.4037 cents 196:211:286:308:332:338:364:392 SD: 0.2464 cents 287:309:419:451:486:495:533:574 SD: 0.2135 cents 338:364:493:531:572:583:628:676 SD: 0.1740 cents 364:392:531:572:616:628:676:728 SD: 0.1307 cents 429:462:626:674:726:740:797:858 SD: 0.1218 cents 455:490:664:715:770:785:845:910 SD: 0.1156 cents 588:633:858:924:995:1014:1092:1176 SD: 0.0922 cents