Scala analysis: xen09-chalmers-tritriadic-10-11-12
Tritriadic scale built from 10:11:12
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 6/5 315.641287 minor third 3: 33/25 480.645516 2 pentatones 4: 36/25 631.282574 classic diminished fifth 5: 5/3 884.358713 major sixth, BP sixth 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 125/108 253.0761 semi-augmented whole tone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 3 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 125/108 253.076 cents semi-augmented whole tone 2: 5 6/5 315.641 cents minor third 2: 1 125/99 403.713 cents 2: 1 275/216 418.080 cents 3: 2 72/55 466.278 cents undecimal semi-diminished fourth 3: 2 33/25 480.646 cents 2 pentatones 3: 3 25/18 568.717 cents classic augmented fourth 4: 3 36/25 631.283 cents classic diminished fifth 4: 2 50/33 719.354 cents 3 pentatones 4: 2 55/36 733.722 cents undecimal semi-augmented fifth 5: 1 432/275 781.920 cents 5: 1 198/125 796.287 cents 5: 5 5/3 884.359 cents major sixth, BP sixth 6: 1 216/125 946.924 cents semi-augmented sixth 6: 3 20/11 1034.996 cents large minor seventh 6: 3 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 : 165.0 315.6 480.6 631.3 884.4 1049.4 1200.0 165.0 : 150.6 315.6 466.3 719.4 884.4 1035.0 1200.0 315.6 : 165.0 315.6 568.7 733.7 884.4 1049.4 1200.0 480.6 : 150.6 403.7 568.7 719.4 884.4 1035.0 1200.0 631.3 : 253.1 418.1 568.7 733.7 884.4 1049.4 1200.0 884.4 : 165.0 315.6 480.6 631.3 796.3 946.9 1200.0 1049.4: 150.6 315.6 466.3 631.3 781.9 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 253.0761 cents 1375/1296, 102.4391 cents 12/11, 150.6371 cents 2: 315.6413 .. 418.0804 cents 1375/1296, 102.4391 cents 648/625, 62.5651 cents 3: 466.2783 .. 568.7174 cents 1375/1296, 102.4391 cents 15552/15125, 48.1980 cents 4: 631.2826 .. 733.7217 cents 1375/1296, 102.4391 cents 648/625, 62.5651 cents 5: 781.9196 .. 884.3587 cents 1375/1296, 102.4391 cents 15552/15125, 48.1980 cents 6: 946.9239 .. 1049.3629 cents 1375/1296, 102.4391 cents 648/625, 62.5651 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 : 125/108, 253.0761 cents Average / Smallest step : 1.138024 Largest / Average step : 1.476277 Largest / Smallest step : 1.680039 Median interval of one step : 11/10, 165.0042 cents, amount: 3 Least squares average step : 170.58089 cents, oct.: 1194.06624 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABABCAB Step pattern size order : MSMSLMS Scale is a Constant Structure, by a margin of 48.19798 cents Scale diversity : 1.323807 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.487805 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 : 121/120, 14.3672 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 165.004 315.641 cents Most common triad is 0.0 315.641 884.359 cents, amount: 3 Number of recognisable fifths : 2, average 719.3545 cents Number of appreciable fifths : 0 Best fifths form a closed circle Best major thirds form a closed circle Scale contains a complete diamond : 3 5 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 102.4391 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 275 (O: 275 U: 275) Highest odd numerator or denominator: 33 Scale harmonicity : 0.020669 Average absolute harmonicity : 0.196268 Specific harmonicity : 0.102994 Fundamental : 1/150, -7.2288 octaves, 1.7442 Hz. Guide tone : 1980, 10.9513 octaves, 518018.619 Hz. Exponens Consonantiae : 2.970000E+05, 18.18010 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 89.5, average 12.78571 Mersenne's string divisions : 55574904 Sum of van Prooijen's expressibility: 6.39718, average 0.91388 Sum of Tenney's harmonic distance : 12.68588, average 1.81227 Vogel's harmonic complexity : 16.28571 Wille's k value : 137 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 69.36527, average 2.47733 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.28571 6 1 3: -1 .. 2 0.28571 6 5: -2 .. 1 -0.71429 7 3 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is JI-epimorphic with val: <7 10 15 23| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 12 15 24| Scale is JI-epimorphic with val: <7 12 17 25| Scale is weakly epimorphic with val: <7 12 18 22|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 29.3974 c. M:-54.4317 c. Lebeng 8: 1 1 1 1 2 1 1 P M ME S SD: 19.3929 c. M: 31.2826 c. 15: 2 2 2 2 3 2 2 SP M ME S SD: 5.6960 c. M: 9.3629 c. 23: 3 3 3 3 5 3 3 SP M DE S SD: 6.2088 c. M: 11.0803 c. 38: 5 5 5 5 8 5 5 SP M DE S SD: 4.6570 c. M: 7.2577 c. 42: 6 5 6 5 9 6 5 SP T3 SD: 4.4484 c. M:-7.7799 c. 50: 7 6 7 6 11 7 6 SP T3 SD: 4.3588 c. M: 7.2826 c. 57: 8 7 8 7 12 8 7 SP T3 SD: 2.2424 c. M:-3.5650 c. 65: 9 8 9 8 14 9 8 SP T3 SD: 2.0614 c. M: 3.5903 c. 72: 10 9 10 9 15 10 9 SP T3 SD: 1.5447 c. M:-2.6878 c. 80: 11 10 11 10 17 11 10 SP T3 SD: 0.6856 c. M: 1.2826 c. 95: 13 12 13 12 20 13 12 SP T3 SD: 0.5432 c. M: 0.9419 c. 152: 21 19 21 19 32 21 19 SP T3 SD: 0.5379 c. M:-0.9334 c. 175: 24 22 24 22 37 24 22 SP T3 SD: 0.3633 c. M: 0.6455 c. 232: 32 29 32 29 49 32 29 SP T3 SD: 0.3611 c. M:-0.6371 c. 247: 34 31 34 31 52 34 31 SP T3 SD: 0.1966 c. M:-0.3261 c. 327: 45 41 45 41 69 45 41 SP T3 SD: 0.0997 c. M:-0.1783 c. 422: 58 53 58 53 89 58 53 SP T3 SD: 0.0493 c. M: 0.0768 c. 749: 103 94 103 94 158 103 94 SP T3 SD: 0.0242 c. M: 0.0409 c. 1171: 161 147 161 147 247 161 147 SP T3 SD: 0.0183 c. M: 0.0307 c. 1840: 253 231 253 231 388 253 231 SP T3 SD: 0.0120 c. M:-0.0218 c. 2167: 298 272 298 272 457 298 272 SP T3 SD: 0.0111 c. M:-0.0190 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 5.7998 cents 4 x 5 x 6 x 7:8 S SD: 32.0891 cents 5 x 6 x 7:8:9:10 S SD: 18.3109 cents 6 x 7:8:9:10:11:12 S SD: 14.6020 cents 7:8 x 9:10:12:13:14 S SD: 16.2636 cents 9:10:11:12:13:15:17:18 SD: 9.3832 cents 12:13:14:16:17:20:22:24 SD: 9.2359 cents 16:18:19:21:23:27:29:32 SD: 7.5629 cents 18:20:22:24:26:30:33:36 SD: 5.7907 cents 19:21:23:25:27:32:35:38 SD: 5.0512 cents 21:23:25:28:30:35:39:42 SD: 5.0280 cents 25:28:30:33:36:42:46:50 SD: 4.9546 cents 28:31:34:37:40:47:51:56 SD: 4.5584 cents 29:32:35:38:42:48:53:58 SD: 3.3832 cents 30:33:36:40:43:50:55:60 SD: 2.7378 cents 40:44:48:53:58:67:73:80 SD: 2.5680 cents 41:45:49:54:59:68:75:82 SD: 1.8466 cents 50:55:60:66:72:83:92:100 SD: 1.3373 cents 59:65:71:78:85:98:108:118 SD: 1.2810 cents 79:87:95:104:114:132:145:158 SD: 1.2403 cents 84:92:101:111:121:140:154:168 SD: 1.2124 cents 90:99:108:119:130:150:165:180 SD: 0.8683 cents 91:100:109:120:131:152:167:182 SD: 0.8302 cents 100:110:120:132:144:167:183:200 SD: 0.6684 cents 141:155:169:186:203:235:259:282 SD: 0.6060 cents 150:165:180:198:216:250:275:300 SD: 0.0000 cents