Scala analysis: xen12-chalmers-tritriadic-dm-11-5-3
Tritriadic D->M scale built from 11:5:3
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: 6/5 315.641287 minor third 3: 72/55 466.278346 undecimal semi-diminished fourth 4: 50/33 719.354484 3 pentatones 5: 5/3 884.358713 major sixth, BP sixth 6: 20/11 1034.995772 large minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/10 165.0042 Ptolemy's second, 4/5-tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 125/108 253.0761 semi-augmented whole tone 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 11/10 165.0042 Ptolemy's second, 4/5-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 : 150.6 315.6 466.3 719.4 884.4 1035.0 1200.0 150.6 : 165.0 315.6 568.7 733.7 884.4 1049.4 1200.0 315.6 : 150.6 403.7 568.7 719.4 884.4 1035.0 1200.0 466.3 : 253.1 418.1 568.7 733.7 884.4 1049.4 1200.0 719.4 : 165.0 315.6 480.6 631.3 796.3 946.9 1200.0 884.4 : 150.6 315.6 466.3 631.3 781.9 1035.0 1200.0 1035.0: 165.0 315.6 480.6 631.3 884.4 1049.4 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 : 172.07101 cents, oct.: 1204.49704 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : SMSLMSM 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 1 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 275 (O: 275 U: 275) Highest odd numerator or denominator: 55 Scale harmonicity : 0.020669 Average absolute harmonicity : 0.192894 Specific harmonicity : 0.101077 Fundamental : 1/165, -7.3663 octaves, 1.5856 Hz. Guide tone : 1800, 10.8138 octaves, 470926.018 Hz. Exponens Consonantiae : 2.970000E+05, 18.18010 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 143.0, average 20.42857 Mersenne's string divisions : 1984153512 Sum of van Prooijen's expressibility: 6.73960, average 0.96280 Sum of Tenney's harmonic distance : 14.23242, average 2.03320 Vogel's harmonic complexity : 16.42857 Wille's k value : 137 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 69.06344, average 2.46655 Lattice compactness (without 2's) : 56.12138, average 2.00433 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.42857 10 1 3: -1 .. 2 0.28571 6 5: -1 .. 2 0.28571 6 2 11: -1 .. 0 -0.57143 4 4 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: 27.7523 c. M:-48.0074 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 16.5571 c. M:-30.6455 c. 15: 2 2 2 3 2 2 2 SP M ME I SD: 6.9632 c. M:-13.7217 c. Miller's Porcupine-7 23: 3 3 3 5 3 3 3 SP M DE I SD: 6.0197 c. M:-11.0803 c. Symmetrical Heptatonic 38: 5 5 5 8 5 5 5 SP M DE I SD: 5.4323 c. M:-7.4059 c. 49: 6 7 6 10 7 6 7 SP T3 SD: 4.6978 c. M: 9.1504 c. 57: 7 8 7 12 8 7 8 SP T3 SD: 2.5312 c. M: 3.5650 c. 65: 8 9 8 14 9 8 9 SP T3 SD: 2.3701 c. M: 4.7399 c. 72: 9 10 9 15 10 9 10 SP T3 SD: 1.3442 c. M: 2.6878 c. 80: 10 11 10 17 11 10 11 SP T3 SD: 0.6844 c. M: 1.2783 c. 95: 12 13 12 20 13 12 13 SP T3 SD: 0.6725 c. M:-1.0901 c. 152: 19 21 19 32 21 19 21 SP T3 SD: 0.5576 c. M: 0.9334 c. 167: 21 23 21 35 23 21 23 SP T3 SD: 0.5264 c. M: 0.7916 c. 175: 22 24 22 37 24 22 24 SP T3 SD: 0.3258 c. M:-0.6455 c. 247: 31 34 31 52 34 31 34 SP T3 SD: 0.1677 c. M: 0.3261 c. 327: 41 45 41 69 45 41 45 SP T3 SD: 0.1261 c. M: 0.2233 c. 422: 53 58 53 89 58 53 58 SP T3 SD: 0.0564 c. M:-0.0768 c. 669: 84 92 84 141 92 84 92 SP T3 SD: 0.0542 c. M:-0.0894 c. 749: 94 103 94 158 103 94 103 SP T3 SD: 0.0284 c. M: 0.0567 c. 1171: 147 161 147 247 161 147 161 SP T3 SD: 0.0157 c. M:-0.0307 c. 1840: 231 253 231 388 253 231 253 SP T3 SD: 0.0131 c. M:-0.0260 c. 2167: 272 298 272 457 298 272 298 SP T3 SD: 0.0118 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: 8.6997 cents 3 x x 4 x 5 x 6 S SD: 10.5889 cents 4 x 5 x 6 x 7:8 S SD: 24.5914 cents 5 x 6:7 x 8:9:10 S SD: 27.4282 cents 6 x 7:8:9:10:11:12 S SD: 10.4041 cents 7:8 x 9:11:12:13:14 SD: 20.5288 cents 8:9:10 x 12:13:15:16 SD: 18.9257 cents 9:10:11:12:14:15:16:18 S SD: 11.6206 cents 10:11:12:13:15:17:18:20 SD: 6.5974 cents 19:21:23:25:29:32:35:38 SD: 6.0965 cents 20:22:24:26:30:33:36:40 SD: 5.0713 cents 23:25:28:30:35:38:42:46 SD: 4.6091 cents 25:27:30:33:38:42:45:50 SD: 4.5910 cents 29:32:35:38:44:48:53:58 SD: 3.8377 cents 33:36:40:43:50:55:60:66 SD: 2.7378 cents 35:38:42:46:53:58:64:70 SD: 2.5234 cents 45:49:54:59:68:75:82:90 SD: 1.0455 cents 99:108:119:130:150:165:180:198 SD: 0.8683 cents 110:120:132:144:167:183:200:220 SD: 0.6684 cents 120:131:144:157:182:200:218:240 SD: 0.3919 cents 165:180:198:216:250:275:300:330 SD: 0.0000 cents