Scala analysis: xen12-chalmers-tritriadic-dm-27-9-5
Tritriadic D->M scale built from 27:9:5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 40/27 680.448711 grave fifth 5: 400/243 862.852423 grave major sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 10/9 182.4037 minor whole tone 4: 10/9 182.4037 minor whole tone 5: 10/9 182.4037 minor whole tone 6: 2187/2000 154.7439 Gorgo limma 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 2187/2000 154.744 cents Gorgo limma 1: 5 10/9 182.404 cents minor whole tone 2: 2 6/5 315.641 cents minor third 2: 2 243/200 337.148 cents acute minor third 2: 3 100/81 364.807 cents grave major third 3: 3 4/3 498.045 cents perfect fourth 3: 3 27/20 519.551 cents acute fourth 3: 1 1000/729 547.211 cents 4: 1 729/500 652.789 cents 4: 3 40/27 680.449 cents grave fifth 4: 3 3/2 701.955 cents perfect fifth 5: 3 81/50 835.193 cents acute minor sixth 5: 2 400/243 862.852 cents grave major sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 6: 5 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 4000/2187 1045.256 cents 6: 1 50/27 1066.762 cents grave major seventh 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 : 182.4 315.6 498.0 680.4 862.9 1017.6 1200.0 182.4 : 133.2 315.6 498.0 680.4 835.2 1017.6 1200.0 315.6 : 182.4 364.8 547.2 702.0 884.4 1066.8 1200.0 498.0 : 182.4 364.8 519.6 702.0 884.4 1017.6 1200.0 680.4 : 182.4 337.1 519.6 702.0 835.2 1017.6 1200.0 862.9 : 154.7 337.1 519.6 652.8 835.2 1017.6 1200.0 1017.6: 182.4 364.8 498.0 680.4 862.9 1045.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 182.4037 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 2: 315.6413 .. 364.8074 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 3: 498.0450 .. 547.2111 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 4: 652.7889 .. 701.9550 cents 250/243, 49.1661 cents 531441/500000, 105.5777 cents 5: 835.1926 .. 884.3587 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 6: 1017.5963 .. 1066.7624 cents 250/243, 49.1661 cents 27/25, 133.2376 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.286638 Largest / Average step : 1.064022 Largest / Smallest step : 1.369011 Median interval of one step : 10/9, 182.4037 cents, amount: 5 Most common interval of one step : 10/9, 182.4037 cents, amount: 5 Least squares average step : 170.35326 cents, oct.: 1192.47280 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : LSLLLML Scale is a Constant Structure, by a margin of 105.57773 cents Scale diversity : 1.255905 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.754169 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 : 81/80, 21.5063 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 519.551 1017.596 cents Most common triad is 0.0 182.404 1017.596 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 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 : 5 9 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 1 and 2 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited transpositions with margin 49.1661 cents: 4 5 Limited inverse transpositions with margin 49.1661 cents: 3 6 -- Rational properties -- Prime limit : 5 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 243 Scale harmonicity : 0.023885 Average absolute harmonicity : 0.224006 Specific harmonicity : 0.137260 Fundamental : 1/1215, -10.2467 octaves, 0.2153 Hz. Guide tone : 3600, 11.8138 octaves, 941852.035 Hz. Exponens Consonantiae : 4.374000E+06, 22.06052 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 382.0, average 54.57143 Mersenne's string divisions : 378165018 Sum of van Prooijen's expressibility: 6.90155, average 0.98594 Sum of Tenney's harmonic distance : 14.48588, average 2.06941 Vogel's harmonic complexity : 19.71429 Wille's k value : 1093 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 10 Triangular lattice diameter : 7 Lattice compactness : 99.07349, average 3.53834 Lattice compactness (without 2's) : 84.04566, average 3.00163 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.71429 12 1 3: -5 .. 2 -1.14286 14 1 5: -1 .. 2 0.28571 6 5 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 13.6575 c. M:-27.2159 c. Lebeng 19: 3 2 3 3 3 2 3 SP M ME I SD: 10.7731 c. M:-21.3581 c. Nineteen-tone Dorian 24: 4 2 4 4 3 3 4 SP D3 S SD: 14.2185 c. M:-19.5513 c. Dastgah-e Nava, Maqam Ushaq Masri 25: 4 3 3 4 4 3 4 SP D3 S SD: 11.9342 c. M:-20.3587 c. 26: 4 3 4 4 4 3 4 SP M ME I SD: 8.4241 c. M:-14.0707 c. 32: 5 3 5 5 5 4 5 SP T3 SD: 7.9066 c. M: 15.6413 c. 33: 5 4 5 5 5 4 5 SP M ME I SD: 8.1497 c. M:-11.6314 c. 34: 5 4 5 5 5 5 5 SP M ME S SD: 7.8968 c. M: 15.7936 c. 39: 6 4 6 6 6 5 6 SP T3 SD: 4.1411 c. M: 7.9490 c. 46: 7 5 7 7 7 6 7 SP T3 SD: 1.7434 c. M: 2.5978 c. 53: 8 6 8 8 8 7 8 SP T3 SD: 1.3421 c. M: 2.4751 c. 99: 15 11 15 15 15 13 15 SP T3 SD: 1.1884 c. M: 2.2464 c. 111: 17 12 17 17 17 14 17 SP T3 SD: 1.3808 c. M: 2.1278 c. 118: 18 13 18 18 18 15 18 SP T3 SD: 0.7832 c. M:-1.5544 c. 125: 19 14 19 19 19 16 19 SP T3 SD: 0.8717 c. M:-1.1587 c. 164: 25 18 25 25 25 21 25 SP T3 SD: 0.5495 c. M: 1.0071 c. 171: 26 19 26 26 26 22 26 SP T3 SD: 0.1793 c. M:-0.3055 c. 388: 59 43 59 59 59 50 59 SP T3 SD: 0.0889 c. M: 0.1774 c. 559: 85 62 85 85 85 72 85 SP T3 SD: 0.0667 c. M:-0.1172 c. 612: 93 68 93 93 93 79 93 SP T3 SD: 0.0560 c. M: 0.1073 c. 783: 119 87 119 119 119 101 119 SP T3 SD: 0.0340 c. M:-0.0675 c. 1000: 152 111 152 152 152 129 152 SP T3 SD: 0.0356 c. M: 0.0524 c. 1171: 178 130 178 178 178 151 178 SP T3 SD: 0.0069 c. M: 0.0136 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: 10.7531 cents 3 x x 4 x 5 x 6 S SD: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 22.1298 cents 5 x 6:7 x 8:9:10 S SD: 19.5469 cents 6 x 7:8:9:10:11:12 S SD: 10.9452 cents 7:8 x 9:10:12:13:14 S SD: 22.4678 cents 8:9:10:11:12:13:14:16 S SD: 15.4091 cents 9:10:11:12:13:15:16:18 SD: 8.8702 cents 15:17:18:20:22:25:27:30 SD: 6.2932 cents 19:21:23:25:28:31:34:38 SD: 5.0698 cents 20:22:24:27:30:33:36:40 S SD: 5.0399 cents 25:28:30:33:37:41:45:50 SD: 3.3111 cents 34:38:41:45:50:56:61:68 SD: 3.3025 cents 35:39:42:47:52:58:63:70 SD: 2.6141 cents 36:40:43:48:53:59:65:72 SD: 2.3406 cents 45:50:54:60:67:74:81:90 SD: 1.2581 cents 54:60:65:72:80:89:97:108 SD: 0.9674 cents 81:90:97:108:120:133:146:162 SD: 0.8705 cents 90:100:108:120:133:148:162:180 SD: 0.6667 cents 125:139:150:167:185:206:225:250 SD: 0.6532 cents 135:150:162:180:200:222:243:270 SD: 0.2474 cents 305:339:366:407:452:502:549:610 SD: 0.2346 cents 324:360:389:432:480:533:583:648 SD: 0.2174 cents 351:390:421:468:520:578:632:702 SD: 0.1702 cents 405:450:486:540:600:667:729:810 SD: 0.1236 cents 486:540:583:648:720:800:875:972 SD: 0.1019 cents 540:600:648:720:800:889:972:1080 SD: 0.0309 cents