Scala analysis: xen12-chalmers-tritriadic-dm-27-25-15
Tritriadic D->M scale built from 27:25:15
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: 125/81 751.121138 5: 5/3 884.358713 major sixth, BP sixth 6: 50/27 1066.762425 grave major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 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: 125/108 253.0761 semi-augmented whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 10/9 182.4037 minor whole tone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 10/9 182.404 cents minor whole tone 1: 1 125/108 253.076 cents semi-augmented whole tone 2: 5 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 1 625/486 435.480 cents 3: 2 162/125 448.879 cents 3: 2 4/3 498.045 cents perfect fourth 3: 3 25/18 568.717 cents classic augmented fourth 4: 3 36/25 631.283 cents classic diminished fifth 4: 2 3/2 701.955 cents perfect fifth 4: 2 125/81 751.121 cents 5: 1 972/625 764.520 cents 5: 1 8/5 813.686 cents minor sixth 5: 5 5/3 884.359 cents major sixth, BP sixth 6: 1 216/125 946.924 cents semi-augmented sixth 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 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 : 182.4 315.6 498.0 751.1 884.4 1066.8 1200.0 182.4 : 133.2 315.6 568.7 702.0 884.4 1017.6 1200.0 315.6 : 182.4 435.5 568.7 751.1 884.4 1066.8 1200.0 498.0 : 253.1 386.3 568.7 702.0 884.4 1017.6 1200.0 751.1 : 133.2 315.6 448.9 631.3 764.5 946.9 1200.0 884.4 : 182.4 315.6 498.0 631.3 813.7 1066.8 1200.0 1066.8: 133.2 315.6 448.9 631.3 884.4 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 253.0761 cents 3125/2916, 119.8386 cents 27/25, 133.2376 cents 2: 315.6413 .. 435.4799 cents 3125/2916, 119.8386 cents 648/625, 62.5651 cents 3: 448.8789 .. 568.7174 cents 3125/2916, 119.8386 cents 78732/78125, 13.3990 cents 4: 631.2826 .. 751.1211 cents 3125/2916, 119.8386 cents 648/625, 62.5651 cents 5: 764.5201 .. 884.3587 cents 3125/2916, 119.8386 cents 78732/78125, 13.3990 cents 6: 946.9239 .. 1066.7624 cents 3125/2916, 119.8386 cents 648/625, 62.5651 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 : 125/108, 253.0761 cents Average / Smallest step : 1.286638 Largest / Average step : 1.476277 Largest / Smallest step : 1.899435 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 175.24767 cents, oct.: 1226.73370 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : MSMLSMS Scale is a Constant Structure, by a margin of 13.39901 cents Scale diversity : 1.413097 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.400807 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 : 78732/78125, 13.3990 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 133.238 315.641 cents Most common triad is 0.0 315.641 884.359 cents, amount: 3 Number of recognisable fifths : 2, average 701.9550 cents Scale contains a complete diamond : 3 5 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 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 5 Odd number limit : 625 (O: 625 U: 625) Highest odd numerator or denominator: 125 Scale harmonicity : 0.024430 Average absolute harmonicity : 0.225972 Specific harmonicity : 0.145410 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 1500, 10.5507 octaves, 392438.348 Hz. Exponens Consonantiae : 6.075000E+05, 19.21252 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 165.5, average 23.64286 Mersenne's string divisions : 3616536 Sum of van Prooijen's expressibility: 6.35758, average 0.90823 Sum of Tenney's harmonic distance : 13.12340, average 1.87477 Vogel's harmonic complexity : 17.85714 Wille's k value : 337 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 78.88443, average 2.81730 Lattice compactness (without 2's) : 71.39702, average 2.54989 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.85714 6 1 3: -4 .. 1 -1.42857 12 1 5: -1 .. 3 0.85714 8 5 Average exponent except 2's :-4 / 7 =-0.57143 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: 32.9550 c. M: 65.4069 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 24.2895 c. M: 48.0450 c. 11: 2 1 2 2 1 2 1 P M ME S SD: 25.4615 c. M:-47.4095 c. 12: 2 1 2 3 1 2 1 N T3 SD: 24.7751 c. M:-48.8789 c. 14: 2 2 2 3 1 2 2 P T3 SD: 23.1040 c. M: 38.1910 c. 15: 2 2 2 3 2 2 2 SP M ME I SD: 19.0874 c. M: 31.1211 c. Miller's Porcupine-7 16: 2 2 3 3 2 2 2 P D3 S SD: 19.0792 c. M: 32.4037 c. 18: 3 2 2 4 2 3 2 P T3 SD: 17.8752 c. M: 31.3783 c. 19: 3 2 3 4 2 3 2 P T3 SD: 5.2905 c. M:-7.2182 c. 27: 4 3 4 6 3 4 3 P T3 SD: 4.8690 c. M: 9.1561 c. 45: 7 5 7 9 5 7 5 SP T3 SD: 4.6346 c. M:-8.6217 c. 46: 7 5 7 10 5 7 5 P T3 SD: 2.8357 c. M:-5.4006 c. 53: 8 6 8 11 6 8 6 SP T3 SD: 1.9873 c. M: 3.9513 c. 72: 11 8 11 15 8 11 8 SP T3 SD: 1.0727 c. M:-1.9550 c. 99: 15 11 15 21 11 15 11 SP T3 SD: 0.5533 c. M: 1.0753 c. 171: 26 19 26 36 19 26 19 SP T3 SD: 0.1491 c. M: 0.2439 c. 270: 41 30 41 57 30 41 30 SP T3 SD: 0.1354 c. M: 0.2672 c. 441: 67 49 67 93 49 67 49 SP T3 SD: 0.0707 c. M: 0.1007 c. 730: 111 81 111 154 81 111 81 SP T3 SD: 0.0615 c. M:-0.1117 c. 901: 137 100 137 190 100 137 100 SP T3 SD: 0.0432 c. M:-0.0682 c. 1000: 152 111 152 211 111 152 111 SP T3 SD: 0.0432 c. M:-0.0789 c. 1171: 178 130 178 247 130 178 130 SP T3 SD: 0.0161 c. M:-0.0317 c. 1342: 204 149 204 283 149 204 149 SP T3 SD: 0.0088 c. M:-0.0176 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: 24.5831 cents 3 x x 4 x 5 x 6 S SD: 0.0000 cents 4 x 5 x 6:7 x 8 S SD: 30.1523 cents 5 x 6:7:8 x 9:10 S SD: 23.2090 cents 6 x 7:8:9:10:11:12 S SD: 11.9007 cents 7:8 x 9:11:12:13:14 SD: 16.4399 cents 8:9:10:11:12:13:15:16 SD: 16.3483 cents 9:10:11:12:14:15:17:18 SD: 6.9616 cents 15:17:18:20:23:25:28:30 SD: 5.5128 cents 20:22:24:27:31:33:37:40 SD: 4.7996 cents 24:27:29:32:37:40:44:48 SD: 4.3137 cents 26:29:31:35:40:43:48:52 SD: 3.7204 cents 27:30:32:36:42:45:50:54 SD: 3.6500 cents 30:33:36:40:46:50:56:60 SD: 3.5473 cents 33:37:40:44:51:55:61:66 SD: 3.3941 cents 35:39:42:47:54:58:65:70 SD: 2.4711 cents 39:43:47:52:60:65:72:78 SD: 2.4334 cents 45:50:54:60:69:75:83:90 SD: 1.8719 cents 54:60:65:72:83:90:100:108 SD: 1.2504 cents 75:83:90:100:116:125:139:150 SD: 1.1524 cents 81:90:97:108:125:135:150:162 SD: 0.5094 cents 135:150:162:180:208:225:250:270 SD: 0.3960 cents 171:190:205:228:264:285:317:342 SD: 0.3697 cents 180:200:216:240:278:300:333:360 SD: 0.3168 cents 216:240:259:288:333:360:400:432 SD: 0.3125 cents 225:250:270:300:347:375:417:450 SD: 0.2533 cents 270:300:324:360:417:450:500:540 SD: 0.1978 cents 315:350:378:420:486:525:583:630 SD: 0.1523 cents 324:360:389:432:500:540:600:648 SD: 0.1272 cents 405:450:486:540:625:675:750:810 SD: 0.0000 cents