Scala analysis: xen12-chalmers-tritriadic-dm-11-27-9
Tritriadic D->M scale built from 11:27:9
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: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 18/11 852.592059 undecimal neutral sixth 6: 81/44 1056.502061 2nd undecimal neutral seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 88/81 143.4979 2nd undecimal neutral second 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 9/8 203.9100 major whole tone 3: 88/81 143.4979 2nd undecimal neutral second 4: 9/8 203.9100 major whole tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 9/8 203.9100 major whole tone 7: 88/81 143.4979 2nd undecimal neutral second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 3 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 11/9 347.408 cents undecimal neutral third 2: 3 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 5 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 243/176 558.457 cents 4: 1 352/243 641.543 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 5 3/2 701.955 cents perfect fifth 5: 3 44/27 845.453 cents neutral sixth 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 81/44 1056.502 cents 2nd undecimal neutral 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 : 150.6 354.5 498.0 702.0 852.6 1056.5 1200.0 150.6 : 203.9 347.4 551.3 702.0 905.9 1049.4 1200.0 354.5 : 143.5 347.4 498.0 702.0 845.5 996.1 1200.0 498.0 : 203.9 354.5 558.5 702.0 852.6 1056.5 1200.0 702.0 : 150.6 354.5 498.0 648.7 852.6 996.1 1200.0 852.6 : 203.9 347.4 498.0 702.0 845.5 1049.4 1200.0 1056.5: 143.5 294.1 498.0 641.5 845.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 203.9100 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 2: 294.1350 .. 354.5471 cents 729/704, 60.4121 cents 256/243, 90.2250 cents 3: 498.0450 .. 558.4571 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 4: 641.5429 .. 701.9550 cents 729/704, 60.4121 cents 61952/59049, 83.0859 cents 5: 845.4529 .. 905.8650 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 6: 996.0900 .. 1056.5021 cents 729/704, 60.4121 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.194641 Largest / Average step : 1.189475 Largest / Smallest step : 1.420996 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 172.59756 cents, oct.: 1208.18294 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : MLSLMLS Scale is a Constant Structure, by a margin of 83.08588 cents Scale diversity : 1.264781 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.697940 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 : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 347.408 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords 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 : 1 3 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 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.028157 Average absolute harmonicity : 0.234396 Specific harmonicity : 0.130547 Fundamental : 1/132, -7.0444 octaves, 1.9820 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 4.276800E+04, 15.38424 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 120.5, average 17.21429 Mersenne's string divisions : 12256125 Sum of van Prooijen's expressibility: 6.37688, average 0.91098 Sum of Tenney's harmonic distance : 12.90133, average 1.84305 Vogel's harmonic complexity : 14.28571 Wille's k value : 121 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 83.08560, average 2.96734 Lattice compactness (without 2's) : 60.30436, average 2.15373 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.28571 10 1 3: -1 .. 4 1.42857 12 2 11: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 6 / 7 = 0.85714 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 25| Scale is JI-epimorphic with val: <7 11 24| = patent Scale is weakly epimorphic with val: <7 12 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 16.4633 c. M: 27.9306 c. Lebeng 16: 2 3 2 2 2 3 2 SP M ME I SD: 19.5502 c. M: 27.5921 c. Armodue-7, Antidorian 17: 2 3 2 3 2 3 2 SP M ME I SD: 4.7650 c. M: 9.4606 c. Neutral Dorian, Maqamic-7 24: 3 4 3 4 3 4 3 SP M ME I SD: 3.3321 c. M: 6.5021 c. Neutral Dorian, Misaelides 2nd Byzantine mode, Iced Fridgian, Maqam Sikah Baladi, Maqamic-7 41: 5 7 5 7 5 7 5 SP M DE I SD: 2.7414 c. M: 4.2956 c. Maqamic-7 65: 8 11 8 11 8 11 8 SP M DE I SD: 2.7303 c. M: 4.1944 c. Maqamic-7 94: 12 16 11 16 12 16 11 SP T3 SD: 2.1337 c. M:-3.0724 c. 101: 13 17 12 17 13 17 12 SP T3 SD: 2.0356 c. M:-3.8184 c. 111: 14 19 13 19 14 19 13 SP T3 SD: 1.5764 c. M:-2.9574 c. 118: 15 20 14 20 15 20 14 SP T3 SD: 1.1745 c. M:-1.9053 c. 135: 17 23 16 23 17 23 16 SP T3 SD: 0.7133 c. M:-1.2757 c. 159: 20 27 19 27 20 27 19 SP T3 SD: 0.1686 c. M:-0.3063 c. 335: 42 57 40 57 42 57 40 SP T3 SD: 0.1349 c. M:-0.2144 c. 494: 62 84 59 84 62 84 59 SP T3 SD: 0.0891 c. M:-0.1781 c. 518: 65 88 62 88 65 88 62 SP T3 SD: 0.0756 c. M: 0.1314 c. 677: 85 115 81 115 85 115 81 SP T3 SD: 0.0394 c. M: 0.0767 c. 1012: 127 172 121 172 127 172 121 SP T3 SD: 0.0232 c. M: 0.0442 c. 1171: 147 199 140 199 147 199 140 SP T3 SD: 0.0158 c. M:-0.0308 c. 1689: 212 287 202 287 212 287 202 SP T3 SD: 0.0130 c. M: 0.0189 c. 1848: 232 314 221 314 232 314 221 SP T3 SD: 0.0071 c. M:-0.0123 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 10.5889 cents 4 x 5 x 6 x 7:8 S SD: 23.3134 cents 5 x 6:7 x 8:9:10 S SD: 21.6108 cents 6 x 7:8:9:10:11:12 S SD: 15.5877 cents 7:8 x 9 x 11:13:14 SD: 24.9763 cents 8:9:10:11:12:13:15:16 SD: 12.6490 cents 10:11:12:13:15:16:18:20 SD: 11.6659 cents 12:13:15:16:18:20:22:24 SD: 6.7230 cents 18:20:22:24:27:29:33:36 SD: 6.1212 cents 21:23:26:28:32:34:39:42 SD: 5.6993 cents 22:24:27:29:33:36:41:44 SD: 4.1471 cents 30:33:37:40:45:49:55:60 SD: 2.6357 cents 36:39:44:48:54:59:66:72 SD: 2.2795 cents 44:48:54:59:66:72:81:88 SD: 1.4012 cents 66:72:81:88:99:108:122:132 SD: 1.0157 cents 88:96:108:117:132:144:162:176 SD: 0.7036 cents 120:131:147:160:180:196:221:240 SD: 0.6783 cents 132:144:162:176:198:216:243:264 SD: 0.0000 cents