Scala analysis: xen15-chalmers-triadic-reversed-diamond-11-9
Triadic reversed diamond for M=11/9, D=3/2
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: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 18/11 852.592059 undecimal neutral 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: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 121/108 196.7709 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 121/108 196.7709 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 121/108 196.771 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 4 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 4 4/3 498.045 cents perfect fourth 3: 1 162/121 505.184 cents 3: 2 11/8 551.318 cents undecimal semi-augmented fourth 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 121/81 694.816 cents two (undecimal neutral third) 4: 4 3/2 701.955 cents perfect fifth 5: 2 44/27 845.453 cents neutral sixth 5: 4 18/11 852.592 cents undecimal neutral sixth 5: 1 121/72 898.726 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 216/121 1003.229 cents 6: 4 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 : 150.6 347.4 498.0 702.0 852.6 1049.4 1200.0 150.6 : 196.8 347.4 551.3 702.0 898.7 1049.4 1200.0 347.4 : 150.6 354.5 505.2 702.0 852.6 1003.2 1200.0 498.0 : 203.9 354.5 551.3 702.0 852.6 1049.4 1200.0 702.0 : 150.6 347.4 498.0 648.7 845.5 996.1 1200.0 852.6 : 196.8 347.4 498.0 694.8 845.5 1049.4 1200.0 1049.4: 150.6 301.3 498.0 648.7 852.6 1003.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 203.9100 cents 33/32, 53.2729 cents 12/11, 150.6371 cents 2: 301.2741 .. 354.5471 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 88/81, 143.4979 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 845.4529 .. 898.7259 cents 33/32, 53.2729 cents 88/81, 143.4979 cents 6: 996.0900 .. 1049.3629 cents 33/32, 53.2729 cents 128/121, 97.3641 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 : 9/8, 203.9100 cents Average / Smallest step : 1.138024 Largest / Average step : 1.189475 Largest / Smallest step : 1.353651 Median interval of one step : 12/11, 150.6371 cents, amount: 4 Most common interval of one step : 12/11, 150.6371 cents, amount: 4 Least squares average step : 172.18961 cents, oct.: 1205.32729 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SMSLSMS Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.243496 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.733635 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 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 Number of recognisable fifths : 5, average 700.5272 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 is a complete diamond : 3 9 11 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 11 Odd number limit : 121 (O: 121 U: 121) Highest odd numerator or denominator: 11 Scale harmonicity : 0.019988 Average absolute harmonicity : 0.237123 Specific harmonicity : 0.107799 Fundamental : 1/198, -7.6294 octaves, 1.3213 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 7.840800E+04, 16.25871 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 52.0, average 7.42857 Mersenne's string divisions : 4762380 Sum of van Prooijen's expressibility: 5.11981, average 0.73140 Sum of Tenney's harmonic distance : 10.39078, average 1.48440 Vogel's harmonic complexity : 18.57143 Wille's k value : 181 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 71.74955, average 2.56248 Lattice compactness (without 2's) : 52.73791, average 1.88350 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -2 .. 2 0.00000 8 2 11: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 25| Scale is weakly epimorphic with val: <7 10 26| Scale is weakly epimorphic with val: <7 11 23| 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: 14.3104 c. M:-20.7915 c. Lebeng 17: 2 3 2 3 2 3 2 SP M ME I SD: 6.2231 c. M:-9.4606 c. Neutral Dorian, Maqamic-7 24: 3 4 3 4 3 4 3 SP M ME I SD: 1.7685 c. M: 2.5921 c. Neutral Dorian, Misaelides 2nd Byzantine mode, Iced Fridgian, Maqam Sikah Baladi, Maqamic-7 87: 11 14 11 15 11 14 11 SP T3 I SD: 1.6962 c. M: 2.5804 c. 104: 13 17 13 18 13 17 13 SP T3 I SD: 1.2598 c. M:-1.8912 c. 111: 14 18 14 19 14 18 14 SP T3 I SD: 0.9572 c. M: 1.4620 c. 128: 16 21 16 22 16 21 16 SP T3 I SD: 0.7670 c. M:-1.1700 c. 135: 17 22 17 23 17 22 17 SP T3 I SD: 0.4915 c. M: 0.7413 c. 152: 19 25 19 26 19 25 19 SP T3 I SD: 0.4972 c. M: 0.6766 c. 159: 20 26 20 27 20 26 20 SP T3 I SD: 0.2106 c. M:-0.3063 c. 183: 23 30 23 31 23 30 23 SP T3 I SD: 0.2075 c. M:-0.3157 c. 311: 39 51 39 53 39 51 39 SP T3 I SD: 0.1937 c. M:-0.2958 c. 335: 42 55 42 57 42 55 42 SP T3 I SD: 0.1275 c. M:-0.1893 c. 470: 59 77 59 80 59 77 59 SP T3 I SD: 0.1310 c. M: 0.1739 c. 494: 62 81 62 84 62 81 62 SP T3 I SD: 0.0455 c. M:-0.0693 c. 677: 85 111 85 115 85 111 85 SP T3 I SD: 0.0240 c. M:-0.0348 c. 1171: 147 192 147 199 147 192 147 SP T3 I SD: 0.0085 c. M: 0.0126 c. 1848: 232 303 232 314 232 303 232 SP T3 I SD: 0.0081 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: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 20.6559 cents 6 x 7:8:9:10:11:12 S SD: 14.4293 cents 7:8 x 9 x 11:13:14 SD: 25.1899 cents 8:9:10:11:12:13:15:16 SD: 13.4384 cents 9:10:11:12:14:15:17:18 SD: 13.2891 cents 10:11:12:13:15:16:18:20 SD: 10.7471 cents 12:13:15:16:18:20:22:24 SD: 7.3794 cents 14:15:17:19:21:23:26:28 SD: 7.2636 cents 18:20:22:24:27:29:33:36 SD: 5.9489 cents 22:24:27:29:33:36:40:44 SD: 3.6390 cents 30:33:37:40:45:49:55:60 SD: 3.0712 cents 36:39:44:48:54:59:66:72 SD: 1.7652 cents 54:59:66:72:81:88:99:108 SD: 1.0888 cents 66:72:81:88:99:108:121:132 SD: 1.0199 cents 90:98:110:120:135:147:165:180 SD: 0.6483 cents 108:118:132:144:162:177:198:216 SD: 0.5393 cents 132:144:161:176:198:216:242:264 SD: 0.5115 cents 144:157:176:192:216:236:264:288 SD: 0.4074 cents 162:177:198:216:243:265:297:324 SD: 0.3907 cents 198:216:242:264:297:324:363:396 SD: 0.0000 cents