Scala analysis: xen15-chalmers-triadic-diamond-7-6
Triadic diamond for M=7/6, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor sixth 6: 12/7 933.129094 septimal major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 7/6 266.8709 septimal minor third 2: 54/49 168.2132 Zalzal's mujannab 3: 28/27 62.9609 Archytas' 1/3-tone 4: 9/8 203.9100 major whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 54/49 168.2132 Zalzal's mujannab 7: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 54/49 168.213 cents Zalzal's mujannab 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 49/36 533.742 cents Arabic lute acute fourth 3: 1 98/81 329.832 cents 3: 2 9/7 435.084 cents septimal major third, BP third 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 2 14/9 764.916 cents septimal minor sixth 4: 1 81/49 870.168 cents two (septimal major third, BP third) 5: 1 72/49 666.258 cents Arabic lute grave fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 2 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 49/27 1031.787 cents 6: 2 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 266.9 435.1 498.0 702.0 764.9 933.1 1200.0 266.9 : 168.2 231.2 435.1 498.0 666.3 933.1 1200.0 435.1 : 63.0 266.9 329.8 498.0 764.9 1031.8 1200.0 498.0 : 203.9 266.9 435.1 702.0 968.8 1137.0 1200.0 702.0 : 63.0 231.2 498.0 764.9 933.1 996.1 1200.0 764.9 : 168.2 435.1 702.0 870.2 933.1 1137.0 1200.0 933.1 : 266.9 533.7 702.0 764.9 968.8 1031.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 266.8709 cents 9/8, 203.9100 cents 28/27, 62.9609 cents 2: 231.1741 .. 533.7418 cents 343/288, 302.5677 cents 48/49,-35.6968 cents 3: 329.8318 .. 701.9550 cents 243/196, 372.1232 cents 8/9,-203.9100 cents 4: 498.0450 .. 870.1682 cents 243/196, 372.1232 cents 8/9,-203.9100 cents 5: 666.2582 .. 968.8259 cents 343/288, 302.5677 cents 8/9,-203.9100 cents 6: 933.1291 .. 1137.0391 cents 9/8, 203.9100 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.722778 Largest / Average step : 1.556747 Largest / Smallest step : 4.238677 Median interval of one step : 54/49, 168.2132 cents, amount: 2 Least squares average step : 166.15963 cents, oct.: 1163.11741 cents Scale is not proper Scale is a mode of a 1277-tone equal temperament with octave 2/1 degrees: 284 463 530 747 814 993 1277 Least number of segments generator : 639 of 600.470 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 700 of 657.792 cents and inv. generated superset size: 69 = 62 more = 985.714% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCBA Step pattern size order : DBACABD Scale is not a Constant Structure Scale diversity : 1.398184 Lumma stability : 0.104935 Lumma impropriety factor : 0.509775 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 64/63, 27.2641 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 3 7 9 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 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 9 Scale harmonicity : 0.029207 Average absolute harmonicity : 0.249965 Specific harmonicity : 0.158341 Fundamental : 1/126, -6.9773 octaves, 2.0764 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 3.175200E+04, 14.95456 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 43.0, average 6.14286 Mersenne's string divisions : 9544080 Sum of van Prooijen's expressibility: 4.55292, average 0.65042 Sum of Tenney's harmonic distance : 9.60560, average 1.37223 Vogel's harmonic complexity : 14.57143 Wille's k value : 94 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 72.04555, average 2.57306 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 7: -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 18| Scale is weakly epimorphic with val: <7 10 19| Scale is weakly epimorphic with val: <7 12 20|
FIT/MODE
7: 2 1 0 1 0 1 2 N I SD: 59.3069 c. M: 79.2016 c. 8: 2 1 0 2 0 1 2 N I SD: 32.1974 c. M:-48.0450 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 26.5986 c. M:-35.2883 c. 12: 3 1 1 2 1 1 3 N I SD: 25.8139 c. M: 35.0841 c. Mela Yagapriya, Raga Kalahamsa 13: 3 2 0 3 0 2 3 N I SD: 24.6901 c. M:-36.5065 c. 14: 3 2 1 2 1 2 3 N G I SD: 10.7013 c. M:-16.2407 c. 17: 4 2 1 3 1 2 4 N I SD: 10.5374 c. M: 15.4820 c. 19: 4 3 1 3 1 3 4 N G I SD: 9.3221 c. M: 14.2393 c. 22: 5 3 1 4 1 3 5 N I SD: 4.9816 c. M:-7.1359 c. 36: 8 5 2 6 2 5 8 N I SD: 1.4070 c. M: 1.9550 c. 77: 17 11 4 13 4 11 17 N I SD: 1.2890 c. M:-1.9358 c. 94: 21 13 5 16 5 13 21 N I SD: 0.8601 c. M: 1.2142 c. 130: 29 18 7 22 7 18 29 N I SD: 0.8247 c. M: 1.2379 c. 135: 30 19 7 23 7 19 30 N I SD: 0.3096 c. M: 0.4715 c. 171: 38 24 9 29 9 24 38 N I SD: 0.1530 c. M: 0.2042 c. 400: 89 56 21 68 21 56 89 N I SD: 0.0858 c. M: 0.1291 c. 535: 119 75 28 91 28 75 119 N I SD: 0.0663 c. M:-0.1011 c. 571: 127 80 30 97 30 80 127 N I SD: 0.0379 c. M: 0.0578 c. 706: 157 99 37 120 37 99 157 N I SD: 0.0288 c. M: 0.0434 c. 1106: 246 155 58 188 58 155 246 N I SD: 0.0269 c. M: 0.0369 c. 1277: 284 179 67 217 67 179 284 N I SD: 0.0030 c. M: 0.0046 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 x 5:6 S SD: 16.2568 cents 4 x 5 x 6 x 7:8 S SD: 15.1096 cents 5:6 x 7 x 8:9:10 S SD: 27.5873 cents 6:7 x 8:9 x 10:12 S SD: 9.7541 cents 7:8:9 x x 11:12:14 SD: 7.9578 cents 8:9:10:11:12 x 14:16 S SD: 17.0415 cents 9:11 x 12 x 14:15:18 SD: 18.8306 cents 10:12:13 x 15:16:17:20 SD: 12.1712 cents 11:13:14:15 x 17:19:22 SD: 8.5302 cents 13:15:17 x x 20:22:26 SD: 9.1476 cents 14:16:18:19:21:22:24:28 SD: 7.1744 cents 15:18:19:20 x 23:26:30 SD: 10.5839 cents 16:19 x 21:24:25:27:32 SD: 8.3084 cents 17:20:22:23 x 26:29:34 SD: 7.2826 cents 18:21:23:24:27:28:31:36 SD: 1.9105 cents 42:49:54:56:63:65:72:84 SD: 1.2651 cents 60:70:77:80:90:93:103:120 SD: 1.0540 cents 66:77:85:88:99:103:113:132 SD: 0.9557 cents 84:98:108:112:126:131:144:168 SD: 0.6301 cents 102:119:131:136:153:159:175:204 SD: 0.6187 cents 108:126:139:144:162:168:185:216 SD: 0.3180 cents 126:147:162:168:189:196:216:252 SD: 0.0000 cents