Scala analysis: xen03-colvig-gamelan-7-11
Colvig's American Gamelan 7-11 scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 11/8 551.317942 undecimal semi-augmented fourth 3: 3/2 701.955001 perfect fifth 4: 7/4 968.825906 harmonic seventh 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 9/8 203.9100 major whole tone 2: 11/9 347.4079 undecimal neutral third 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 7/6 266.8709 septimal minor third 5: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 2 4/3 498.045 cents perfect fourth 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 2 3/2 701.955 cents perfect fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 11/7 782.492 cents undecimal augmented fifth 4: 1 18/11 852.592 cents undecimal neutral sixth 4: 1 12/7 933.129 cents septimal major sixth 4: 1 7/4 968.826 cents harmonic seventh 4: 1 16/9 996.090 cents Pythagorean minor seventh 4: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.50000 = 9/2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 203.9 551.3 702.0 968.8 1200.0 203.9 : 347.4 498.0 764.9 996.1 1200.0 551.3 : 150.6 417.5 648.7 852.6 1200.0 702.0 : 266.9 498.0 702.0 1049.4 1200.0 968.8 : 231.2 435.1 782.5 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 347.4079 cents 121/108, 196.7709 cents 12/11, 150.6371 cents 2: 417.5080 .. 551.3179 cents 121/112, 133.8100 cents 126/121, 70.1000 cents 3: 648.6821 .. 782.4920 cents 121/112, 133.8100 cents 128/121, 97.3641 cents 4: 852.5921 .. 1049.3629 cents 121/108, 196.7709 cents 126/121, 70.1000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 1.593233 Largest / Average step : 1.447533 Largest / Smallest step : 2.306258 Median interval of one step : 8/7, 231.1741 cents, amount: 1 Least squares average step : 241.59481 cents, oct.: 1207.97405 cents Scale is strictly proper Step pattern alph. order: ABCDE Step pattern size order : BEADC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.10002 cents Scale diversity : 1.647401 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.449032 Rothenberg efficiency : 0.440000 redundancy: 0.560000 Efficiency x scale size : 2.200000 Number of different interval sizes : 18 = 4.50000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.50000 = 9/2 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 99/98, 17.5761 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 2 Most common triad is 0.0 498.045 1049.363 cents, amount: 1 Number of recognisable fifths : 2, average 701.9550 cents Best fifths form a closed circle Length of longest harmonic part : 3 at degree 3 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 20.0000% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.304266 Specific harmonicity : 0.173909 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 1386, 10.4367 octaves, 362613.034 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 27.5, average 5.50000 Mersenne's string divisions : 53295 Sum of van Prooijen's expressibility: 3.31785, average 0.66357 Sum of Tenney's harmonic distance : 6.32815, average 1.26563 Vogel's harmonic complexity : 6.80000 Wille's k value : 5 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 38.24691, average 2.54979 Lattice compactness (without 2's) : 19.71478, average 1.31432 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.60000 10 1 3: 0 .. 2 0.60000 3 2 7: 0 .. 1 0.20000 1 1 11: 0 .. 1 0.20000 1 1 Average exponent except 2's : 5 / 5 = 1.00000 Average absolute exponent except 2's: 5 / 5 = 1.00000 Scale is weakly epimorphic with val: <5 7 13 16| Scale is JI-epimorphic with val: <5 8 14 17| = patent
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 36.8572 c. M: 71.3179 c. 7: 1 2 1 2 1 P M ME I SD: 35.3828 c. M:-59.7455 c. Thai mode 2 9: 1 3 1 2 2 P D3 S SD: 39.5209 c. M: 70.5767 c. 10: 2 3 1 2 2 P T3 SD: 28.5515 c. M:-48.6821 c. 11: 2 3 1 3 2 SP D3 I SD: 23.0414 c. M: 47.4095 c. Swooning Rushes 12: 2 4 1 3 2 P SD: 25.9263 c. M:-48.6821 c. 14: 2 4 2 3 3 SP D3 S SD: 25.9406 c. M: 37.0322 c. 15: 3 4 2 3 3 SP T3 SD: 18.8753 c. M:-36.0900 c. 16: 3 4 2 4 3 SP D3 I SD: 19.5044 c. M: 26.9550 c. 17: 3 5 2 4 3 SP SD: 11.2524 c. M:-19.4094 c. 22: 4 6 3 5 4 SP SD: 9.5685 c. M:-14.2718 c. 24: 4 7 3 5 5 SP SD: 8.6633 c. M: 18.8259 c. 31: 5 9 4 7 6 SP SD: 6.6844 c. M: 10.3616 c. 41: 7 12 5 9 8 SP SD: 2.5632 c. M:-4.7796 c. 63: 11 18 8 14 12 SP SD: 3.0756 c. M:-5.6138 c. 72: 12 21 9 16 14 SP SD: 2.2587 c. M: 3.9100 c. 87: 15 25 11 19 17 SP SD: 2.1101 c. M: 3.3087 c. 89: 15 26 11 20 17 SP SD: 1.3801 c. M:-1.9606 c. 94: 16 27 12 21 18 SP SD: 1.2446 c. M: 2.3818 c. 130: 22 38 16 29 25 SP SD: 1.2185 c. M:-2.5282 c. 135: 23 39 17 30 26 SP SD: 0.2842 c. M:-0.5344 c. 342: 58 99 43 76 66 SP SD: 0.3345 c. M: 0.4407 c. 359: 61 104 45 80 69 SP SD: 0.2571 c. M:-0.5334 c. 477: 81 138 60 106 92 SP SD: 0.2181 c. M: 0.3745 c. 494: 84 143 62 110 95 SP SD: 0.1989 c. M:-0.4049 c. 566: 96 164 71 126 109 SP SD: 0.1949 c. M: 0.3764 c. 607: 103 176 76 135 117 SP SD: 0.1894 c. M: 0.2856 c. 612: 104 177 77 136 118 SP SD: 0.1752 c. M: 0.3376 c. 629: 107 182 79 140 121 SP SD: 0.1863 c. M:-0.3315 c. 653: 111 189 82 145 126 SP SD: 0.1706 c. M: 0.3726 c. 701: 119 203 88 156 135 SP SD: 0.1161 c. M: 0.2010 c. 742: 126 215 93 165 143 SP SD: 0.1086 c. M:-0.1645 c. 836: 142 242 105 186 161 SP SD: 0.0758 c. M: 0.1218 c. 877: 149 254 110 195 169 SP SD: 0.0594 c. M:-0.1074 c. 1012: 172 293 127 225 195 SP SD: 0.0428 c. M:-0.0655 c. 1713: 291 496 215 381 330 SP SD: 0.0286 c. M: 0.0571 c. 1848: 314 535 232 411 356 SP SD: 0.0113 c. M: 0.0192 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.0000 cents 3 x 4 x 5:6 S SD: 33.2878 cents 4 x x 6:7:8 S SD: 0.0000 cents