Scala analysis: xen09-wilson-marwa-03-01
Marwa permutation 1 from Figure 3, Ptolemy 16/15 9/8 10/9
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: 81/64 407.820003 Pythagorean major third 3: 45/32 590.223716 diatonic tritone 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 243/128 1109.775004 Pythagorean major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 10/9 182.4037 minor whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 9/8 203.9100 major whole tone 6: 9/8 203.9100 major whole tone 7: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 4 9/8 203.910 cents major whole tone 2: 3 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 2 81/64 407.820 cents Pythagorean major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 40/27 680.449 cents grave fifth 4: 5 3/2 701.955 cents perfect fifth 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.66667 = 11/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 407.8 590.2 702.0 905.9 1109.8 1200.0 203.9 : 203.9 386.3 498.0 702.0 905.9 996.1 1200.0 407.8 : 182.4 294.1 498.0 702.0 792.2 996.1 1200.0 590.2 : 111.7 315.6 519.6 609.8 813.7 1017.6 1200.0 702.0 : 203.9 407.8 498.0 702.0 905.9 1088.3 1200.0 905.9 : 203.9 294.1 498.0 702.0 884.4 996.1 1200.0 1109.8: 90.2 294.1 498.0 680.4 792.2 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1109.7750 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.900012 Largest / Average step : 1.189475 Largest / Smallest step : 2.260017 Median interval of one step : 9/8, 203.9100 cents, amount: 4 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 179.90012 cents, oct.: 1259.30081 cents Scale is strictly proper Step pattern alph. order: AABCAAD Step pattern size order : DDCBDDA Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.461397 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.467419 Rothenberg efficiency : 0.496599 redundancy: 0.503401 Efficiency x scale size : 3.476190 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.66667 = 11/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Scale contains two identical disjunct "tetrachords" of 3 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 113.6850 cents: 3 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.036058 Average absolute harmonicity : 0.235000 Specific harmonicity : 0.208831 Fundamental : 1/128, -7.0000 octaves, 2.0439 Hz. Guide tone : 2430, 11.2467 octaves, 635750.124 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 330.5, average 47.21429 Mersenne's string divisions : 1297696785 Sum of van Prooijen's expressibility: 8.81003, average 1.25858 Sum of Tenney's harmonic distance : 16.93784, average 2.41969 Vogel's harmonic complexity : 11.42857 Wille's k value : 121 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 119.31012, average 4.26108 Lattice compactness (without 2's) : 63.69891, average 2.27496 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -3.57143 27 1 3: 0 .. 5 2.42857 17 5 5: 0 .. 1 0.14286 1 1 Average exponent except 2's : 18 / 7 = 2.57143 Average absolute exponent except 2's: 18 / 7 = 2.57143 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: 53.8164 c. M: 81.2036 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 39.0911 c. M: 59.7750 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 33.4399 c. M:-54.1350 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 6.6094 c. M:-9.7763 c. G.Hypolydian, M.Lydian, G.M.Hypolocrian, Rut biscale ascending, Kalyan That (Yaman), Mela Mecakalyani, Raga Chandrakant, Malarani, Shuddh Kalyan, Ping, Kung, Gu: China 29: 5 5 4 3 5 5 2 SP SD: 5.8766 c. M: 10.9134 c. 41: 7 7 6 4 7 7 3 SP SD: 2.2830 c. M: 4.8579 c. 53: 9 9 8 5 9 9 4 SP SD: 0.6143 c. M: 1.5445 c. 118: 20 20 18 11 20 20 9 SP SD: 0.7440 c. M: 1.3004 c. 171: 29 29 26 16 29 29 13 SP SD: 0.6298 c. M: 1.0031 c. 224: 38 38 34 21 38 38 17 SP SD: 0.5923 c. M: 0.9380 c. 277: 47 47 42 26 47 47 21 SP SD: 0.5791 c. M: 1.0540 c. 330: 56 56 50 31 56 56 25 SP SD: 0.5748 c. M: 1.1328 c. 335: 57 57 51 31 57 57 25 SP SD: 0.4884 c. M:-0.8211 c. 347: 59 59 53 32 59 59 26 SP SD: 0.4617 c. M:-1.1308 c. 388: 66 66 59 36 66 66 29 SP SD: 0.3537 c. M:-0.5343 c. 400: 68 68 61 37 68 68 30 SP SD: 0.3194 c. M:-0.7763 c. 441: 75 75 67 41 75 75 33 SP SD: 0.2588 c. M:-0.4291 c. 453: 77 77 69 42 77 77 34 SP SD: 0.2105 c. M:-0.5048 c. 494: 84 84 75 46 84 84 37 SP SD: 0.1955 c. M:-0.3465 c. 506: 86 86 77 47 86 86 38 SP SD: 0.1248 c. M:-0.2901 c. 547: 93 93 83 51 93 93 41 SP SD: 0.1610 c. M:-0.2798 c. 559: 95 95 85 52 95 95 42 SP SD: 0.0567 c. M:-0.1162 c. 612: 104 104 93 57 104 104 46 SP SD: 0.0193 c. M:-0.0289 c. 2395: 407 407 364 223 407 407 180 SP SD: 0.0209 c. M:-0.0371 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 4 x x 5 x 6 S SD: 30.9176 cents 4 x 5 x 6:7 x 8 S SD: 16.6332 cents 5 x 6:7 x 8 x 10 S SD: 32.6471 cents 6:7:8 x 9:10:11:12 S SD: 21.2242 cents 7:8:9:10:11:12:13:14 H SD: 14.9210 cents 8:9:10:11:12:14:15:16 S SD: 11.4310 cents 10:11:13:14:15:17:19:20 SD: 8.9109 cents 14:16:18:20:21:24:27:28 S SD: 8.7092 cents 15:17:19:21:23:25:28:30 SD: 7.8100 cents 16:18:20:23:24:27:30:32 SD: 6.9589 cents 18:20:23:25:27:30:34:36 SD: 5.9547 cents 22:25:28:31:33:37:42:44 SD: 3.3097 cents 30:34:38:42:45:51:57:60 SD: 2.8212 cents 38:43:48:53:57:64:72:76 SD: 2.6291 cents 42:47:53:59:63:71:80:84 SD: 1.7851 cents 56:63:71:79:84:95:106:112 SD: 1.7429 cents 64:72:81:90:96:108:122:128 SD: 1.0157 cents 86:97:109:121:129:145:163:172 SD: 0.8701 cents 98:110:124:138:147:165:186:196 SD: 0.8668 cents 106:119:134:149:159:179:201:212 SD: 0.6900 cents 128:144:162:180:192:216:243:256 SD: 0.0000 cents