Scala analysis: xen09-wilson-marwa-13-08
Marwa permutation 8 from Figure 13, Al-Farabi 10/9 10/9 27/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 36/25 631.282574 classic diminished fifth 5: 8/5 813.686286 minor sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 10/9 182.4037 minor whole tone 3: 10/9 182.4037 minor whole tone 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.4037 minor whole tone 6: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 4 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 3 6/5 315.641 cents minor third 2: 1 243/200 337.148 cents acute minor third 2: 2 100/81 364.807 cents grave major third 2: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 81/50 835.193 cents acute minor sixth 5: 1 400/243 862.852 cents grave major sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 50/27 1066.762 cents grave major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 133.2 315.6 498.0 631.3 813.7 996.1 1200.0 133.2 : 182.4 364.8 498.0 680.4 862.9 1066.8 1200.0 315.6 : 182.4 315.6 498.0 680.4 884.4 1017.6 1200.0 498.0 : 133.2 315.6 498.0 702.0 835.2 1017.6 1200.0 631.3 : 182.4 364.8 568.7 702.0 884.4 1066.8 1200.0 813.7 : 182.4 386.3 519.6 702.0 884.4 1017.6 1200.0 996.1 : 203.9 337.1 519.6 702.0 835.2 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 203.9100 cents 25/24, 70.6724 cents 27/25, 133.2376 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 498.0450 .. 568.7174 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 4: 631.2826 .. 701.9550 cents 25/24, 70.6724 cents 648/625, 62.5651 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1066.7624 cents 25/24, 70.6724 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.286638 Largest / Average step : 1.189475 Largest / Smallest step : 1.530424 Median interval of one step : 10/9, 182.4037 cents, amount: 4 Most common interval of one step : 10/9, 182.4037 cents, amount: 4 Least squares average step : 165.91969 cents, oct.: 1161.43784 cents Scale is strictly proper Step pattern alph. order: ABBABBC Step pattern size order : SMMSMML Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.349275 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.646638 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Most common triad is 0.0 701.955 1017.596 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is 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 70.6724 cents: 4 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.033186 Average absolute harmonicity : 0.232127 Specific harmonicity : 0.174133 Fundamental : 1/225, -7.8138 octaves, 1.1628 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 9.720000E+04, 16.56867 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 86.0, average 12.28571 Mersenne's string divisions : 18318300 Sum of van Prooijen's expressibility: 5.65861, average 0.80837 Sum of Tenney's harmonic distance : 12.40130, average 1.77161 Vogel's harmonic complexity : 14.85714 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 83.88367, average 2.99585 Lattice compactness (without 2's) : 62.72863, average 2.24031 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.85714 13 1 3: -2 .. 3 0.42857 9 2 5: -2 .. 0 -0.85714 6 4 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 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: 34.5777 c. M:-54.4317 c. Lebeng 10: 1 2 1 1 2 1 2 P M ME S SD: 27.8825 c. M:-44.3587 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 19.0278 c. M: 33.2376 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 16: 2 2 3 1 3 2 3 P D3 SD: 20.0128 c. M: 31.2826 c. 17: 2 2 3 2 3 2 3 SP M ME S SD: 18.4316 c. M:-33.3725 c. Safi al-Din's maqam Higazi 19: 2 3 3 2 3 3 3 SP M ME S SD: 7.1991 c. M:-14.4363 c. Nineteen-tone Locrian 33: 4 5 5 3 5 5 6 SP SD: 11.7667 c. M: 14.2718 c. 34: 4 5 5 4 5 5 6 SP T3 SD: 4.8396 c. M:-7.9389 c. 46: 5 7 7 5 7 7 8 SP SD: 3.6865 c. M: 5.1956 c. 53: 6 8 8 6 8 8 9 SP SD: 1.5947 c. M:-2.6797 c. 99: 11 15 15 11 15 15 17 SP SD: 1.1612 c. M: 2.1506 c. 118: 13 18 18 13 18 18 20 SP SD: 0.5572 c. M: 1.0342 c. 171: 19 26 26 19 26 26 29 SP SD: 0.2512 c. M:-0.4012 c. 289: 32 44 44 32 44 44 49 SP SD: 0.2493 c. M:-0.4498 c. 388: 43 59 59 43 59 59 66 SP SD: 0.2257 c. M: 0.3547 c. 441: 49 67 67 49 67 67 75 SP SD: 0.0867 c. M: 0.1716 c. 559: 62 85 85 62 85 85 95 SP SD: 0.0923 c. M: 0.1556 c. 612: 68 93 93 68 93 93 104 SP SD: 0.0548 c. M:-0.0958 c. 730: 81 111 111 81 111 111 124 SP SD: 0.0503 c. M: 0.0869 c. 1171: 130 178 178 130 178 178 199 SP SD: 0.0177 c. M: 0.0272 c. 1783: 198 271 271 198 271 271 303 SP SD: 0.0118 c. M:-0.0210 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 25.8995 cents 5 x 6 x 7:8:9:10 S SD: 10.6603 cents 6 x 7:8:9:10:11:12 S SD: 20.5519 cents 7 x 8:9:10:11:12:14 S SD: 21.2304 cents 8:9:10:11:12:13:14:16 S SD: 19.8389 cents 9:10:11:12:13:14:16:18 S SD: 10.9110 cents 10:11:12:13:14:16:18:20 S SD: 10.8528 cents 12:13:14:16:17:19:21:24 SD: 9.3447 cents 13:14:16:17:19:21:23:26 SD: 9.1254 cents 14:15:17:19:20:22:25:28 SD: 7.5212 cents 15:16:18:20:22:24:27:30 S SD: 6.2827 cents 21:23:25:28:30:34:37:42 SD: 5.7672 cents 23:25:28:31:33:37:41:46 SD: 5.0386 cents 24:26:29:32:35:38:43:48 SD: 4.8694 cents 25:27:30:33:36:40:44:50 SD: 3.5152 cents 35:38:42:47:50:56:62:70 SD: 3.0771 cents 36:39:43:48:52:58:64:72 SD: 2.3256 cents 45:49:54:60:65:72:80:90 SD: 2.1658 cents 50:54:60:67:72:80:89:100 SD: 1.2716 cents 75:81:90:100:108:120:133:150 SD: 0.6191 cents 125:135:150:167:180:200:222:250 SD: 0.5526 cents 150:162:180:200:216:240:267:300 SD: 0.3090 cents 225:243:270:300:324:360:400:450 SD: 0.0000 cents