Scala analysis: xen09-wilson-marwa-13-05
Marwa permutation 5 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: 81/50 835.192576 acute minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor 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: 9/8 203.9100 major whole tone 6: 10/9 182.4037 minor whole tone 7: 10/9 182.4037 minor 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 : 133.2 315.6 498.0 631.3 835.2 1017.6 1200.0 133.2 : 182.4 364.8 498.0 702.0 884.4 1066.8 1200.0 315.6 : 182.4 315.6 519.6 702.0 884.4 1017.6 1200.0 498.0 : 133.2 337.1 519.6 702.0 835.2 1017.6 1200.0 631.3 : 203.9 386.3 568.7 702.0 884.4 1066.8 1200.0 835.2 : 182.4 364.8 498.0 680.4 862.9 996.1 1200.0 1017.6: 182.4 315.6 498.0 680.4 813.7 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 : 167.60947 cents, oct.: 1173.26630 cents Scale is strictly proper Step pattern alph. order: ABBACBB Step pattern size order : SMMSLMM Scale is sum-free (all different intervals) 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 0.0 182.404 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord 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 4 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 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: 81 Scale harmonicity : 0.034325 Average absolute harmonicity : 0.219638 Specific harmonicity : 0.168865 Fundamental : 1/150, -7.2288 octaves, 1.7442 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 4.860000E+04, 15.56867 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 139.5, average 19.92857 Mersenne's string divisions : 95987892 Sum of van Prooijen's expressibility: 6.86812, average 0.98116 Sum of Tenney's harmonic distance : 13.90155, average 1.98594 Vogel's harmonic complexity : 13.71429 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 79.32808, average 2.83315 Lattice compactness (without 2's) : 66.43683, average 2.37274 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.71429 7 1 3: -1 .. 4 1.57143 13 1 5: -2 .. 0 -1.14286 8 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 21 / 7 = 3.00000 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: 29.3455 c. M:-54.4317 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 34.9331 c. M:-49.0704 c. 11: 1 2 2 1 2 1 2 P M ME S SD: 29.7516 c. M:-47.4095 c. Orgone-7 12: 1 2 2 1 2 2 2 P M ME S SD: 23.5431 c. M: 35.1926 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 15: 2 2 2 2 2 3 2 SP M ME S SD: 20.2741 c. M: 35.1926 c. 17: 2 2 3 2 3 2 3 SP M ME S SD: 17.7504 c. M: 33.2883 c. Safi al-Din's maqam Higazi 19: 2 3 3 2 3 3 3 SP M ME S SD: 7.0715 c. M: 14.1399 c. Nineteen-tone Locrian 26: 3 4 4 3 4 4 4 SP M ME S SD: 7.7576 c. M:-14.8713 c. 27: 3 4 4 3 5 4 4 SP T3 SD: 6.4747 c. M:-9.2519 c. 34: 4 5 5 4 6 5 5 SP T3 SD: 6.2630 c. M:-11.8662 c. 45: 5 7 7 5 7 7 7 SP M DE S SD: 6.0968 c. M:-8.7174 c. 46: 5 7 7 5 8 7 7 SP SD: 2.6059 c. M: 5.1956 c. 53: 6 8 8 6 9 8 8 SP SD: 1.8472 c. M:-2.6797 c. 72: 8 11 11 8 12 11 11 SP SD: 1.3841 c. M:-2.0508 c. 99: 11 15 15 11 17 15 15 SP SD: 0.7634 c. M:-1.1711 c. 118: 13 18 18 13 20 18 18 SP SD: 0.7541 c. M: 1.2943 c. 171: 19 26 26 19 29 26 26 SP SD: 0.1572 c. M:-0.2964 c. 441: 49 67 67 49 75 67 67 SP SD: 0.0909 c. M:-0.1816 c. 559: 62 85 85 62 95 85 85 SP SD: 0.1014 c. M: 0.1556 c. 612: 68 93 93 68 104 93 93 SP SD: 0.0678 c. M:-0.1015 c. 730: 81 111 111 81 124 111 111 SP SD: 0.0668 c. M: 0.1241 c. 901: 100 137 137 100 153 137 137 SP SD: 0.0607 c. M: 0.1204 c. 1000: 111 152 152 111 170 152 152 SP SD: 0.0415 c. M: 0.0826 c. 1171: 130 178 178 130 199 178 178 SP SD: 0.0143 c. M: 0.0272 c. 1342: 149 204 204 149 228 204 204 SP SD: 0.0127 c. M: 0.0212 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: 16.3887 cents 4 x 5 x 6 x 7:8 S SD: 27.8026 cents 5 x 6 x 7:8:9:10 S SD: 10.6603 cents 6 x 7:8:9:10:11:12 S SD: 17.3202 cents 7 x 8:9:10:11:13:14 SD: 21.7267 cents 8:9:10:11:12:13:14:16 S SD: 20.3183 cents 9:10:11:12:13:15:16:18 SD: 11.3701 cents 10:11:12:13:14:16:18:20 S SD: 10.8528 cents 11:12:13:15:16:18:20:22 SD: 8.3584 cents 14:15:17:19:20:23:25:28 SD: 7.1684 cents 15:16:18:20:22:24:27:30 S SD: 6.2827 cents 21:23:25:28:30:34:38:42 SD: 4.6367 cents 24:26:29:32:35:39:43:48 SD: 3.8985 cents 30:32:36:40:43:49:54:60 SD: 3.8556 cents 34:37:41:45:49:55:61:68 SD: 3.0248 cents 36:39:43:48:52:58:65:72 SD: 2.2162 cents 39:42:47:52:56:63:70:78 SD: 1.7618 cents 50:54:60:67:72:81:90:100 SD: 1.2335 cents 75:81:90:100:108:122:135:150 SD: 1.0157 cents 84:91:101:112:121:136:151:168 SD: 0.9779 cents 90:97:108:120:130:146:162:180 SD: 0.9774 cents 100:108:120:133:144:162:180:200 SD: 0.6191 cents 111:120:133:148:160:180:200:222 SD: 0.6189 cents 150:162:180:200:216:243:270:300 SD: 0.0000 cents