Scala analysis: xen09-wilson-marwa-10-13
Marwa permutation 13 from Figure 10, Ptolemy 7/6 12/11 22/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 11/7 782.492036 undecimal augmented fifth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 22/21 80.5370 undecimal minor semitone 2: 9/8 203.9100 major whole tone 3: 112/99 213.5980 4: 9/8 203.9100 major whole tone 5: 22/21 80.5370 undecimal minor semitone 6: 7/6 266.8709 septimal minor third 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 2 33/28 284.447 cents undecimal minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 3 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 3 11/7 782.492 cents undecimal augmented fifth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 2 56/33 915.553 cents 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 1 99/56 986.402 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 80.5 284.4 498.0 702.0 782.5 1049.4 1200.0 80.5 : 203.9 417.5 621.4 702.0 968.8 1119.5 1200.0 284.4 : 213.6 417.5 498.0 764.9 915.6 996.1 1200.0 498.0 : 203.9 284.4 551.3 702.0 782.5 986.4 1200.0 702.0 : 80.5 347.4 498.0 578.6 782.5 996.1 1200.0 782.5 : 266.9 417.5 498.0 702.0 915.6 1119.5 1200.0 1049.4: 150.6 231.2 435.1 648.7 852.6 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 231.1741 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.556747 Largest / Smallest step : 3.313642 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 168.28589 cents, oct.: 1178.00120 cents Scale is not proper Step pattern alph. order: ABCBADE Step pattern size order : ACDCAEB Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.570782 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 896/891, 9.6880 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% 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 class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.232744 Specific harmonicity : 0.114042 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 77.0, average 11.00000 Mersenne's string divisions : 28092330 Sum of van Prooijen's expressibility: 5.87776, average 0.83968 Sum of Tenney's harmonic distance : 11.49471, average 1.64210 Vogel's harmonic complexity : 14.85714 Wille's k value : 49 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 64.11016, average 2.28965 Lattice compactness (without 2's) : 41.66292, average 1.48796 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 8 1 3: -1 .. 1 -0.14286 5 2 7: -1 .. 0 -0.42857 3 11: 0 .. 1 0.57143 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 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 48.4481 c. M: 80.5370 c. 8: 1 1 1 2 0 2 1 P D3 S SD: 39.1696 c. M:-69.4630 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 29.7611 c. M:-52.7963 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 21.9466 c. M: 49.3629 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 14: 1 2 3 2 1 3 2 P T3 SD: 16.2768 c. M: 27.3042 c. 17: 1 3 3 3 1 4 2 N SD: 6.0942 c. M: 9.9488 c. 31: 2 5 6 5 2 7 4 N SD: 6.8828 c. M: 13.4793 c. 41: 3 7 7 7 3 9 5 N SD: 5.3407 c. M:-8.2359 c. 46: 3 8 8 8 3 10 6 N SD: 2.8679 c. M: 5.8847 c. 58: 4 10 10 10 4 13 7 N SD: 3.4655 c. M:-5.8095 c. 63: 4 11 11 11 4 14 8 N SD: 2.4398 c. M: 4.3466 c. 72: 5 12 13 12 5 16 9 N SD: 1.5954 c. M:-2.7963 c. 89: 6 15 16 15 6 20 11 N SD: 1.1225 c. M:-2.3225 c. 118: 8 20 21 20 8 26 15 N SD: 0.8313 c. M: 1.9053 c. 135: 9 23 24 23 9 30 17 N SD: 0.3227 c. M: 0.5370 c. 342: 23 58 61 58 23 76 43 N SD: 0.1783 c. M: 0.2401 c. 477: 32 81 85 81 32 106 60 N SD: 0.1433 c. M: 0.3063 c. 701: 47 119 125 119 47 156 88 N SD: 0.1408 c. M: 0.2816 c. 836: 56 142 149 142 56 186 105 N SD: 0.1351 c. M: 0.2365 c. 877: 59 149 156 149 59 195 110 N SD: 0.1251 c. M:-0.1927 c. 1012: 68 172 180 172 68 225 127 N SD: 0.0798 c. M:-0.1379 c. 1147: 77 195 204 195 77 255 144 N SD: 0.0604 c. M:-0.1214 c. 1236: 83 210 220 210 83 275 155 N SD: 0.0619 c. M:-0.1516 c. 1282: 86 218 228 218 86 285 161 N SD: 0.0647 c. M:-0.1083 c. 1354: 91 230 241 230 91 301 170 N SD: 0.0584 c. M:-0.1129 c. 1371: 92 233 244 233 92 305 172 N SD: 0.0357 c. M:-0.0900 c. 1489: 100 253 265 253 100 331 187 N SD: 0.0403 c. M: 0.0681 c. 1506: 101 256 268 256 101 335 189 N SD: 0.0348 c. M: 0.0589 c. 1713: 115 291 305 291 115 381 215 N SD: 0.0237 c. M: 0.0337 c. 1848: 124 314 329 314 124 411 232 N SD: 0.0175 c. M: 0.0315 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 5 x 6 S SD: 33.9556 cents 4 x 5 x 6 x 7:8 S SD: 32.4644 cents 5 x 6:7 x 8:9:10 S SD: 20.0898 cents 6 x 7:8:9 x 11:12 SD: 3.5152 cents 7 x 8:9 x 11:13:14 SD: 17.0893 cents 8 x 9:11:12:13:15:16 SD: 19.8648 cents 9:10:11:12 x 14:17:18 SD: 21.9348 cents 10:11:12:13:15:16:18:20 SD: 15.6565 cents 11:12:13:15 x 17:20:22 SD: 14.4235 cents 12:13:14:16:18:19:22:24 SD: 8.8615 cents 13:14:15:17 x 20:24:26 SD: 13.1777 cents 14:15:17:19:21:22:26:28 SD: 10.7121 cents 15:16:18:20:23:24:28:30 SD: 10.4395 cents 16:17:19:21:24:25:29:32 SD: 6.3873 cents 18:19:21:24:27:28:33:36 SD: 4.0116 cents 24:25:28:32:36:38:44:48 SD: 3.4314 cents 38:40:45:51:57:60:70:76 SD: 2.8644 cents 40:42:47:53:60:63:73:80 SD: 2.2063 cents 44:46:52:59:66:69:81:88 SD: 1.9975 cents 56:59:66:75:84:88:103:112 SD: 1.9544 cents 60:63:71:80:90:94:110:120 SD: 1.3686 cents 66:69:78:88:99:104:121:132 SD: 1.0897 cents 84:88:99:112:126:132:154:168 SD: 0.0000 cents