Scala analysis: xen09-wilson-marwa-10-07
Marwa permutation 7 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: 11/8 551.317942 undecimal semi-augmented 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: 7/6 266.8709 septimal minor third 4: 12/11 150.6371 undecimal neutral second, 3/4-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: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 1 33/28 284.447 cents undecimal minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 21/16 470.781 cents narrow fourth 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: 1 32/21 729.219 cents wide fifth 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 56/33 915.553 cents 5: 2 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 80.5 284.4 551.3 702.0 782.5 1049.4 1200.0 80.5 : 203.9 470.8 621.4 702.0 968.8 1119.5 1200.0 284.4 : 266.9 417.5 498.0 764.9 915.6 996.1 1200.0 551.3 : 150.6 231.2 498.0 648.7 729.2 933.1 1200.0 702.0 : 80.5 347.4 498.0 578.6 782.5 1049.4 1200.0 782.5 : 266.9 417.5 498.0 702.0 968.8 1119.5 1200.0 1049.4: 150.6 231.2 435.1 702.0 852.6 933.1 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 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 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 : 12/11, 150.6371 cents, amount: 2 Least squares average step : 169.42745 cents, oct.: 1185.99214 cents Scale is not proper Step pattern alph. order: ABCDACD Step pattern size order : ACDBADB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.595742 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 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: 4 Most common triad is 0.0 701.955 1119.463 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypophrygian octave species of abstract tetrachord All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is 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 : 63 (O: 63 U: 63) Highest odd numerator or denominator: 33 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.208876 Specific harmonicity : 0.118956 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 66, 6.0444 octaves, 17267.287 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 83.0, average 11.85714 Mersenne's string divisions : 76250610 Sum of van Prooijen's expressibility: 6.44203, average 0.92029 Sum of Tenney's harmonic distance : 12.36001, average 1.76572 Vogel's harmonic complexity : 17.14286 Wille's k value : 115 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 65.73174, average 2.34756 Lattice compactness (without 2's) : 39.30980, average 1.40392 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.71429 9 1 3: -1 .. 1 0.00000 4 1 7: -1 .. 0 -0.42857 3 11: 0 .. 1 0.71429 5 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 22 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 50.0544 c. M: 80.5370 c. 8: 1 1 2 1 0 2 1 N D3 SD: 39.2818 c. M:-69.4630 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 27.4597 c. M:-52.7963 c. 12: 1 2 3 1 1 3 1 N SD: 28.9460 c. M:-50.6371 c. Todi That, Mela Shubhapantuvarali, Raga Gamakasamantam, Hemavanti, Kaam Ranjani, Multani, Harsh Minor, Chromatic Lydian inverse, Maqam Athar Kurd 14: 1 2 3 2 1 3 2 P T3 SD: 20.5710 c. M: 37.0322 c. 15: 1 3 3 2 1 3 2 N SD: 17.1527 c. M:-35.5530 c. 16: 1 3 3 2 1 4 2 N SD: 19.8130 c. M: 32.4920 c. 17: 1 3 4 2 1 4 2 N SD: 7.7808 c. M:-13.3879 c. 26: 2 4 6 3 2 6 3 N SD: 7.9944 c. M:-12.1755 c. 31: 2 5 7 4 2 7 4 N SD: 7.4910 c. M: 13.4793 c. 41: 3 7 9 5 3 9 5 N SD: 5.6350 c. M:-8.2359 c. 46: 3 8 10 6 3 10 6 N SD: 3.0247 c. M: 5.8847 c. 63: 4 11 14 8 4 14 8 N SD: 2.2335 c. M: 4.3466 c. 72: 5 12 16 9 5 16 9 N SD: 1.4992 c. M:-2.7963 c. 89: 6 15 20 11 6 20 11 N SD: 1.2161 c. M:-2.3225 c. 118: 8 20 26 15 8 26 15 N SD: 1.1624 c. M: 2.1654 c. 135: 9 23 30 17 9 30 17 N SD: 0.3163 c. M: 0.5370 c. 342: 23 58 76 43 23 76 43 N SD: 0.2319 c. M: 0.4407 c. 359: 24 61 80 45 24 80 45 N SD: 0.2390 c. M: 0.3245 c. 477: 32 81 106 60 32 106 60 N SD: 0.1998 c. M: 0.3745 c. 566: 38 96 126 71 38 126 71 N SD: 0.1695 c. M: 0.3481 c. 701: 47 119 156 88 47 156 88 N SD: 0.1413 c. M: 0.2816 c. 805: 54 137 179 101 54 179 101 N SD: 0.1585 c. M:-0.2735 c. 836: 56 142 186 105 56 186 105 N SD: 0.1419 c. M: 0.2365 c. 877: 59 149 195 110 59 195 110 N SD: 0.1314 c. M:-0.1927 c. 1012: 68 172 225 127 68 225 127 N SD: 0.0832 c. M:-0.1379 c. 1147: 77 195 255 144 77 255 144 N SD: 0.0588 c. M:-0.1214 c. 1282: 86 218 285 161 86 285 161 N SD: 0.0586 c. M:-0.1083 c. 1371: 92 233 305 172 92 305 172 N SD: 0.0530 c. M:-0.1044 c. 1417: 95 241 315 178 95 315 178 N SD: 0.0719 c. M: 0.1039 c. 1489: 100 253 331 187 100 331 187 N SD: 0.0493 c. M: 0.0755 c. 1506: 101 256 335 189 101 335 189 N SD: 0.0430 c. M:-0.0765 c. 1578: 106 268 351 198 106 351 198 N SD: 0.0451 c. M:-0.0713 c. 1713: 115 291 381 215 115 381 215 N SD: 0.0211 c. M: 0.0337 c. 1848: 124 314 411 232 124 411 232 N SD: 0.0188 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: 38.3186 cents 4 x 5 x 6 x 7:8 S SD: 32.4644 cents 5 x 6:7 x 8:9:10 S SD: 12.5353 cents 6 x 7:8:9 x 11:12 SD: 11.2195 cents 7 x 8:10 x 11:13:14 SD: 17.5676 cents 8 x 9:11:12:13:15:16 SD: 17.7701 cents 9:10:11:12 x 14:17:18 SD: 23.6637 cents 10:11:12:14:15:16:18:20 S SD: 15.0259 cents 11:12:13:15 x 17:20:22 SD: 13.1044 cents 12:13:14:17:18:19:22:24 SD: 11.5342 cents 13:14:15:18 x 20:24:26 S SD: 12.0956 cents 14:15:17:19:21:22:26:28 SD: 10.2975 cents 16:17:19:22:24:25:29:32 SD: 5.0624 cents 18:19:21:25:27:28:33:36 SD: 4.7193 cents 22:23:26:30:33:35:40:44 SD: 4.2935 cents 24:25:28:33:36:38:44:48 SD: 3.4314 cents 38:40:45:52:57:60:70:76 SD: 2.6423 cents 40:42:47:55:60:63:73:80 SD: 1.5695 cents 62:65:73:85:93:97:114:124 SD: 1.5272 cents 66:69:78:91:99:104:121:132 SD: 1.2847 cents 80:84:94:110:120:126:147:160 SD: 1.2284 cents 84:88:99:116:126:132:154:168 SD: 1.0683 cents 102:107:120:140:153:160:187:204 SD: 0.8326 cents 112:117:132:154:168:176:205:224 SD: 0.8103 cents 128:134:151:176:192:201:235:256 SD: 0.4897 cents 168:176:198:231:252:264:308:336 S SD: 0.0000 cents