Scala analysis: xen09-wilson-marwa-15a-04
Marwa permutation 4 from Figure 15a, Ptolemy 12/11 22/21 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 112/99 213.597962 2: 14/11 417.507964 undecimal diminished fourth or major third 3: 63/44 621.417966 4: 14/9 764.915905 septimal minor sixth 5: 56/33 915.552963 6: 21/11 1119.462965 undecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 112/99 213.5980 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 88/81 143.4979 2nd undecimal neutral second 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 9/8 203.9100 major whole tone 7: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 3 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 81/64 407.820 cents Pythagorean major third 2: 1 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: 1 11/7 782.492 cents undecimal augmented fifth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 1 56/33 915.553 cents 6: 1 99/56 986.402 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 6: 1 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 213.6 417.5 621.4 764.9 915.6 1119.5 1200.0 213.6 : 203.9 407.8 551.3 702.0 905.9 986.4 1200.0 417.5 : 203.9 347.4 498.0 702.0 782.5 996.1 1200.0 621.4 : 143.5 294.1 498.0 578.6 792.2 996.1 1200.0 764.9 : 150.6 354.5 435.1 648.7 852.6 1056.5 1200.0 915.6 : 203.9 284.4 498.0 702.0 905.9 1049.4 1200.0 1119.5: 80.5 294.1 498.0 702.0 845.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 213.5980 cents 392/363, 133.0609 cents 22/21, 80.5370 cents 2: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 3267/3136, 70.8491 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 .. 915.5530 cents 392/363, 133.0609 cents 99/98, 17.5761 cents 6: 986.4020 .. 1119.4630 cents 392/363, 133.0609 cents 3267/3136, 70.8491 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 : 112/99, 213.5980 cents Average / Smallest step : 2.128568 Largest / Average step : 1.245988 Largest / Smallest step : 2.652171 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 183.33624 cents, oct.: 1283.35370 cents Scale is not proper Step pattern alph. order: ABBCDBE Step pattern size order : EDDBCDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.582054 Lumma stability : 0.281604 Lumma impropriety factor : 0.035697 Rothenberg efficiency : 0.383673 redundancy: 0.616327 Efficiency x scale size : 2.685714 Number of different interval sizes : 30 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.022156 Average absolute harmonicity : 0.172844 Specific harmonicity : 0.110569 Fundamental : 1/396, -8.6294 octaves, 0.6607 Hz. Guide tone : 1008, 9.9773 octaves, 263718.570 Hz. Exponens Consonantiae : 3.991680E+05, 18.60664 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 245.0, average 35.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.63134, average 1.23305 Sum of Tenney's harmonic distance : 17.70688, average 2.52955 Vogel's harmonic complexity : 17.42857 Wille's k value : 283 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 86.69514, average 3.09625 Lattice compactness (without 2's) : 55.96239, average 1.99866 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.14286 12 1 3: -2 .. 2 -0.28571 8 7: 0 .. 1 0.85714 6 1 11: -1 .. 0 -0.71429 5 5 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 19 25| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 72.4808 c. M: 107.1323 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 39.3676 c. M: 69.4630 c. 9: 2 1 2 1 1 1 1 N D3 S SD: 36.8486 c. M:-53.0687 c. 11: 2 2 2 1 1 2 1 N D3 SD: 24.2751 c. M: 42.8257 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 28.7475 c. M: 64.9159 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 13: 2 3 2 1 2 2 1 N G T3 S SD: 24.7431 c. M:-44.0305 c. 14: 2 3 2 2 2 2 1 P T3 SD: 21.2943 c. M: 42.1694 c. 15: 3 2 3 2 1 3 1 N SD: 23.4341 c. M: 35.5530 c. 16: 3 3 2 2 2 3 1 P T3 SD: 17.4827 c. M:-32.4920 c. 17: 3 3 3 2 2 3 1 N SD: 8.1857 c. M:-13.8762 c. 33: 6 5 6 4 4 6 2 N SD: 7.9499 c. M: 17.5080 c. 35: 6 6 6 4 5 6 2 N SD: 8.2533 c. M:-11.9656 c. 38: 7 6 7 4 5 6 3 N SD: 8.0936 c. M: 14.1998 c. 39: 7 7 6 5 5 6 3 N SD: 7.8306 c. M:-13.2613 c. 41: 7 7 7 5 5 7 3 N SD: 6.7435 c. M: 8.7199 c. 44: 8 7 8 5 6 7 3 N SD: 6.1733 c. M:-11.7198 c. 46: 8 8 8 5 6 8 3 N SD: 4.2726 c. M: 8.3942 c. 58: 10 10 10 7 7 10 4 N SD: 3.6186 c. M: 6.7014 c. 60: 11 10 10 7 8 10 4 N SD: 3.6535 c. M:-6.4020 c. 71: 13 12 12 8 9 12 5 N SD: 4.1609 c. M:-6.1203 c. 72: 13 12 12 9 9 12 5 N SD: 2.5305 c. M: 4.7513 c. 77: 14 13 13 9 10 13 5 N SD: 2.9143 c. M:-4.5839 c. 89: 16 15 15 11 11 15 6 N SD: 1.7380 c. M:-3.6234 c. 100: 18 17 17 12 12 17 7 N SD: 2.7458 c. M: 3.5530 c. 101: 18 17 17 12 13 17 7 N SD: 2.4964 c. M: 4.5199 c. 106: 19 18 18 13 13 18 7 N SD: 2.1797 c. M:-4.8954 c. 118: 21 20 20 14 15 20 8 N SD: 1.0068 c. M: 2.2040 c. 135: 24 23 23 16 17 23 9 N SD: 0.4310 c. M:-0.8043 c. 342: 61 58 58 41 43 58 23 N SD: 0.2417 c. M:-0.4371 c. 477: 85 81 81 57 60 81 32 N SD: 0.1294 c. M:-0.2385 c. 612: 109 104 104 73 77 104 41 N SD: 0.1420 c. M: 0.2100 c. 877: 156 149 149 105 110 149 59 N SD: 0.1508 c. M: 0.2093 c. 894: 159 152 152 107 112 152 60 N SD: 0.1104 c. M:-0.1848 c. 1012: 180 172 172 121 127 172 68 N SD: 0.1078 c. M: 0.1592 c. 1147: 204 195 195 137 144 195 77 N SD: 0.0998 c. M: 0.1716 c. 1236: 220 210 210 148 155 210 83 N SD: 0.0592 c. M:-0.1326 c. 1371: 244 233 233 164 172 233 92 N SD: 0.0326 c. M:-0.0732 c. 1713: 305 291 291 205 215 291 115 N SD: 0.0408 c. M:-0.0623 c. 1848: 329 314 314 221 232 314 124 N SD: 0.0235 c. M:-0.0384 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: 31.4805 cents 3 x 4 x x 5 x 6 S SD: 28.7891 cents 4 x 5 x 6:7 x 8 S SD: 22.0442 cents 5 x 6:7:8 x x 10 S SD: 29.8633 cents 6:7:8 x 9:10:11:12 S SD: 23.0792 cents 7:8:9:10:11:12:13:14 H SD: 8.4904 cents 14:16:18:20:22:24:27:28 S SD: 5.6425 cents 21:24:27:30:33:36:40:42 S SD: 5.0841 cents 22:25:28:32:34:37:42:44 SD: 4.8887 cents 23:26:29:33:36:39:44:46 SD: 2.8812 cents 30:34:38:43:47:51:57:60 SD: 2.5187 cents 40:45:51:57:62:68:76:80 SD: 2.4239 cents 44:50:56:63:68:75:84:88 SD: 2.2413 cents 47:53:60:67:73:80:90:94 SD: 1.9120 cents 54:61:69:77:84:92:103:108 SD: 1.7726 cents 62:70:79:89:96:105:118:124 SD: 1.6921 cents 63:71:80:90:98:107:120:126 SD: 1.3744 cents 67:76:85:96:104:114:128:134 SD: 1.3545 cents 69:78:88:99:107:117:132:138 SD: 1.2044 cents 70:79:89:100:109:119:134:140 SD: 1.2038 cents 76:86:97:109:118:129:145:152 SD: 0.9501 cents 92:104:117:132:143:156:176:184 SD: 0.8191 cents 99:112:126:142:154:168:189:198 SD: 0.4358 cents 176:199:224:252:274:299:336:352 SD: 0.3680 cents 220:249:280:315:342:373:420:440 SD: 0.2946 cents 275:311:350:394:428:467:525:550 SD: 0.2831 cents 290:328:369:415:451:492:554:580 SD: 0.2440 cents 297:336:378:425:462:504:567:594 SD: 0.1454 cents 396:448:504:567:616:672:756:792 SD: 0.0000 cents