Scala analysis: xen09-wilson-marwa-16a-04
Marwa permutation 4 from Figure 16a, Schlesinger 16/15 15/13 13/12
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 128/117 155.5623 5: 13/12 138.5727 tridecimal 2/3-tone 6: 9/8 203.9100 major whole tone 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 128/117 155.562 cents 1: 1 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 5/4 386.314 cents major third 2: 1 81/64 407.820 cents Pythagorean major third 3: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 117/64 1044.438 cents 6: 1 24/13 1061.427 cents tridecimal neutral seventh 6: 1 15/8 1088.269 cents classic 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 : 182.4 386.3 590.2 745.8 884.4 1088.3 1200.0 182.4 : 203.9 407.8 563.4 702.0 905.9 1017.6 1200.0 386.3 : 203.9 359.5 498.0 702.0 813.7 996.1 1200.0 590.2 : 155.6 294.1 498.0 609.8 792.2 996.1 1200.0 745.8 : 138.6 342.5 454.2 636.6 840.5 1044.4 1200.0 884.4 : 203.9 315.6 498.0 702.0 905.9 1061.4 1200.0 1088.3: 111.7 294.1 498.0 702.0 857.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 454.2139 .. 590.2237 cents 225/208, 136.0098 cents 416/405, 46.3939 cents 4: 609.7763 .. 745.7861 cents 225/208, 136.0098 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 416/405, 46.3939 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 179.00180 cents, oct.: 1253.01262 cents Scale is strictly proper Step pattern alph. order: ABBCDBE Step pattern size order : DEECBEA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.558029 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.430211 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 : 512/507, 16.9897 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 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 109.1684 cents: 4 -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 45 Scale harmonicity : 0.021635 Average absolute harmonicity : 0.211891 Specific harmonicity : 0.155638 Fundamental : 1/3744, -11.8704 octaves, 0.0699 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 6.739200E+05, 19.36222 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 86.0, average 12.28571 Mersenne's string divisions : 2422728 Sum of van Prooijen's expressibility: 6.29543, average 0.89935 Sum of Tenney's harmonic distance : 12.38491, average 1.76927 Vogel's harmonic complexity : 25.57143 Wille's k value : 2632 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 95.57730, average 3.41348 Lattice compactness (without 2's) : 47.73012, average 1.70465 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -0.85714 14 1 3: -2 .. 2 0.00000 6 5: 0 .. 1 0.85714 6 5 13: -1 .. 0 -0.14286 1 1 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 16 26| Scale is JI-epimorphic with val: <7 11 16 26| = patent Scale is weakly epimorphic with val: <7 12 15 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 47.3416 c. M: 75.9380 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 31.4607 c. M:-63.6863 c. 9: 1 2 1 2 1 1 1 N D3 S SD: 40.7712 c. M: 56.8904 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 32.4768 c. M: 62.4037 c. 11: 2 2 1 2 1 2 1 P M ME S SD: 29.8813 c. M:-50.0499 c. 12: 2 2 2 1 2 2 1 P M ME S SD: 20.9460 c. M: 45.7861 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 2 2 2 2 2 1 SP M ME S SD: 22.5201 c. M:-38.7182 c. Ryonian 15: 2 3 2 2 2 2 2 SP M ME S SD: 25.6807 c. M: 48.2687 c. Miller's Porcupine-7 Major 16: 2 3 3 2 2 3 1 P SD: 20.3019 c. M:-36.7313 c. 18: 3 3 3 2 2 3 2 P D3 SD: 14.7709 c. M: 21.6020 c. 19: 3 3 3 3 2 3 2 SP D3 S SD: 11.5817 c. M: 21.8027 c. 22: 3 4 4 3 2 4 2 P S SD: 11.5195 c. M: 18.7673 c. 24: 4 4 4 3 3 4 2 P SD: 11.9077 c. M:-17.5963 c. 26: 4 4 5 3 3 5 2 P SD: 11.2027 c. M:-19.4236 c. 29: 4 5 5 4 3 5 3 SP S SD: 11.8879 c. M: 16.8865 c. 30: 5 5 5 4 3 5 3 P SD: 11.2245 c. M:-17.5963 c. 31: 5 5 5 4 4 5 3 SP SD: 7.3447 c. M:-11.1447 c. 34: 5 6 6 4 4 6 3 P SD: 5.2638 c. M:-9.7763 c. 47: 7 8 8 6 6 8 4 SP SD: 5.8589 c. M:-9.6036 c. 53: 8 9 9 7 6 9 5 SP SD: 1.3024 c. M: 1.5445 c. 130: 20 22 22 17 15 22 12 SP SD: 1.4576 c. M:-2.2117 c. 140: 21 24 24 18 16 24 13 SP SD: 1.1917 c. M: 2.4037 c. 171: 26 29 29 22 20 29 16 SP SD: 0.8213 c. M: 1.9264 c. 183: 28 31 31 24 21 31 17 SP SD: 0.9031 c. M:-1.7549 c. 217: 33 37 37 28 25 37 20 SP SD: 0.8332 c. M:-1.4814 c. 224: 34 38 38 29 26 38 21 SP SD: 0.6959 c. M: 1.1432 c. 270: 41 46 46 35 31 46 25 SP SD: 0.5493 c. M:-0.8874 c. 301: 46 51 51 39 35 51 28 SP SD: 0.4966 c. M:-0.9850 c. 323: 49 55 55 42 37 55 30 SP SD: 0.4470 c. M:-0.9632 c. 335: 51 57 57 43 39 57 31 SP SD: 0.5619 c. M:-0.8211 c. 354: 54 60 60 46 41 60 33 SP SD: 0.3290 c. M:-0.6471 c. 388: 59 66 66 50 45 66 36 SP SD: 0.3160 c. M:-0.4979 c. 407: 62 69 69 53 47 69 38 SP SD: 0.2940 c. M: 0.5431 c. 441: 67 75 75 57 51 75 41 SP SD: 0.1461 c. M:-0.2525 c. 494: 75 84 84 64 57 84 46 SP SD: 0.1072 c. M: 0.2175 c. 848: 129 144 144 110 98 144 79 SP SD: 0.0826 c. M:-0.1435 c. 1289: 196 219 219 167 149 219 120 SP SD: 0.0479 c. M: 0.0917 c. 1342: 204 228 228 174 155 228 125 SP SD: 0.0322 c. M: 0.0598 c. 1783: 271 303 303 231 206 303 166 SP SD: 0.0305 c. M: 0.0766 c. 1836: 279 312 312 238 212 312 171 SP SD: 0.0363 c. M: 0.0508 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: 21.9155 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x 6:7 x 8 S SD: 23.7906 cents 5 x 6:7:8 x 9:10 S SD: 24.2149 cents 6:7 x 8:9:10:11:12 S SD: 23.0135 cents 7:8:9:10:11:12:13:14 H SD: 13.9246 cents 8:9:10:11:12:13:15:16 SD: 10.8970 cents 9:10:11:13:14:15:17:18 SD: 9.2530 cents 15:17:19:21:23:25:28:30 SD: 6.1503 cents 17:19:21:24:26:28:32:34 SD: 4.8208 cents 24:27:30:34:37:40:45:48 SD: 3.6105 cents 35:39:44:49:54:58:66:70 SD: 2.8618 cents 37:41:46:52:57:62:69:74 SD: 2.4399 cents 39:43:49:55:60:65:73:78 SD: 2.4335 cents 44:49:55:62:68:73:83:88 SD: 2.3076 cents 45:50:56:63:69:75:84:90 SD: 2.0791 cents 52:58:65:73:80:87:98:104 SD: 1.8927 cents 56:62:70:79:86:93:105:112 SD: 1.5414 cents 63:70:79:89:97:105:118:126 SD: 1.4149 cents 71:79:89:100:109:118:133:142 SD: 1.2526 cents 72:80:90:101:111:120:135:144 SD: 0.7992 cents 108:120:135:152:166:180:203:216 SD: 0.6826 cents 128:142:160:180:197:213:240:256 SD: 0.5554 cents 143:159:179:201:220:238:268:286 SD: 0.5439 cents 145:161:181:204:223:242:272:290 SD: 0.5431 cents 152:169:190:214:234:253:285:304 SD: 0.4925 cents 160:178:200:225:246:267:300:320 SD: 0.4635 cents 180:200:225:253:277:300:338:360 SD: 0.3920 cents 216:240:270:304:332:360:405:432 SD: 0.3064 cents 271:301:339:381:417:452:508:542 SD: 0.2905 cents 280:311:350:394:431:467:525:560 SD: 0.2849 cents 288:320:360:405:443:480:540:576 SD: 0.0429 cents