Scala analysis: xen09-wilson-marwa-10-20
Marwa permutation 20 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: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 44/27 845.452940 neutral sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 22/21 80.5370 undecimal minor semitone 2: 112/99 213.5980 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 88/81 143.4979 2nd undecimal neutral second 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 9/8 203.9100 major whole tone
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 : 80.5 294.1 498.0 702.0 845.5 996.1 1200.0 80.5 : 213.6 417.5 621.4 764.9 915.6 1119.5 1200.0 294.1 : 203.9 407.8 551.3 702.0 905.9 986.4 1200.0 498.0 : 203.9 347.4 498.0 702.0 782.5 996.1 1200.0 702.0 : 143.5 294.1 498.0 578.6 792.2 996.1 1200.0 845.5 : 150.6 354.5 435.1 648.7 852.6 1056.5 1200.0 996.1 : 203.9 284.4 498.0 702.0 905.9 1049.4 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 : 168.38976 cents, oct.: 1178.72834 cents Scale is not proper Step pattern alph. order: ABCCDEC Step pattern size order : AEDDBCD 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 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% -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 27 Scale harmonicity : 0.022156 Average absolute harmonicity : 0.248240 Specific harmonicity : 0.131457 Fundamental : 1/378, -8.5622 octaves, 0.6921 Hz. Guide tone : 1056, 10.0444 octaves, 276276.597 Hz. Exponens Consonantiae : 3.991680E+05, 18.60664 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 106.5, average 15.21429 Mersenne's string divisions : 94566675 Sum of van Prooijen's expressibility: 6.09343, average 0.87049 Sum of Tenney's harmonic distance : 12.99270, average 1.85610 Vogel's harmonic complexity : 17.28571 Wille's k value : 283 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 90.34816, average 3.22672 Lattice compactness (without 2's) : 55.84336, average 1.99441 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 5 2.00000 16 1 3: -3 .. 1 -1.28571 11 4 7: -1 .. 0 -0.14286 1 11: 0 .. 1 0.28571 2 2 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 14 / 7 = 2.00000 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: 0 2 1 1 1 1 1 N T3 SD: 38.8758 c. M: 80.5370 c. 10: 1 1 2 2 1 1 2 P D3 S SD: 30.4053 c. M: 54.1350 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 18.9062 c. M: 45.4529 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 13: 1 2 2 3 1 2 2 N T3 SD: 22.9538 c. M:-36.5065 c. 14: 1 2 3 2 2 2 2 P T3 SD: 21.0931 c. M: 36.9921 c. 15: 1 3 2 3 2 1 3 N SD: 23.3499 c. M: 36.0900 c. 16: 1 3 2 3 2 2 3 P D3 SD: 23.7939 c. M: 48.0450 c. 17: 1 3 3 3 2 2 3 N SD: 6.8964 c. M: 11.7821 c. 41: 3 7 7 7 5 5 7 N SD: 3.1032 c. M:-7.2678 c. 48: 3 9 8 8 6 6 8 N SD: 3.9400 c. M:-5.8650 c. 58: 4 10 10 10 7 7 10 N SD: 2.5733 c. M: 4.4798 c. 77: 5 14 13 13 9 10 13 N SD: 2.0166 c. M: 3.8945 c. 89: 6 16 15 15 11 11 15 N SD: 1.9413 c. M:-3.9853 c. 94: 6 17 16 16 11 12 16 N SD: 1.8666 c. M: 3.9413 c. 101: 7 18 17 17 12 13 17 N SD: 1.8691 c. M:-2.8947 c. 106: 7 19 18 18 13 13 18 N SD: 1.4504 c. M:-3.6037 c. 118: 8 21 20 20 14 15 20 N SD: 0.7175 c. M: 1.3851 c. 135: 9 24 23 23 16 17 23 N SD: 0.5827 c. M: 1.0085 c. 224: 15 40 38 38 27 28 38 N SD: 0.4495 c. M:-0.9756 c. 301: 20 54 51 51 36 38 51 N SD: 0.5362 c. M:-0.8816 c. 311: 21 55 53 53 37 39 53 N SD: 0.4993 c. M: 0.8874 c. 342: 23 61 58 58 41 43 58 N SD: 0.3063 c. M:-0.6018 c. 359: 24 64 61 61 43 45 61 N SD: 0.1473 c. M: 0.3142 c. 477: 32 85 81 81 57 60 81 N SD: 0.1194 c. M:-0.2046 c. 836: 56 149 142 142 100 105 142 N SD: 0.0838 c. M: 0.1543 c. 877: 59 156 149 149 105 110 149 N SD: 0.0971 c. M:-0.1927 c. 971: 65 173 165 165 116 122 165 N SD: 0.0944 c. M: 0.2075 c. 1012: 68 180 172 172 121 127 172 N SD: 0.0477 c. M:-0.0954 c. 1371: 92 244 233 233 164 172 233 N SD: 0.0316 c. M:-0.0613 c. 1489: 100 265 253 253 178 187 253 N SD: 0.0306 c. M:-0.0540 c. 1848: 124 329 314 314 221 232 314 N SD: 0.0122 c. M:-0.0208 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: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 19.0461 cents 6 x 7:8:9:10:11:12 S SD: 11.8965 cents 7 x 8:9 x 11:12:14 SD: 25.1844 cents 8 x 9:11:12:13:14:16 SD: 18.0633 cents 10:11:12:13:15:16:18:20 SD: 14.9762 cents 11:12:13:15:17:18:20:22 SD: 14.7687 cents 12:13:14:16:18:20:21:24 S SD: 11.4004 cents 14:15:17:19:21:23:25:28 SD: 9.5527 cents 15:16:18:20:23:24:27:30 SD: 9.4276 cents 16:17:19:21:24:26:28:32 SD: 6.5754 cents 18:19:21:24:27:29:32:36 SD: 5.1617 cents 21:22:25:28:32:34:37:42 SD: 4.8887 cents 22:23:26:29:33:36:39:44 SD: 3.2064 cents 36:38:43:48:54:59:64:72 SD: 3.0252 cents 38:40:45:51:57:62:68:76 SD: 2.6044 cents 42:44:50:56:63:68:75:84 SD: 2.2413 cents 44:46:52:59:66:72:78:88 SD: 2.0629 cents 48:50:57:64:72:78:85:96 SD: 1.9107 cents 54:57:64:72:81:88:96:108 SD: 1.8666 cents 60:63:71:80:90:98:107:120 SD: 1.1728 cents 81:85:96:108:122:132:144:162 SD: 1.0976 cents 86:90:102:115:129:140:153:172 SD: 0.8466 cents 102:107:121:136:153:166:181:204 SD: 0.6909 cents 108:113:128:144:162:176:192:216 SD: 0.3125 cents 210:220:249:280:315:342:373:420 SD: 0.2946 cents 270:283:320:360:405:440:480:540 SD: 0.1249 cents 378:396:448:504:567:616:672:756 SD: 0.0000 cents