Scala analysis: xen09-wilson-marwa-15b-02
Marwa permutation 2 from Figure 15b, Ptolemy 22/21 12/11 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 11/9 347.407941 undecimal neutral third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 14/9 764.915905 septimal minor sixth 5: 7/4 968.825906 harmonic seventh 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: 7/6 266.8709 septimal minor third 2: 22/21 80.5370 undecimal minor semitone 3: 9/8 203.9100 major whole tone 4: 112/99 213.5980 5: 9/8 203.9100 major whole tone 6: 22/21 80.5370 undecimal minor semitone 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 : 266.9 347.4 551.3 764.9 968.8 1049.4 1200.0 266.9 : 80.5 284.4 498.0 702.0 782.5 933.1 1200.0 347.4 : 203.9 417.5 621.4 702.0 852.6 1119.5 1200.0 551.3 : 213.6 417.5 498.0 648.7 915.6 996.1 1200.0 764.9 : 203.9 284.4 435.1 702.0 782.5 986.4 1200.0 968.8 : 80.5 231.2 498.0 578.6 782.5 996.1 1200.0 1049.4: 150.6 417.5 498.0 702.0 915.6 1119.5 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 : 180.11151 cents, oct.: 1260.78057 cents Scale is not proper Step pattern alph. order: ABCDCBE Step pattern size order : EACDCAB Scale is sum-free (all different intervals) 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 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Best minor thirds form a closed circle 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 n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 11 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.192677 Specific harmonicity : 0.116643 Fundamental : 1/72, -6.1699 octaves, 3.6337 Hz. Guide tone : 154, 7.2668 octaves, 40290.337 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 53.0, average 7.57143 Mersenne's string divisions : 63740820 Sum of van Prooijen's expressibility: 5.76862, average 0.82409 Sum of Tenney's harmonic distance : 11.23147, average 1.60450 Vogel's harmonic complexity : 13.42857 Wille's k value : 49 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 67.95210, average 2.42686 Lattice compactness (without 2's) : 42.67095, average 1.52396 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.71429 9 1 3: -2 .. 0 -0.85714 6 7: 0 .. 1 0.42857 3 3 11: 0 .. 1 0.42857 3 3 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: 2 0 1 1 2 0 1 N T3 SD: 49.9152 c. M: 79.2016 c. 8: 2 0 2 1 1 1 1 P D3 S SD: 39.0510 c. M: 68.8259 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 28.9814 c. M:-52.5921 c. 10: 2 1 2 1 2 1 1 P M ME S SD: 29.9631 c. M:-48.6821 c. 11: 2 1 2 2 2 1 1 N D3 SD: 25.9311 c. M: 48.6891 c. 13: 3 1 2 2 2 1 2 P D3 SD: 25.4418 c. M: 45.7490 c. 14: 3 1 2 3 2 1 2 P T3 SD: 19.4047 c. M: 37.0322 c. 16: 4 1 2 3 3 1 2 N SD: 20.0446 c. M:-33.1291 c. 17: 4 1 3 3 3 1 2 N SD: 12.2433 c. M:-19.4094 c. 22: 5 1 4 4 4 1 3 N SD: 10.7804 c. M: 20.1352 c. 24: 5 2 4 4 4 2 3 P SD: 11.1508 c. M: 18.8259 c. 27: 6 2 4 5 5 2 3 N SD: 11.0650 c. M: 17.9846 c. 30: 7 2 5 5 5 2 4 N SD: 9.2276 c. M:-13.1291 c. 31: 7 2 5 6 5 2 4 N SD: 5.4860 c. M: 9.3825 c. 41: 9 3 7 7 7 3 5 N SD: 3.6279 c. M:-4.7796 c. 58: 13 4 10 10 10 4 7 N SD: 4.1975 c. M:-7.3027 c. 63: 14 4 11 11 11 4 8 N SD: 2.4132 c. M: 4.5508 c. 72: 16 5 12 13 12 5 9 N SD: 1.5414 c. M:-2.5921 c. 135: 30 9 23 24 23 9 17 N SD: 0.3937 c. M: 0.7413 c. 207: 46 14 35 37 35 14 26 N SD: 0.4090 c. M: 0.7100 c. 342: 76 23 58 61 58 23 43 N SD: 0.2561 c. M: 0.4407 c. 477: 106 32 81 85 81 32 60 N SD: 0.2465 c. M: 0.3745 c. 494: 110 33 84 88 84 33 62 N SD: 0.2267 c. M:-0.4049 c. 612: 136 41 104 109 104 41 77 N SD: 0.2616 c. M: 0.3491 c. 629: 140 42 107 112 107 42 79 N SD: 0.1745 c. M:-0.3315 c. 670: 149 45 114 119 114 45 84 N SD: 0.1604 c. M:-0.3238 c. 701: 156 47 119 125 119 47 88 N SD: 0.1381 c. M:-0.2767 c. 805: 179 54 137 143 137 54 101 N SD: 0.1315 c. M:-0.2349 c. 836: 186 56 142 149 142 56 105 N SD: 0.0969 c. M:-0.1559 c. 877: 195 59 149 156 149 59 110 N SD: 0.0889 c. M:-0.1405 c. 971: 216 65 165 173 165 65 122 N SD: 0.0999 c. M: 0.1371 c. 1012: 225 68 172 180 172 68 127 N SD: 0.0579 c. M: 0.0938 c. 1506: 335 101 256 268 256 101 189 N SD: 0.0554 c. M:-0.0984 c. 1641: 365 110 279 292 279 110 206 N SD: 0.0496 c. M:-0.0955 c. 1713: 381 115 291 305 291 115 215 N SD: 0.0329 c. M:-0.0578 c. 1848: 411 124 314 329 314 124 232 N SD: 0.0125 c. M: 0.0192 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 x 4 x 5 x 6 S SD: 33.2878 cents 4 x 5 x 6:7 x 8 S SD: 18.5029 cents 5 x 6:7:8 x 9:10 S SD: 14.6559 cents 6:7 x 8:9 x 11:12 SD: 16.4949 cents 8:9:10:11:12:14:15:16 S SD: 14.9526 cents 9 x 11:12:14:16:17:18 SD: 13.1787 cents 10 x 12:14:16 x 18:20 S SD: 14.6559 cents 11:13 x 15:17:19:20:22 SD: 6.5642 cents 13:15:16:18:20:23:24:26 SD: 5.5816 cents 15 x 18:21:23:26:28:30 SD: 10.3418 cents 16:19:20:22:25:28:29:32 SD: 7.6978 cents 17:20:21:23:26:30:31:34 SD: 7.1288 cents 18:21:22:25:28:32:33:36 SD: 4.6204 cents 23:27:28:32:36:40:42:46 SD: 4.1813 cents 24:28:29:33:37:42:44:48 SD: 3.5930 cents 31:36:38:43:48:54:57:62 SD: 3.1075 cents 32:37:39:44:50:56:59:64 SD: 2.9313 cents 36:42:44:50:56:63:66:72 SD: 2.4856 cents 40:47:49:55:62:70:73:80 SD: 2.3380 cents 48:56:59:66:75:84:88:96 SD: 1.7824 cents 54:63:66:74:84:95:99:108 SD: 1.5489 cents 59:69:72:81:92:103:108:118 SD: 1.2293 cents 67:78:82:92:104:117:123:134 SD: 1.0834 cents 72:84:88:99:112:126:132:144 SD: 0.0000 cents