Scala analysis: xen09-wilson-marwa-17b-04
Marwa permutation 4 from Figure 17b, Archytas 36/35 28/27 5/4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 9/7 435.084095 septimal major third, BP third 3: 81/56 638.994097 4: 5/3 884.358713 major sixth, BP sixth 5: 12/7 933.129094 septimal major sixth 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 8/7 231.1741 septimal whole tone 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 280/243 245.3646 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 9/8 203.9100 major whole tone 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 3 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 280/243 245.365 cents 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 81/64 407.820 cents Pythagorean major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 1 140/81 947.320 cents 6: 1 243/140 954.635 cents 6: 1 7/4 968.826 cents harmonic seventh 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/14 1137.039 cents septimal major seventh 6: 1 35/18 1151.230 cents septimal semi-diminished octave 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 : 231.2 435.1 639.0 884.4 933.1 1137.0 1200.0 231.2 : 203.9 407.8 653.2 702.0 905.9 968.8 1200.0 435.1 : 203.9 449.3 498.0 702.0 764.9 996.1 1200.0 639.0 : 245.4 294.1 498.0 561.0 792.2 996.1 1200.0 884.4 : 48.8 252.7 315.6 546.8 750.7 954.6 1200.0 933.1 : 203.9 266.9 498.0 702.0 905.9 1151.2 1200.0 1137.0: 63.0 294.1 498.0 702.0 947.3 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 245.3646 cents 2450/2187, 196.5942 cents 36/35, 48.7704 cents 2: 252.6804 .. 449.2746 cents 2450/2187, 196.5942 cents 19683/19600, 7.3158 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 750.7254 .. 947.3196 cents 2450/2187, 196.5942 cents 162/175,-133.6333 cents 6: 954.6354 .. 1151.2296 cents 2450/2187, 196.5942 cents 19683/19600, 7.3158 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 280/243, 245.3646 cents Average / Smallest step : 3.515014 Largest / Average step : 1.431294 Largest / Smallest step : 5.031017 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 : 188.88314 cents, oct.: 1322.18197 cents Scale is not proper Step pattern alph. order: ABBCDBE Step pattern size order : DCCEACB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.456709 Lumma stability : 0.093477 Lumma impropriety factor : 0.311363 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 : 19683/19600, 7.3158 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 Length of longest harmonic part : 2 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 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 337.5433 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.027763 Average absolute harmonicity : 0.201438 Specific harmonicity : 0.155685 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 3240, 11.6618 octaves, 847666.832 Hz. Exponens Consonantiae : 5.443200E+05, 19.05410 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 119.5, average 17.07143 Mersenne's string divisions : 25613520 Sum of van Prooijen's expressibility: 6.68326, average 0.95475 Sum of Tenney's harmonic distance : 13.18309, average 1.88330 Vogel's harmonic complexity : 12.85714 Wille's k value : 121 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 92.77475, average 3.31338 Lattice compactness (without 2's) : 63.63672, average 2.27274 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.28571 10 1 3: -1 .. 4 1.28571 11 5: 0 .. 1 0.14286 1 1 7: -1 .. 0 -0.71429 5 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 80.9827 c. M: 124.7084 c. 8: 2 1 1 2 0 2 0 N D3 S SD: 41.0336 c. M:-68.8259 c. 9: 2 1 2 2 0 2 0 N SD: 37.0695 c. M:-62.9609 c. 10: 2 2 1 2 1 1 1 N D3 SD: 36.9538 c. M: 57.0391 c. 11: 2 2 2 2 1 1 1 N S SD: 26.8493 c. M:-48.6891 c. 12: 2 2 2 3 0 2 1 N SD: 30.3252 c. M: 38.9941 c. 13: 3 2 2 3 0 2 1 N SD: 27.5304 c. M:-45.7490 c. 14: 3 2 2 3 1 2 1 N T3 S SD: 22.6476 c. M: 38.9941 c. 15: 3 2 3 3 1 2 1 N SD: 18.2881 c. M: 35.0841 c. 17: 3 3 3 3 1 3 1 N D3 S SD: 17.7807 c. M: 37.2999 c. 19: 4 3 3 4 1 3 1 N S SD: 10.4712 c. M:-21.4575 c. 22: 4 4 4 4 1 4 1 N D3 S SD: 9.6561 c. M:-15.5514 c. 30: 6 5 5 6 1 5 2 N SD: 9.1400 c. M: 17.0391 c. 34: 6 6 6 7 1 6 2 N SD: 10.8616 c. M: 19.4094 c. 35: 7 6 6 7 1 6 2 N SD: 8.2976 c. M:-12.4345 c. 36: 7 6 6 8 1 6 2 N SD: 6.5268 c. M:-15.6413 c. 41: 8 7 7 8 2 7 2 N S SD: 4.1367 c. M: 6.3099 c. 53: 10 9 9 11 2 9 3 N SD: 4.1691 c. M: 5.0318 c. 58: 11 10 10 12 2 10 3 N SD: 2.7297 c. M:-5.2965 c. 77: 15 13 13 16 3 13 4 N SD: 2.0043 c. M:-3.9530 c. 94: 18 16 16 19 4 16 5 N SD: 1.6047 c. M: 3.5076 c. 99: 19 17 17 20 4 17 5 N SD: 1.6898 c. M:-3.4301 c. 113: 22 19 19 23 5 19 6 N SD: 1.7156 c. M: 2.9428 c. 118: 23 20 20 24 5 20 6 N SD: 1.8942 c. M:-2.7242 c. 130: 25 22 22 27 5 22 7 N SD: 1.3427 c. M: 2.0710 c. 152: 29 26 26 31 6 26 8 N SD: 1.0964 c. M: 2.2267 c. 171: 33 29 29 35 7 29 9 N SD: 0.2463 c. M:-0.4049 c. 441: 85 75 75 90 18 75 23 N SD: 0.2657 c. M:-0.4617 c. 494: 95 84 84 101 20 84 26 N SD: 0.2463 c. M: 0.4049 c. 571: 110 97 97 117 23 97 30 N SD: 0.1642 c. M:-0.4049 c. 612: 118 104 104 125 25 104 32 N SD: 0.1784 c. M:-0.2216 c. 665: 128 113 113 136 27 113 35 N SD: 0.1756 c. M: 0.1971 c. 742: 143 126 126 152 30 126 39 N SD: 0.1378 c. M:-0.2774 c. 913: 176 155 155 187 37 155 48 N SD: 0.1371 c. M: 0.2208 c. 935: 180 159 159 191 38 159 49 N SD: 0.0971 c. M: 0.1581 c. 1106: 213 188 188 226 45 188 58 N SD: 0.0534 c. M: 0.0911 c. 1277: 246 217 217 261 52 217 67 N SD: 0.0375 c. M: 0.0987 c. 1677: 323 285 285 343 68 285 88 N SD: 0.0378 c. M:-0.0778 c. 1848: 356 314 314 378 75 314 97 N SD: 0.0282 c. M:-0.0569 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 31.4805 cents 3 x 4 x 5 x x 6 S SD: 20.9870 cents 4 x 5:6 x 7 x 8 S SD: 21.8187 cents 5:6 x 7:8:9 x 10 S SD: 29.9695 cents 6:7:8:9:10 x x 12 S SD: 19.1858 cents 7:8:9:10 x 12 x 14 S SD: 4.3013 cents 9:10:12:13:15 x 17:18 SD: 14.5715 cents 10:11:13:14 x 17:19:20 SD: 15.6455 cents 11:13:14:16:18:19:21:22 SD: 10.3605 cents 13:15:17:19 x 22:25:26 SD: 7.4211 cents 14:16:18:20:23:24:27:28 SD: 4.7014 cents 16:18:21:23:27 x 31:32 SD: 8.5942 cents 17:19:22:25:28:29:33:34 SD: 7.9027 cents 18:21:23:26:30:31:35:36 SD: 5.8207 cents 20:23:26:29:33:34:39:40 SD: 5.3052 cents 21:24:27:30:35:36:41:42 SD: 4.3184 cents 27:31:35:39:45:46:52:54 SD: 2.8267 cents 36:41:46:52:60:62:69:72 SD: 2.6174 cents 41:47:53:59:68:70:79:82 SD: 2.5480 cents 42:48:54:61:70:72:81:84 SD: 1.0157 cents 56:64:72:81:93:96:108:112 SD: 0.8849 cents 98:112:126:142:163:168:189:196 SD: 0.6672 cents 105:120:135:152:175:180:203:210 SD: 0.6430 cents 112:128:144:162:187:192:216:224 SD: 0.4412 cents 126:144:162:182:210:216:243:252 SD: 0.3395 cents 168:192:216:243:280:288:324:336 SD: 0.0000 cents