Scala analysis: xen09-wilson-marwa-17b-03
Marwa permutation 3 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: 5/4 386.313714 major third 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: 5/4 386.3137 major third 2: 36/35 48.7704 septimal diesis, 1/4-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: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 280/243 245.365 cents 1: 1 5/4 386.314 cents major third 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 7/6 266.871 cents septimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 2 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: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 2 140/81 947.320 cents 6: 1 8/5 813.686 cents minor sixth 6: 1 243/140 954.635 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 386.3 435.1 639.0 884.4 933.1 1137.0 1200.0 386.3 : 48.8 252.7 498.0 546.8 750.7 813.7 1200.0 435.1 : 203.9 449.3 498.0 702.0 764.9 1151.2 1200.0 639.0 : 245.4 294.1 498.0 561.0 947.3 996.1 1200.0 884.4 : 48.8 252.7 315.6 702.0 750.7 954.6 1200.0 933.1 : 203.9 266.9 653.2 702.0 905.9 1151.2 1200.0 1137.0: 63.0 449.3 498.0 702.0 947.3 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 252.6804 .. 449.2746 cents 2450/2187, 196.5942 cents 162/175,-133.6333 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: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 162/175,-133.6333 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 : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 189.99128 cents, oct.: 1329.93895 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EACDACB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.470169 Lumma stability : 0.081284 Lumma impropriety factor : 0.416298 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 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: 2 Number of recognisable fifths : 4, average 701.9550 cents 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 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.028556 Average absolute harmonicity : 0.207692 Specific harmonicity : 0.143378 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 1620, 10.6618 octaves, 423833.416 Hz. Exponens Consonantiae : 2.721600E+05, 18.05410 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 116.5, average 16.64286 Mersenne's string divisions : 15368112 Sum of van Prooijen's expressibility: 6.53713, average 0.93388 Sum of Tenney's harmonic distance : 12.73594, average 1.81942 Vogel's harmonic complexity : 13.85714 Wille's k value : 121 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 89.66002, average 3.20214 Lattice compactness (without 2's) : 64.64547, average 2.30877 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 9 1 3: -1 .. 4 1.28571 11 5: 0 .. 1 0.28571 2 2 7: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is weakly epimorphic with val: <7 10 18 21| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 12 16 21| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 0 1 2 0 1 1 N T3 SD: 79.4861 c. M: 124.7084 c. 8: 3 0 1 2 0 2 0 N SD: 39.8304 c. M:-63.6863 c. 9: 3 0 2 2 0 2 0 N SD: 34.9420 c. M:-62.9609 c. 10: 3 1 1 2 1 1 1 N T3 SD: 38.1231 c. M: 57.0391 c. 11: 4 0 2 2 1 1 1 N SD: 32.4750 c. M:-50.0499 c. 12: 4 0 2 3 0 2 1 N SD: 28.4174 c. M: 38.9941 c. 13: 4 1 2 3 0 2 1 N SD: 22.3744 c. M:-38.7182 c. 14: 4 1 2 3 1 2 1 N SD: 26.1984 c. M: 43.4566 c. 15: 5 0 3 3 1 2 1 N SD: 18.7106 c. M: 35.0841 c. 17: 5 1 3 3 1 3 1 N D3 SD: 20.5290 c. M: 37.2999 c. 18: 6 1 3 3 1 3 1 N SD: 18.0370 c. M:-31.5826 c. 19: 6 1 3 4 1 3 1 N SD: 7.1849 c. M:-14.2393 c. 34: 11 1 6 7 1 6 2 N SD: 8.0426 c. M: 15.4820 c. 35: 11 2 6 7 1 6 2 N SD: 8.3509 c. M:-12.4345 c. 36: 12 1 6 8 1 6 2 N SD: 8.2881 c. M:-15.6413 c. 37: 12 1 7 7 2 6 2 N SD: 7.7152 c. M: 13.4625 c. 41: 13 2 7 8 2 7 2 N SD: 4.5496 c. M: 6.3099 c. 53: 17 2 9 11 2 9 3 N SD: 3.7985 c. M: 5.0318 c. 58: 19 2 10 12 2 10 3 N SD: 3.4926 c. M:-6.7897 c. 72: 23 3 12 15 3 12 4 N SD: 2.8987 c. M: 5.6608 c. 77: 25 3 13 16 3 13 4 N SD: 2.1470 c. M:-3.9530 c. 94: 30 4 16 19 4 16 5 N SD: 1.9721 c. M: 3.5076 c. 99: 32 4 17 20 4 17 5 N SD: 1.7598 c. M:-3.4301 c. 111: 36 4 19 23 4 19 6 N SD: 2.2786 c. M: 3.3994 c. 113: 36 5 19 23 5 19 6 N SD: 2.0936 c. M: 4.0128 c. 118: 38 5 20 24 5 20 6 N SD: 1.5906 c. M:-2.4641 c. 130: 42 5 22 27 5 22 7 N SD: 1.4321 c. M: 2.0710 c. 149: 48 6 25 31 6 25 8 N SD: 1.3856 c. M: 2.7525 c. 152: 49 6 26 31 6 26 8 N SD: 0.7306 c. M: 1.5501 c. 171: 55 7 29 35 7 29 9 N SD: 0.2337 c. M: 0.3976 c. 441: 142 18 75 90 18 75 23 N SD: 0.2637 c. M:-0.4617 c. 494: 159 20 84 101 20 84 26 N SD: 0.1952 c. M: 0.3356 c. 612: 197 25 104 125 25 104 32 N SD: 0.1626 c. M:-0.2216 c. 665: 214 27 113 136 27 113 35 N SD: 0.1686 c. M: 0.1971 c. 742: 239 30 126 152 30 126 39 N SD: 0.1550 c. M:-0.2774 c. 764: 246 31 130 156 31 130 40 N SD: 0.1326 c. M:-0.2729 c. 783: 252 32 133 160 32 133 41 N SD: 0.1243 c. M:-0.2042 c. 935: 301 38 159 191 38 159 49 N SD: 0.0766 c. M:-0.1503 c. 1106: 356 45 188 226 45 188 58 N SD: 0.0510 c. M: 0.0911 c. 1277: 411 52 217 261 52 217 67 N SD: 0.0521 c. M: 0.0987 c. 1677: 540 68 285 343 68 285 88 N SD: 0.0478 c. M:-0.0906 c. 1848: 595 75 314 378 75 314 97 N SD: 0.0338 c. M:-0.0569 c. 2019: 650 82 343 413 82 343 106 N SD: 0.0336 c. M: 0.0639 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 4:5 x 6 x 7 x 8 S SD: 18.0941 cents 5:6 x 7:8:9 x 10 S SD: 28.5055 cents 6 x 8:9:10 x x 12 S SD: 22.2600 cents 7 x 9:10 x 12 x 14 SD: 5.3766 cents 8:10 x 12:13:14:15:16 S SD: 16.2772 cents 9:11:12:13:15 x 17:18 SD: 13.7224 cents 10 x 13:14 x 17:19:20 SD: 13.3173 cents 11 x 14:16:18:19:21:22 SD: 7.2486 cents 12:15 x 17:20:21:23:24 SD: 8.6357 cents 13:16:17:19 x 22:25:26 SD: 8.2135 cents 14 x 18:20:23:24:27:28 SD: 5.4849 cents 15:19 x 22:25:26:29:30 SD: 6.4305 cents 16:20:21:23:27 x 31:32 SD: 7.2947 cents 17:21:22:25:28:29:33:34 SD: 6.3708 cents 18 x 23:26:30:31:35:36 SD: 3.2740 cents 19:24 x 27:32:33:37:38 SD: 8.1485 cents 20:25:26:29:33:34:39:40 SD: 5.0765 cents 21:26:27:30:35:36:41:42 SD: 4.9244 cents 22 x 28:32:37:38:42:44 SD: 5.5973 cents 24:30:31:35:40:41:46:48 SD: 2.9154 cents 26 x 33:38:43:45:50:52 SD: 6.0099 cents 27:34:35:39:45:46:52:54 SD: 3.1649 cents 31:39:40:45:52:53:60:62 SD: 2.8020 cents 32:40:41:46:53:55:62:64 SD: 2.6848 cents 36:45:46:52:60:62:69:72 SD: 2.4720 cents 43:54:55:62:72:74:83:86 SD: 2.4185 cents 45:56:58:65:75:77:87:90 SD: 1.5110 cents 56:70:72:81:93:96:108:112 SD: 0.8849 cents 87:109:112:126:145:149:168:174 SD: 0.8232 cents 105:131:135:152:175:180:203:210 SD: 0.7973 cents 108:135:139:156:180:185:208:216 SD: 0.5759 cents 112:140:144:162:187:192:216:224 SD: 0.4412 cents 168:210:216:243:280:288:324:336 SD: 0.0000 cents