Scala analysis: xen09-wilson-marwa-17b-02
Marwa permutation 2 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: 15/8 1088.268715 classic major seventh 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: 9/8 203.9100 major whole tone 6: 36/35 48.7704 septimal diesis, 1/4-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: 1 16/15 111.731 cents minor diatonic semitone 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 9/7 435.084 cents septimal major third, BP third 2: 3 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: 3 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 140/81 947.320 cents 5: 1 15/8 1088.269 cents classic major seventh 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 386.3 435.1 639.0 884.4 1088.3 1137.0 1200.0 386.3 : 48.8 252.7 498.0 702.0 750.7 813.7 1200.0 435.1 : 203.9 449.3 653.2 702.0 764.9 1151.2 1200.0 639.0 : 245.4 449.3 498.0 561.0 947.3 996.1 1200.0 884.4 : 203.9 252.7 315.6 702.0 750.7 954.6 1200.0 1088.3: 48.8 111.7 498.0 546.8 750.7 996.1 1200.0 1137.0: 63.0 449.3 498.0 702.0 947.3 1151.2 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: 111.7313 .. 449.2746 cents 175/144, 337.5433 cents 64/75,-274.5824 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 .. 1088.2687 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 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 : 195.53198 cents, oct.: 1368.72386 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 7.31577 cents Scale diversity : 1.557433 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 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 : 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 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 : 0.029395 Average absolute harmonicity : 0.209977 Specific harmonicity : 0.141503 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 810, 9.6618 octaves, 211916.708 Hz. Exponens Consonantiae : 1.360800E+05, 17.05410 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 118.5, average 16.92857 Mersenne's string divisions : 18603504 Sum of van Prooijen's expressibility: 6.86812, average 0.98116 Sum of Tenney's harmonic distance : 12.89084, average 1.84155 Vogel's harmonic complexity : 14.85714 Wille's k value : 157 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 88.80677, average 3.17167 Lattice compactness (without 2's) : 64.96210, average 2.32007 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.14286 10 1 3: -1 .. 4 1.28571 11 5: 0 .. 1 0.42857 3 3 7: -1 .. 0 -0.42857 3 3 Average exponent except 2's : 9 / 7 = 1.28571 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| Scale is weakly epimorphic with val: <7 12 18 19|
FIT/MODE
7: 2 0 1 2 1 0 1 N T3 SD: 77.4746 c. M: 124.7084 c. 8: 3 0 1 2 1 1 0 N SD: 40.4831 c. M:-63.6863 c. 9: 3 0 2 2 1 1 0 N SD: 35.8832 c. M:-62.9609 c. 11: 4 0 2 2 2 0 1 N G SD: 26.7761 c. M:-50.0499 c. 12: 4 0 2 3 2 0 1 N SD: 25.8924 c. M: 38.9941 c. 13: 4 1 2 3 2 0 1 N SD: 23.2395 c. M:-38.7182 c. 15: 5 0 3 3 3 0 1 N SD: 19.7680 c. M: 35.0841 c. 16: 5 1 3 3 3 0 1 N SD: 21.9925 c. M:-36.7313 c. 17: 5 1 3 3 3 1 1 N T3 SD: 22.6066 c. M: 37.2999 c. 19: 6 1 3 4 3 1 1 N SD: 7.2832 c. M: 14.5845 c. 34: 11 1 6 7 6 1 2 N SD: 5.9438 c. M: 11.5547 c. 41: 13 2 7 8 7 2 2 N SD: 4.8030 c. M: 6.3099 c. 53: 17 2 9 11 9 2 3 N SD: 3.3781 c. M: 5.0318 c. 72: 23 3 12 15 12 3 4 N SD: 3.4462 c. M: 5.6608 c. 75: 24 3 13 15 13 3 4 N SD: 2.2686 c. M: 4.3587 c. 77: 25 3 13 16 13 3 4 N SD: 2.2517 c. M:-3.9530 c. 94: 30 4 16 19 16 4 5 N SD: 2.2599 c. M: 3.5076 c. 96: 31 4 16 20 16 4 5 N SD: 1.6965 c. M:-3.1413 c. 99: 32 4 17 20 17 4 5 N SD: 2.0216 c. M:-3.4301 c. 118: 38 5 20 24 20 5 6 N SD: 1.2904 c. M:-2.2040 c. 130: 42 5 22 27 22 5 7 N SD: 1.4446 c. M: 2.0710 c. 149: 48 6 25 31 25 6 8 N SD: 1.3770 c. M: 2.7525 c. 152: 49 6 26 31 26 6 8 N SD: 0.6308 c. M:-1.2050 c. 171: 55 7 29 35 29 7 9 N SD: 0.3029 c. M: 0.5494 c. 323: 104 13 55 66 55 13 17 N SD: 0.2100 c. M: 0.4092 c. 494: 159 20 84 101 84 20 26 N SD: 0.1485 c. M: 0.2663 c. 612: 197 25 104 125 104 25 32 N SD: 0.1437 c. M:-0.2216 c. 665: 214 27 113 136 113 27 35 N SD: 0.1614 c. M: 0.1971 c. 764: 246 31 130 156 130 31 40 N SD: 0.1451 c. M:-0.2729 c. 783: 252 32 133 160 133 32 41 N SD: 0.1120 c. M:-0.1649 c. 935: 301 38 159 191 159 38 49 N SD: 0.0755 c. M:-0.1503 c. 1106: 356 45 188 226 188 45 58 N SD: 0.0498 c. M: 0.0911 c. 1525: 491 62 259 312 259 62 80 N SD: 0.0511 c. M:-0.1003 c. 1600: 515 65 272 327 272 65 84 N SD: 0.0596 c. M: 0.1087 c. 1696: 546 69 288 347 288 69 89 N SD: 0.0522 c. M: 0.0790 c. 1848: 595 75 314 378 314 75 97 N SD: 0.0373 c. M:-0.0569 c. 2019: 650 82 343 413 343 82 106 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 6:7 x x 8 S SD: 26.3377 cents 5:6 x 7:8:9 x 10 S SD: 26.9622 cents 6 x 8:9:10:11 x 12 S SD: 19.4338 cents 7 x 9:10:12:13 x 14 SD: 11.1634 cents 8:10 x 12:13:15 x 16 SD: 15.3431 cents 9:11:12:13:15:17 x 18 SD: 12.5240 cents 10 x 13:14:17:19 x 20 SD: 14.5014 cents 11 x 14:16:18 x 21:22 SD: 8.2965 cents 12:15 x 17:20 x 23:24 SD: 7.5112 cents 14 x 18:20:23:26:27:28 SD: 6.1407 cents 15:19 x 22:25:28:29:30 SD: 5.7304 cents 18 x 23:26:30:34:35:36 SD: 3.6711 cents 19:24 x 27:32:36:37:38 SD: 7.8295 cents 20:25:26:29:33:38:39:40 SD: 5.6761 cents 21:26:27:30:35:39:41:42 SD: 5.4636 cents 22 x 28:32:37:41:42:44 SD: 5.4465 cents 24:30:31:35:40:45:46:48 SD: 2.7856 cents 26 x 33:38:43:49:50:52 SD: 5.5384 cents 27:34:35:39:45:51:52:54 SD: 3.3171 cents 31:39:40:45:52:58:60:62 SD: 2.7734 cents 32:40:41:46:53:60:62:64 SD: 2.6066 cents 39:49:50:56:65:73:75:78 SD: 2.4579 cents 45:56:58:65:75:84:87:90 SD: 1.8129 cents 56:70:72:81:93:105:108:112 SD: 0.8849 cents 81:101:104:117:135:152:156:162 SD: 0.8724 cents 87:109:112:126:145:163:168:174 SD: 0.8108 cents 112:140:144:162:187:210:216:224 SD: 0.4412 cents 168:210:216:243:280:315:324:336 SD: 0.0000 cents