Scala analysis: xen09-wilson-marwa-17a-08
Marwa permutation 8 from Figure 17a, Archytas 28/27 36/35 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: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 3: 4/3 498.044999 perfect fourth 4: 5/3 884.358713 major sixth, BP sixth 5: 140/81 947.319617 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: 5/4 386.3137 major third 2: 28/27 62.9609 Archytas' 1/3-tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 5/4 386.3137 major third 5: 28/27 62.9609 Archytas' 1/3-tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 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 2: 1 45/32 590.224 cents diatonic tritone 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 64/45 609.776 cents 2nd tritone 5: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 140/81 947.320 cents 5: 2 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 386.3 449.3 498.0 884.4 947.3 996.1 1200.0 386.3 : 63.0 111.7 498.0 561.0 609.8 813.7 1200.0 449.3 : 48.8 435.1 498.0 546.8 750.7 1137.0 1200.0 498.0 : 386.3 449.3 498.0 702.0 1088.3 1151.2 1200.0 884.4 : 63.0 111.7 315.6 702.0 764.9 813.7 1200.0 947.3 : 48.8 252.7 639.0 702.0 750.7 1137.0 1200.0 996.1 : 203.9 590.2 653.2 702.0 1088.3 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 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 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 : 28/27, 62.9609 cents, amount: 2 Least squares average step : 181.63979 cents, oct.: 1271.47854 cents Scale is not proper Step pattern alph. order: ABCABCD Step pattern size order : DBADBAC Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.578397 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 701.955 1151.230 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.029983 Average absolute harmonicity : 0.232192 Specific harmonicity : 0.154033 Fundamental : 1/324, -8.3399 octaves, 0.8075 Hz. Guide tone : 560, 9.1293 octaves, 146510.317 Hz. Exponens Consonantiae : 1.814400E+05, 17.46913 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 167.5, average 23.92857 Mersenne's string divisions : 86322600 Sum of van Prooijen's expressibility: 6.28186, average 0.89741 Sum of Tenney's harmonic distance : 13.04574, average 1.86368 Vogel's harmonic complexity : 15.14286 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 90.39932, average 3.22855 Lattice compactness (without 2's) : 57.64284, average 2.05867 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.00000 11 1 3: -4 .. 0 -1.57143 11 2 5: 0 .. 1 0.57143 4 2 7: 0 .. 1 0.28571 2 2 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 11 16 18| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 1 0 2 1 0 1 N T3 SD: 45.9445 c. M:-81.2518 c. 8: 3 0 0 3 0 1 1 N SD: 40.9789 c. M:-63.6863 c. 9: 3 0 1 3 0 0 2 N SD: 38.5322 c. M: 62.7567 c. 10: 3 1 0 3 1 0 2 N SD: 27.7567 c. M: 44.3587 c. 12: 4 0 1 4 0 1 2 N SD: 27.0402 c. M: 49.2746 c. 13: 4 1 0 5 0 1 2 N SD: 24.5940 c. M:-38.7182 c. 15: 5 1 0 5 1 0 3 N SD: 20.4913 c. M: 36.0900 c. 16: 5 1 1 5 1 0 3 N SD: 18.1688 c. M:-27.6804 c. 18: 6 1 0 6 1 1 3 N SD: 16.8959 c. M: 31.3783 c. 19: 6 1 1 6 1 1 3 N SD: 7.2328 c. M:-14.4363 c. 24: 8 1 1 8 1 1 4 N SD: 8.0957 c. M:-15.6413 c. 34: 11 2 1 11 2 1 6 N SD: 5.4461 c. M:-9.5489 c. 41: 13 2 2 13 2 2 7 N SD: 6.4942 c. M: 10.7343 c. 43: 14 2 2 14 2 2 7 N SD: 5.2894 c. M:-8.6645 c. 46: 15 2 2 15 2 2 8 N SD: 4.7950 c. M: 8.1892 c. 53: 17 3 2 17 3 2 9 N SD: 2.0555 c. M:-3.6238 c. 94: 30 5 4 30 5 4 16 N SD: 2.2872 c. M: 3.5076 c. 96: 31 5 4 31 5 4 16 N SD: 2.3329 c. M:-3.9100 c. 99: 32 5 4 32 5 4 17 N SD: 1.3402 c. M: 2.1506 c. 118: 38 6 5 38 6 5 20 N SD: 0.9434 c. M: 1.8170 c. 152: 49 8 6 49 8 6 26 N SD: 0.6675 c. M: 1.3532 c. 171: 55 9 7 55 9 7 29 N SD: 0.2300 c. M:-0.4012 c. 323: 104 17 13 104 17 13 55 N SD: 0.2144 c. M: 0.4244 c. 441: 142 23 18 142 23 18 75 N SD: 0.1984 c. M: 0.3808 c. 494: 159 26 20 159 26 20 84 N SD: 0.0989 c. M: 0.1482 c. 665: 214 35 27 214 35 27 113 N SD: 0.0834 c. M: 0.1483 c. 935: 301 49 38 301 49 38 159 N SD: 0.0969 c. M: 0.1542 c. 1106: 356 58 45 356 58 45 188 N SD: 0.0758 c. M: 0.1225 c. 1277: 411 67 52 411 67 52 217 N SD: 0.0740 c. M: 0.0996 c. 1525: 491 80 62 491 80 62 259 N SD: 0.0717 c. M:-0.1067 c. 1600: 515 84 65 515 84 65 272 N SD: 0.0670 c. M: 0.1087 c. 1677: 540 88 68 540 88 68 285 N SD: 0.0680 c. M:-0.0993 c. 1771: 570 93 72 570 93 72 301 N SD: 0.0632 c. M: 0.1125 c. 1795: 578 94 73 578 94 73 305 N SD: 0.0529 c. M:-0.0981 c. 1848: 595 97 75 595 97 75 314 N SD: 0.0516 c. M:-0.0830 c. 1966: 633 103 80 633 103 80 334 N SD: 0.0430 c. M:-0.0767 c. 2019: 650 106 82 650 106 82 343 N SD: 0.0450 c. M:-0.0801 c. 2137: 688 112 87 688 112 87 363 N SD: 0.0429 c. M:-0.0728 c. 2289: 737 120 93 737 120 93 389 N SD: 0.0288 c. M:-0.0559 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: 91.2019 cents 3 x x 4:5 x x 6 S SD: 0.0000 cents 4:5 x x x 7 x 8 SD: 7.1688 cents 5:6 x 7:8 x 9:10 S SD: 26.5228 cents 6 x x 8:10 x 11:12 S SD: 13.3182 cents 7 x 9 x x 12 x 14 SD: 6.6895 cents 8:10 x 11:13:14 x 16 SD: 14.4522 cents 9:11 x 12:15 x 16:18 SD: 7.7812 cents 10 x 13 x x 17:18:20 SD: 9.0462 cents 11:14 x 15:18:19:20:22 SD: 11.7978 cents 12:15 x 16:20:21 x 24 S SD: 4.3013 cents 13:16:17 x 22 x 23:26 SD: 8.2905 cents 14 x 18:19:23:24:25:28 SD: 7.4938 cents 15:19 x 20:25:26:27:30 SD: 5.3039 cents 16:20:21 x 27:28 x 32 SD: 7.4500 cents 17:21:22:23:28:29:30:34 SD: 6.6474 cents 18 x 23:24:30:31:32:36 SD: 4.2781 cents 19:24 x 25:32:33:34:38 SD: 6.1986 cents 20:25:26:27:33:35:36:40 SD: 5.9156 cents 21:26:27:28:35:36:37:42 SD: 4.3290 cents 22:28 x 29:37:38:39:44 SD: 6.7403 cents 23:29:30:31:38:40:41:46 SD: 4.6412 cents 24:30:31:32:40:41:43:48 SD: 3.5812 cents 27:34:35:36:45:47:48:54 SD: 2.5358 cents 33:41:43:44:55:57:59:66 SD: 2.4273 cents 36:45:47:48:60:62:64:72 SD: 1.9702 cents 44:55:57:59:73:76:78:88 SD: 1.9441 cents 45:56:58:60:75:78:80:90 SD: 1.9288 cents 48:60:62:64:80:83:85:96 SD: 1.3161 cents 60:75:78:80:100:104:107:120 SD: 1.2615 cents 72:90:93:96:120:124:128:144 S SD: 1.2514 cents 81:101:105:108:135:140:144:162 SD: 0.6114 cents 108:135:140:144:180:187:192:216 SD: 0.4412 cents 132:165:171:176:220:228:235:264 SD: 0.4182 cents 180:225:233:240:300:311:320:360 SD: 0.3644 cents 189:236:245:252:315:327:336:378 SD: 0.3636 cents 192:240:249:256:320:332:341:384 SD: 0.2877 cents 216:270:280:288:360:373:384:432 SD: 0.2209 cents 243:304:315:324:405:420:432:486 SD: 0.2035 cents 324:405:420:432:540:560:576:648 S SD: 0.0000 cents