Scala analysis: xen09-wilson-marwa-17a-02
Marwa permutation 2 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: 35/24 653.184619 septimal semi-diminished fifth 4: 5/3 884.358713 major sixth, BP sixth 5: 15/8 1088.268715 classic major seventh 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 5/4 386.3137 major third 2: 28/27 62.9609 Archytas' 1/3-tone 3: 9/8 203.9100 major whole tone 4: 8/7 231.1741 septimal whole tone 5: 9/8 203.9100 major whole tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 7/6 266.871 cents septimal minor third 2: 3 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: 3 14/9 764.916 cents septimal minor sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 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: 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 : 386.3 449.3 653.2 884.4 1088.3 1151.2 1200.0 386.3 : 63.0 266.9 498.0 702.0 764.9 813.7 1200.0 449.3 : 203.9 435.1 639.0 702.0 750.7 1137.0 1200.0 653.2 : 231.2 435.1 498.0 546.8 933.1 996.1 1200.0 884.4 : 203.9 266.9 315.6 702.0 764.9 968.8 1200.0 1088.3: 63.0 111.7 498.0 561.0 764.9 996.1 1200.0 1151.2: 48.8 435.1 498.0 702.0 933.1 1137.0 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 : 196.64695 cents, oct.: 1376.52865 cents Scale is not proper Step pattern alph. order: ABCDCBE Step pattern size order : EBCDCBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.577632 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 : 245/243, 14.1905 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 1 = 14.2857% Scale is 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 : 81 (O: 81 U: 81) Highest odd numerator or denominator: 35 Scale harmonicity : 0.031896 Average absolute harmonicity : 0.205843 Specific harmonicity : 0.162814 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 210, 7.7142 octaves, 54941.369 Hz. Exponens Consonantiae : 4.536000E+04, 15.46913 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 108.5, average 15.50000 Mersenne's string divisions : 160527672 Sum of van Prooijen's expressibility: 7.20624, average 1.02946 Sum of Tenney's harmonic distance : 13.55638, average 1.93663 Vogel's harmonic complexity : 15.57143 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 78.15764, average 2.79134 Lattice compactness (without 2's) : 51.63748, average 1.84420 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.14286 10 1 3: -3 .. 1 -0.85714 8 5: 0 .. 1 0.85714 6 3 7: 0 .. 1 0.42857 3 3 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is weakly epimorphic with val: <7 10 15 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 2 1 1 1 1 1 0 N T3 SD: 44.4910 c. M:-65.0111 c. 8: 3 0 1 2 1 1 0 N SD: 39.5921 c. M:-63.6863 c. 9: 3 0 2 2 1 1 0 N SD: 33.8922 c. M: 49.2746 c. 11: 4 0 2 2 2 1 0 N SD: 27.2406 c. M:-50.0499 c. 13: 4 1 2 3 2 0 1 N SD: 24.6795 c. M: 43.5373 c. 15: 5 1 2 3 3 0 1 N SD: 21.7333 c. M:-31.7313 c. 16: 5 1 3 3 3 0 1 N SD: 20.3058 c. M:-36.7313 c. 18: 6 1 3 3 3 1 1 N SD: 15.9082 c. M: 21.6020 c. 19: 6 1 3 4 3 1 1 N SD: 11.9056 c. M: 21.6057 c. 22: 7 1 4 4 4 1 1 N T3 SD: 7.2148 c. M: 12.9110 c. 41: 13 2 7 8 7 2 2 N SD: 7.4536 c. M: 10.2502 c. 42: 14 2 7 8 7 2 2 N SD: 7.0036 c. M:-13.6863 c. 43: 14 2 7 9 7 2 2 N SD: 6.3221 c. M: 11.3242 c. 46: 15 2 8 9 8 2 2 N SD: 4.3486 c. M:-7.3835 c. 53: 17 3 9 10 9 3 2 N SD: 2.4626 c. M:-3.5556 c. 72: 23 4 12 14 12 4 3 N SD: 2.5766 c. M: 4.9354 c. 75: 24 4 13 14 13 4 3 N SD: 2.2222 c. M: 4.3587 c. 77: 25 4 13 15 13 4 3 N SD: 2.5783 c. M:-3.9530 c. 94: 30 5 16 18 16 5 4 N SD: 2.6529 c. M: 3.5076 c. 96: 31 5 16 19 16 5 4 N SD: 1.8534 c. M: 3.1846 c. 99: 32 5 17 19 17 5 4 N SD: 1.3211 c. M:-2.6404 c. 118: 38 6 20 23 20 6 5 N SD: 1.3764 c. M: 2.3372 c. 149: 48 8 25 29 25 8 6 N SD: 1.0285 c. M:-1.7321 c. 152: 49 8 26 29 26 8 6 N SD: 1.1062 c. M:-2.0785 c. 171: 55 9 29 33 29 9 7 N SD: 0.3583 c. M: 0.5530 c. 270: 87 14 46 52 46 14 11 N SD: 0.3166 c. M:-0.6202 c. 419: 135 22 71 81 71 22 17 N SD: 0.3055 c. M:-0.6055 c. 441: 142 23 75 85 75 23 18 N SD: 0.1605 c. M: 0.2950 c. 494: 159 26 84 95 84 26 20 N SD: 0.1430 c. M:-0.2567 c. 612: 197 32 104 118 104 32 25 N SD: 0.1652 c. M: 0.2550 c. 665: 214 35 113 128 113 35 27 N SD: 0.1022 c. M: 0.1484 c. 935: 301 49 159 180 159 49 38 N SD: 0.0583 c. M: 0.0806 c. 1106: 356 58 188 213 188 58 45 N SD: 0.0576 c. M: 0.0911 c. 1525: 491 80 259 294 259 80 62 N SD: 0.0518 c. M:-0.1003 c. 1848: 595 97 314 356 314 97 75 N SD: 0.0560 c. M:-0.0760 c. 1966: 633 103 334 379 334 103 80 N SD: 0.0555 c. M: 0.0819 c. 2019: 650 106 343 389 343 106 82 N SD: 0.0300 c. M:-0.0567 c. 2190: 705 115 372 422 372 115 89 N SD: 0.0293 c. M: 0.0495 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: 24.3852 cents 3 x 4 x 5 x x 6 S SD: 16.2568 cents 4:5 x 6:7 x x 8 S SD: 24.3840 cents 5:6 x 7:8:9 x 10 S SD: 28.2690 cents 6 x 8:9:10:11 x 12 S SD: 15.8376 cents 7 x 9:10:12:13 x 14 SD: 12.8509 cents 8:10 x 12:13:15 x 16 SD: 13.1144 cents 9:11:12:13:15:17 x 18 SD: 10.9670 cents 10 x 13:15:17:19 x 20 SD: 12.8126 cents 11:14 x 16:18:21 x 22 SD: 10.9097 cents 12:15:16:18:20 x 23:24 SD: 12.2220 cents 13:16:17:19:22:24:25:26 SD: 7.4909 cents 14 x 18:20:23:26:27:28 SD: 8.4525 cents 15:19 x 22:25:28:29:30 SD: 4.6578 cents 18 x 23:26:30:34:35:36 SD: 5.4217 cents 20:25:26:29:33:38:39:40 SD: 4.4625 cents 24:30:31:35:40:45:47:48 SD: 1.9702 cents 48:60:62:70:80:90:93:96 SD: 1.2514 cents 57:71:74:83:95:107:111:114 SD: 1.1198 cents 72:90:93:105:120:135:140:144 SD: 0.8849 cents 87:109:113:127:145:163:169:174 SD: 0.8451 cents 104:130:135:152:173:195:202:208 SD: 0.8430 cents 105:131:136:153:175:197:204:210 SD: 0.6078 cents 111:139:144:162:185:208:216:222 SD: 0.5741 cents 129:161:167:188:215:242:251:258 SD: 0.5708 cents 144:180:187:210:240:270:280:288 SD: 0.4412 cents 159:199:206:232:265:298:309:318 SD: 0.4009 cents 168:210:218:245:280:315:327:336 SD: 0.3567 cents 192:240:249:280:320:360:373:384 SD: 0.2470 cents 216:270:280:315:360:405:420:432 S SD: 0.0000 cents