Scala analysis: xen09-wilson-marwa-10-03
Marwa permutation 3 from Figure 10, Ptolemy 7/6 12/11 22/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 33/28 284.447037 undecimal minor third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 11/7 782.492036 undecimal augmented fifth 6: 99/56 986.402038 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 112/99 213.5980 1: 9/8 203.9100 major whole tone 2: 22/21 80.5370 undecimal minor semitone 3: 7/6 266.8709 septimal minor third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 22/21 80.5370 undecimal minor semitone 6: 9/8 203.9100 major whole tone 7: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 2 33/28 284.447 cents undecimal minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 3 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 3 11/7 782.492 cents undecimal augmented fifth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 2 56/33 915.553 cents 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 1 99/56 986.402 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 21/11 1119.463 cents undecimal major seventh 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 : 203.9 284.4 551.3 702.0 782.5 986.4 1200.0 203.9 : 80.5 347.4 498.0 578.6 782.5 996.1 1200.0 284.4 : 266.9 417.5 498.0 702.0 915.6 1119.5 1200.0 551.3 : 150.6 231.2 435.1 648.7 852.6 933.1 1200.0 702.0 : 80.5 284.4 498.0 702.0 782.5 1049.4 1200.0 782.5 : 203.9 417.5 621.4 702.0 968.8 1119.5 1200.0 986.4 : 213.6 417.5 498.0 764.9 915.6 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 231.1741 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.556747 Largest / Smallest step : 3.313642 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 167.61036 cents, oct.: 1173.27252 cents Scale is not proper Step pattern alph. order: ABCDBAE Step pattern size order : CAEBACD Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.570782 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 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 : 896/891, 9.6880 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 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 class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.026454 Average absolute harmonicity : 0.218917 Specific harmonicity : 0.111719 Fundamental : 1/56, -5.8074 octaves, 4.6719 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 139.0, average 19.85714 Mersenne's string divisions : 54971370 Sum of van Prooijen's expressibility: 7.02830, average 1.00404 Sum of Tenney's harmonic distance : 13.47698, average 1.92528 Vogel's harmonic complexity : 14.28571 Wille's k value : 49 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 72.80572, average 2.60020 Lattice compactness (without 2's) : 42.96614, average 1.53451 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.57143 13 1 3: 0 .. 2 0.85714 6 2 7: -1 .. 0 -0.42857 3 11: 0 .. 1 0.57143 4 4 Average exponent except 2's : 7 / 7 = 1.00000 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 18 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 43.8389 c. M:-74.6508 c. Lebeng 8: 1 1 2 1 0 2 1 N D3 SD: 42.9732 c. M:-63.5980 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 37.7752 c. M: 70.5767 c. Pseudo Pelog, Pelogic-7, Antiionian 11: 2 1 2 1 1 2 2 N D3 SD: 25.9018 c. M: 47.4095 c. 12: 2 1 3 1 1 2 2 N T3 SD: 21.1200 c. M:-48.6821 c. Minor Gipsy, Mela Sanmukhapriya, Raga Camara, Chinthamani 13: 2 1 3 2 0 3 2 N SD: 25.4858 c. M: 44.0305 c. 14: 2 1 3 2 1 2 3 P T3 SD: 27.9138 c. M: 43.5449 c. 17: 3 1 4 2 1 3 3 N SD: 6.5505 c. M:-13.3879 c. 29: 5 2 6 4 2 5 5 N SD: 6.2814 c. M: 13.3869 c. 39: 7 2 9 5 2 7 7 N SD: 7.6218 c. M: 13.2613 c. 41: 7 3 9 5 3 7 7 N SD: 5.7068 c. M:-8.7199 c. 46: 8 3 10 6 3 8 8 N SD: 3.1885 c. M:-4.9023 c. 63: 11 4 14 8 4 11 11 N SD: 2.9544 c. M:-5.6138 c. 72: 12 5 16 9 5 12 13 N SD: 2.1452 c. M: 3.9100 c. 89: 15 6 20 11 6 15 16 N SD: 1.3169 c. M: 2.1324 c. 118: 20 8 26 15 8 20 21 N SD: 0.8808 c. M: 2.1654 c. 135: 23 9 30 17 9 23 24 N SD: 0.2784 c. M:-0.5344 c. 342: 58 23 76 43 23 58 61 N SD: 0.3033 c. M: 0.4407 c. 359: 61 24 80 45 24 61 64 N SD: 0.2274 c. M: 0.3296 c. 477: 81 32 106 60 32 81 85 N SD: 0.1927 c. M: 0.3745 c. 494: 84 33 110 62 33 84 88 N SD: 0.1737 c. M: 0.3058 c. 612: 104 41 136 77 41 104 109 N SD: 0.1547 c. M: 0.3376 c. 629: 107 42 140 79 42 107 112 N SD: 0.1659 c. M: 0.2981 c. 742: 126 50 165 93 50 126 132 N SD: 0.1544 c. M:-0.2573 c. 747: 127 50 166 94 50 127 133 N SD: 0.1485 c. M: 0.3139 c. 836: 142 56 186 105 56 142 149 N SD: 0.1667 c. M: 0.2776 c. 877: 149 59 195 110 59 149 156 N SD: 0.1133 c. M:-0.1762 c. 1012: 172 68 225 127 68 172 180 N SD: 0.0960 c. M:-0.1592 c. 1101: 187 74 245 138 74 187 196 N SD: 0.0845 c. M:-0.1807 c. 1147: 195 77 255 144 77 195 204 N SD: 0.0949 c. M:-0.1716 c. 1219: 207 82 271 153 82 207 217 N SD: 0.0772 c. M: 0.1364 c. 1236: 210 83 275 155 83 210 220 N SD: 0.0554 c. M:-0.1384 c. 1354: 230 91 301 170 91 230 241 N SD: 0.0507 c. M:-0.0781 c. 1371: 233 92 305 172 92 233 244 N SD: 0.0434 c. M:-0.1044 c. 1489: 253 100 331 187 100 253 265 N SD: 0.0391 c. M: 0.0755 c. 1713: 291 115 381 215 115 291 305 N SD: 0.0361 c. M: 0.0623 c. 1848: 314 124 411 232 124 314 329 N SD: 0.0229 c. M: 0.0384 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 38.3186 cents 4 x 5 x 6 x 7:8 S SD: 25.8430 cents 5 x 6:7 x 8:9:10 S SD: 12.4777 cents 6 x 7:8:9 x 11:12 SD: 16.8654 cents 7:8 x 10 x 11:12:14 S SD: 17.8435 cents 8:9 x 11:12:13:14:16 SD: 10.1065 cents 9:10:11:12 x 14:16:18 S SD: 14.5939 cents 10:11:12:14:15:16:18:20 S SD: 10.5036 cents 11:12:13:15 x 17:19:22 SD: 12.3786 cents 12 x 14:17:18:19:21:24 SD: 9.8031 cents 13 x 15:18 x 20:23:26 SD: 10.6621 cents 14:16:17:19:21:22:25:28 SD: 9.2904 cents 16:18:19:22:24:25:28:32 SD: 3.4314 cents 32:36:38:44:48:50:57:64 SD: 2.9923 cents 34:38:40:47:51:53:60:68 SD: 2.9541 cents 38:43:45:52:57:60:67:76 SD: 2.5898 cents 40:45:47:55:60:63:71:80 SD: 1.3686 cents 56:63:66:77:84:88:99:112 SD: 0.0000 cents