Scala analysis: xen09-wilson-marwa-10-04
Marwa permutation 4 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: 22/21 80.537035 undecimal minor semitone 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: 22/21 80.5370 undecimal minor semitone 2: 9/8 203.9100 major whole tone 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 32/27 294.135 cents Pythagorean minor third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 21/16 470.781 cents narrow fourth 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: 1 32/21 729.219 cents wide fifth 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 27/16 905.865 cents Pythagorean major 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: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 80.5 284.4 551.3 702.0 782.5 986.4 1200.0 80.5 : 203.9 470.8 621.4 702.0 905.9 1119.5 1200.0 284.4 : 266.9 417.5 498.0 702.0 915.6 996.1 1200.0 551.3 : 150.6 231.2 435.1 648.7 729.2 933.1 1200.0 702.0 : 80.5 284.4 498.0 578.6 782.5 1049.4 1200.0 782.5 : 203.9 417.5 498.0 702.0 968.8 1119.5 1200.0 986.4 : 213.6 294.1 498.0 764.9 915.6 996.1 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 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 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 : 166.72912 cents, oct.: 1167.10387 cents Scale is not proper Step pattern alph. order: ABCDABE Step pattern size order : ACEBACD Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.506814 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 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 : 896/891, 9.6880 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 class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.024711 Average absolute harmonicity : 0.206219 Specific harmonicity : 0.112353 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 198, 7.6294 octaves, 51801.862 Hz. Exponens Consonantiae : 3.326400E+04, 15.02167 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 152.0, average 21.71429 Mersenne's string divisions : 139045230 Sum of van Prooijen's expressibility: 7.39628, average 1.05661 Sum of Tenney's harmonic distance : 14.28429, average 2.04061 Vogel's harmonic complexity : 17.14286 Wille's k value : 148 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 74.12544, average 2.64734 Lattice compactness (without 2's) : 43.46212, average 1.55222 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.00000 11 1 3: -1 .. 2 0.42857 5 1 7: -1 .. 0 -0.57143 4 11: 0 .. 1 0.71429 5 5 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 22| Scale is weakly epimorphic with val: <7 12 18 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 81.9132 c. M: 129.2592 c. 8: 0 1 2 1 1 1 2 N D3 SD: 87.6221 c. M: 134.4470 c. 9: 0 2 2 1 1 1 2 N T3 SD: 40.5214 c. M: 80.5370 c. 11: 1 2 2 1 1 2 2 P D3 S SD: 27.5369 c. M: 47.4095 c. 12: 1 2 3 1 1 2 2 N SD: 22.3156 c. M:-48.6821 c. Mela Bhavapriya, Raga Bhavani, Kalamurti, Neveseri ascending: Greece 14: 1 2 3 2 1 2 3 P T3 SD: 25.1454 c. M: 43.5449 c. Superpelog-Pelog 15: 1 3 3 2 1 2 3 N SD: 19.5262 c. M:-35.5530 c. 16: 1 3 3 2 1 3 3 P SD: 20.2749 c. M: 32.4920 c. Gorgo-Pelog 17: 1 3 4 2 1 3 3 N SD: 6.9451 c. M:-13.3879 c. 29: 2 5 6 4 2 5 5 N SD: 6.2359 c. M: 13.3869 c. 39: 3 6 9 5 2 7 7 N SD: 7.6860 c. M: 13.2613 c. 41: 3 7 9 5 3 7 7 N SD: 6.3230 c. M:-8.7199 c. 43: 3 7 10 5 3 7 8 N SD: 5.3236 c. M: 9.6579 c. 46: 3 8 10 6 3 8 8 N SD: 2.7631 c. M:-4.9023 c. 63: 4 11 14 8 4 11 11 N SD: 2.6316 c. M: 4.3466 c. 72: 5 12 16 9 5 12 13 N SD: 1.8801 c. M: 3.0687 c. 89: 6 15 20 11 6 15 16 N SD: 1.1653 c. M: 2.1324 c. 118: 8 20 26 15 8 20 21 N SD: 0.9126 c. M: 2.1654 c. 135: 9 23 30 17 9 23 24 N SD: 0.2791 c. M: 0.5370 c. 342: 23 58 76 43 23 58 61 N SD: 0.2699 c. M: 0.4407 c. 359: 24 61 80 45 24 61 64 N SD: 0.2565 c. M: 0.3296 c. 477: 32 81 106 60 32 81 85 N SD: 0.1861 c. M: 0.3745 c. 612: 41 104 136 77 41 104 109 N SD: 0.1640 c. M: 0.3376 c. 742: 50 126 165 93 50 126 132 N SD: 0.1906 c. M:-0.3255 c. 747: 50 127 166 94 50 127 133 N SD: 0.1646 c. M: 0.3139 c. 836: 56 142 186 105 56 142 149 N SD: 0.1738 c. M: 0.2776 c. 877: 59 149 195 110 59 149 156 N SD: 0.1341 c. M:-0.1927 c. 966: 65 164 215 121 65 164 172 N SD: 0.1340 c. M:-0.2349 c. 1012: 68 172 225 127 68 172 180 N SD: 0.1013 c. M:-0.1592 c. 1101: 74 187 245 138 74 187 196 N SD: 0.0883 c. M:-0.1807 c. 1147: 77 195 255 144 77 195 204 N SD: 0.0873 c. M:-0.1716 c. 1236: 83 210 275 155 83 210 220 N SD: 0.0571 c. M:-0.1384 c. 1354: 91 230 301 170 91 230 241 N SD: 0.0608 c. M:-0.1129 c. 1371: 92 233 305 172 92 233 244 N SD: 0.0423 c. M:-0.1044 c. 1489: 100 253 331 187 100 253 265 N SD: 0.0437 c. M: 0.0755 c. 1624: 109 276 361 204 109 276 289 N SD: 0.0415 c. M: 0.0864 c. 1713: 115 291 381 215 115 291 305 N SD: 0.0303 c. M: 0.0623 c. 1848: 124 314 411 232 124 314 329 N SD: 0.0233 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 x 8:10 x 11:12:14 S SD: 20.0544 cents 8 x 9:11:12:13:14:16 SD: 16.8022 cents 9:10:11:12 x 14:16:18 S SD: 22.0993 cents 10:11:12:14:15:16:18:20 S SD: 15.0014 cents 11:12:13:15 x 17:19:22 SD: 14.5223 cents 12:13:14:17:18:19:21:24 SD: 11.8043 cents 13:14:15:18 x 20:23:26 SD: 11.9294 cents 14:15:17:19:21:22:25:28 SD: 10.1012 cents 16:17:19:22:24:25:28:32 SD: 4.8932 cents 21:22:25:29:32:33:37:42 SD: 4.8151 cents 22:23:26:30:33:35:39:44 SD: 3.8321 cents 34:36:40:47:51:53:60:68 SD: 3.6082 cents 38:40:45:52:57:60:67:76 SD: 2.4538 cents 40:42:47:55:60:63:71:80 SD: 1.4793 cents 56:59:66:77:84:88:99:112 SD: 1.4012 cents 78:82:92:107:117:123:138:156 SD: 1.3774 cents 80:84:94:110:120:126:141:160 SD: 1.3256 cents 82:86:97:113:123:129:145:164 SD: 1.1341 cents 86:90:101:118:129:135:152:172 SD: 1.0846 cents 102:107:120:140:153:160:180:204 SD: 0.9423 cents 106:111:125:146:159:167:187:212 SD: 0.9403 cents 107:112:126:147:161:168:189:214 SD: 0.9015 cents 112:117:132:154:168:176:198:224 SD: 0.7036 cents 128:134:151:176:192:201:226:256 SD: 0.4628 cents 168:176:198:231:252:264:297:336 SD: 0.0000 cents