Scala analysis: xen09-wilson-marwa-10-15
Marwa permutation 15 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: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 11/7 782.492036 undecimal augmented fifth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 22/21 80.5370 undecimal minor semitone 2: 7/6 266.8709 septimal minor third 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 22/21 80.5370 undecimal minor semitone 6: 7/6 266.8709 septimal minor third 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 33/28 284.447 cents undecimal minor third 2: 2 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 2 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: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 56/33 915.553 cents 5: 1 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 80.5 347.4 498.0 702.0 782.5 1049.4 1200.0 80.5 : 266.9 417.5 621.4 702.0 968.8 1119.5 1200.0 347.4 : 150.6 354.5 435.1 702.0 852.6 933.1 1200.0 498.0 : 203.9 284.4 551.3 702.0 782.5 1049.4 1200.0 702.0 : 80.5 347.4 498.0 578.6 845.5 996.1 1200.0 782.5 : 266.9 417.5 498.0 764.9 915.6 1119.5 1200.0 1049.4: 150.6 231.2 498.0 648.7 852.6 933.1 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 : 12/11, 150.6371 cents, amount: 2 Least squares average step : 169.18533 cents, oct.: 1184.29729 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ADBCADB Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.579325 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 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 : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Scale contains a complete diamond : 1 3 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 : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.025337 Average absolute harmonicity : 0.234508 Specific harmonicity : 0.121134 Fundamental : 1/126, -6.9773 octaves, 2.0764 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 1.663200E+04, 14.02167 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 56.5, average 8.07143 Mersenne's string divisions : 921060 Sum of van Prooijen's expressibility: 5.40064, average 0.77152 Sum of Tenney's harmonic distance : 10.52467, average 1.50352 Vogel's harmonic complexity : 16.85714 Wille's k value : 115 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 59.12073, average 2.11145 Lattice compactness (without 2's) : 42.79795, average 1.52850 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.28571 6 1 3: -2 .. 1 -0.57143 6 2 7: -1 .. 0 -0.28571 2 11: 0 .. 1 0.57143 4 4 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 18 26| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 43.1600 c. M: 80.5370 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 35.1524 c. M:-52.7963 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 30.7360 c. M:-57.5080 c. 12: 1 2 2 2 1 2 2 P M ME S SD: 27.7159 c. M: 49.3629 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 13: 1 3 1 3 0 3 2 N SD: 30.1744 c. M: 44.0305 c. 14: 1 3 2 2 1 3 2 P T3 SD: 12.7039 c. M: 20.7915 c. 17: 1 4 2 3 1 4 2 N SD: 6.3942 c. M: 9.9488 c. 31: 2 7 4 5 2 7 4 N SD: 4.6426 c. M: 8.2985 c. 41: 3 9 5 7 3 9 5 N SD: 4.5726 c. M:-7.7519 c. 46: 3 10 6 8 3 10 6 N SD: 4.1368 c. M: 8.2775 c. 48: 3 11 6 8 3 11 6 N SD: 3.8090 c. M: 7.4920 c. 55: 4 12 7 9 4 12 7 N SD: 3.5821 c. M:-6.7357 c. 58: 4 13 7 10 4 13 7 N SD: 3.2858 c. M:-5.8095 c. 63: 4 14 8 11 4 14 8 N SD: 2.9465 c. M: 4.5508 c. 72: 5 16 9 12 5 16 9 N SD: 1.8243 c. M:-2.7963 c. 89: 6 20 11 15 6 20 11 N SD: 1.5618 c. M:-3.1539 c. 104: 7 23 13 18 7 23 13 N SD: 1.3987 c. M:-2.1233 c. 118: 8 26 15 20 8 26 15 N SD: 1.0320 c. M: 1.9053 c. 135: 9 30 17 23 9 30 17 N SD: 0.4273 c. M: 0.7413 c. 207: 14 46 26 35 14 46 26 N SD: 0.3955 c. M:-0.6224 c. 311: 21 69 39 53 21 69 39 N SD: 0.3930 c. M:-0.7877 c. 342: 23 76 43 58 23 76 43 N SD: 0.1550 c. M: 0.2401 c. 477: 32 106 60 81 32 106 60 N SD: 0.1565 c. M: 0.3063 c. 670: 45 149 84 114 45 149 84 N SD: 0.1290 c. M:-0.1945 c. 701: 47 156 88 119 47 156 88 N SD: 0.0990 c. M: 0.1811 c. 805: 54 179 101 137 54 179 101 N SD: 0.1047 c. M:-0.1568 c. 836: 56 186 105 142 56 186 105 N SD: 0.1024 c. M: 0.1954 c. 1012: 68 225 127 172 68 225 127 N SD: 0.0610 c. M:-0.1167 c. 1147: 77 255 144 195 77 255 144 N SD: 0.0468 c. M:-0.0712 c. 1371: 92 305 172 233 92 305 172 N SD: 0.0453 c. M:-0.0900 c. 1489: 100 331 187 253 100 331 187 N SD: 0.0439 c. M: 0.0681 c. 1506: 101 335 189 256 101 335 189 N SD: 0.0344 c. M: 0.0589 c. 1713: 115 381 215 291 115 381 215 N SD: 0.0282 c. M:-0.0527 c. 1848: 124 411 232 314 124 411 232 N SD: 0.0130 c. M: 0.0245 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: 33.9556 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 20.1256 cents 6 x 7:8:9 x 11:12 SD: 16.1074 cents 7 x x 9 x 11:13:14 SD: 16.7016 cents 9:10:11:12 x 14:17:18 SD: 19.2619 cents 10:11:12:13:15:16:18:20 SD: 15.6800 cents 11:12:13:15 x 17:20:22 SD: 17.3635 cents 12:13:15:16:18:19:22:24 SD: 10.1544 cents 13:14:16:17 x 20:24:26 SD: 11.8435 cents 14:15:17:19:21:22:26:28 SD: 7.9267 cents 17:18:21:23:26:27:31:34 SD: 7.6568 cents 18:19:22:24:27:28:33:36 SD: 3.1287 cents 36:38:44:48:54:57:66:72 SD: 2.6397 cents 40:42:49:53:60:63:73:80 SD: 2.1493 cents 42:44:51:56:63:66:77:84 SD: 1.6112 cents 60:63:73:80:90:94:110:120 SD: 1.4657 cents 66:69:81:88:99:104:121:132 SD: 1.3284 cents 82:86:100:109:123:129:150:164 SD: 1.1503 cents 84:88:103:112:126:132:154:168 SD: 0.8017 cents 108:113:132:144:162:170:198:216 SD: 0.5203 cents 126:132:154:168:189:198:231:252 S SD: 0.0000 cents