Scala analysis: xen09-wilson-marwa-10-06
Marwa permutation 6 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: 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: 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: 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 : 203.9 284.4 551.3 702.0 782.5 1049.4 1200.0 203.9 : 80.5 347.4 498.0 578.6 845.5 996.1 1200.0 284.4 : 266.9 417.5 498.0 764.9 915.6 1119.5 1200.0 551.3 : 150.6 231.2 498.0 648.7 852.6 933.1 1200.0 702.0 : 80.5 347.4 498.0 702.0 782.5 1049.4 1200.0 782.5 : 266.9 417.5 621.4 702.0 968.8 1119.5 1200.0 1049.4: 150.6 354.5 435.1 702.0 852.6 933.1 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 : 170.30868 cents, oct.: 1192.16079 cents Scale is not proper Step pattern alph. order: ABCDBCD Step pattern size order : CADBADB Scale is sum-free (all different intervals) 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 Hypodorian octave species of abstract tetrachord Best fifths form a closed circle 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 : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 33 Scale harmonicity : 0.024711 Average absolute harmonicity : 0.221573 Specific harmonicity : 0.118371 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 : 70.0, average 10.00000 Mersenne's string divisions : 1773270 Sum of van Prooijen's expressibility: 6.07406, average 0.86772 Sum of Tenney's harmonic distance : 11.55270, average 1.65039 Vogel's harmonic complexity : 17.28571 Wille's k value : 115 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 69.50340, average 2.48226 Lattice compactness (without 2's) : 42.56188, average 1.52007 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.28571 11 1 3: -1 .. 2 0.42857 5 2 7: -1 .. 0 -0.28571 2 11: 0 .. 1 0.57143 4 4 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 11 / 7 = 1.57143 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: 1 0 2 1 0 2 1 N T3 SD: 60.0733 c. M: 113.0185 c. 8: 1 1 2 1 0 2 1 N D3 SD: 35.6222 c. M: 53.9100 c. 9: 2 0 2 1 1 2 1 N D3 SD: 30.3061 c. M:-62.7567 c. 11: 2 1 2 1 1 3 1 N T3 SD: 30.2404 c. M: 47.4095 c. 12: 2 1 3 1 1 3 1 N T3 S SD: 28.0346 c. M:-50.6371 c. Double Harmonic Minor, Hungarian Minor, Egyptian Heptatonic, Mela Simhendramadhyama, Raga Madhava Manohari, Shimendra Madyam, Maqam Nawa Athar, Hisar, Flamenco Mode, Niavent: Greece 13: 2 1 3 1 1 3 2 N SD: 30.8041 c. M: 55.8012 c. 14: 2 1 3 2 1 3 2 P T3 SD: 23.8759 c. M: 37.0322 c. 15: 3 1 3 2 1 3 2 N T3 SD: 21.9144 c. M:-36.0900 c. 16: 3 1 3 2 1 4 2 N SD: 21.2537 c. M: 32.4920 c. 17: 3 1 4 2 1 4 2 N SD: 7.4307 c. M:-13.3879 c. 31: 5 2 7 4 2 7 4 N SD: 8.3704 c. M: 13.4793 c. 37: 6 3 8 5 2 8 5 N SD: 7.7970 c. M:-11.5585 c. 39: 7 2 9 5 2 9 5 N SD: 7.6881 c. M: 13.2613 c. 41: 7 3 9 5 3 9 5 N SD: 4.9337 c. M:-8.2359 c. 46: 8 3 10 6 3 10 6 N SD: 3.4176 c. M: 5.8847 c. 63: 11 4 14 8 4 14 8 N SD: 2.6061 c. M:-5.6138 c. 72: 12 5 16 9 5 16 9 N SD: 1.8206 c. M: 3.9100 c. 89: 15 6 20 11 6 20 11 N SD: 1.3620 c. M:-2.3225 c. 118: 20 8 26 15 8 26 15 N SD: 1.1376 c. M: 2.1654 c. 135: 23 9 30 17 9 30 17 N SD: 0.3156 c. M:-0.5344 c. 342: 58 23 76 43 23 76 43 N SD: 0.2700 c. M: 0.4407 c. 359: 61 24 80 45 24 80 45 N SD: 0.2075 c. M: 0.3245 c. 477: 81 32 106 60 32 106 60 N SD: 0.2059 c. M: 0.3745 c. 494: 84 33 110 62 33 110 62 N SD: 0.1622 c. M: 0.3058 c. 629: 107 42 140 79 42 140 79 N SD: 0.1662 c. M: 0.2981 c. 701: 119 47 156 88 47 156 88 N SD: 0.1575 c. M: 0.2816 c. 742: 126 50 165 93 50 165 93 N SD: 0.1717 c. M:-0.2573 c. 836: 142 56 186 105 56 186 105 N SD: 0.1330 c. M: 0.2365 c. 877: 149 59 195 110 59 195 110 N SD: 0.1100 c. M:-0.1762 c. 1012: 172 68 225 127 68 225 127 N SD: 0.0767 c. M:-0.1379 c. 1147: 195 77 255 144 77 255 144 N SD: 0.0695 c. M:-0.1214 c. 1354: 230 91 301 170 91 301 170 N SD: 0.0517 c. M:-0.0781 c. 1371: 233 92 305 172 92 305 172 N SD: 0.0539 c. M:-0.1044 c. 1489: 253 100 331 187 100 331 187 N SD: 0.0452 c. M: 0.0755 c. 1506: 256 101 335 189 101 335 189 N SD: 0.0462 c. M:-0.0765 c. 1713: 291 115 381 215 115 381 215 N SD: 0.0289 c. M: 0.0571 c. 1848: 314 124 411 232 124 411 232 N SD: 0.0183 c. M: 0.0315 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: 32.4644 cents 5 x 6:7 x 8:9:10 S SD: 12.5353 cents 6 x 7:8:9 x 11:12 SD: 11.2195 cents 7:8 x 10 x 11:13:14 SD: 14.9944 cents 8:9 x 11:12:13:15:16 SD: 11.6450 cents 9:10:11:12 x 14:17:18 SD: 16.8693 cents 10:11:12:14:15:16:18:20 S SD: 10.5386 cents 11:12:13:15 x 17:20:22 SD: 10.6798 cents 12 x 14:17:18:19:22:24 SD: 9.3552 cents 13 x 15:18 x 20:24:26 SD: 10.9284 cents 14:16:17:19:21:22:26:28 SD: 9.5036 cents 16:18:19:22:24:25:29:32 SD: 3.6687 cents 24:27:28:33:36:38:44:48 SD: 3.1287 cents 32:36:38:44:48:50:59:64 SD: 2.7264 cents 40:45:47:55:60:63:73:80 SD: 1.4657 cents 56:63:66:77:84:88:103:112 SD: 0.8017 cents 72:81:85:99:108:113:132:144 SD: 0.5203 cents 96:108:113:132:144:151:176:192 SD: 0.3904 cents 152:171:179:209:228:239:279:304 SD: 0.3850 cents 168:189:198:231:252:264:308:336 S SD: 0.0000 cents