Scala analysis: xen09-wilson-marwa-10-12
Marwa permutation 12 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: 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: 9/8 203.9100 major whole tone 2: 22/21 80.5370 undecimal minor semitone 3: 112/99 213.5980 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: 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: 2 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 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: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 56/33 915.553 cents 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 : 203.9 284.4 498.0 702.0 782.5 1049.4 1200.0 203.9 : 80.5 294.1 498.0 578.6 845.5 996.1 1200.0 284.4 : 213.6 417.5 498.0 764.9 915.6 1119.5 1200.0 498.0 : 203.9 284.4 551.3 702.0 905.9 986.4 1200.0 702.0 : 80.5 347.4 498.0 702.0 782.5 996.1 1200.0 782.5 : 266.9 417.5 621.4 702.0 915.6 1119.5 1200.0 1049.4: 150.6 354.5 435.1 648.7 852.6 933.1 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: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 99/98, 17.5761 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 .. 915.5530 cents 392/363, 133.0609 cents 99/98, 17.5761 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 99/98, 17.5761 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 : 169.16712 cents, oct.: 1184.16985 cents Scale is not proper Step pattern alph. order: ABCABDE Step pattern size order : CADCAEB Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.581147 Lumma stability : 0.192815 Lumma impropriety factor : 0.035697 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 : 243/242, 7.1391 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 Best fifths form a closed circle Best major thirds form a closed circle Scale contains a complete diamond : 1 3 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 n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.024115 Average absolute harmonicity : 0.245441 Specific harmonicity : 0.118338 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 64.0, average 9.14286 Mersenne's string divisions : 653310 Sum of van Prooijen's expressibility: 5.50978, average 0.78711 Sum of Tenney's harmonic distance : 10.68740, average 1.52677 Vogel's harmonic complexity : 16.00000 Wille's k value : 94 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 73.98729, average 2.64240 Lattice compactness (without 2's) : 45.67893, average 1.63139 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.57143 10 1 3: -1 .. 2 0.28571 6 3 7: -1 .. 0 -0.28571 2 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 21 26| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 21 23| 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: 39.6401 c. M:-74.6508 c. Lebeng 8: 1 1 1 2 0 2 1 P D3 S SD: 35.4984 c. M: 53.9100 c. 9: 2 0 2 1 1 2 1 N D3 SD: 32.4060 c. M:-62.7567 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 20.7297 c. M: 49.3629 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 14: 2 1 3 2 1 3 2 P T3 SD: 20.2935 c. M: 32.4814 c. 17: 3 1 3 3 1 4 2 N SD: 5.6403 c. M:-9.4606 c. 41: 7 3 7 7 3 9 5 N SD: 4.5947 c. M:-8.2359 c. 46: 8 3 8 8 3 10 6 N SD: 3.2797 c. M: 5.8847 c. 58: 10 4 10 10 4 13 7 N SD: 3.5467 c. M:-5.8095 c. 63: 11 4 11 11 4 14 8 N SD: 2.7849 c. M:-5.6138 c. 72: 12 5 13 12 5 16 9 N SD: 1.9006 c. M: 3.9100 c. 89: 15 6 16 15 6 20 11 N SD: 1.2792 c. M:-2.3225 c. 118: 20 8 21 20 8 26 15 N SD: 0.7962 c. M: 1.9053 c. 135: 23 9 24 23 9 30 17 N SD: 0.3220 c. M:-0.5344 c. 342: 58 23 61 58 23 76 43 N SD: 0.2256 c. M: 0.4012 c. 359: 61 24 64 61 24 80 45 N SD: 0.1910 c. M: 0.3245 c. 477: 81 32 85 81 32 106 60 N SD: 0.1517 c. M: 0.3063 c. 494: 84 33 88 84 33 110 62 N SD: 0.1600 c. M: 0.3058 c. 612: 104 41 109 104 41 136 77 N SD: 0.1489 c. M: 0.3433 c. 629: 107 42 112 107 42 140 79 N SD: 0.1710 c. M: 0.2981 c. 701: 119 47 125 119 47 156 88 N SD: 0.1571 c. M: 0.2816 c. 742: 126 50 132 126 50 165 93 N SD: 0.1621 c. M:-0.2573 c. 836: 142 56 149 142 56 186 105 N SD: 0.1258 c. M: 0.2365 c. 877: 149 59 156 149 59 195 110 N SD: 0.1025 c. M:-0.1762 c. 1012: 172 68 180 172 68 225 127 N SD: 0.0730 c. M:-0.1379 c. 1147: 195 77 204 195 77 255 144 N SD: 0.0709 c. M:-0.1214 c. 1236: 210 83 220 210 83 275 155 N SD: 0.0603 c. M:-0.1516 c. 1354: 230 91 241 230 91 301 170 N SD: 0.0478 c. M:-0.0781 c. 1371: 233 92 244 233 92 305 172 N SD: 0.0371 c. M:-0.0900 c. 1489: 253 100 265 253 100 331 187 N SD: 0.0352 c. M: 0.0681 c. 1713: 291 115 305 291 115 381 215 N SD: 0.0308 c. M: 0.0571 c. 1848: 314 124 329 314 124 411 232 N SD: 0.0170 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: 33.9556 cents 4 x 5 x 6 x 7:8 S SD: 32.4644 cents 5 x 6:7 x 8:9:10 S SD: 20.0898 cents 6 x 7:8:9 x 11:12 SD: 3.5152 cents 7:8 x 9 x 11:13:14 SD: 14.4311 cents 8:9 x 11:12:13:15:16 SD: 14.6437 cents 9:10:11:12 x 14:17:18 SD: 14.3436 cents 10:11:12:13:15:16:18:20 SD: 11.4197 cents 11:12:13:15 x 17:20:22 SD: 12.2626 cents 12 x 14:16:18:19:22:24 SD: 3.6501 cents 13 x 15:17 x 20:24:26 SD: 12.6021 cents 14:16:17:19:21:22:26:28 SD: 9.9513 cents 15:17:18:20:23:24:28:30 SD: 9.6154 cents 16:18:19:21:24:25:29:32 SD: 5.3506 cents 18:20:21:24:27:28:33:36 SD: 4.6955 cents 24:27:28:32:36:38:44:48 SD: 3.1287 cents 38:43:45:51:57:60:70:76 SD: 2.9817 cents 40:45:47:53:60:63:73:80 SD: 2.1337 cents 54:61:64:72:81:85:99:108 SD: 1.7664 cents 56:63:66:75:84:88:103:112 SD: 1.3625 cents 66:74:78:88:99:104:121:132 SD: 1.2734 cents 72:81:85:96:108:113:132:144 SD: 0.5203 cents 96:108:113:128:144:151:176:192 SD: 0.3904 cents 168:189:198:224:252:264:308:336 SD: 0.0000 cents