Scala analysis: xen09-wilson-marwa-03-15
Marwa permutation 15 from Figure 3, Ptolemy 16/15 9/8 10/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 128/81 792.179997 Pythagorean minor sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 10/9 182.4037 minor whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 9/8 203.9100 major whole tone 4: 9/8 203.9100 major whole tone 5: 256/243 90.2250 limma, Pythagorean minor second 6: 9/8 203.9100 major whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 4 9/8 203.910 cents major whole tone 2: 3 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 2 81/64 407.820 cents Pythagorean major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 40/27 680.449 cents grave fifth 4: 5 3/2 701.955 cents perfect fifth 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.66667 = 11/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 294.1 498.0 702.0 792.2 996.1 1200.0 182.4 : 111.7 315.6 519.6 609.8 813.7 1017.6 1200.0 294.1 : 203.9 407.8 498.0 702.0 905.9 1088.3 1200.0 498.0 : 203.9 294.1 498.0 702.0 884.4 996.1 1200.0 702.0 : 90.2 294.1 498.0 680.4 792.2 996.1 1200.0 792.2 : 203.9 407.8 590.2 702.0 905.9 1109.8 1200.0 996.1 : 203.9 386.3 498.0 702.0 905.9 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1109.7750 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.900012 Largest / Average step : 1.189475 Largest / Smallest step : 2.260017 Median interval of one step : 9/8, 203.9100 cents, amount: 4 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 167.21478 cents, oct.: 1170.50343 cents Scale is strictly proper Step pattern alph. order: ABCCDCC Step pattern size order : CBDDADD Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.461397 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.467419 Rothenberg efficiency : 0.496599 redundancy: 0.503401 Efficiency x scale size : 3.476190 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.66667 = 11/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 6 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 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 113.6850 cents: 6 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.036058 Average absolute harmonicity : 0.258031 Specific harmonicity : 0.222376 Fundamental : 1/162, -7.3399 octaves, 1.6150 Hz. Guide tone : 1920, 10.9069 octaves, 502321.085 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 163.5, average 23.35714 Mersenne's string divisions : 6473775 Sum of van Prooijen's expressibility: 6.20258, average 0.88608 Sum of Tenney's harmonic distance : 13.22318, average 1.88903 Vogel's harmonic complexity : 11.71429 Wille's k value : 121 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 111.45986, average 3.98071 Lattice compactness (without 2's) : 59.69891, average 2.13210 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 7 2.71429 21 1 3: -4 .. 1 -1.57143 13 5 5: 0 .. 1 0.14286 1 1 Average exponent except 2's :-10 / 7 =-1.42857 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.4281 c. M:-64.9629 c. Lebeng 8: 1 1 1 2 0 2 1 P D3 S SD: 38.5199 c. M:-53.9100 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 37.1339 c. M: 62.7567 c. Pseudo Pelog, Pelogic-7, Antiionian 12: 2 1 2 2 1 2 2 P M ME S SD: 7.8204 c. M:-17.5963 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 29: 4 3 5 5 2 5 5 SP SD: 7.1142 c. M: 16.8865 c. 32: 5 3 5 6 2 6 5 P SD: 9.0550 c. M:-16.4100 c. 33: 5 3 6 5 3 5 6 SP T3 SD: 8.6157 c. M: 14.2718 c. 34: 5 3 6 6 2 6 6 P SD: 8.5636 c. M: 15.7094 c. 36: 5 4 6 6 3 6 6 SP SD: 7.2322 c. M: 15.7370 c. First plagal Byzantine Liturgical mode descending 39: 6 4 6 7 3 6 7 SP SD: 7.9941 c. M:-13.5573 c. 41: 6 4 7 7 3 7 7 SP SD: 2.7625 c. M: 6.7940 c. 53: 8 5 9 9 4 9 9 SP SD: 0.5016 c. M: 1.2716 c. Makam Ussak, Acem, Arazbar 118: 18 11 20 20 9 20 20 SP SD: 0.5995 c. M:-1.0403 c. 171: 26 16 29 29 13 29 29 SP SD: 0.4226 c. M:-0.8025 c. 224: 34 21 38 38 17 38 38 SP SD: 0.3696 c. M:-0.6771 c. 277: 42 26 47 47 21 47 47 SP SD: 0.3592 c. M:-0.5998 c. 330: 50 31 56 56 25 56 56 SP SD: 0.3632 c. M: 0.5855 c. 335: 51 31 57 57 25 57 57 SP SD: 0.3027 c. M: 0.5382 c. 388: 59 36 66 66 29 66 66 SP SD: 0.2264 c. M: 0.4274 c. 441: 67 41 75 75 33 75 75 SP SD: 0.1838 c. M: 0.3433 c. 453: 69 42 77 77 34 77 77 SP SD: 0.1576 c. M:-0.3777 c. 494: 75 46 84 84 37 84 84 SP SD: 0.1674 c. M: 0.2772 c. 506: 77 47 86 86 38 86 86 SP SD: 0.0895 c. M:-0.2050 c. 559: 85 52 95 95 42 95 95 SP SD: 0.0365 c. M:-0.0650 c. 612: 93 57 104 104 46 104 104 SP SD: 0.0227 c. M: 0.0508 c. 1171: 178 109 199 199 88 199 199 SP SD: 0.0193 c. M: 0.0365 c. 1783: 271 166 303 303 134 303 303 SP SD: 0.0177 c. M: 0.0319 c. 2395: 364 223 407 407 180 407 407 SP SD: 0.0180 c. M: 0.0297 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: 30.7262 cents 4 x 5 x 6 x 7:8 S SD: 24.0316 cents 5 x 6:7 x 8:9:10 S SD: 18.4632 cents 6 x 7:8:9 x 11:12 SD: 11.9689 cents 7:8 x 9 x 11:12:14 SD: 20.3966 cents 8:9 x 11:12:13:14:16 SD: 13.3139 cents 9:10:11:12 x 14:16:18 S SD: 9.9740 cents 10:11:12:13:15:16:18:20 SD: 8.5851 cents 11:12:13:15 x 17:20:22 SD: 12.4122 cents 12:13:14:16:18:19:21:24 SD: 8.3535 cents 16:18:19:21:24:25:28:32 SD: 6.9148 cents 17:19:20:23:26:27:30:34 SD: 6.8134 cents 18:20:21:24:27:28:32:36 S SD: 5.5082 cents 24:27:28:32:36:38:43:48 SD: 5.3429 cents 26:29:31:35:39:41:46:52 SD: 3.2234 cents 36:40:43:48:54:57:64:72 SD: 1.9842 cents 48:53:57:64:72:76:85:96 SD: 1.9512 cents 54:60:64:72:81:85:96:108 SD: 0.9680 cents 90:100:107:120:135:142:160:180 SD: 0.8632 cents 98:109:116:131:147:155:174:196 SD: 0.8408 cents 108:120:128:144:162:171:192:216 SD: 0.4826 cents 162:180:192:216:243:256:288:324 SD: 0.0000 cents