Scala analysis: xen09-wilson-marwa-03-10
Marwa permutation 10 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: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major 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: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 256/243 90.2250 limma, Pythagorean minor second 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 : 203.9 386.3 498.0 702.0 905.9 996.1 1200.0 203.9 : 182.4 294.1 498.0 702.0 792.2 996.1 1200.0 386.3 : 111.7 315.6 519.6 609.8 813.7 1017.6 1200.0 498.0 : 203.9 407.8 498.0 702.0 905.9 1088.3 1200.0 702.0 : 203.9 294.1 498.0 702.0 884.4 996.1 1200.0 905.9 : 90.2 294.1 498.0 680.4 792.2 996.1 1200.0 996.1 : 203.9 407.8 590.2 702.0 905.9 1109.8 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 : 172.74541 cents, oct.: 1209.21787 cents Scale is strictly proper Step pattern alph. order: ABCAADA Step pattern size order : DCBDDAD 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 9 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% 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: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.036058 Average absolute harmonicity : 0.273791 Specific harmonicity : 0.230935 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 2160, 11.0768 octaves, 565111.221 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 54.5, average 7.78571 Mersenne's string divisions : 1151325 Sum of van Prooijen's expressibility: 4.99306, average 0.71329 Sum of Tenney's harmonic distance : 10.11057, average 1.44437 Vogel's harmonic complexity : 11.57143 Wille's k value : 121 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 108.72090, average 3.88289 Lattice compactness (without 2's) : 56.46284, average 2.01653 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 -0.42857 17 1 3: -2 .. 3 0.42857 9 5 5: 0 .. 1 0.14286 1 1 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 10 / 7 = 1.42857 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: 31.3959 c. M: 48.7221 c. Lebeng 10: 2 1 1 2 2 0 2 P D3 S SD: 31.3488 c. M:-54.1350 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 6.0937 c. M:-13.6863 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 29: 5 4 3 5 5 2 5 SP SD: 5.8012 c. M: 13.8999 c. 34: 6 5 3 6 6 2 6 P SD: 6.5110 c. M:-11.7821 c. 37: 6 6 3 7 6 3 6 SP SD: 8.0539 c. M:-11.5585 c. 40: 7 6 4 6 7 3 7 P SD: 7.6346 c. M:-11.9550 c. 41: 7 6 4 7 7 3 7 SP SD: 2.3419 c. M: 5.8259 c. 53: 9 8 5 9 9 4 9 SP SD: 0.5439 c. M: 1.4081 c. 65: 11 10 6 11 11 5 11 SP SD: 0.8617 c. M:-1.3786 c. 118: 20 18 11 20 20 9 20 SP SD: 0.4312 c. M: 0.7803 c. 171: 29 26 16 29 29 13 29 SP SD: 0.3558 c. M: 0.6018 c. 224: 38 34 21 38 38 17 38 SP SD: 0.3593 c. M: 0.5994 c. 323: 55 49 30 55 55 24 55 SP SD: 0.3504 c. M:-0.6365 c. 335: 57 51 31 57 57 25 57 SP SD: 0.3044 c. M:-0.5520 c. 376: 64 57 35 64 64 28 64 SP SD: 0.2896 c. M:-0.5180 c. 388: 66 59 36 66 66 29 66 SP SD: 0.2062 c. M:-0.3206 c. 441: 75 67 41 75 75 33 75 SP SD: 0.1446 c. M:-0.2574 c. 494: 84 75 46 84 84 37 84 SP SD: 0.1180 c. M:-0.2079 c. 506: 86 77 47 86 86 38 86 SP SD: 0.0999 c. M:-0.2476 c. 547: 93 83 51 93 93 41 93 SP SD: 0.1211 c. M: 0.2077 c. 559: 95 85 52 95 95 42 95 SP SD: 0.0402 c. M:-0.0906 c. 612: 104 93 57 104 104 46 104 SP SD: 0.0176 c. M: 0.0392 c. 1171: 199 178 109 199 199 88 199 SP SD: 0.0173 c. M:-0.0274 c. 1783: 303 271 166 303 303 134 303 SP SD: 0.0132 c. M:-0.0239 c. 2395: 407 364 223 407 407 180 407 SP SD: 0.0127 c. M:-0.0223 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: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 6.8160 cents 5 x 6:7 x 8:9:10 S SD: 29.0439 cents 6:7 x 8:9:10:11:12 S SD: 14.2054 cents 7:8:9 x 11:12 x 14 SD: 20.3484 cents 8:9:10:11:12 x 14:16 S SD: 9.9740 cents 10:11 x 13:15:17:18:20 SD: 10.6205 cents 12:14:15:16:18:20:21:24 S SD: 10.2717 cents 14:16:18:19:21:24:25:28 SD: 9.9628 cents 15:17:19:20:23:25:27:30 SD: 7.9050 cents 16:18:20:21:24:27:28:32 S SD: 5.5082 cents 23:26:29:31:35:39:41:46 SD: 5.2621 cents 24:27:30:32:36:41:43:48 SD: 3.5935 cents 32:36:40:43:48:54:57:64 SD: 1.9842 cents 48:54:60:64:72:81:85:96 SD: 0.9680 cents 80:90:100:107:120:135:142:160 SD: 0.8632 cents 96:108:120:128:144:162:171:192 SD: 0.4826 cents 144:162:180:192:216:243:256:288 SD: 0.0000 cents