Scala analysis: xen09-wilson-marwa-03-07
Marwa permutation 7 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: 15/8 1088.268715 classic major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 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: 10/9 182.4037 minor whole tone 7: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 386.3 498.0 702.0 905.9 1088.3 1200.0 203.9 : 182.4 294.1 498.0 702.0 884.4 996.1 1200.0 386.3 : 111.7 315.6 519.6 702.0 813.7 1017.6 1200.0 498.0 : 203.9 407.8 590.2 702.0 905.9 1088.3 1200.0 702.0 : 203.9 386.3 498.0 702.0 884.4 996.1 1200.0 905.9 : 182.4 294.1 498.0 680.4 792.2 996.1 1200.0 1088.3: 111.7 315.6 498.0 609.8 813.7 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 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 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 176.69593 cents, oct.: 1236.87149 cents Scale is strictly proper Step pattern alph. order: ABCAABC Step pattern size order : LMSLLMS Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.415885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.503263 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 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: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Phrygian octave species of abstract tetrachord Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords 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 All steps are superparticular (epimoric) Length of longest harmonic part : 2 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 n-1 differentially coherent in interval classes 2 and 3 combined Scale is 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: 2 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 27 Scale harmonicity : 0.043353 Average absolute harmonicity : 0.270323 Specific harmonicity : 0.245398 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 2.592000E+04, 14.66178 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 53.5, average 7.64286 Mersenne's string divisions : 5296095 Sum of van Prooijen's expressibility: 5.21491, average 0.74499 Sum of Tenney's harmonic distance : 10.03139, average 1.43306 Vogel's harmonic complexity : 9.57143 Wille's k value : 40 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 89.22730, average 3.18669 Lattice compactness (without 2's) : 47.94155, average 1.71220 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.42857 16 1 3: -1 .. 3 0.85714 8 4 5: 0 .. 1 0.28571 2 2 Average exponent except 2's : 8 / 7 = 1.14286 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: 36.6619 c. M: 59.6973 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 33.4609 c. M:-62.7567 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 28.3980 c. M:-54.1350 c. Pseudo Rast 12: 2 2 1 2 2 2 1 P M ME S SD: 7.3898 c. M:-13.6863 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 29: 5 4 3 5 5 4 3 SP SD: 7.3735 c. M: 13.8999 c. 31: 5 5 3 5 5 5 3 SP M DE S SD: 7.7696 c. M: 15.5424 c. Thirty-one tone Major, Intense Diatonic Lydian, M.Ionian 34: 6 5 3 6 6 5 3 P SD: 6.2021 c. M:-11.7821 c. 41: 7 6 4 7 7 6 4 SP SD: 3.0704 c. M: 5.8259 c. 53: 9 8 5 9 9 8 5 SP SD: 0.7775 c. M: 1.4763 c. Makam Sazkar 65: 11 10 6 11 11 10 6 SP SD: 0.8806 c. M:-1.3786 c. 118: 20 18 11 20 20 18 11 SP SD: 0.3870 c. M: 0.7803 c. 171: 29 26 16 29 29 26 16 SP SD: 0.3831 c. M: 0.6018 c. 289: 49 44 27 49 49 44 27 SP SD: 0.3638 c. M: 0.6747 c. 323: 55 49 30 55 55 49 30 SP SD: 0.3286 c. M:-0.6365 c. 376: 64 57 35 64 64 57 35 SP SD: 0.2587 c. M:-0.5180 c. 388: 66 59 36 66 66 59 36 SP SD: 0.2405 c. M:-0.3911 c. 441: 75 67 41 75 75 67 41 SP SD: 0.1438 c. M:-0.2574 c. 494: 84 75 46 84 84 75 46 SP SD: 0.1058 c. M:-0.2079 c. 547: 93 83 51 93 93 83 51 SP SD: 0.1271 c. M: 0.2077 c. 559: 95 85 52 95 95 85 52 SP SD: 0.0552 c. M:-0.1034 c. 612: 104 93 57 104 104 93 57 SP SD: 0.0212 c. M: 0.0392 c. 1171: 199 178 109 199 199 178 109 SP SD: 0.0199 c. M:-0.0319 c. 1783: 303 271 166 303 303 271 166 SP SD: 0.0122 c. M:-0.0239 c. 2395: 407 364 223 407 407 364 223 SP SD: 0.0114 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 6:7 x 8 S SD: 15.7402 cents 5 x 6:7 x 8:9:10 S SD: 32.0130 cents 6:7 x 8:9:10:11:12 S SD: 12.8455 cents 7:8:9 x 11:12:13:14 SD: 17.1803 cents 8:9:10:11:12:14:15:16 S SD: 11.7821 cents 9:10:11:12:14:15:17:18 SD: 11.5759 cents 10:11 x 13:15:17:19:20 SD: 10.7029 cents 14:16:18:19:21:24:26:28 SD: 10.1806 cents 15:17:19:20:23:25:28:30 SD: 7.3664 cents 16:18:20:21:24:27:30:32 S SD: 3.8949 cents 24:27:30:32:36:41:45:48 SD: 3.0346 cents 32:36:40:43:48:54:60:64 SD: 1.9247 cents 48:54:60:64:72:81:90:96 S SD: 0.0000 cents