Scala analysis: xen09-wilson-marwa-18b-06
Marwa permutation 6 from Figure 18b, Ptolemy 10/9 11/10 12/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 8/5 813.686286 minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 10/9 182.4037 minor whole tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 9/8 203.9100 major whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 2 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 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: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 15/11 536.951 cents undecimal augmented fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 5: 1 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 33/20 866.959 cents 5: 2 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 20/11 1034.996 cents large minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 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 : 165.0 315.6 498.0 663.0 813.7 1017.6 1200.0 165.0 : 150.6 333.0 498.0 648.7 852.6 1035.0 1200.0 315.6 : 182.4 347.4 498.0 702.0 884.4 1049.4 1200.0 498.0 : 165.0 315.6 519.6 702.0 867.0 1017.6 1200.0 663.0 : 150.6 354.5 537.0 702.0 852.6 1035.0 1200.0 813.7 : 203.9 386.3 551.3 702.0 884.4 1049.4 1200.0 1017.6: 182.4 347.4 498.0 680.4 845.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 203.9100 cents 33/32, 53.2729 cents 12/11, 150.6371 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 16/15, 111.7313 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1049.3629 cents 33/32, 53.2729 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.138024 Largest / Average step : 1.189475 Largest / Smallest step : 1.353651 Median interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 167.97591 cents, oct.: 1175.83139 cents Scale is strictly proper Step pattern alph. order: ABCABDC Step pattern size order : BACBADC Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.313255 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.704636 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 Lydian octave species of abstract tetrachord Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 4 at degree 5 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 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 70.6724 cents: 5 -- Rational properties -- Prime limit : 11 Odd number limit : 33 (O: 33 U: 33) Highest odd numerator or denominator: 15 Scale harmonicity : 0.027336 Average absolute harmonicity : 0.225674 Specific harmonicity : 0.146169 Fundamental : 1/30, -4.9069 octaves, 8.7209 Hz. Guide tone : 792, 9.6294 octaves, 207207.448 Hz. Exponens Consonantiae : 2.376000E+04, 14.53625 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 53.0, average 7.57143 Mersenne's string divisions : 222222 Sum of van Prooijen's expressibility: 5.04679, average 0.72097 Sum of Tenney's harmonic distance : 10.67251, average 1.52464 Vogel's harmonic complexity : 10.00000 Wille's k value : 16 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 65.42956, average 2.33677 Lattice compactness (without 2's) : 44.01476, average 1.57196 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.00000 9 1 3: -1 .. 2 0.14286 5 1 5: -1 .. 0 -0.71429 5 3 11: 0 .. 1 0.28571 2 2 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 18 26| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 17 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 22.5780 c. M:-43.4566 c. Lebeng 12: 2 1 2 2 1 2 2 P M ME S SD: 21.8288 c. M:-36.9508 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 15: 2 2 2 2 2 3 2 SP M ME S SD: 15.0721 c. M: 23.0492 c. 20: 3 2 3 3 3 3 3 SP M ME S SD: 14.6513 c. M:-26.3137 c. Minor quasi-equal Heptatonic 21: 3 3 3 3 2 4 3 SP T3 SD: 16.3323 c. M:-27.2159 c. 22: 3 3 3 3 3 4 3 SP M ME S SD: 9.5080 c. M:-18.7673 c. 24: 3 3 4 3 3 4 4 SP D3 S SD: 12.7662 c. M: 17.5963 c. Maqam Ouchairan-Hussaini, Bayatan, Neutral Diatonic Mixolydian 26: 4 3 4 3 4 4 4 SP D3 S SD: 12.6216 c. M:-19.6112 c. 27: 4 3 4 4 3 5 4 SP T3 SD: 8.3608 c. M: 13.6863 c. 31: 4 4 5 4 4 5 5 SP D3 S SD: 6.7126 c. M: 11.1447 c. Neutral Diatonic Mixolydian 34: 5 4 5 5 4 6 5 SP T3 SD: 5.9360 c. M:-11.4664 c. 38: 5 5 6 5 5 6 6 SP D3 S SD: 5.4370 c. M:-7.3663 c. 46: 6 6 7 6 6 8 7 SP SD: 5.7027 c. M: 10.8753 c. 53: 7 7 8 7 7 9 8 SP SD: 3.5731 c. M: 6.5137 c. 58: 8 7 9 8 7 10 9 SP SD: 3.6267 c. M: 6.7897 c. 60: 8 8 9 8 8 10 9 SP SD: 3.8322 c. M:-6.3137 c. 65: 9 8 10 9 8 11 10 SP SD: 1.4123 c. M: 2.2117 c. 118: 16 15 18 16 15 20 18 SP SD: 1.1975 c. M: 2.2924 c. 152: 21 19 23 21 19 26 23 SP SD: 0.5435 c. M:-0.8248 c. 217: 30 27 33 30 27 37 33 SP SD: 0.5382 c. M:-0.8944 c. 270: 37 34 41 37 34 46 41 SP SD: 0.4198 c. M: 0.8270 c. 277: 38 35 42 38 35 47 42 SP SD: 0.4414 c. M:-0.7541 c. 335: 46 42 51 46 42 57 51 SP SD: 0.3296 c. M: 0.5520 c. 342: 47 43 52 47 43 58 52 SP SD: 0.1719 c. M:-0.3488 c. 494: 68 62 75 68 62 84 75 SP SD: 0.1330 c. M:-0.2175 c. 677: 93 85 103 93 85 115 103 SP SD: 0.1174 c. M: 0.1665 c. 829: 114 104 126 114 104 141 126 SP SD: 0.0876 c. M: 0.1760 c. 1019: 140 128 155 140 128 173 155 SP SD: 0.0842 c. M: 0.1367 c. 1106: 152 139 168 152 139 188 168 SP SD: 0.0846 c. M:-0.1252 c. 1171: 161 147 178 161 147 199 178 SP SD: 0.0160 c. M: 0.0262 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: 19.4529 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 23.5675 cents 5 x 6 x 7:8:9:10 S SD: 16.1074 cents 6 x 7:8:9:10:11:12 S SD: 16.5797 cents 7:8 x 9:10:11:13:14 SD: 19.9436 cents 8:9:10:11:12:13:14:16 S SD: 16.8783 cents 9:10:11:12:13:14:16:18 S SD: 9.9504 cents 10:11:12:13:15:16:18:20 SD: 8.3725 cents 15:17:18:20:22:24:27:30 SD: 7.3832 cents 18:20:22:24:26:29:32:36 SD: 7.3075 cents 19:21:23:25:28:30:34:38 SD: 5.5694 cents 20:22:24:27:29:32:36:40 SD: 4.1747 cents 30:33:36:40:44:48:54:60 S SD: 0.0000 cents