Scala analysis: xen09-wilson-marwa-18a-05
Marwa permutation 5 from Figure 18a, Ptolemy 12/11 11/10 10/9
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: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 33/20 866.959229 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: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 10/9 182.4037 minor whole tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 11/10 165.0042 Ptolemy's second, 4/5-tone 5: 9/8 203.9100 major whole tone 6: 10/9 182.4037 minor whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-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: 2 40/33 333.041 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 99/80 368.914 cents 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: 1 160/99 831.086 cents 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 2 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 : 165.0 347.4 498.0 663.0 867.0 1049.4 1200.0 165.0 : 182.4 333.0 498.0 702.0 884.4 1035.0 1200.0 347.4 : 150.6 315.6 519.6 702.0 852.6 1017.6 1200.0 498.0 : 165.0 368.9 551.3 702.0 867.0 1049.4 1200.0 663.0 : 203.9 386.3 537.0 702.0 884.4 1035.0 1200.0 867.0 : 182.4 333.0 498.0 680.4 831.1 996.1 1200.0 1049.4: 150.6 315.6 498.0 648.7 813.7 1017.6 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 : 171.69376 cents, oct.: 1201.85629 cents Scale is strictly proper Step pattern alph. order: ABCADBC Step pattern size order : BCABDCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.315972 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 : 121/120, 14.3672 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Phrygian 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 : 2 at degree 4 Length of longest subharmonic part : 3 at degree 6 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 Limited inverse transpositions with margin 53.2729 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.027336 Average absolute harmonicity : 0.201608 Specific harmonicity : 0.129889 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 2.376000E+04, 14.53625 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 79.0, average 11.28571 Mersenne's string divisions : 14001540 Sum of van Prooijen's expressibility: 6.29590, average 0.89941 Sum of Tenney's harmonic distance : 12.57484, average 1.79641 Vogel's harmonic complexity : 17.00000 Wille's k value : 148 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 65.73218, average 2.34758 Lattice compactness (without 2's) : 43.53000, average 1.55464 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 8 1 3: -2 .. 1 -0.57143 6 1 5: -1 .. 0 -0.42857 3 11: 0 .. 1 0.71429 5 5 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 18 23| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 12 16 22|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 13.9801 c. M:-22.6651 c. Lebeng 15: 2 2 2 2 3 2 2 SP M ME S SD: 16.4354 c. M: 27.4079 c. 17: 2 3 2 2 3 3 2 SP D3 S SD: 16.3431 c. M: 27.7551 c. Dastgah-e Sehgah 22: 3 3 3 3 4 3 3 SP M ME S SD: 10.2315 c. M: 20.1352 c. 24: 3 4 3 3 4 4 3 SP D3 S SD: 9.9568 c. M: 16.9592 c. Dastgah-e Sehgah, Neutral Diatonic Lydian 29: 4 4 4 4 5 4 4 SP M ME S SD: 8.4261 c. M: 16.3735 c. 31: 4 5 4 4 5 5 4 SP D3 S SD: 7.6452 c. M: 15.3463 c. Neutral Diatonic Lydian 32: 4 5 4 5 5 5 4 SP D3 SD: 9.2397 c. M: 15.0042 c. 34: 5 5 4 5 6 5 4 SP T3 S SD: 8.9508 c. M:-15.3937 c. 36: 5 5 5 5 6 5 5 SP M ME S SD: 8.2358 c. M: 16.0296 c. Equal Diatonic Phrygian 37: 5 6 4 5 7 5 5 SP SD: 9.6010 c. M: 14.4006 c. 38: 5 6 5 5 6 6 5 SP D3 S SD: 7.1775 c. M: 14.3277 c. 41: 6 6 5 6 7 6 5 SP T3 S SD: 7.2812 c. M:-11.0896 c. 45: 6 7 6 6 8 6 6 SP T3 SD: 7.2775 c. M:-13.0408 c. 46: 6 7 6 6 8 7 6 SP SD: 6.9301 c. M: 10.8753 c. 48: 7 7 6 7 8 7 6 SP T3 S SD: 6.7436 c. M:-11.9508 c. 49: 7 7 6 7 8 8 6 SP SD: 5.8967 c. M: 9.8164 c. 51: 7 8 6 7 9 8 6 SP SD: 4.8794 c. M:-9.4606 c. 53: 7 8 7 7 9 8 7 SP SD: 5.9712 c. M: 7.8535 c. 55: 8 8 7 7 10 8 7 SP SD: 5.5813 c. M:-9.5412 c. 56: 8 8 7 8 9 9 7 SP SD: 5.1712 c. M: 9.8164 c. 58: 8 9 7 8 10 9 7 SP SD: 2.9243 c. M:-5.8095 c. 65: 9 10 8 9 11 10 8 SP SD: 1.8691 c. M:-3.3613 c. 80: 11 12 10 11 14 12 10 SP SD: 2.2045 c. M: 3.0492 c. 87: 12 13 11 12 15 13 11 SP SD: 1.4793 c. M: 2.5804 c. 118: 16 18 15 16 20 18 15 SP SD: 1.7850 c. M: 2.5524 c. 137: 19 21 17 19 23 21 17 SP SD: 1.7844 c. M:-2.9570 c. 145: 20 22 18 20 25 22 18 SP SD: 1.2133 c. M:-2.0063 c. 152: 21 23 19 21 26 23 19 SP SD: 0.7202 c. M:-1.4618 c. 159: 22 24 20 22 27 24 20 SP SD: 0.6937 c. M:-1.1017 c. 224: 31 34 28 31 38 34 28 SP SD: 0.8070 c. M:-1.2365 c. 241: 33 37 30 33 41 37 30 SP SD: 0.7885 c. M:-1.2595 c. 246: 34 37 31 34 42 37 31 SP SD: 0.7878 c. M:-1.3335 c. 248: 34 38 31 34 42 38 31 SP SD: 0.5892 c. M:-0.9792 c. 270: 37 41 34 37 46 41 34 SP SD: 0.5249 c. M: 0.8270 c. 328: 45 50 41 45 56 50 41 SP SD: 0.4695 c. M: 0.8541 c. 335: 46 51 42 46 57 51 42 SP SD: 0.1887 c. M: 0.3627 c. 342: 47 52 43 47 58 52 43 SP SD: 0.1713 c. M: 0.2926 c. 494: 68 75 62 68 84 75 62 SP SD: 0.1264 c. M:-0.2472 c. 677: 93 103 85 93 115 103 85 SP SD: 0.1073 c. M: 0.1941 c. 829: 114 126 104 114 141 126 104 SP SD: 0.0726 c. M:-0.1095 c. 836: 115 127 105 115 142 127 105 SP SD: 0.0619 c. M:-0.1087 c. 1171: 161 178 147 161 199 178 147 SP SD: 0.0136 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: 5.7998 cents 4 x 5 x 6 x 7:8 S SD: 24.3843 cents 5 x 6 x 7:8:9:10 S SD: 21.3002 cents 6 x 7:8:9:10:11:12 S SD: 15.1864 cents 7:8 x 9:10:12:13:14 S SD: 20.6127 cents 8:9:10:11:12:13:15:16 SD: 13.9907 cents 9:10:11:12:13:15:17:18 SD: 9.0070 cents 17:19:21:23:25:28:31:34 SD: 6.1516 cents 18:20:22:24:26:30:33:36 SD: 5.1589 cents 22:24:27:29:32:36:40:44 SD: 5.0872 cents 23:25:28:31:34:38:42:46 SD: 4.6551 cents 28:31:34:37:41:46:51:56 SD: 3.7400 cents 30:33:37:40:44:50:55:60 SD: 3.3448 cents 32:35:39:43:47:53:59:64 SD: 3.0243 cents 39:43:48:52:57:64:72:78 SD: 2.9736 cents 40:44:49:53:59:66:73:80 SD: 2.4398 cents 41:45:50:55:60:68:75:82 SD: 2.2572 cents 49:54:60:65:72:81:90:98 SD: 1.6282 cents 60:66:73:80:88:99:110:120 SD: 1.1267 cents 90:99:110:120:132:149:165:180 SD: 0.8313 cents 108:119:132:144:158:178:198:216 SD: 0.8008 cents 120:132:147:160:176:198:220:240 SD: 0.5615 cents 171:188:209:228:251:282:314:342 SD: 0.4783 cents 180:198:220:240:264:297:330:360 S SD: 0.0000 cents