Scala analysis: xen09-wilson-marwa-18a-02
Marwa permutation 2 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: 11/8 551.317942 undecimal semi-augmented 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: 9/8 203.9100 major whole tone 4: 16/15 111.7313 minor diatonic semitone 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: 1 16/15 111.731 cents minor diatonic semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 2 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 3 6/5 315.641 cents minor third 2: 1 40/33 333.041 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 2 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: 2 8/5 813.686 cents minor sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 33/20 866.959 cents 5: 3 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 15/8 1088.269 cents classic major seventh 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 : 165.0 347.4 551.3 663.0 867.0 1049.4 1200.0 165.0 : 182.4 386.3 498.0 702.0 884.4 1035.0 1200.0 347.4 : 203.9 315.6 519.6 702.0 852.6 1017.6 1200.0 551.3 : 111.7 315.6 498.0 648.7 813.7 996.1 1200.0 663.0 : 203.9 386.3 537.0 702.0 884.4 1088.3 1200.0 867.0 : 182.4 333.0 498.0 680.4 884.4 996.1 1200.0 1049.4: 150.6 315.6 498.0 702.0 813.7 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: 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 .. 1088.2687 cents 135/128, 92.1787 cents 16/15, 111.7313 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 Least squares average step : 172.83532 cents, oct.: 1209.84723 cents Scale is strictly proper Step pattern alph. order: ABCDCBE Step pattern size order : CDEAEDB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.395193 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.639793 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 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 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents 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 : 4 at degree 6 Formal octave complements present : 1 = 14.2857% Scale is 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 -- Rational properties -- Prime limit : 11 Odd number limit : 33 (O: 33 U: 33) Highest odd numerator or denominator: 33 Scale harmonicity : 0.027336 Average absolute harmonicity : 0.177740 Specific harmonicity : 0.145947 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 66, 6.0444 octaves, 17267.287 Hz. Exponens Consonantiae : 2.376000E+04, 14.53625 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 85.0, average 12.14286 Mersenne's string divisions : 266029260 Sum of van Prooijen's expressibility: 6.86018, average 0.98003 Sum of Tenney's harmonic distance : 13.44014, average 1.92002 Vogel's harmonic complexity : 19.28571 Wille's k value : 247 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 67.92132, average 2.42576 Lattice compactness (without 2's) : 42.34846, average 1.51245 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.71429 9 1 3: -2 .. 1 -0.42857 5 5: -1 .. 0 -0.42857 3 11: 0 .. 1 0.85714 6 6 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 15 23| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 12 18 22|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 18.8062 c. M: 37.0322 c. Lebeng 13: 2 2 2 1 2 2 2 SP M ME I SD: 22.7311 c. M: 36.1900 c. Horthatian 15: 2 2 3 1 3 2 2 SP D3 I SD: 15.3092 c. M: 27.4079 c. 21: 3 3 4 2 3 3 3 SP T3 SD: 14.6812 c. M:-22.6651 c. 22: 3 3 4 2 4 3 3 SP D3 I SD: 10.1154 c. M: 20.1352 c. Symmetric Diminished Porcupine 24: 3 4 4 2 4 4 3 SP D3 I SD: 9.9419 c. M: 16.9592 c. Maqam Su'ar, Naghmeh Abuata, Naghmeh Afshari 29: 4 4 5 3 5 4 4 SP D3 I SD: 9.8123 c. M: 16.3735 c. 31: 4 5 5 3 5 5 4 SP D3 I SD: 8.1970 c. M: 15.3463 c. 32: 4 5 6 3 5 5 4 SP SD: 9.3461 c. M: 15.0042 c. 35: 5 5 6 3 6 6 4 SP SD: 8.3068 c. M:-13.4942 c. 41: 6 6 7 4 7 6 5 SP SD: 7.4998 c. M:-11.0896 c. 42: 6 6 7 4 7 7 5 SP SD: 6.8174 c. M: 9.8164 c. 46: 6 7 8 4 8 7 6 SP I SD: 6.9964 c. M: 10.8753 c. 48: 7 7 8 5 8 7 6 SP SD: 6.7215 c. M:-11.9508 c. 50: 7 8 8 5 8 8 6 SP SD: 6.5566 c. M:-12.5921 c. 51: 7 8 8 5 9 8 6 SP SD: 6.0248 c. M: 10.1415 c. 53: 7 8 9 5 9 8 7 SP I SD: 6.6798 c. M: 7.9217 c. 54: 7 9 9 5 9 8 7 SP SD: 5.4900 c. M: 9.4487 c. 56: 8 8 10 5 9 9 7 SP SD: 5.2673 c. M: 9.8164 c. 58: 8 9 10 5 10 9 7 SP SD: 3.9814 c. M:-7.3027 c. 65: 9 10 11 6 11 10 8 SP SD: 2.0933 c. M:-3.3613 c. 72: 10 11 12 7 12 11 9 SP SD: 1.8821 c. M:-3.6174 c. 87: 12 13 15 8 15 13 11 SP SD: 1.3760 c. M: 2.5804 c. 118: 16 18 20 11 20 18 15 SP SD: 1.9613 c. M: 2.5524 c. 137: 19 21 23 13 23 21 17 SP SD: 1.7339 c. M:-2.9570 c. 145: 20 22 25 13 25 22 18 SP SD: 1.6076 c. M:-3.1648 c. 152: 21 23 26 14 26 23 19 SP SD: 0.8365 c. M:-1.4618 c. 159: 22 24 27 15 27 24 20 SP SD: 0.7076 c. M:-1.1017 c. 183: 25 28 31 17 31 28 23 SP SD: 0.7495 c. M: 1.3855 c. 224: 31 34 38 21 38 34 28 SP SD: 0.8237 c. M:-1.2365 c. 246: 34 37 42 23 42 37 31 SP SD: 0.7671 c. M:-1.3335 c. 248: 34 38 42 23 42 38 31 SP SD: 0.5856 c. M:-0.9792 c. 270: 37 41 46 25 46 41 34 SP SD: 0.5210 c. M: 0.8270 c. 335: 46 51 57 31 57 51 42 SP SD: 0.2191 c. M: 0.3627 c. 342: 47 52 58 32 58 52 43 SP SD: 0.2266 c. M: 0.4407 c. 494: 68 75 84 46 84 75 62 SP SD: 0.1292 c. M:-0.2472 c. 677: 93 103 115 63 115 103 85 SP SD: 0.1091 c. M: 0.1941 c. 829: 114 126 141 77 141 126 104 SP SD: 0.0955 c. M:-0.1899 c. 836: 115 127 142 78 142 127 105 SP SD: 0.0756 c. M: 0.1218 c. 1171: 161 178 199 109 199 178 147 SP SD: 0.0133 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: 18.6808 cents 4 x 5 x 6 x 7:8 S SD: 24.3843 cents 5 x 6:7 x 8:9:10 S SD: 15.2700 cents 6 x 7:8:9:10:11:12 S SD: 17.5915 cents 7:8:9 x 10:12:13:14 S SD: 22.9848 cents 8:9:10:11:12:13:15:16 SD: 11.7397 cents 11:12:13:15:16:18:20:22 SD: 9.4966 cents 13:14:16:18:19:21:24:26 SD: 8.0408 cents 17:19:21:23:25:28:31:34 SD: 6.3878 cents 18:20:22:25:26:30:33:36 SD: 5.7265 cents 19:21:23:26:28:31:35:38 SD: 4.3535 cents 30:33:37:41:44:50:55:60 SD: 3.6672 cents 31:34:38:43:45:51:57:62 SD: 3.6480 cents 32:35:39:44:47:53:59:64 SD: 2.3328 cents 40:44:49:55:59:66:73:80 SD: 1.8837 cents 49:54:60:67:72:81:90:98 SD: 1.7194 cents 58:64:71:80:85:96:106:116 SD: 1.6088 cents 69:76:84:95:101:114:127:138 SD: 1.5712 cents 71:78:87:98:104:117:130:142 SD: 1.3041 cents 72:79:88:99:106:119:132:144 SD: 1.1993 cents 77:85:94:106:113:127:141:154 SD: 1.0253 cents 90:99:110:124:132:149:165:180 SD: 0.9697 cents 109:120:133:150:160:180:200:218 SD: 0.6189 cents 120:132:147:165:176:198:220:240 SD: 0.5615 cents 131:144:160:180:192:216:240:262 SD: 0.4206 cents 208:229:254:286:305:343:381:416 SD: 0.4049 cents 221:243:270:304:324:365:405:442 SD: 0.3287 cents 229:252:280:315:336:378:420:458 SD: 0.2404 cents 320:352:391:440:469:528:587:640 SD: 0.2357 cents 328:361:401:451:481:541:601:656 SD: 0.2276 cents 360:396:440:495:528:594:660:720 S SD: 0.0000 cents