Scala analysis: xen09-wilson-marwa-18b-01
Marwa permutation 1 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: 99/80 368.914230 3: 27/20 519.551289 acute fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 33/20 866.959229 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: 9/8 203.9100 major whole tone 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 88/81 143.4979 2nd undecimal neutral second 5: 9/8 203.9100 major whole tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 2 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: 1 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 40/33 333.041 cents 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 99/80 368.914 cents 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: 1 160/99 831.086 cents 5: 2 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: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 20/11 1034.996 cents large minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 81/44 1056.502 cents 2nd undecimal neutral seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 165.0 368.9 519.6 663.0 867.0 1017.6 1200.0 165.0 : 203.9 354.5 498.0 702.0 852.6 1035.0 1200.0 368.9 : 150.6 294.1 498.0 648.7 831.1 996.1 1200.0 519.6 : 143.5 347.4 498.0 680.4 845.5 1049.4 1200.0 663.0 : 203.9 354.5 537.0 702.0 905.9 1056.5 1200.0 867.0 : 150.6 333.0 498.0 702.0 852.6 996.1 1200.0 1017.6: 182.4 347.4 551.3 702.0 845.5 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 203.9100 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 2: 294.1350 .. 368.9142 cents 2673/2560, 74.7792 cents 256/243, 90.2250 cents 3: 498.0450 .. 551.3179 cents 33/32, 53.2729 cents 320/297, 129.1308 cents 4: 648.6821 .. 701.9550 cents 33/32, 53.2729 cents 128/121, 97.3641 cents 5: 831.0858 .. 905.8650 cents 2673/2560, 74.7792 cents 320/297, 129.1308 cents 6: 996.0900 .. 1056.5021 cents 729/704, 60.4121 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.194641 Largest / Average step : 1.189475 Largest / Smallest step : 1.420996 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 171.10041 cents, oct.: 1197.70287 cents Scale is strictly proper Step pattern alph. order: ABCDBCE Step pattern size order : CEBAEBD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.330006 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.685893 Rothenberg efficiency : 0.408163 redundancy: 0.591837 Efficiency x scale size : 2.857143 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 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 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 Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 74.7792 cents: 6 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.024846 Average absolute harmonicity : 0.183481 Specific harmonicity : 0.117493 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 594, 9.2143 octaves, 155405.586 Hz. Exponens Consonantiae : 1.425600E+05, 17.12121 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 177.0, average 25.28571 Mersenne's string divisions : 692911506 Sum of van Prooijen's expressibility: 8.11724, average 1.15961 Sum of Tenney's harmonic distance : 15.96481, average 2.28069 Vogel's harmonic complexity : 16.00000 Wille's k value : 148 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 84.67212, average 3.02400 Lattice compactness (without 2's) : 55.20053, average 1.97145 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.00000 11 1 3: -1 .. 3 1.00000 9 5: -1 .. 0 -0.85714 6 2 11: 0 .. 1 0.57143 4 4 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 17 22| Scale is JI-epimorphic with val: <7 11 16 24| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 14.5332 c. M: 26.0571 c. Lebeng 20: 3 3 3 2 3 3 3 SP M ME I SD: 14.4636 c. M: 26.9592 c. 22: 3 4 3 2 4 3 3 SP D3 SD: 13.6128 c. M:-25.9033 c. 23: 3 4 3 3 4 3 3 SP M ME S SD: 14.0995 c. M:-25.8820 c. Mavila-7, Antiaeolian 24: 3 4 3 3 4 3 4 SP M ME S SD: 15.7328 c. M: 19.5513 c. Neutral Mixolydian, Iced Blizzard 25: 3 5 3 3 4 3 4 SP T3 SD: 11.4711 c. M: 21.0042 c. 26: 4 4 3 3 5 3 4 SP T3 SD: 11.4328 c. M:-19.6112 c. 29: 4 5 4 3 5 4 4 SP D3 SD: 9.5653 c. M:-18.3797 c. 30: 4 5 4 4 5 3 5 SP D3 SD: 11.1594 c. M: 17.5963 c. 32: 4 6 4 4 5 4 5 SP T3 SD: 8.2854 c. M: 15.0042 c. 35: 5 6 4 4 6 5 5 SP T3 S SD: 8.3543 c. M: 11.6207 c. 36: 5 6 5 4 6 5 5 SP D3 SD: 8.0940 c. M:-15.7370 c. 39: 5 7 5 4 7 5 6 SP SD: 8.0779 c. M: 16.8954 c. 40: 5 7 5 5 7 5 6 SP T3 S SD: 7.7473 c. M: 15.0042 c. 42: 6 7 5 5 7 6 6 SP T3 S SD: 6.8350 c. M:-10.9751 c. 46: 6 8 6 5 8 6 7 SP SD: 5.9258 c. M: 10.8753 c. 50: 7 8 7 6 8 6 8 SP SD: 6.9773 c. M: 9.5963 c. 51: 7 9 6 6 9 6 8 SP SD: 4.2401 c. M:-7.5564 c. 53: 7 9 7 6 9 7 8 SP SD: 4.9940 c. M: 6.6501 c. 58: 8 10 7 7 10 7 9 SP SD: 2.3082 c. M: 3.8032 c. 65: 9 11 8 8 11 8 10 SP SD: 1.5218 c. M: 2.6282 c. 152: 21 26 19 18 26 19 23 SP SD: 1.2114 c. M:-2.1384 c. 159: 22 27 20 19 27 20 24 SP SD: 1.0060 c. M:-1.2716 c. 205: 28 35 26 24 35 26 31 SP SD: 1.0029 c. M: 1.5858 c. 212: 29 36 27 25 36 27 32 SP SD: 0.9440 c. M:-1.2716 c. 217: 30 37 27 26 37 27 33 SP SD: 0.8666 c. M:-1.5927 c. 224: 31 38 28 27 38 28 34 SP SD: 0.7636 c. M:-1.2365 c. 263: 36 45 33 31 45 33 40 SP SD: 0.7055 c. M: 1.4523 c. 270: 37 46 34 32 46 34 41 SP SD: 0.4339 c. M: 0.8270 c. 277: 38 47 35 33 47 35 42 SP SD: 0.4228 c. M: 0.6832 c. 335: 46 57 42 40 57 42 51 SP SD: 0.2056 c. M: 0.3627 c. 494: 68 84 62 59 84 62 75 SP SD: 0.2185 c. M:-0.3165 c. 612: 84 104 77 73 104 77 93 SP SD: 0.2252 c. M: 0.3041 c. 677: 93 115 85 81 115 85 103 SP SD: 0.1687 c. M: 0.2289 c. 771: 106 131 97 92 131 97 117 SP SD: 0.1608 c. M:-0.3025 c. 829: 114 141 104 99 141 104 126 SP SD: 0.1025 c. M:-0.2052 c. 836: 115 142 105 100 142 105 127 SP SD: 0.0688 c. M:-0.1087 c. 1171: 161 199 147 140 199 147 178 SP SD: 0.0124 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: 9.2211 cents 4 x 5 x 6 x 7:8 S SD: 16.1921 cents 5 x 6:7 x 8:9:10 S SD: 19.6368 cents 6:7 x 8:9:10:11:12 S SD: 19.4828 cents 7:8:9 x 10:12:13:14 S SD: 22.4466 cents 8:9:10:11:12:13:14:16 S SD: 12.3026 cents 9:10:11:12:13:15:16:18 SD: 7.4116 cents 17:19:21:23:25:28:31:34 SD: 5.1890 cents 20:22:25:27:29:33:36:40 SD: 3.7640 cents 29:32:36:39:43:48:52:58 SD: 3.2990 cents 34:37:42:46:50:56:61:68 SD: 2.9737 cents 37:41:46:50:54:61:67:74 SD: 2.8966 cents 39:43:48:53:57:64:70:78 SD: 2.8114 cents 41:45:51:55:60:68:74:82 SD: 2.6019 cents 43:47:53:58:63:71:77:86 SD: 2.2895 cents 49:54:61:66:72:81:88:98 SD: 1.8531 cents 51:56:63:69:75:84:92:102 SD: 1.2648 cents 60:66:74:81:88:99:108:120 SD: 0.8341 cents 80:88:99:108:117:132:144:160 SD: 0.7036 cents 109:120:135:147:160:180:196:218 SD: 0.5452 cents 131:144:162:177:192:216:236:262 SD: 0.4537 cents 160:176:198:216:235:264:288:320 SD: 0.3511 cents 180:198:223:243:264:297:324:360 SD: 0.2774 cents 240:264:297:324:352:396:432:480 SD: 0.0000 cents