Scala analysis: xen09-wilson-marwa-15a-10
Marwa permutation 10 from Figure 15a, Ptolemy 12/11 22/21 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 112/99 213.597962 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 14/9 764.915905 septimal minor sixth 5: 56/33 915.552963 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 112/99 213.5980 2: 22/21 80.5370 undecimal minor semitone 3: 9/8 203.9100 major whole tone 4: 7/6 266.8709 septimal minor third 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 22/21 80.5370 undecimal minor semitone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 2 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 21/16 470.781 cents narrow fourth 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 32/21 729.219 cents wide fifth 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 56/33 915.553 cents 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 1 99/56 986.402 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 21/11 1119.463 cents undecimal major 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 : 213.6 294.1 498.0 764.9 915.6 996.1 1200.0 213.6 : 80.5 284.4 551.3 702.0 782.5 986.4 1200.0 294.1 : 203.9 470.8 621.4 702.0 905.9 1119.5 1200.0 498.0 : 266.9 417.5 498.0 702.0 915.6 996.1 1200.0 764.9 : 150.6 231.2 435.1 648.7 729.2 933.1 1200.0 915.6 : 80.5 284.4 498.0 578.6 782.5 1049.4 1200.0 996.1 : 203.9 417.5 498.0 702.0 968.8 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 22/21, 80.5370 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 2.128568 Largest / Average step : 1.556747 Largest / Smallest step : 3.313642 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 173.64265 cents, oct.: 1215.49857 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : DACEBAC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.506814 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 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 : 896/891, 9.6880 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 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 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 99 Scale harmonicity : 0.024115 Average absolute harmonicity : 0.216324 Specific harmonicity : 0.121719 Fundamental : 1/297, -8.2143 octaves, 0.8809 Hz. Guide tone : 224, 7.8074 octaves, 58604.127 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 208.5, average 29.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.33112, average 1.04730 Sum of Tenney's harmonic distance : 15.88701, average 2.26957 Vogel's harmonic complexity : 18.00000 Wille's k value : 148 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 79.29081, average 2.83181 Lattice compactness (without 2's) : 46.55193, average 1.66257 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 5 2.85714 20 1 3: -3 .. 0 -1.57143 11 3 7: 0 .. 1 0.42857 3 1 11: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-10 / 7 =-1.42857 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 22| Scale is weakly epimorphic with val: <7 12 18 24| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 46.5304 c. M: 79.2016 c. Lebeng 8: 1 1 1 2 1 0 2 N D3 SD: 47.9361 c. M: 96.0900 c. 9: 2 0 2 2 1 1 1 N T3 SD: 40.2566 c. M:-70.5767 c. 11: 2 1 2 2 1 1 2 P D3 S SD: 27.7904 c. M:-47.4095 c. 12: 2 1 2 3 1 1 2 N SD: 15.6351 c. M:-35.0841 c. 16: 3 1 3 3 2 1 3 P SD: 16.0363 c. M:-26.9550 c. 17: 3 1 3 4 2 1 3 N SD: 7.1434 c. M: 11.7821 c. 29: 5 2 5 6 4 2 5 N SD: 8.5088 c. M: 20.0883 c. 33: 6 2 6 7 4 2 6 N SD: 7.5641 c. M: 14.2718 c. 41: 7 3 7 9 5 3 7 N SD: 4.8207 c. M: 8.7199 c. 46: 8 3 8 10 6 3 8 N SD: 5.0843 c. M: 8.3942 c. 58: 10 4 10 13 7 4 10 N SD: 3.8473 c. M: 6.7014 c. 60: 11 4 10 13 8 4 10 N SD: 4.4471 c. M:-6.4020 c. 63: 11 4 11 14 8 4 11 N SD: 4.4332 c. M: 8.4207 c. 69: 12 5 12 15 9 4 12 N SD: 4.2648 c. M:-6.3028 c. 72: 13 5 12 16 9 5 12 N SD: 3.0991 c. M:-5.8650 c. 77: 14 5 13 17 10 5 13 N SD: 2.5101 c. M:-4.5839 c. 89: 16 6 15 20 11 6 15 N SD: 2.0370 c. M:-3.6234 c. 94: 17 6 16 21 12 6 16 N SD: 1.9329 c. M:-3.5960 c. 111: 20 7 19 25 14 7 19 N SD: 2.1727 c. M:-3.3660 c. 113: 20 8 19 25 14 8 19 N SD: 1.8040 c. M:-3.2101 c. 118: 21 8 20 26 15 8 20 N SD: 0.9177 c. M: 2.2040 c. 130: 23 9 22 29 16 9 22 N SD: 1.1045 c. M: 1.7068 c. 135: 24 9 23 30 17 9 23 N SD: 0.4296 c. M: 0.8017 c. 342: 61 23 58 76 43 23 58 N SD: 0.3403 c. M:-0.6018 c. 359: 64 24 61 80 45 24 61 N SD: 0.2699 c. M:-0.5437 c. 477: 85 32 81 106 60 32 81 N SD: 0.1556 c. M:-0.2385 c. 612: 109 41 104 136 77 41 104 N SD: 0.1060 c. M: 0.2100 c. 742: 132 50 126 165 93 50 126 N SD: 0.1295 c. M:-0.2046 c. 877: 156 59 149 195 110 59 149 N SD: 0.0854 c. M: 0.1596 c. 1012: 180 68 172 225 127 68 172 N SD: 0.0922 c. M: 0.1592 c. 1236: 220 83 210 275 155 83 210 N SD: 0.0540 c. M:-0.1326 c. 1354: 241 91 230 301 170 91 230 N SD: 0.0585 c. M:-0.1043 c. 1371: 244 92 233 305 172 92 233 N SD: 0.0368 c. M:-0.0732 c. 1848: 329 124 314 411 232 124 314 N SD: 0.0224 c. M:-0.0384 c. 1983: 353 133 337 441 249 133 337 N SD: 0.0217 c. M: 0.0351 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: 31.4805 cents 3 x x 4 x 5 x 6 S SD: 10.3981 cents 4 x 5 x 6 x 7:8 S SD: 28.7275 cents 5 x 6:7:8 x 9:10 S SD: 20.4336 cents 6 x 7:8:9:10:11:12 S SD: 15.3826 cents 7:8 x 9:11:12 x 14 SD: 13.9869 cents 8:9 x 11:12 x 14:16 SD: 17.4806 cents 9:10:11:12:14:15:16:18 S SD: 9.8811 cents 12 x 14:16:19:20:21:24 SD: 9.7164 cents 13:15 x 17:20:22:23:26 SD: 8.7466 cents 14:16:17:19:22:24:25:28 SD: 8.6764 cents 15:17:18:20:23:25:27:30 SD: 7.1830 cents 16:18:19:21:25:27:28:32 SD: 5.9680 cents 21:24:25:28:33:36:37:42 SD: 5.0047 cents 22:25:26:29:34:37:39:44 SD: 4.2082 cents 23:26:27:31:36:39:41:46 SD: 3.9502 cents 27:31:32:36:42:46:48:54 SD: 3.7823 cents 31:35:37:41:48:53:55:62 SD: 3.4989 cents 32:36:38:43:50:54:57:64 SD: 3.0356 cents 36:41:43:48:56:61:64:72 SD: 2.5621 cents 39:44:46:52:61:66:69:78 SD: 2.3672 cents 45:51:53:60:70:76:80:90 SD: 1.9982 cents 54:61:64:72:84:92:96:108 SD: 1.0464 cents 76:86:90:101:118:129:135:152 SD: 0.9849 cents 99:112:117:132:154:168:176:198 SD: 0.7036 cents 108:122:128:144:168:183:192:216 SD: 0.5209 cents 135:153:160:180:210:229:240:270 SD: 0.4520 cents 162:183:192:216:252:275:288:324 SD: 0.3773 cents 189:214:224:252:294:321:336:378 SD: 0.2973 cents 243:275:288:324:378:412:432:486 SD: 0.2330 cents 297:336:352:396:462:504:528:594 SD: 0.0000 cents