Scala analysis: xen09-wilson-marwa-15b-01
Marwa permutation 1 from Figure 15b, Ptolemy 22/21 12/11 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 21/16 470.780907 narrow fourth 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 14/9 764.915905 septimal minor sixth 5: 7/4 968.825906 harmonic seventh 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: 7/6 266.8709 septimal minor third 2: 9/8 203.9100 major whole tone 3: 22/21 80.5370 undecimal minor semitone 4: 112/99 213.5980 5: 9/8 203.9100 major whole tone 6: 22/21 80.5370 undecimal minor semitone 7: 12/11 150.6371 undecimal neutral second, 3/4-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 : 266.9 470.8 551.3 764.9 968.8 1049.4 1200.0 266.9 : 203.9 284.4 498.0 702.0 782.5 933.1 1200.0 470.8 : 80.5 294.1 498.0 578.6 729.2 996.1 1200.0 551.3 : 213.6 417.5 498.0 648.7 915.6 1119.5 1200.0 764.9 : 203.9 284.4 435.1 702.0 905.9 986.4 1200.0 968.8 : 80.5 231.2 498.0 702.0 782.5 996.1 1200.0 1049.4: 150.6 417.5 621.4 702.0 915.6 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 : 181.87398 cents, oct.: 1273.11787 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : ECADCAB 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 Length of longest harmonic part : 1 at degree 0 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 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 21 Scale harmonicity : 0.024115 Average absolute harmonicity : 0.195029 Specific harmonicity : 0.122820 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 462, 8.8517 octaves, 120871.011 Hz. Exponens Consonantiae : 6.652800E+04, 16.02167 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 61.5, average 8.78571 Mersenne's string divisions : 117920517 Sum of van Prooijen's expressibility: 6.04944, average 0.86421 Sum of Tenney's harmonic distance : 11.76217, average 1.68031 Vogel's harmonic complexity : 14.57143 Wille's k value : 94 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 78.33680, average 2.79774 Lattice compactness (without 2's) : 42.61303, average 1.52189 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.28571 13 1 3: -2 .. 1 -0.42857 5 7: 0 .. 1 0.57143 4 4 11: 0 .. 1 0.28571 2 2 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 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: 81.0850 c. M: 127.9238 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 35.5753 c. M: 68.8259 c. 9: 2 2 0 2 1 1 1 N T3 SD: 31.6822 c. M:-62.5524 c. 10: 2 2 1 1 2 1 1 P D3 S SD: 29.7872 c. M:-48.6821 c. 11: 2 2 1 2 2 1 1 P D3 S SD: 27.9951 c. M: 48.6891 c. 13: 3 2 1 2 2 1 2 N G T3 S SD: 24.3199 c. M: 45.7490 c. 14: 3 2 1 3 2 1 2 P T3 SD: 25.0620 c. M: 42.2095 c. 15: 3 3 1 3 2 1 2 N SD: 18.0431 c. M:-35.0841 c. 16: 3 3 1 3 3 1 2 P SD: 21.1750 c. M: 41.8709 c. 17: 4 3 1 3 3 1 2 N SD: 14.9440 c. M:-23.3367 c. 22: 5 4 1 4 4 1 3 N SD: 10.7785 c. M:-20.1282 c. 26: 6 4 2 5 4 2 3 N SD: 10.2074 c. M:-19.6995 c. 27: 6 5 1 5 5 2 3 N SD: 12.6410 c. M:-18.1080 c. 28: 6 5 2 5 5 1 4 N SD: 11.2688 c. M: 20.7915 c. 30: 7 5 2 5 5 2 4 N SD: 8.6394 c. M:-13.1291 c. 31: 7 5 2 6 5 2 4 N SD: 5.9638 c. M: 9.3825 c. 41: 9 7 3 7 7 3 5 N SD: 3.4599 c. M:-4.7796 c. 63: 14 11 4 11 11 4 8 N SD: 2.6543 c. M:-5.4096 c. 72: 16 12 5 13 12 5 9 N SD: 1.9581 c. M: 4.1142 c. 89: 20 15 6 16 15 6 11 N SD: 2.1929 c. M:-3.6234 c. 94: 21 16 6 17 16 6 12 N SD: 1.6524 c. M: 2.5544 c. 130: 29 22 9 23 22 9 16 N SD: 1.5782 c. M:-2.9448 c. 135: 30 23 9 24 23 9 17 N SD: 0.3034 c. M: 0.4741 c. 342: 76 58 23 61 58 23 43 N SD: 0.3431 c. M: 0.6055 c. 477: 106 81 32 85 81 32 60 N SD: 0.2631 c. M: 0.3745 c. 535: 119 91 36 95 91 36 67 N SD: 0.2462 c. M:-0.4578 c. 566: 126 96 38 101 96 38 71 N SD: 0.2120 c. M:-0.4551 c. 612: 136 104 41 109 104 41 77 N SD: 0.2373 c. M: 0.3433 c. 629: 140 107 42 112 107 42 79 N SD: 0.2310 c. M:-0.4433 c. 670: 149 114 45 119 114 45 84 N SD: 0.1877 c. M:-0.3238 c. 701: 156 119 47 125 119 47 88 N SD: 0.1337 c. M:-0.2767 c. 742: 165 126 50 132 126 50 93 N SD: 0.1300 c. M:-0.2327 c. 836: 186 142 56 149 142 56 105 N SD: 0.0966 c. M:-0.1559 c. 877: 195 149 59 156 149 59 110 N SD: 0.0783 c. M:-0.1239 c. 1012: 225 172 68 180 172 68 127 N SD: 0.0583 c. M: 0.0938 c. 1578: 351 268 106 281 268 106 198 N SD: 0.0549 c. M:-0.1031 c. 1713: 381 291 115 305 291 115 215 N SD: 0.0282 c. M:-0.0578 c. 1848: 411 314 124 329 314 124 232 N SD: 0.0124 c. M: 0.0192 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 4 x x 5 x 6 S SD: 29.5861 cents 4 x 5 x 6:7 x 8 S SD: 26.3377 cents 5:6 x 7:8 x 9:10 S SD: 16.4187 cents 6:7:8 x 9 x 11:12 SD: 13.7221 cents 7:8:9:10:11:12:13:14 H SD: 13.5595 cents 8:9 x 11:12:14:15:16 SD: 16.1948 cents 9:11:12 x 14:16:17:18 SD: 17.1949 cents 10:12:13:14:16 x 18:20 S SD: 13.9580 cents 11:13:14:15:17:19:20:22 SD: 9.4645 cents 12:14:16:17:19:21:22:24 SD: 9.4257 cents 13:15:17:18:20:23:24:26 SD: 5.3858 cents 16:19:21:22:25:28:29:32 SD: 5.3259 cents 19:22:25:26:30:33:35:38 SD: 4.8763 cents 23:27:30:32:36:40:42:46 SD: 4.3472 cents 25:29:33:34:39:44:46:50 SD: 3.8267 cents 29:34:38:40:45:51:53:58 SD: 2.1664 cents 48:56:63:66:75:84:88:96 SD: 1.1016 cents 61:71:80:84:95:107:112:122 SD: 1.0312 cents 77:90:101:106:120:135:141:154 SD: 0.9080 cents 83:97:109:114:129:145:152:166 SD: 0.7581 cents 96:112:126:132:149:168:176:192 SD: 0.5527 cents 115:134:151:158:179:201:211:230 SD: 0.5473 cents 131:153:172:180:204:229:240:262 SD: 0.5340 cents 144:168:189:198:224:252:264:288 SD: 0.0000 cents