Scala analysis: xen09-wilson-marwa-15a-01
Marwa permutation 1 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: 7/6 266.870906 septimal minor third 2: 21/16 470.780907 narrow fourth 3: 63/44 621.417966 4: 14/9 764.915905 septimal minor sixth 5: 7/4 968.825906 harmonic seventh 6: 21/11 1119.462965 undecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 7/6 266.8709 septimal minor third 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: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 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: 2 9/8 203.910 cents major whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 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 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 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 7/4 968.826 cents harmonic seventh 6: 1 12/7 933.129 cents septimal major sixth 6: 2 16/9 996.090 cents Pythagorean 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 6: 1 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 : 266.9 470.8 621.4 764.9 968.8 1119.5 1200.0 266.9 : 203.9 354.5 498.0 702.0 852.6 933.1 1200.0 470.8 : 150.6 294.1 498.0 648.7 729.2 996.1 1200.0 621.4 : 143.5 347.4 498.0 578.6 845.5 1049.4 1200.0 764.9 : 203.9 354.5 435.1 702.0 905.9 1056.5 1200.0 968.8 : 150.6 231.2 498.0 702.0 852.6 996.1 1200.0 1119.5: 80.5 347.4 551.3 702.0 845.5 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 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 : 12/11, 150.6371 cents, amount: 2 Least squares average step : 186.38041 cents, oct.: 1304.66288 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : EDCBDCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 1.600163 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 : 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 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 : 81 (O: 81 U: 81) Highest odd numerator or denominator: 63 Scale harmonicity : 0.022658 Average absolute harmonicity : 0.190325 Specific harmonicity : 0.125998 Fundamental : 1/1584, -10.6294 octaves, 0.1652 Hz. Guide tone : 126, 6.9773 octaves, 32964.821 Hz. Exponens Consonantiae : 1.995840E+05, 17.60664 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 113.0, average 16.14286 Mersenne's string divisions : 1250030496 Sum of van Prooijen's expressibility: 7.08822, average 1.01260 Sum of Tenney's harmonic distance : 13.80455, average 1.97208 Vogel's harmonic complexity : 23.28571 Wille's k value : 1039 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 82.07593, average 2.93128 Lattice compactness (without 2's) : 50.24030, average 1.79430 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.00000 11 1 3: -2 .. 2 0.14286 7 7: 0 .. 1 0.85714 6 4 11: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 22 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 18 25| 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: 95.5871 c. M: 127.9238 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 41.0099 c. M: 69.4630 c. 10: 2 2 1 1 2 1 1 P D3 S SD: 26.5072 c. M: 44.9159 c. 12: 3 2 1 2 2 1 1 N SD: 26.7035 c. M:-35.0841 c. 13: 3 2 2 1 2 2 1 N T3 SD: 23.0827 c. M: 45.7490 c. 14: 3 2 2 2 2 2 1 P T3 SD: 20.9714 c. M: 42.2095 c. 15: 3 3 2 2 2 2 1 N SD: 18.7518 c. M:-35.0841 c. 17: 4 3 2 2 3 2 1 N SD: 15.0526 c. M:-23.3367 c. 23: 5 4 3 3 4 2 2 N SD: 14.3654 c. M: 23.8108 c. 24: 5 4 3 3 4 3 2 P SD: 17.4475 c. M: 21.4180 c. 25: 6 4 3 3 4 3 2 N SD: 11.1138 c. M:-21.1291 c. 27: 6 5 3 3 5 3 2 N SD: 8.9928 c. M:-18.1080 c. 31: 7 5 4 4 5 4 2 N SD: 4.7398 c. M:-9.2776 c. 41: 9 7 5 5 7 5 3 N SD: 4.4935 c. M: 7.2678 c. 58: 13 10 7 7 10 7 4 N SD: 2.6432 c. M:-5.0812 c. 72: 16 12 9 9 12 9 5 N SD: 2.8054 c. M: 4.7513 c. 77: 17 13 10 9 13 10 5 N SD: 2.1821 c. M: 3.2484 c. 89: 20 15 11 11 15 11 6 N SD: 1.9856 c. M:-3.6234 c. 94: 21 16 12 11 16 12 6 N SD: 2.3716 c. M:-4.1139 c. 99: 22 17 12 12 17 12 7 N SD: 2.2452 c. M: 4.3114 c. 104: 23 18 13 12 18 13 7 N SD: 1.7671 c. M: 3.3774 c. 118: 26 20 15 14 20 15 8 N SD: 2.0386 c. M: 2.9843 c. 130: 29 22 16 16 22 16 9 N SD: 1.5840 c. M: 2.9564 c. 135: 30 23 17 16 23 17 9 N SD: 0.4330 c. M:-0.8043 c. 301: 67 51 38 36 51 38 20 N SD: 0.4422 c. M:-0.8028 c. 311: 69 53 39 37 53 39 21 N SD: 0.4868 c. M: 0.9288 c. 342: 76 58 43 41 58 43 23 N SD: 0.3236 c. M: 0.6055 c. 359: 80 61 45 43 61 45 24 N SD: 0.4381 c. M:-0.5437 c. 400: 89 68 50 48 68 50 27 N SD: 0.2649 c. M: 0.4630 c. 477: 106 81 60 57 81 60 32 N SD: 0.1900 c. M: 0.3407 c. 535: 119 91 67 64 91 67 36 N SD: 0.1434 c. M:-0.2471 c. 612: 136 104 77 73 104 77 41 N SD: 0.1716 c. M: 0.2100 c. 670: 149 114 84 80 114 84 45 N SD: 0.1282 c. M:-0.2639 c. 701: 156 119 88 84 119 88 47 N SD: 0.1314 c. M:-0.2767 c. 836: 186 142 105 100 142 105 56 N SD: 0.1073 c. M:-0.1559 c. 1012: 225 172 127 121 172 127 68 N SD: 0.0678 c. M: 0.0954 c. 1147: 255 195 144 137 195 144 77 N SD: 0.0652 c. M: 0.1382 c. 1682: 374 286 211 201 286 211 113 N SD: 0.0649 c. M: 0.1121 c. 1713: 381 291 215 205 291 215 115 N SD: 0.0343 c. M:-0.0578 c. 1848: 411 314 232 221 314 232 124 N SD: 0.0118 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 7:8:9 x 10 S SD: 18.6003 cents 6:7:8 x 9 x 11:12 SD: 19.6178 cents 7:8:9:10:11:12:13:14 H SD: 11.4538 cents 8:9 x 11:12:14:15:16 SD: 19.5897 cents 9:11:12:13:14:16:17:18 SD: 13.2041 cents 11:13:14:16:17:19:21:22 SD: 9.8143 cents 12:14:16:17:19:21:23:24 SD: 6.4972 cents 16:19:21:23:25:28:31:32 SD: 5.8891 cents 19:22:25:27:30:33:36:38 SD: 5.2864 cents 23:27:30:33:36:40:44:46 SD: 3.1564 cents 32:37:42:46:50:56:61:64 SD: 2.6886 cents 35:41:46:50:54:61:67:70 SD: 2.6510 cents 41:48:54:59:64:72:78:82 SD: 2.2906 cents 47:55:62:67:73:82:90:94 SD: 2.1404 cents 48:56:63:69:75:84:92:96 SD: 1.7699 cents 54:63:71:77:84:95:103:108 SD: 1.7266 cents 60:70:79:86:93:105:115:120 SD: 1.5573 cents 65:76:85:93:101:114:124:130 SD: 1.2462 cents 67:78:88:96:104:117:128:134 SD: 0.9637 cents 90:105:118:129:140:158:172:180 SD: 0.9055 cents 97:113:127:139:151:170:185:194 SD: 0.8763 cents 108:126:142:155:168:189:206:216 SD: 0.7583 cents 121:141:159:173:188:212:231:242 SD: 0.6845 cents 132:154:173:189:205:231:252:264 SD: 0.5376 cents 144:168:189:206:224:252:275:288 SD: 0.2330 cents 252:294:331:361:392:441:481:504 SD: 0.2294 cents 317:370:416:454:493:555:605:634 SD: 0.1967 cents 384:448:504:550:597:672:733:768 SD: 0.1634 cents 396:462:520:567:616:693:756:792 SD: 0.1189 cents 528:616:693:756:821:924:1008:1056 SD: 0.1004 cents