Scala analysis: xen09-wilson-marwa-15a-09
Marwa permutation 9 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: 14/11 417.507964 undecimal diminished fourth or major 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: 9/8 203.9100 major whole tone 3: 22/21 80.5370 undecimal minor semitone 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 11/9 347.408 cents undecimal neutral third 2: 3 14/11 417.508 cents undecimal diminished fourth or major third 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: 3 11/7 782.492 cents undecimal augmented fifth 5: 1 18/11 852.592 cents undecimal neutral 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: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 213.6 417.5 498.0 764.9 915.6 996.1 1200.0 213.6 : 203.9 284.4 551.3 702.0 782.5 986.4 1200.0 417.5 : 80.5 347.4 498.0 578.6 782.5 996.1 1200.0 498.0 : 266.9 417.5 498.0 702.0 915.6 1119.5 1200.0 764.9 : 150.6 231.2 435.1 648.7 852.6 933.1 1200.0 915.6 : 80.5 284.4 498.0 702.0 782.5 1049.4 1200.0 996.1 : 203.9 417.5 621.4 702.0 968.8 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 .. 417.5080 cents 49/44, 186.3339 cents 48/49,-35.6968 cents 3: 435.0841 .. 621.4180 cents 49/44, 186.3339 cents 99/98, 17.5761 cents 4: 578.5820 .. 764.9159 cents 49/44, 186.3339 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 968.8259 cents 49/44, 186.3339 cents 99/98, 17.5761 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 : 175.40512 cents, oct.: 1227.83587 cents Scale is not proper Step pattern alph. order: ABCDECB Step pattern size order : DCAEBAC Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.570782 Lumma stability : 0.163522 Lumma impropriety factor : 0.095191 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 : 896/891, 9.6880 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 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 : 0.026454 Average absolute harmonicity : 0.210183 Specific harmonicity : 0.112815 Fundamental : 1/99, -6.6294 octaves, 2.6427 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 1.108800E+04, 13.43671 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 191.5, average 27.35714 Mersenne's string divisions : 226756425 Sum of van Prooijen's expressibility: 6.94115, average 0.99159 Sum of Tenney's harmonic distance : 15.13802, average 2.16257 Vogel's harmonic complexity : 15.14286 Wille's k value : 49 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 71.13211, average 2.54043 Lattice compactness (without 2's) : 44.20221, average 1.57865 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.28571 16 1 3: -2 .. 0 -1.14286 8 2 7: 0 .. 1 0.57143 4 1 11: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-7 / 7 =-1.00000 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 18 23| Scale is JI-epimorphic with val: <7 11 19 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: 51.2061 c. M: 79.2016 c. Lebeng 8: 1 2 0 2 1 1 1 P D3 S SD: 39.2418 c. M: 63.5980 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 39.4537 c. M:-70.5767 c. 10: 2 1 1 2 2 0 2 P D3 S SD: 37.0816 c. M: 57.5080 c. 11: 2 2 1 2 1 1 2 N D3 SD: 25.8113 c. M:-47.4095 c. 12: 2 2 1 3 1 1 2 N T3 SD: 16.8325 c. M:-35.0841 c. 16: 3 3 1 3 2 1 3 N SD: 20.0766 c. M:-32.4920 c. 17: 3 3 1 4 2 1 3 N SD: 6.0313 c. M:-11.5547 c. 41: 7 7 3 9 5 3 7 N SD: 5.6145 c. M: 8.7199 c. 46: 8 8 3 10 6 3 8 N SD: 4.3001 c. M: 8.3942 c. 55: 10 9 4 12 7 4 9 N SD: 3.8409 c. M:-7.5464 c. 58: 10 10 4 13 7 4 10 N SD: 3.7291 c. M: 6.7014 c. 60: 11 10 4 13 8 4 10 N SD: 3.9686 c. M:-6.4020 c. 63: 11 11 4 14 8 4 11 N SD: 3.1404 c. M: 5.6138 c. 72: 13 12 5 16 9 5 12 N SD: 2.1889 c. M:-3.9100 c. 89: 16 15 6 20 11 6 15 N SD: 1.8144 c. M:-3.6234 c. 113: 20 19 8 25 14 8 19 N SD: 1.8396 c. M: 3.3487 c. 118: 21 20 8 26 15 8 20 N SD: 0.8943 c. M: 2.2040 c. 130: 23 22 9 29 16 9 22 N SD: 1.2810 c. M: 2.1233 c. 135: 24 23 9 30 17 9 23 N SD: 0.3212 c. M: 0.5344 c. 342: 61 58 23 76 43 23 58 N SD: 0.2534 c. M:-0.4371 c. 477: 85 81 32 106 60 32 81 N SD: 0.1405 c. M:-0.2385 c. 612: 109 104 41 136 77 41 104 N SD: 0.1181 c. M: 0.2100 c. 877: 156 149 59 195 110 59 149 N SD: 0.1066 c. M: 0.1762 c. 1012: 180 172 68 225 127 68 172 N SD: 0.0993 c. M: 0.1592 c. 1101: 196 187 74 245 138 74 187 N SD: 0.0926 c. M:-0.2067 c. 1147: 204 195 77 255 144 77 195 N SD: 0.1076 c. M: 0.1716 c. 1219: 217 207 82 271 153 82 207 N SD: 0.0759 c. M:-0.1364 c. 1236: 220 210 83 275 155 83 210 N SD: 0.0533 c. M:-0.1326 c. 1354: 241 230 91 301 170 91 230 N SD: 0.0523 c. M: 0.0781 c. 1371: 244 233 92 305 172 92 233 N SD: 0.0331 c. M:-0.0732 c. 1713: 305 291 115 381 215 115 291 N SD: 0.0422 c. M:-0.0623 c. 1848: 329 314 124 411 232 124 314 N SD: 0.0229 c. M:-0.0384 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: 18.8423 cents 5 x 6:7:8 x 9:10 S SD: 28.5325 cents 6:7 x 8:9:10:11:12 S SD: 17.1700 cents 7:8:9 x 11:12 x 14 SD: 7.0305 cents 8:9:10:11:12 x 14:16 S SD: 15.4671 cents 9:10:11:12:14:15:16:18 S SD: 11.8323 cents 10:11:13 x 16:17:18:20 SD: 13.4982 cents 11:12:14:15:17:19:20:22 SD: 12.8234 cents 12:14:15:16:19:20:21:24 SD: 11.4877 cents 13:15 x 17:20:22:23:26 SD: 8.7466 cents 14:16:18:19:22:24:25:28 SD: 6.7523 cents 15:17:19:20:23:25:27:30 SD: 6.5992 cents 18:20:23:24:28:31:32:36 SD: 5.8450 cents 21:24:27:28:33:36:37:42 SD: 5.4898 cents 22:25:28:29:34:37:39:44 SD: 4.1490 cents 23:26:29:31:36:39:41:46 SD: 3.9214 cents 29:33:37:39:45:49:52:58 SD: 3.6025 cents 30:34:38:40:47:51:53:60 SD: 2.6993 cents 36:41:46:48:56:61:64:72 SD: 1.9544 cents 45:51:57:60:70:76:80:90 SD: 1.7268 cents 54:61:69:72:84:92:96:108 SD: 1.4333 cents 63:71:80:84:98:107:112:126 SD: 1.1218 cents 85:96:108:113:132:144:151:170 SD: 1.1207 cents 92:104:117:123:143:156:164:184 SD: 1.0240 cents 99:112:126:132:154:168:176:198 SD: 0.0000 cents