Scala analysis: xen09-wilson-marwa-15a-07
Marwa permutation 7 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: 21/11 1119.462965 undecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 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: 9/8 203.9100 major whole tone 7: 22/21 80.5370 undecimal minor semitone
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: 2 33/28 284.447 cents undecimal minor third 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 2 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: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 2 56/33 915.553 cents 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 : 213.6 417.5 498.0 764.9 915.6 1119.5 1200.0 213.6 : 203.9 284.4 551.3 702.0 905.9 986.4 1200.0 417.5 : 80.5 347.4 498.0 702.0 782.5 996.1 1200.0 498.0 : 266.9 417.5 621.4 702.0 915.6 1119.5 1200.0 764.9 : 150.6 354.5 435.1 648.7 852.6 933.1 1200.0 915.6 : 203.9 284.4 498.0 702.0 782.5 1049.4 1200.0 1119.5: 80.5 294.1 498.0 578.6 845.5 996.1 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: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 99/98, 17.5761 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 .. 915.5530 cents 392/363, 133.0609 cents 99/98, 17.5761 cents 6: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 99/98, 17.5761 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 : 180.69254 cents, oct.: 1264.84776 cents Scale is not proper Step pattern alph. order: ABCDEBC Step pattern size order : DCAEBCA Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.581147 Lumma stability : 0.192815 Lumma impropriety factor : 0.035697 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 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: 99 Scale harmonicity : 0.024711 Average absolute harmonicity : 0.199466 Specific harmonicity : 0.109490 Fundamental : 1/99, -6.6294 octaves, 2.6427 Hz. Guide tone : 336, 8.3923 octaves, 87906.190 Hz. Exponens Consonantiae : 3.326400E+04, 15.02167 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 195.0, average 27.85714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.30912, average 1.04416 Sum of Tenney's harmonic distance : 15.34327, average 2.19190 Vogel's harmonic complexity : 15.28571 Wille's k value : 94 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 70.59959, average 2.52141 Lattice compactness (without 2's) : 47.68232, average 1.70294 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.71429 12 1 3: -2 .. 1 -0.71429 7 1 7: 0 .. 1 0.71429 5 1 11: -1 .. 0 -0.57143 4 4 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 21 26| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 21 23| 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: 60.4278 c. M: 90.8915 c. Lebeng 8: 1 2 0 2 1 1 1 P D3 S SD: 42.5915 c. M: 69.4630 c. 9: 2 1 1 2 1 1 1 P M ME S SD: 35.2594 c. M:-53.0687 c. 11: 2 2 1 2 1 2 1 P M ME S SD: 27.4518 c. M:-47.4095 c. 12: 2 2 1 3 1 2 1 P D3 SD: 18.3102 c. M:-35.0841 c. Ionian Augmented, Ionian sharp 5 14: 3 2 1 3 2 2 1 P T3 SD: 21.0342 c. M:-43.5449 c. 16: 3 3 1 3 2 3 1 P T3 S SD: 18.5447 c. M:-32.4920 c. 17: 3 3 1 4 2 3 1 N SD: 6.4577 c. M:-11.5547 c. 41: 7 7 3 9 5 7 3 N SD: 6.2397 c. M: 8.7199 c. 46: 8 8 3 10 6 8 3 N SD: 3.9949 c. M: 8.3942 c. 55: 10 9 4 12 7 9 4 N SD: 3.6192 c. M: 6.7357 c. 58: 10 10 4 13 7 10 4 N SD: 3.6520 c. M: 6.7014 c. 60: 11 10 4 13 8 10 4 N SD: 3.6888 c. M:-6.4020 c. 63: 11 11 4 14 8 11 4 N SD: 2.8388 c. M:-4.3466 c. 72: 13 12 5 16 9 12 5 N SD: 1.9299 c. M:-3.0687 c. 89: 16 15 6 20 11 15 6 N SD: 1.7076 c. M:-3.6234 c. 118: 21 20 8 26 15 20 8 N SD: 0.9257 c. M: 2.2040 c. 135: 24 23 9 30 17 23 9 N SD: 0.3218 c. M:-0.5370 c. 342: 61 58 23 76 43 58 23 N SD: 0.2124 c. M:-0.4371 c. 477: 85 81 32 106 60 81 32 N SD: 0.1313 c. M:-0.2385 c. 612: 109 104 41 136 77 104 41 N SD: 0.1301 c. M: 0.2100 c. 877: 156 149 59 195 110 149 59 N SD: 0.1285 c. M: 0.1927 c. 894: 159 152 60 199 112 152 60 N SD: 0.1104 c. M:-0.1848 c. 1012: 180 172 68 225 127 172 68 N SD: 0.1044 c. M: 0.1592 c. 1029: 183 175 69 229 129 175 69 N SD: 0.0982 c. M: 0.1869 c. 1101: 196 187 74 245 138 187 74 N SD: 0.0961 c. M:-0.2067 c. 1219: 217 207 82 271 153 207 82 N SD: 0.0894 c. M: 0.1849 c. 1236: 220 210 83 275 155 210 83 N SD: 0.0551 c. M:-0.1326 c. 1354: 241 230 91 301 170 230 91 N SD: 0.0622 c. M: 0.1129 c. 1371: 244 233 92 305 172 233 92 N SD: 0.0315 c. M:-0.0732 c. 1506: 268 256 101 335 189 256 101 N SD: 0.0356 c. M:-0.0589 c. 1713: 305 291 115 381 215 291 115 N SD: 0.0373 c. M:-0.0623 c. 1848: 329 314 124 411 232 314 124 N SD: 0.0233 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 6:7 x 8 S SD: 22.0442 cents 5 x 6:7:8 x x 10 S SD: 35.2580 cents 6:7 x 8:9:10:11:12 S SD: 18.7744 cents 7:8:9 x 11:12:13:14 SD: 9.8838 cents 10:11:13 x 16:17:19:20 SD: 13.0863 cents 11:12:14:15:17:19:21:22 SD: 11.5563 cents 12:14:15:16:19:20:23:24 SD: 10.8516 cents 13:15 x 17:20:22:25:26 SD: 8.8885 cents 14:16:18:19:22:24:27:28 SD: 7.1193 cents 15:17:19:20:23:25:29:30 SD: 6.6219 cents 18:20:23:24:28:31:34:36 SD: 6.4099 cents 21:24:27:28:33:36:40:42 SD: 5.0530 cents 22:25:28:29:34:37:42:44 SD: 4.0889 cents 23:26:29:31:36:39:44:46 SD: 3.8973 cents 29:33:37:39:45:49:55:58 SD: 3.3358 cents 30:34:38:40:47:51:57:60 SD: 2.5051 cents 36:41:46:48:56:61:69:72 SD: 2.1861 cents 45:51:57:60:70:76:86:90 SD: 1.7465 cents 54:61:69:72:84:92:103:108 SD: 1.4498 cents 63:71:80:84:98:107:120:126 SD: 1.2545 cents 69:78:88:92:107:117:132:138 SD: 1.0904 cents 92:104:117:123:143:156:176:184 SD: 0.9272 cents 99:112:126:132:154:168:189:198 SD: 0.0000 cents