Scala analysis: xen09-wilson-marwa-15a-08
Marwa permutation 8 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: 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: 7/6 266.8709 septimal minor third 2: 12/11 150.6371 undecimal neutral second, 3/4-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: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 1 33/28 284.447 cents undecimal minor third 2: 1 11/9 347.408 cents undecimal neutral 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 18/11 852.592 cents undecimal neutral sixth 5: 1 56/33 915.553 cents 5: 2 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 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 : 266.9 417.5 498.0 764.9 915.6 996.1 1200.0 266.9 : 150.6 231.2 498.0 648.7 729.2 933.1 1200.0 417.5 : 80.5 347.4 498.0 578.6 782.5 1049.4 1200.0 498.0 : 266.9 417.5 498.0 702.0 968.8 1119.5 1200.0 764.9 : 150.6 231.2 435.1 702.0 852.6 933.1 1200.0 915.6 : 80.5 284.4 551.3 702.0 782.5 1049.4 1200.0 996.1 : 203.9 470.8 621.4 702.0 968.8 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 .. 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 : 175.78564 cents, oct.: 1230.49951 cents Scale is not proper Step pattern alph. order: ABCABCD Step pattern size order : DBADBAC Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.595742 Lumma stability : 0.134228 Lumma impropriety factor : 0.154686 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 99/98, 17.5761 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 701.955 1119.463 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords All steps are superparticular (epimoric) 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 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 : 63 (O: 63 U: 63) Highest odd numerator or denominator: 33 Scale harmonicity : 0.025773 Average absolute harmonicity : 0.216643 Specific harmonicity : 0.126045 Fundamental : 1/198, -7.6294 octaves, 1.3213 Hz. Guide tone : 112, 6.8074 octaves, 29302.063 Hz. Exponens Consonantiae : 2.217600E+04, 14.43671 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 92.5, average 13.21429 Mersenne's string divisions : 13970775 Sum of van Prooijen's expressibility: 5.79061, average 0.82723 Sum of Tenney's harmonic distance : 12.71642, average 1.81663 Vogel's harmonic complexity : 17.42857 Wille's k value : 115 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 71.67533, average 2.55983 Lattice compactness (without 2's) : 40.81382, average 1.45764 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.57143 13 1 3: -2 .. 0 -1.00000 7 2 7: 0 .. 1 0.57143 4 2 11: -1 .. 0 -0.28571 2 2 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 22 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 12 18 22| 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: 60.5751 c. M: 95.4423 c. Lebeng 8: 2 1 0 2 1 1 1 N D3 SD: 33.4499 c. M:-53.9100 c. 9: 2 1 1 2 1 0 2 N SD: 31.7069 c. M: 62.7567 c. 12: 3 1 1 3 1 1 2 N SD: 20.3398 c. M:-35.0841 c. Chromatic Hypodorian inverse 14: 3 2 1 3 2 1 2 P T3 SD: 18.2200 c. M:-32.4814 c. 17: 4 2 1 4 2 1 3 N SD: 8.3749 c. M:-15.4820 c. 31: 7 4 2 7 4 2 5 N SD: 8.3462 c. M:-13.4793 c. 37: 8 5 2 9 4 3 6 N SD: 8.6923 c. M:-13.4625 c. 39: 9 5 2 9 5 2 7 N SD: 8.5917 c. M:-13.2613 c. 41: 9 5 3 9 5 3 7 N SD: 4.7293 c. M: 8.2359 c. 46: 10 6 3 10 6 3 8 N SD: 4.4947 c. M: 8.3942 c. 55: 12 7 4 12 7 4 9 N SD: 3.9240 c. M:-7.5464 c. 58: 13 7 4 13 7 4 10 N SD: 2.8491 c. M: 5.2081 c. 63: 14 8 4 14 8 4 11 N SD: 2.7381 c. M: 5.6138 c. 72: 16 9 5 16 9 5 12 N SD: 1.8580 c. M:-3.9100 c. 89: 20 11 6 20 11 6 15 N SD: 1.9381 c. M:-3.6234 c. 113: 25 14 8 25 14 8 19 N SD: 1.8572 c. M: 3.3487 c. 118: 26 15 8 26 15 8 20 N SD: 1.2911 c. M: 2.4641 c. 130: 29 16 9 29 16 9 22 N SD: 1.2245 c. M: 2.1233 c. 135: 30 17 9 30 17 9 23 N SD: 0.3148 c. M: 0.5344 c. 342: 76 43 23 76 43 23 58 N SD: 0.2071 c. M:-0.4012 c. 477: 106 60 32 106 60 32 81 N SD: 0.1325 c. M: 0.2042 c. 612: 136 77 41 136 77 41 104 N SD: 0.1326 c. M: 0.2100 c. 836: 186 105 56 186 105 56 142 N SD: 0.1414 c. M:-0.2365 c. 877: 195 110 59 195 110 59 149 N SD: 0.0940 c. M: 0.1762 c. 1012: 225 127 68 225 127 68 172 N SD: 0.0836 c. M: 0.1379 c. 1147: 255 144 77 255 144 77 195 N SD: 0.0920 c. M: 0.1382 c. 1219: 271 153 82 271 153 82 207 N SD: 0.0836 c. M:-0.1364 c. 1236: 275 155 83 275 155 83 210 N SD: 0.0698 c. M:-0.1326 c. 1354: 301 170 91 301 170 91 230 N SD: 0.0657 c. M: 0.1058 c. 1371: 305 172 92 305 172 92 233 N SD: 0.0453 c. M:-0.0875 c. 1506: 335 189 101 335 189 101 256 N SD: 0.0413 c. M: 0.0741 c. 1713: 381 215 115 381 215 115 291 N SD: 0.0367 c. M:-0.0578 c. 1848: 411 232 124 411 232 124 314 N SD: 0.0183 c. M:-0.0315 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 5:6 x 7:8 x 9:10 S SD: 22.2300 cents 6:7 x 8:9:10:11:12 S SD: 14.6961 cents 7:8:9 x 11:12 x 14 SD: 9.3830 cents 8:9:10:11:12 x 14:16 S SD: 18.6209 cents 9 x 11:12:14:15:16:18 SD: 12.7879 cents 10:12:13 x 16:17:18:20 SD: 13.5159 cents 11:13:14:15:17:19:20:22 SD: 9.6811 cents 12:14:15:16:19:20:21:24 SD: 8.6052 cents 13:15 x 17:20:22:23:26 SD: 7.3679 cents 18:21:23:24:28:31:32:36 SD: 3.7823 cents 29:34:37:39:45:49:52:58 SD: 3.5177 cents 30:35:38:40:47:51:53:60 SD: 2.6629 cents 36:42:46:48:56:61:64:72 SD: 1.0464 cents 95:111:121:127:148:161:169:190 SD: 0.9305 cents 96:112:122:128:149:163:171:192 SD: 0.8325 cents 102:119:130:136:159:173:181:204 SD: 0.7830 cents 121:141:154:161:188:205:215:242 SD: 0.7811 cents 126:147:160:168:196:214:224:252 SD: 0.5995 cents 132:154:168:176:205:224:235:264 SD: 0.5336 cents 144:168:183:192:224:244:256:288 SD: 0.5209 cents 162:189:206:216:252:275:288:324 SD: 0.2330 cents 198:231:252:264:308:336:352:396 S SD: 0.0000 cents