Scala analysis: xen09-wilson-marwa-15a-03
Marwa permutation 3 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: 63/44 621.417966 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: 7/6 266.8709 septimal minor third 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 9/8 203.9100 major whole tone 4: 88/81 143.4979 2nd undecimal neutral second 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: 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 33/28 284.447 cents undecimal minor third 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 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: 1 11/7 782.492 cents undecimal augmented 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 56/33 915.553 cents 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 : 266.9 417.5 621.4 764.9 915.6 1119.5 1200.0 266.9 : 150.6 354.5 498.0 648.7 852.6 933.1 1200.0 417.5 : 203.9 347.4 498.0 702.0 782.5 1049.4 1200.0 621.4 : 143.5 294.1 498.0 578.6 845.5 996.1 1200.0 764.9 : 150.6 354.5 435.1 702.0 852.6 1056.5 1200.0 915.6 : 203.9 284.4 551.3 702.0 905.9 1049.4 1200.0 1119.5: 80.5 347.4 498.0 702.0 845.5 996.1 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 : 12/11, 150.6371 cents, amount: 2 Least squares average step : 183.71676 cents, oct.: 1286.01735 cents Scale is not proper Step pattern alph. order: ABCDBCE Step pattern size order : ECDBCDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.579089 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 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 : 0.179303 Specific harmonicity : 0.111757 Fundamental : 1/396, -8.6294 octaves, 0.6607 Hz. Guide tone : 504, 8.9773 octaves, 131859.285 Hz. Exponens Consonantiae : 1.995840E+05, 17.60664 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 146.0, average 20.85714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.48081, average 1.06869 Sum of Tenney's harmonic distance : 15.28528, average 2.18361 Vogel's harmonic complexity : 18.71429 Wille's k value : 283 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 76.49491, average 2.73196 Lattice compactness (without 2's) : 51.70440, average 1.84659 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.42857 9 1 3: -2 .. 2 -0.14286 7 7: 0 .. 1 0.85714 6 2 11: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is weakly epimorphic with val: <7 10 21 22| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 21 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: 79.3772 c. M: 107.1323 c. Lebeng 8: 2 1 1 1 1 1 1 P M ME S SD: 33.5974 c. M: 69.4630 c. 9: 2 1 2 1 1 1 1 N D3 S SD: 30.9112 c. M: 52.7963 c. 11: 2 2 2 1 1 2 1 N D3 SD: 30.4129 c. M: 48.6891 c. 12: 3 1 2 2 1 2 1 P D3 SD: 23.0353 c. M:-35.0841 c. Aeolian flat 1 13: 3 2 2 1 2 2 1 N T3 SD: 22.5090 c. M:-44.0305 c. 14: 3 2 2 2 2 2 1 P T3 SD: 14.5921 c. M:-27.3042 c. 17: 4 2 3 2 2 3 1 N SD: 10.0383 c. M:-15.4820 c. 31: 7 4 5 4 4 5 2 N SD: 7.2446 c. M:-13.4793 c. 35: 8 4 6 4 5 6 2 N SD: 8.1910 c. M:-11.9656 c. 41: 9 5 7 5 5 7 3 N SD: 6.0265 c. M: 8.2359 c. 46: 10 6 8 5 6 8 3 N SD: 4.4685 c. M: 8.3942 c. 58: 13 7 10 7 7 10 4 N SD: 2.7029 c. M: 5.2081 c. 71: 16 9 12 8 9 12 5 N SD: 3.7100 c. M:-5.0272 c. 72: 16 9 12 9 9 12 5 N SD: 2.2504 c. M: 4.7513 c. 77: 17 10 13 9 10 13 5 N SD: 2.4549 c. M:-3.9276 c. 89: 20 11 15 11 11 15 6 N SD: 1.8667 c. M:-3.6234 c. 100: 22 13 17 12 12 17 7 N SD: 2.8093 c. M: 3.5530 c. 104: 23 13 18 12 13 18 7 N SD: 2.3005 c. M: 4.0145 c. 118: 26 15 20 14 15 20 8 N SD: 1.3714 c. M: 2.4641 c. 135: 30 17 23 16 17 23 9 N SD: 0.4263 c. M:-0.8043 c. 342: 76 43 58 41 43 58 23 N SD: 0.1926 c. M: 0.3653 c. 477: 106 60 81 57 60 81 32 N SD: 0.1207 c. M: 0.2042 c. 1012: 225 127 172 121 127 172 68 N SD: 0.0936 c. M: 0.1379 c. 1147: 255 144 195 137 144 195 77 N SD: 0.0828 c. M: 0.1382 c. 1236: 275 155 210 148 155 210 83 N SD: 0.0744 c. M:-0.1326 c. 1371: 305 172 233 164 172 233 92 N SD: 0.0449 c. M:-0.0875 c. 1506: 335 189 256 180 189 256 101 N SD: 0.0504 c. M:-0.0960 c. 1713: 381 215 291 205 215 291 115 N SD: 0.0351 c. M:-0.0578 c. 1848: 411 232 314 221 232 314 124 N SD: 0.0190 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 4 x x 5 x 6 S SD: 28.7891 cents 4 x 5 x 6:7 x 8 S SD: 22.0442 cents 5:6 x 7:8 x x 10 S SD: 19.7970 cents 6:7:8 x 9:10:11:12 S SD: 21.3030 cents 7:8:9:10:11:12:13:14 H SD: 9.5806 cents 9 x 11:13:14:15:17:18 SD: 13.3929 cents 10:12:13:14:16:17:19:20 SD: 12.5323 cents 11:13:14:16:17:19:21:22 SD: 6.8638 cents 18:21:23:26:28:31:34:36 SD: 5.0934 cents 23:27:29:33:36:39:44:46 SD: 3.2573 cents 30:35:38:43:47:51:57:60 SD: 2.4797 cents 43:50:55:62:67:73:82:86 SD: 2.3304 cents 47:55:60:67:73:80:90:94 SD: 1.8919 cents 54:63:69:77:84:92:103:108 SD: 1.7339 cents 56:65:71:80:87:95:107:112 SD: 1.7218 cents 65:76:83:93:101:110:124:130 SD: 1.2490 cents 77:90:98:110:120:131:147:154 SD: 1.0642 cents 88:103:112:126:137:149:168:176 SD: 0.9942 cents 95:111:121:136:148:161:181:190 SD: 0.8154 cents 102:119:130:146:159:173:195:204 SD: 0.7293 cents 121:141:154:173:188:205:231:242 SD: 0.6780 cents 132:154:168:189:205:224:252:264 SD: 0.4018 cents 162:189:206:232:252:275:309:324 SD: 0.3229 cents 227:265:289:325:353:385:433:454 SD: 0.3135 cents 234:273:298:335:364:397:447:468 SD: 0.2234 cents 264:308:336:378:411:448:504:528 SD: 0.2007 cents 373:435:475:534:580:633:712:746 SD: 0.2007 cents 385:449:490:551:599:653:735:770 SD: 0.1976 cents 389:454:495:557:605:660:743:778 SD: 0.1709 cents 396:462:504:567:616:672:756:792 SD: 0.0000 cents