Scala analysis: xen09-wilson-marwa-10-05
Marwa permutation 5 from Figure 10, Ptolemy 7/6 12/11 22/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 33/28 284.447037 undecimal minor third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 9/8 203.9100 major whole tone 2: 22/21 80.5370 undecimal minor semitone 3: 7/6 266.8709 septimal minor third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 9/8 203.9100 major whole tone 6: 88/81 143.4979 2nd undecimal neutral second 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
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 : 203.9 284.4 551.3 702.0 905.9 1049.4 1200.0 203.9 : 80.5 347.4 498.0 702.0 845.5 996.1 1200.0 284.4 : 266.9 417.5 621.4 764.9 915.6 1119.5 1200.0 551.3 : 150.6 354.5 498.0 648.7 852.6 933.1 1200.0 702.0 : 203.9 347.4 498.0 702.0 782.5 1049.4 1200.0 905.9 : 143.5 294.1 498.0 578.6 845.5 996.1 1200.0 1049.4: 150.6 354.5 435.1 702.0 852.6 1056.5 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: 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 : 174.71486 cents, oct.: 1223.00403 cents Scale is not proper Step pattern alph. order: ABCDAED Step pattern size order : DAECDBC 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: 33 Scale harmonicity : 0.022658 Average absolute harmonicity : 0.228460 Specific harmonicity : 0.124579 Fundamental : 1/336, -8.3923 octaves, 0.7786 Hz. Guide tone : 594, 9.2143 octaves, 155405.586 Hz. Exponens Consonantiae : 1.995840E+05, 17.60664 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 82.5, average 11.78571 Mersenne's string divisions : 12708435 Sum of van Prooijen's expressibility: 6.46403, average 0.92343 Sum of Tenney's harmonic distance : 12.30170, average 1.75739 Vogel's harmonic complexity : 18.42857 Wille's k value : 283 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 80.78239, average 2.88509 Lattice compactness (without 2's) : 50.87257, average 1.81688 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.85714 15 1 3: -1 .. 3 0.85714 8 3 7: -1 .. 0 -0.14286 1 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 8 / 7 = 1.14286 Average absolute exponent except 2's: 12 / 7 = 1.71429 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 0 2 1 1 1 1 N T3 SD: 51.0875 c. M: 113.0185 c. 8: 1 1 2 1 1 1 1 P M ME S SD: 33.5117 c. M: 53.9100 c. 9: 2 0 2 1 2 1 1 N D3 SD: 31.3441 c. M:-62.7567 c. 11: 2 1 2 1 2 2 1 P M ME S SD: 31.9463 c. M: 47.4095 c. 12: 2 1 3 1 2 1 2 P D3 SD: 26.9975 c. M: 49.3629 c. Mela Hemavati, Raga Desisimharavam, Maqam Nakriz, Tunisian, Dorian sharp 4, Misheberekh: Jewish, Nigriz, Pimenikos, Souzinak (Peiraiotikos Minor): Greece, Ukrainian Dorian, Ukrainian Minor, Kaffa, Gnossiennes 13: 2 1 3 2 2 1 2 N T3 SD: 21.4436 c. M:-36.5065 c. 15: 3 1 3 2 2 2 2 SP D3 S SD: 23.0656 c. M:-36.0900 c. 16: 3 1 3 2 3 2 2 P D3 SD: 17.4875 c. M: 26.9550 c. 17: 3 1 4 2 3 2 2 N SD: 8.3586 c. M:-13.3879 c. 24: 4 2 5 3 4 3 3 P SD: 6.5197 c. M:-15.5530 c. 37: 6 3 8 5 6 4 5 N SD: 7.6873 c. M:-11.5585 c. 41: 7 3 9 5 7 5 5 N SD: 4.0073 c. M:-8.2359 c. 46: 8 3 10 6 8 5 6 N SD: 4.3635 c. M:-7.1785 c. 58: 10 4 13 7 10 7 7 N SD: 4.5579 c. M:-7.3027 c. 63: 11 4 14 8 11 7 8 N SD: 4.0722 c. M:-8.4207 c. 65: 11 4 15 8 11 8 8 N SD: 3.2536 c. M: 7.5240 c. 70: 12 5 15 9 12 8 9 N SD: 3.4015 c. M:-6.9815 c. 72: 12 5 16 9 12 9 9 N SD: 2.8509 c. M: 5.8650 c. 77: 13 5 17 10 13 9 10 N SD: 3.4424 c. M: 5.8634 c. 81: 14 5 18 10 14 10 10 N SD: 3.2505 c. M: 5.6587 c. 87: 15 6 19 11 15 10 11 N SD: 2.9201 c. M:-5.2081 c. 89: 15 6 20 11 15 11 11 N SD: 1.6469 c. M: 2.4942 c. 94: 16 6 21 12 16 11 12 N SD: 1.9104 c. M: 3.5960 c. 111: 19 7 25 14 19 13 14 N SD: 1.6762 c. M: 3.3660 c. 118: 20 8 26 15 20 14 15 N SD: 1.1561 c. M: 2.1654 c. 135: 23 9 30 17 23 16 17 N SD: 0.4255 c. M:-0.8017 c. 224: 38 15 50 28 38 27 28 N SD: 0.4301 c. M:-0.6371 c. 342: 58 23 76 43 58 41 43 N SD: 0.3528 c. M: 0.6018 c. 359: 61 24 80 45 61 43 45 N SD: 0.1688 c. M: 0.3245 c. 494: 84 33 110 62 84 59 62 N SD: 0.1383 c. M: 0.2365 c. 742: 126 50 165 93 126 89 93 N SD: 0.1613 c. M:-0.2327 c. 836: 142 56 186 105 142 100 105 N SD: 0.1201 c. M: 0.2365 c. 877: 149 59 195 110 149 105 110 N SD: 0.0896 c. M:-0.1596 c. 1012: 172 68 225 127 172 121 127 N SD: 0.0672 c. M:-0.1379 c. 1354: 230 91 301 170 230 162 170 N SD: 0.0579 c. M: 0.1043 c. 1371: 233 92 305 172 233 164 172 N SD: 0.0563 c. M:-0.1044 c. 1489: 253 100 331 187 253 178 187 N SD: 0.0425 c. M: 0.0755 c. 1713: 291 115 381 215 291 205 215 N SD: 0.0433 c. M: 0.0857 c. 1848: 314 124 411 232 314 221 232 N SD: 0.0177 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 19.1501 cents 4 x 5 x 6:7 x 8 S SD: 29.9384 cents 5 x 6:7 x 8:9:10 S SD: 21.4030 cents 6 x 7:8:9:10:11:12 S SD: 10.0131 cents 7:8 x 10:11:12:13:14 S SD: 18.8932 cents 8:9 x 11:12:14:15:16 SD: 12.3353 cents 10:11:12:14:15:17:18:20 SD: 9.7229 cents 12 x 14:17:18:20:22:24 SD: 9.7788 cents 13 x 15:18:20:22:24:26 SD: 9.9775 cents 16:18:19:22:24:27:29:32 SD: 3.3872 cents 32:36:38:44:48:54:59:64 SD: 2.3340 cents 40:45:47:55:60:68:73:80 SD: 2.2725 cents 48:54:57:66:72:81:88:96 SD: 1.8666 cents 56:63:66:77:84:95:103:112 SD: 1.5317 cents 66:74:78:91:99:111:121:132 SD: 1.5223 cents 72:81:85:99:108:122:132:144 SD: 1.0976 cents 80:90:94:110:120:135:147:160 SD: 0.9373 cents 90:101:106:124:135:152:165:180 SD: 0.8319 cents 96:108:113:132:144:162:176:192 SD: 0.3125 cents 208:234:245:286:312:351:381:416 SD: 0.2599 cents 224:252:264:308:336:378:411:448 SD: 0.2007 cents 240:270:283:330:360:405:440:480 SD: 0.1249 cents 336:378:396:462:504:567:616:672 SD: 0.0000 cents