Scala analysis: xen09-wilson-marwa-15b-04
Marwa permutation 4 from Figure 15b, Ptolemy 22/21 12/11 7/6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 2: 11/9 347.407941 undecimal neutral third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 14/9 764.915905 septimal minor sixth 5: 44/27 845.452940 neutral 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: 88/81 143.4979 2nd undecimal neutral second 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 112/99 213.5980 5: 22/21 80.5370 undecimal minor semitone 6: 9/8 203.9100 major whole tone 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: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 3 9/8 203.910 cents major whole tone 1: 1 112/99 213.598 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 2 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: 1 81/64 407.820 cents Pythagorean major third 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: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 44/27 845.453 cents neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 1 56/33 915.553 cents 6: 1 99/56 986.402 cents 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 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: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 143.5 347.4 551.3 764.9 845.5 1049.4 1200.0 143.5 : 203.9 407.8 621.4 702.0 905.9 1056.5 1200.0 347.4 : 203.9 417.5 498.0 702.0 852.6 996.1 1200.0 551.3 : 213.6 294.1 498.0 648.7 792.2 996.1 1200.0 764.9 : 80.5 284.4 435.1 578.6 782.5 986.4 1200.0 845.5 : 203.9 354.5 498.0 702.0 905.9 1119.5 1200.0 1049.4: 150.6 294.1 498.0 702.0 915.6 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 213.5980 cents 392/363, 133.0609 cents 22/21, 80.5370 cents 2: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 3267/3136, 70.8491 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: 986.4020 .. 1119.4630 cents 392/363, 133.0609 cents 3267/3136, 70.8491 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 : 112/99, 213.5980 cents Average / Smallest step : 2.128568 Largest / Average step : 1.245988 Largest / Smallest step : 2.652171 Median interval of one step : 9/8, 203.9100 cents, amount: 3 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 174.82410 cents, oct.: 1223.76868 cents Scale is not proper Step pattern alph. order: ABBCDBE Step pattern size order : BDDEADC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.582054 Lumma stability : 0.281604 Lumma impropriety factor : 0.035697 Rothenberg efficiency : 0.383673 redundancy: 0.616327 Efficiency x scale size : 2.685714 Number of different interval sizes : 30 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 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: 3 Number of recognisable fifths : 4, average 701.9550 cents Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 81 Scale harmonicity : 0.022156 Average absolute harmonicity : 0.180365 Specific harmonicity : 0.118725 Fundamental : 1/648, -9.3399 octaves, 0.4037 Hz. Guide tone : 616, 9.2668 octaves, 161161.348 Hz. Exponens Consonantiae : 3.991680E+05, 18.60664 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 161.0, average 23.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.41827, average 1.05975 Sum of Tenney's harmonic distance : 15.08885, average 2.15555 Vogel's harmonic complexity : 19.14286 Wille's k value : 445 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 88.96768, average 3.17742 Lattice compactness (without 2's) : 58.12076, average 2.07574 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.42857 11 1 3: -4 .. 0 -1.71429 12 7: 0 .. 1 0.14286 1 1 11: 0 .. 1 0.71429 5 5 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 12 19 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: 35.8848 c. M: 79.2016 c. Lebeng 8: 1 1 2 1 1 1 1 P M ME S SD: 33.5048 c. M:-54.5471 c. 9: 1 2 1 2 0 2 1 N D3 SD: 31.1425 c. M:-52.5921 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 29.4387 c. M:-48.6821 c. 11: 1 2 2 2 1 2 1 N D3 SD: 24.1875 c. M:-41.5461 c. 13: 2 2 2 2 1 2 2 SP M ME S SD: 24.6207 c. M:-41.1174 c. Glacial-7, Lobonian 14: 2 2 2 3 1 2 2 P T3 SD: 19.9412 c. M: 37.0322 c. 15: 2 2 3 3 1 2 2 N SD: 22.7123 c. M:-35.0841 c. 16: 2 3 2 3 1 3 2 P D3 SD: 17.4742 c. M:-27.5921 c. 17: 2 3 3 3 1 3 2 N SD: 7.9358 c. M:-13.3879 c. 24: 3 4 4 4 2 4 3 P SD: 6.4840 c. M: 14.9159 c. 31: 4 5 5 6 2 5 4 N SD: 7.1642 c. M:-11.3408 c. 41: 5 7 7 7 3 7 5 N SD: 3.5958 c. M:-4.7796 c. 58: 7 10 10 10 4 10 7 N SD: 4.0674 c. M:-7.3027 c. 72: 9 12 12 13 5 12 9 N SD: 3.2706 c. M:-6.5021 c. 85: 10 15 14 15 6 14 11 N SD: 3.1024 c. M:-5.5332 c. 89: 11 15 15 16 6 15 11 N SD: 3.1572 c. M:-4.8167 c. 91: 11 15 16 16 6 16 11 N SD: 2.9984 c. M:-5.5821 c. 94: 11 16 16 17 6 16 12 N SD: 2.3473 c. M: 3.0724 c. 111: 13 19 19 20 7 19 14 N SD: 1.8248 c. M: 2.9574 c. 118: 14 20 20 21 8 20 15 N SD: 1.6505 c. M: 2.2040 c. 135: 16 23 23 24 9 23 17 N SD: 0.7254 c. M: 1.2757 c. 176: 21 30 30 31 12 30 22 N SD: 0.6715 c. M: 1.2795 c. 224: 27 38 38 40 15 38 28 N SD: 0.8343 c. M:-1.1555 c. 287: 34 49 49 51 19 49 36 N SD: 0.6637 c. M: 1.3377 c. 301: 36 51 51 54 20 51 38 N SD: 0.6254 c. M: 1.1518 c. 311: 37 53 53 55 21 53 39 N SD: 0.5123 c. M: 0.9288 c. 318: 38 54 54 57 21 54 40 N SD: 0.4764 c. M:-1.1218 c. 342: 41 58 58 61 23 58 43 N SD: 0.2421 c. M: 0.4407 c. 359: 43 61 61 64 24 61 45 N SD: 0.2797 c. M:-0.5437 c. 477: 57 81 81 85 32 81 60 N SD: 0.2231 c. M: 0.3745 c. 494: 59 84 84 88 33 84 62 N SD: 0.1346 c. M:-0.2663 c. 836: 100 142 142 149 56 142 105 N SD: 0.0837 c. M:-0.1559 c. 971: 116 165 165 173 65 165 122 N SD: 0.1187 c. M: 0.1406 c. 1012: 121 172 172 180 68 172 127 N SD: 0.0477 c. M: 0.0938 c. 1354: 162 230 230 241 91 230 170 N SD: 0.0498 c. M:-0.0767 c. 1506: 180 256 256 268 101 256 189 N SD: 0.0453 c. M:-0.0765 c. 1848: 221 314 314 329 124 314 232 N SD: 0.0119 c. M: 0.0192 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: 21.9891 cents 4 x 5 x 6 x 7:8 S SD: 27.3450 cents 5 x 6:7 x 8:9:10 S SD: 12.6498 cents 6 x 7:8:9:10:11:12 S SD: 20.2772 cents 7:8:9:10:11 x 13:14 SD: 23.8983 cents 8:9:10:11:12:13:15:16 SD: 14.7533 cents 9:10:11:12:14:15:17:18 SD: 13.1990 cents 10:11:12:14 x 16:18:20 S SD: 11.1342 cents 11:12:13:15:17:18:20:22 SD: 9.0678 cents 13:14:16:18:20:21:24:26 S SD: 5.0803 cents 22:24:27:30:34:36:40:44 SD: 3.7605 cents 24:26:29:33:37:39:44:48 SD: 3.7282 cents 32:35:39:44:50:52:59:64 SD: 2.6331 cents 35:38:43:48:54:57:64:70 SD: 2.5750 cents 45:49:55:62:70:73:83:90 SD: 2.0167 cents 54:59:66:74:84:88:99:108 SD: 1.6307 cents 59:64:72:81:92:96:108:118 SD: 1.0416 cents 72:78:88:99:112:117:132:144 SD: 0.9951 cents 90:98:110:124:140:147:165:180 SD: 0.9379 cents 94:102:115:129:146:153:172:188 SD: 0.9144 cents 103:112:126:142:160:168:189:206 SD: 0.8579 cents 117:127:143:161:182:191:215:234 SD: 0.7758 cents 126:137:154:173:196:205:231:252 SD: 0.5738 cents 149:162:182:205:232:243:273:298 SD: 0.4423 cents 162:176:198:223:252:264:297:324 SD: 0.2774 cents 288:313:352:396:448:469:528:576 SD: 0.1964 cents 360:391:440:495:560:587:660:720 SD: 0.1571 cents 427:464:522:587:664:696:783:854 SD: 0.1439 cents 486:528:594:668:756:792:891:972 SD: 0.0925 cents