Scala analysis: met24-wilson_rast-bayyati17_Dup
Tempering of Wilson's Rast-Bayyati Matrix (17)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 82.031 cents 82.031250 2: 150.000 cents 150.000000 3: 207.422 cents 207.421880 4: 289.453 cents 289.453130 5: 357.422 cents 357.421880 6: 439.453 cents 439.453130 7: 496.875 cents 496.875000 8: 564.844 cents 564.843750 9: 646.875 cents 646.875000 10: 704.297 cents 704.296880 11: 785.156 cents 785.156250 12: 854.297 cents 854.296880 13: 911.719 cents 911.718750 14: 992.578 cents 992.578130 15: 1061.719 cents 1061.718750 16: 1142.578 cents 1142.578120 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 57.4219 cents 57.4219 1: 82.0313 cents 82.0313 2: 67.9687 cents 67.9687 3: 57.4219 cents 57.4219 4: 82.0313 cents 82.0313 5: 67.9687 cents 67.9687 6: 82.0312 cents 82.0312 7: 57.4219 cents 57.4219 8: 67.9687 cents 67.9687 9: 82.0313 cents 82.0313 10: 57.4219 cents 57.4219 11: 80.8594 cents 80.8594 12: 69.1406 cents 69.1406 13: 57.4219 cents 57.4219 14: 80.8594 cents 80.8594 15: 69.1406 cents 69.1406 16: 80.8594 cents 80.8594 17: 57.4219 cents 57.4219
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 57.42188 cents 1: 3 67.96875 cents 1: 2 69.14063 cents 1: 3 80.85937 cents 1: 4 82.03125 cents 2: 2 125.39063 cents 2: 1 126.56250 cents 2: 3 138.28125 cents 2: 4 139.45313 cents 2: 7 150.00000 cents 3: 13 207.42188 cents 3: 2 220.31250 cents 3: 1 230.85937 cents 3: 1 232.03125 cents 4: 3 264.84375 cents 4: 2 275.39063 cents 4: 1 276.56250 cents 4: 5 288.28125 cents 4: 6 289.45313 cents 5: 4 345.70312 cents 5: 4 346.87500 cents 5: 8 357.42188 cents 5: 1 370.31250 cents 6: 9 414.84375 cents 6: 4 427.73437 cents 6: 2 438.28124 cents 6: 2 439.45313 cents 7: 1 472.26562 cents 7: 1 482.81250 cents 7: 7 495.70312 cents 7: 8 496.87500 cents 8: 3 553.12500 cents 8: 3 554.29688 cents 8: 6 564.84375 cents 8: 5 577.73437 cents 9: 5 622.26563 cents 9: 6 635.15625 cents 9: 3 645.70312 cents 9: 3 646.87500 cents 10: 8 703.12500 cents 10: 7 704.29688 cents 10: 1 717.18750 cents 10: 1 727.73438 cents 11: 2 760.54687 cents 11: 2 761.71875 cents 11: 4 772.26563 cents 11: 9 785.15625 cents 12: 1 829.68750 cents 12: 8 842.57813 cents 12: 4 853.12499 cents 12: 4 854.29688 cents 13: 6 910.54688 cents 13: 5 911.71875 cents 13: 1 923.43750 cents 13: 2 924.60937 cents 13: 3 935.15624 cents 14: 1 967.96875 cents 14: 1 969.14063 cents 14: 2 979.68750 cents 14: 13 992.57813 cents 15: 7 1050.00000 cents 15: 4 1060.54687 cents 15: 3 1061.71875 cents 15: 1 1073.43750 cents 15: 2 1074.60937 cents 16: 4 1117.96875 cents 16: 3 1119.14063 cents 16: 2 1130.85937 cents 16: 3 1132.03125 cents 16: 5 1142.57812 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.37500 = 35/8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 82.0 150.0 207.4 289.5 357.4 439.5 496.9 564.8 646.9 704.3 785.2 854.3 911.7 992.6 1061.7 1142.6 1200.0 82.0 : 68.0 125.4 207.4 275.4 357.4 414.8 482.8 564.8 622.3 703.1 772.3 829.7 910.5 979.7 1060.5 1118.0 1200.0 150.0 : 57.4 139.5 207.4 289.5 346.9 414.8 496.9 554.3 635.2 704.3 761.7 842.6 911.7 992.6 1050.0 1132.0 1200.0 207.4 : 82.0 150.0 232.0 289.5 357.4 439.5 496.9 577.7 646.9 704.3 785.2 854.3 935.2 992.6 1074.6 1142.6 1200.0 289.5 : 68.0 150.0 207.4 275.4 357.4 414.8 495.7 564.8 622.3 703.1 772.3 853.1 910.5 992.6 1060.5 1118.0 1200.0 357.4 : 82.0 139.5 207.4 289.5 346.9 427.7 496.9 554.3 635.2 704.3 785.2 842.6 924.6 992.6 1050.0 1132.0 1200.0 439.5 : 57.4 125.4 207.4 264.8 345.7 414.8 472.3 553.1 622.3 703.1 760.5 842.6 910.5 968.0 1050.0 1118.0 1200.0 496.9 : 68.0 150.0 207.4 288.3 357.4 414.8 495.7 564.8 645.7 703.1 785.2 853.1 910.5 992.6 1060.5 1142.6 1200.0 564.8 : 82.0 139.5 220.3 289.5 346.9 427.7 496.9 577.7 635.2 717.2 785.2 842.6 924.6 992.6 1074.6 1132.0 1200.0 646.9 : 57.4 138.3 207.4 264.8 345.7 414.8 495.7 553.1 635.2 703.1 760.5 842.6 910.5 992.6 1050.0 1118.0 1200.0 704.3 : 80.9 150.0 207.4 288.3 357.4 438.3 495.7 577.7 645.7 703.1 785.2 853.1 935.2 992.6 1060.5 1142.6 1200.0 785.2 : 69.1 126.6 207.4 276.6 357.4 414.8 496.9 564.8 622.3 704.3 772.3 854.3 911.7 979.7 1061.7 1119.1 1200.0 854.3 : 57.4 138.3 207.4 288.3 345.7 427.7 495.7 553.1 635.2 703.1 785.2 842.6 910.5 992.6 1050.0 1130.9 1200.0 911.7 : 80.9 150.0 230.9 288.3 370.3 438.3 495.7 577.7 645.7 727.7 785.2 853.1 935.2 992.6 1073.4 1142.6 1200.0 992.6 : 69.1 150.0 207.4 289.5 357.4 414.8 496.9 564.8 646.9 704.3 772.3 854.3 911.7 992.6 1061.7 1119.1 1200.0 1061.7: 80.9 138.3 220.3 288.3 345.7 427.7 495.7 577.7 635.2 703.1 785.2 842.6 923.4 992.6 1050.0 1130.9 1200.0 1142.6: 57.4 139.5 207.4 264.8 346.9 414.8 496.9 554.3 622.3 704.3 761.7 842.6 911.7 969.1 1050.0 1119.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.4219 .. 82.0313 cents 24.60937 cents 57.42188 cents 2: 125.3906 .. 150.0000 cents 24.60937 cents 43.35938 cents 3: 207.4219 .. 232.0312 cents 24.60937 cents 57.42188 cents 4: 264.8438 .. 289.4531 cents 24.60938 cents 32.81250 cents 5: 345.7031 .. 370.3125 cents 24.60938 cents 56.24999 cents 6: 414.8438 .. 439.4531 cents 24.60938 cents 44.53125 cents 7: 472.2656 .. 496.8750 cents 24.60938 cents 32.81249 cents 8: 553.1250 .. 577.7344 cents 24.60937 cents 56.25000 cents 9: 622.2656 .. 646.8750 cents 24.60937 cents 44.53126 cents 10: 703.1250 .. 727.7344 cents 24.60938 cents 56.25000 cents 11: 760.5469 .. 785.1563 cents 24.60938 cents 32.81249 cents 12: 829.6875 .. 854.2969 cents 24.60938 cents 44.53125 cents 13: 910.5469 .. 935.1562 cents 24.60936 cents 56.25000 cents 14: 967.9687 .. 992.5781 cents 24.60938 cents 32.81251 cents 15: 1050.0000 .. 1074.6094 cents 24.60937 cents 57.42187 cents 16: 1117.9687 .. 1142.5781 cents 24.60937 cents 43.35938 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 57.42187 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 82.03125 cents Average / Smallest step : 1.229292 Largest / Average step : 1.162109 Largest / Smallest step : 1.428572 Median interval of one step : 69.14063 cents, amount: 2 Most common interval of one step : 57.42188 cents, amount: 5 Least squares average step : 70.97558 cents, oct.: 1206.58482 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 70 128 177 247 305 375 424 482 552 601 670 729 778 847 906 975 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 831 of 973.828 cents and inv. generated superset size: 262 = 245 more = 1541.176% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABACBACDECDEDC Step pattern size order : EBAEBEABEADCADCDA Scale is a Constant Structure, by a margin of 32.81249 cents Scale diversity : 1.229929 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.671875 Number of different interval sizes : 70 = 4.37500 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.37500 = 35/8 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17187 cents Most common intervals : 207.42188 cents & inv., amount: 13 Most common triad is 0.0 207.422 992.578 cents, amount: 9 Number of recognisable fifths : 16, average 704.5166 cents Number of appreciable fifths : 15, average 703.6719 cents Best fifths form a closed circle Formal octave complements present : 3 = 17.6471% Limited inverse transpositions with margin 24.6094 cents: 14 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.8947 c. M: 15.9237 c. 38: 3 2 2 2 2 3 2 2 2 2 3 2 2 2 3 2 2 P D3 SD: 8.9230 c. M: 15.2961 c. 41: 3 2 2 3 2 3 2 2 3 2 3 2 2 3 2 3 2 SP M ME S SD: 4.4715 c. M: 8.7462 c. 46: 3 3 2 3 3 3 2 3 3 2 3 3 2 3 3 3 2 SP M ME S SD: 4.8238 c. M:-9.0693 c. 58: 4 3 3 4 3 4 3 3 4 3 4 3 3 4 3 4 3 SP M ME S SD: 3.8994 c. M: 6.5463 c. 63: 4 4 3 4 4 4 3 4 4 3 4 4 3 4 4 4 3 SP M ME S SD: 3.3279 c. M:-6.5848 c. 70: 5 4 3 5 4 5 3 4 5 3 5 4 3 5 4 5 3 SP T3 SD: 3.2362 c. M:-6.2612 c. 87: 6 5 4 6 5 6 4 5 6 4 6 5 4 6 5 6 4 SP T3 SD: 1.1226 c. M:-2.2495 c. 104: 7 6 5 7 6 7 5 6 7 5 7 6 5 7 6 7 5 SP T3 SD: 0.5915 c. M: 1.2620 c. 191: 13 11 9 13 11 13 9 11 13 9 13 11 9 13 11 13 9 SP T3 SD: 0.4865 c. M:-0.8774 c. 295: 20 17 14 20 17 20 14 17 20 14 20 17 14 20 17 20 14 SP T3 SD: 0.4193 c. M: 0.6753 c. 440: 30 25 21 30 25 30 21 25 30 21 30 25 21 30 25 30 21 SP T3 SD: 0.4393 c. M: 0.8097 c. 486: 33 28 23 33 28 33 23 28 33 23 33 28 23 33 28 33 23 SP T3 SD: 0.4320 c. M:-0.6318 c. 497: 34 28 24 34 28 34 24 28 34 24 33 29 24 33 29 33 24 SP SD: 0.4307 c. M:-0.9573 c. 527: 36 30 25 36 30 36 25 30 36 25 36 30 25 36 30 36 25 SP T3 SD: 0.4062 c. M: 0.9028 c. 538: 37 30 26 37 30 37 26 30 37 26 36 31 26 36 31 36 26 SP SD: 0.3902 c. M: 0.5707 c. 544: 37 31 26 37 31 37 26 31 37 26 37 31 26 37 31 37 26 SP T3 SD: 0.4216 c. M: 0.6893 c. 567: 39 32 27 39 32 39 27 32 39 27 38 33 27 38 33 38 27 SP SD: 0.4596 c. M:-0.7585 c. 584: 40 33 28 40 33 40 28 33 40 28 39 34 28 39 34 39 28 SP SD: 0.3310 c. M:-0.6100 c. 625: 43 35 30 43 35 43 30 35 43 30 42 36 30 42 36 42 30 SP SD: 0.2750 c. M:-0.5287 c. 642: 44 36 31 44 36 44 31 36 44 31 43 37 31 43 37 43 31 SP SD: 0.2895 c. M: 0.5220 c. 671: 46 38 32 46 38 46 32 38 46 32 45 39 32 45 39 45 32 SP SD: 0.3265 c. M:-0.5763 c. 688: 47 39 33 47 39 47 33 39 47 33 46 40 33 46 40 46 33 SP SD: 0.2505 c. M:-0.4906 c. 729: 50 41 35 50 41 50 35 41 50 35 49 42 35 49 42 49 35 SP SD: 0.1697 c. M:-0.2733 c. 816: 56 46 39 56 46 56 39 46 56 39 55 47 39 55 47 55 39 SP SD: 0.1508 c. M:-0.3217 c. 833: 57 47 40 57 47 57 40 47 57 40 56 48 40 56 48 56 40 SP SD: 0.1115 c. M: 0.2012 c. 920: 63 52 44 63 52 63 44 52 63 44 62 53 44 62 53 62 44 SP SD: 0.0669 c. M:-0.1427 c. 1024: 70 58 49 70 58 70 49 58 70 49 69 59 49 69 59 69 49 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.1709 cents 3 .. 6 match: 3 H SD: 9.1283 cents 4 .. 8 match: 4 H SD: 9.3688 cents 5 .. 10 match: 5 H SD: 9.8749 cents 6 .. 12 match: 6 H SD: 6.2762 cents 7 .. 14 match: 7 H SD: 6.4079 cents 8 .. 16 match: 8 H SD: 6.2427 cents 9 .. 18 match: 9 H SD: 6.6201 cents 10 .. 20 match: 10 H SD: 6.2601 cents 11 .. 22 match: 11 H SD: 6.2302 cents 12 .. 24 match: 12 H SD: 5.7591 cents 13 .. 26 match: 13 H SD: 5.4886 cents 14 .. 28 match: 14 H SD: 4.8444 cents 15 .. 30 match: 14 SD: 5.9597 cents 16 .. 32 match: 15 S SD: 4.3761 cents 17 .. 34 match: 16 SD: 4.3877 cents 18 .. 36 match: 16 SD: 3.9244 cents 19 .. 38 match: 16 SD: 5.0927 cents 20 .. 40 match: 17 SD: 4.4310 cents 21 .. 42 match: 17 SD: 3.5862 cents 22 .. 44 match: 17 SD: 3.1675 cents 26 .. 52 match: 17 SD: 3.1073 cents 30 .. 60 match: 17 SD: 3.0182 cents 31 .. 62 match: 17 SD: 2.6084 cents 33 .. 66 match: 17 SD: 2.4443 cents 34 .. 68 match: 17 SD: 2.4437 cents 36 .. 72 match: 17 SD: 2.4353 cents 38 .. 76 match: 17 SD: 2.1264 cents 39 .. 78 match: 17 SD: 1.8682 cents 42 .. 84 match: 17 SD: 1.7509 cents 44 .. 88 match: 17 SD: 1.4929 cents 55 .. 110 match: 17 SD: 1.4227 cents 56 .. 112 match: 17 SD: 1.3518 cents 62 .. 124 match: 17 SD: 1.2087 cents 65 .. 130 match: 17 SD: 1.1721 cents 66 .. 132 match: 17 SD: 0.9407 cents 78 .. 156 match: 17 SD: 0.8045 cents 99 .. 198 match: 17 SD: 0.7744 cents 100 .. 200 match: 17 SD: 0.7682 cents 101 .. 202 match: 17 SD: 0.7491 cents 104 .. 208 match: 17 SD: 0.7091 cents 108 .. 216 match: 17 SD: 0.6607 cents 110 .. 220 match: 17 SD: 0.6326 cents 121 .. 242 match: 17 SD: 0.5943 cents 124 .. 248 match: 17 SD: 0.5557 cents 132 .. 264 match: 17 SD: 0.5489 cents 141 .. 282 match: 17 SD: 0.4942 cents 143 .. 286 match: 17 SD: 0.4448 cents 163 .. 326 match: 17 SD: 0.4307 cents 165 .. 330 match: 17 SD: 0.3834 cents 166 .. 332 match: 17 SD: 0.3501 cents 187 .. 374 match: 17 SD: 0.2951 cents 243 .. 486 match: 17 SD: 0.2691 cents 265 .. 530 match: 17 SD: 0.2384 cents 267 .. 534 match: 17 SD: 0.2312 cents 274 .. 548 match: 17 SD: 0.2256 cents 291 .. 582 match: 17 SD: 0.2170 cents 307 .. 614 match: 17 SD: 0.2103 cents 309 .. 618 match: 17 SD: 0.2099 cents 331 .. 662 match: 17 SD: 0.1847 cents 353 .. 706 match: 17 SD: 0.1664 cents 384 .. 768 match: 17 SD: 0.1655 cents 418 .. 836 match: 17 SD: 0.1595 cents 430 .. 860 match: 17 SD: 0.1445 cents 472 .. 944 match: 17 SD: 0.1358 cents 488 .. 976 match: 17 SD: 0.1181 cents 550 .. 1100 match: 17 SD: 0.1116 cents 598 .. 1196 match: 17 SD: 0.1020 cents