Scala analysis: semineutral_36-ED2
Semineutral tuning in 36-EDO, 0-433.33-866.67 cents
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.667 cents 66.666670 2: 133.333 cents 133.333330 3: 200.000 cents 200.000000 4: 266.667 cents 266.666670 5: 366.667 cents 366.666660 6: 433.333 cents 433.333330 7: 500.000 cents 500.000000 8: 566.667 cents 566.666670 9: 633.333 cents 633.333330 10: 700.000 cents 700.000000 11: 766.667 cents 766.666670 12: 866.667 cents 866.666670 13: 933.333 cents 933.333330 14: 1000.000 cents 1000.000000 15: 1066.667 cents 1066.666670 16: 1133.333 cents 1133.333330 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 66.6667 cents 66.6667 1: 66.6667 cents 66.6667 2: 66.6667 cents 66.6667 3: 66.6667 cents 66.6667 4: 66.6667 cents 66.6667 5: 100.0000 cents 100.0000 6: 66.6667 cents 66.6667 7: 66.6667 cents 66.6667 8: 66.6667 cents 66.6667 9: 66.6667 cents 66.6667 10: 66.6667 cents 66.6667 11: 66.6667 cents 66.6667 12: 100.0000 cents 100.0000 13: 66.6667 cents 66.6667 14: 66.6667 cents 66.6667 15: 66.6667 cents 66.6667 16: 66.6667 cents 66.6667 17: 66.6667 cents 66.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 15 66.66667 cents 1: 2 99.99999 cents 2: 13 133.33333 cents 2: 4 166.66666 cents 3: 11 200.00000 cents 3: 6 233.33333 cents 4: 9 266.66667 cents 4: 8 299.99999 cents 5: 7 333.33334 cents 5: 10 366.66666 cents 6: 5 400.00001 cents 6: 12 433.33333 cents 7: 3 466.66666 cents 7: 14 500.00000 cents 8: 2 533.33333 cents 8: 14 566.66667 cents 8: 1 600.00000 cents 9: 1 600.00000 cents 9: 14 633.33333 cents 9: 2 666.66667 cents 10: 14 700.00000 cents 10: 3 733.33334 cents 11: 12 766.66667 cents 11: 5 800.00000 cents 12: 10 833.33334 cents 12: 7 866.66667 cents 13: 8 900.00001 cents 13: 9 933.33333 cents 14: 6 966.66667 cents 14: 11 1000.00000 cents 15: 4 1033.33334 cents 15: 13 1066.66667 cents 16: 2 1100.00001 cents 16: 15 1133.33333 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.12500 = 17/8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 66.7 133.3 200.0 266.7 366.7 433.3 500.0 566.7 633.3 700.0 766.7 866.7 933.3 1000.0 1066.7 1133.3 1200.0 66.7 : 66.7 133.3 200.0 300.0 366.7 433.3 500.0 566.7 633.3 700.0 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 133.3 : 66.7 133.3 233.3 300.0 366.7 433.3 500.0 566.7 633.3 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 200.0 : 66.7 166.7 233.3 300.0 366.7 433.3 500.0 566.7 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 266.7 : 100.0 166.7 233.3 300.0 366.7 433.3 500.0 600.0 666.7 733.3 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 366.7 : 66.7 133.3 200.0 266.7 333.3 400.0 500.0 566.7 633.3 700.0 766.7 833.3 900.0 966.7 1033.3 1100.0 1200.0 433.3 : 66.7 133.3 200.0 266.7 333.3 433.3 500.0 566.7 633.3 700.0 766.7 833.3 900.0 966.7 1033.3 1133.3 1200.0 500.0 : 66.7 133.3 200.0 266.7 366.7 433.3 500.0 566.7 633.3 700.0 766.7 833.3 900.0 966.7 1066.7 1133.3 1200.0 566.7 : 66.7 133.3 200.0 300.0 366.7 433.3 500.0 566.7 633.3 700.0 766.7 833.3 900.0 1000.0 1066.7 1133.3 1200.0 633.3 : 66.7 133.3 233.3 300.0 366.7 433.3 500.0 566.7 633.3 700.0 766.7 833.3 933.3 1000.0 1066.7 1133.3 1200.0 700.0 : 66.7 166.7 233.3 300.0 366.7 433.3 500.0 566.7 633.3 700.0 766.7 866.7 933.3 1000.0 1066.7 1133.3 1200.0 766.7 : 100.0 166.7 233.3 300.0 366.7 433.3 500.0 566.7 633.3 700.0 800.0 866.7 933.3 1000.0 1066.7 1133.3 1200.0 866.7 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 600.0 700.0 766.7 833.3 900.0 966.7 1033.3 1100.0 1200.0 933.3 : 66.7 133.3 200.0 266.7 333.3 400.0 466.7 533.3 633.3 700.0 766.7 833.3 900.0 966.7 1033.3 1133.3 1200.0 1000.0: 66.7 133.3 200.0 266.7 333.3 400.0 466.7 566.7 633.3 700.0 766.7 833.3 900.0 966.7 1066.7 1133.3 1200.0 1066.7: 66.7 133.3 200.0 266.7 333.3 400.0 500.0 566.7 633.3 700.0 766.7 833.3 900.0 1000.0 1066.7 1133.3 1200.0 1133.3: 66.7 133.3 200.0 266.7 333.3 433.3 500.0 566.7 633.3 700.0 766.7 833.3 933.3 1000.0 1066.7 1133.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6667 .. 100.0000 cents 33.33332 cents 66.66667 cents 2: 133.3333 .. 166.6667 cents 33.33333 cents 33.33334 cents 3: 200.0000 .. 233.3333 cents 33.33333 cents 33.33334 cents 4: 266.6667 .. 300.0000 cents 33.33332 cents 33.33334 cents 5: 333.3333 .. 366.6667 cents 33.33332 cents 33.33335 cents 6: 400.0000 .. 433.3333 cents 33.33332 cents 33.33335 cents 7: 466.6667 .. 500.0000 cents 33.33334 cents 33.33333 cents 8: 533.3333 .. 600.0000 cents 66.66667 cents 33.33333 cents 9: 600.0000 .. 666.6667 cents 66.66667 cents 1/1, 0.0000 cents 10: 700.0000 .. 733.3333 cents 33.33334 cents 33.33333 cents 11: 766.6667 .. 800.0000 cents 33.33333 cents 33.33333 cents 12: 833.3333 .. 866.6667 cents 33.33333 cents 33.33334 cents 13: 900.0000 .. 933.3333 cents 33.33332 cents 33.33334 cents 14: 966.6667 .. 1000.0000 cents 33.33333 cents 33.33334 cents 15: 1033.3333 .. 1066.6667 cents 33.33333 cents 33.33334 cents 16: 1100.0000 .. 1133.3333 cents 33.33332 cents 33.33334 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 66.66666 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 99.99999 cents Average / Smallest step : 1.058824 Largest / Average step : 1.416667 Largest / Smallest step : 1.500000 Median interval of one step : 66.66667 cents, amount: 15 Most common interval of one step : 66.66667 cents, amount: 15 Least squares average step : 70.96172 cents, oct.: 1206.34921 cents Scale is proper Scale is 3-distributional even Scale is a mode of a 36-tone equal temperament with octave 2/1 degrees: 2 4 6 8 11 13 15 17 19 21 23 26 28 30 32 34 36 Least number of segments generator : 19 of 633.333 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 19 of 633.333 cents and inv. generated superset size: 19 = 2 more = 111.765% Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAABAAAAAABAAAAA Step pattern size order : SSSSLSSSSSSLSSSSS Interval vector is [ 0 15 2 13 4 11 6 9 8 7 10 5 12 3 14 2 14 1 ] Scale is not a Constant Structure Scale diversity : 1.227637 Rothenberg stability : 0.992647 = 135/136 Lumma stability : 0.500000 Number of different interval sizes : 33 = 2.06250 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.12500 = 17/8 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 33.33332 cents Most common intervals : 66.66667 cents & inv., amount: 15 Number of recognisable fifths : 14, average 700.0000 cents Scale contains two identical conjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 15 = 88.2353% Limited inverse transpositions : 16 Inversional symmetry on degrees : 8 Inversional symmetry on intervals : 16-17 -- 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: 10.1885 c. M: 19.6078 c. 19: 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 N D3 S SD: 9.1161 c. M:-17.5439 c. 34: 2 2 2 2 2 2 2 2 2 2 2 3 1 2 2 2 2 P T3 SD: 9.7808 c. M:-15.6863 c. 36: 2 2 2 2 3 2 2 2 2 2 2 3 2 2 2 2 2 P D3 S 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: 0.9775 cents 3 .. 6 match: 3 H SD: 5.9332 cents 4 .. 8 match: 4 H SD: 9.2251 cents 5 .. 10 match: 5 H SD: 14.3806 cents 6 .. 12 match: 6 H SD: 4.1503 cents 7 .. 14 match: 7 H SD: 5.5362 cents 8 .. 16 match: 8 H SD: 6.5698 cents 9 .. 18 match: 9 H SD: 5.0540 cents 10 .. 20 match: 10 H SD: 8.5549 cents 11 .. 22 match: 11 H SD: 5.6812 cents 12 .. 24 match: 12 H SD: 5.1434 cents 13 .. 26 match: 13 H SD: 5.1150 cents 14 .. 28 match: 14 H SD: 4.2464 cents 15 .. 30 match: 14 SD: 5.8945 cents 16 .. 32 match: 15 SD: 5.2614 cents 17 .. 34 match: 15 SD: 5.2720 cents 18 .. 36 match: 16 SD: 3.1381 cents 19 .. 38 match: 16 SD: 5.6342 cents 20 .. 40 match: 16 SD: 4.2248 cents 22 .. 44 match: 17 SD: 3.7827 cents 23 .. 46 match: 17 SD: 3.5229 cents 24 .. 48 match: 17 SD: 2.8011 cents 25 .. 50 match: 17 SD: 2.5332 cents 34 .. 68 match: 17 SD: 2.2815 cents 38 .. 76 match: 17 SD: 2.1769 cents 41 .. 82 match: 17 SD: 1.9253 cents 42 .. 84 match: 17 SD: 1.7416 cents 47 .. 94 match: 17 SD: 1.7065 cents 48 .. 96 match: 17 SD: 1.4733 cents 50 .. 100 match: 17 SD: 1.3641 cents 54 .. 108 match: 17 SD: 1.2621 cents 59 .. 118 match: 17 SD: 1.2324 cents 66 .. 132 match: 17 SD: 1.1991 cents 72 .. 144 match: 17 SD: 0.9798 cents 74 .. 148 match: 17 SD: 0.9295 cents 77 .. 154 match: 17 SD: 0.8350 cents 95 .. 190 match: 17 SD: 0.8340 cents 97 .. 194 match: 17 SD: 0.8295 cents 98 .. 196 match: 17 SD: 0.7122 cents 101 .. 202 match: 17 SD: 0.6982 cents 102 .. 204 match: 17 SD: 0.6839 cents 120 .. 240 match: 17 SD: 0.6370 cents 122 .. 244 match: 17 SD: 0.5380 cents 147 .. 294 match: 17 SD: 0.5022 cents 149 .. 298 match: 17 SD: 0.4728 cents 161 .. 322 match: 17 SD: 0.4157 cents 173 .. 346 match: 17 SD: 0.4153 cents 174 .. 348 match: 17 SD: 0.4016 cents 179 .. 358 match: 17 SD: 0.3736 cents 186 .. 372 match: 17 SD: 0.3584 cents 197 .. 394 match: 17 SD: 0.3325 cents 203 .. 406 match: 17 SD: 0.3019 cents 228 .. 456 match: 17 SD: 0.2756 cents 251 .. 502 match: 17 SD: 0.2386 cents 263 .. 526 match: 17 SD: 0.2364 cents 277 .. 554 match: 17 SD: 0.2344 cents 302 .. 604 match: 17 SD: 0.2221 cents 325 .. 650 match: 17 SD: 0.2218 cents 326 .. 652 match: 17 SD: 0.2091 cents 335 .. 670 match: 17 SD: 0.1898 cents 377 .. 754 match: 17 SD: 0.1791 cents 385 .. 770 match: 17 SD: 0.1616 cents 433 .. 866 match: 17 SD: 0.1593 cents 439 .. 878 match: 17 SD: 0.1553 cents 457 .. 914 match: 17 SD: 0.1534 cents 463 .. 926 match: 17 SD: 0.1499 cents 475 .. 950 match: 17 SD: 0.1464 cents 514 .. 1028 match: 17 SD: 0.1177 cents 588 .. 1176 match: 17 SD: 0.1036 cents