Scala analysis: simplemint24
Rank 3 temperament (2-3-7-9-11-13), 704c 5th, 58c spacing (1200-EDO)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.000 cents 58.000000 2: 128.000 cents 128.000000 3: 186.000 cents 186.000000 4: 208.000 cents 208.000000 5: 266.000 cents 266.000000 6: 288.000 cents 288.000000 7: 346.000 cents 346.000000 8: 416.000 cents 416.000000 9: 474.000 cents 474.000000 10: 496.000 cents 496.000000 11: 554.000 cents 554.000000 12: 624.000 cents 624.000000 13: 682.000 cents 682.000000 14: 704.000 cents 704.000000 15: 762.000 cents 762.000000 16: 832.000 cents 832.000000 17: 890.000 cents 890.000000 18: 912.000 cents 912.000000 19: 970.000 cents 970.000000 20: 992.000 cents 992.000000 21: 1050.000 cents 1050.000000 22: 1120.000 cents 1120.000000 23: 1178.000 cents 1178.000000 24: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22.0000 cents 22.0000 1: 58.0000 cents 58.0000 2: 70.0000 cents 70.0000 3: 58.0000 cents 58.0000 4: 22.0000 cents 22.0000 5: 58.0000 cents 58.0000 6: 22.0000 cents 22.0000 7: 58.0000 cents 58.0000 8: 70.0000 cents 70.0000 9: 58.0000 cents 58.0000 10: 22.0000 cents 22.0000 11: 58.0000 cents 58.0000 12: 70.0000 cents 70.0000 13: 58.0000 cents 58.0000 14: 22.0000 cents 22.0000 15: 58.0000 cents 58.0000 16: 70.0000 cents 70.0000 17: 58.0000 cents 58.0000 18: 22.0000 cents 22.0000 19: 58.0000 cents 58.0000 20: 22.0000 cents 22.0000 21: 58.0000 cents 58.0000 22: 70.0000 cents 70.0000 23: 58.0000 cents 58.0000 24: 22.0000 cents 22.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 22.00000 cents 1: 12 58.00000 cents 1: 5 70.00000 cents 2: 14 80.00000 cents 2: 10 128.00000 cents 3: 2 102.00000 cents 3: 7 138.00000 cents 3: 10 150.00000 cents 3: 5 186.00000 cents 4: 4 160.00000 cents 4: 20 208.00000 cents 5: 2 218.00000 cents 5: 9 230.00000 cents 5: 10 266.00000 cents 5: 3 278.00000 cents 6: 18 288.00000 cents 6: 6 336.00000 cents 7: 4 310.00000 cents 7: 9 346.00000 cents 7: 8 358.00000 cents 7: 3 394.00000 cents 8: 8 368.00000 cents 8: 16 416.00000 cents 9: 4 426.00000 cents 9: 11 438.00000 cents 9: 8 474.00000 cents 9: 1 486.00000 cents 10: 22 496.00000 cents 10: 2 544.00000 cents 11: 6 518.00000 cents 11: 11 554.00000 cents 11: 6 566.00000 cents 11: 1 602.00000 cents 12: 12 576.00000 cents 12: 12 624.00000 cents 13: 1 598.00000 cents 13: 6 634.00000 cents 13: 11 646.00000 cents 13: 6 682.00000 cents 14: 2 656.00000 cents 14: 22 704.00000 cents 15: 1 714.00000 cents 15: 8 726.00000 cents 15: 11 762.00000 cents 15: 4 774.00000 cents 16: 16 784.00000 cents 16: 8 832.00000 cents 17: 3 806.00000 cents 17: 8 842.00000 cents 17: 9 854.00000 cents 17: 4 890.00000 cents 18: 6 864.00000 cents 18: 18 912.00000 cents 19: 3 922.00000 cents 19: 10 934.00000 cents 19: 9 970.00000 cents 19: 2 982.00000 cents 20: 20 992.00000 cents 20: 4 1040.00000 cents 21: 5 1014.00000 cents 21: 10 1050.00000 cents 21: 7 1062.00000 cents 21: 2 1098.00000 cents 22: 10 1072.00000 cents 22: 14 1120.00000 cents 23: 5 1130.00000 cents 23: 12 1142.00000 cents 23: 7 1178.00000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.95652 = 68/23
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0.0 : 58.0 128.0 186.0 208.0 266.0 288.0 346.0 416.0 474.0 496.0 554.0 624.0 682.0 704.0 762.0 832.0 890.0 912.0 970.0 992.0 1050.0 1120.0 1178.0 1200.0 58.0 : 70.0 128.0 150.0 208.0 230.0 288.0 358.0 416.0 438.0 496.0 566.0 624.0 646.0 704.0 774.0 832.0 854.0 912.0 934.0 992.0 1062.0 1120.0 1142.0 1200.0 128.0 : 58.0 80.0 138.0 160.0 218.0 288.0 346.0 368.0 426.0 496.0 554.0 576.0 634.0 704.0 762.0 784.0 842.0 864.0 922.0 992.0 1050.0 1072.0 1130.0 1200.0 186.0 : 22.0 80.0 102.0 160.0 230.0 288.0 310.0 368.0 438.0 496.0 518.0 576.0 646.0 704.0 726.0 784.0 806.0 864.0 934.0 992.0 1014.0 1072.0 1142.0 1200.0 208.0 : 58.0 80.0 138.0 208.0 266.0 288.0 346.0 416.0 474.0 496.0 554.0 624.0 682.0 704.0 762.0 784.0 842.0 912.0 970.0 992.0 1050.0 1120.0 1178.0 1200.0 266.0 : 22.0 80.0 150.0 208.0 230.0 288.0 358.0 416.0 438.0 496.0 566.0 624.0 646.0 704.0 726.0 784.0 854.0 912.0 934.0 992.0 1062.0 1120.0 1142.0 1200.0 288.0 : 58.0 128.0 186.0 208.0 266.0 336.0 394.0 416.0 474.0 544.0 602.0 624.0 682.0 704.0 762.0 832.0 890.0 912.0 970.0 1040.0 1098.0 1120.0 1178.0 1200.0 346.0 : 70.0 128.0 150.0 208.0 278.0 336.0 358.0 416.0 486.0 544.0 566.0 624.0 646.0 704.0 774.0 832.0 854.0 912.0 982.0 1040.0 1062.0 1120.0 1142.0 1200.0 416.0 : 58.0 80.0 138.0 208.0 266.0 288.0 346.0 416.0 474.0 496.0 554.0 576.0 634.0 704.0 762.0 784.0 842.0 912.0 970.0 992.0 1050.0 1072.0 1130.0 1200.0 474.0 : 22.0 80.0 150.0 208.0 230.0 288.0 358.0 416.0 438.0 496.0 518.0 576.0 646.0 704.0 726.0 784.0 854.0 912.0 934.0 992.0 1014.0 1072.0 1142.0 1200.0 496.0 : 58.0 128.0 186.0 208.0 266.0 336.0 394.0 416.0 474.0 496.0 554.0 624.0 682.0 704.0 762.0 832.0 890.0 912.0 970.0 992.0 1050.0 1120.0 1178.0 1200.0 554.0 : 70.0 128.0 150.0 208.0 278.0 336.0 358.0 416.0 438.0 496.0 566.0 624.0 646.0 704.0 774.0 832.0 854.0 912.0 934.0 992.0 1062.0 1120.0 1142.0 1200.0 624.0 : 58.0 80.0 138.0 208.0 266.0 288.0 346.0 368.0 426.0 496.0 554.0 576.0 634.0 704.0 762.0 784.0 842.0 864.0 922.0 992.0 1050.0 1072.0 1130.0 1200.0 682.0 : 22.0 80.0 150.0 208.0 230.0 288.0 310.0 368.0 438.0 496.0 518.0 576.0 646.0 704.0 726.0 784.0 806.0 864.0 934.0 992.0 1014.0 1072.0 1142.0 1200.0 704.0 : 58.0 128.0 186.0 208.0 266.0 288.0 346.0 416.0 474.0 496.0 554.0 624.0 682.0 704.0 762.0 784.0 842.0 912.0 970.0 992.0 1050.0 1120.0 1178.0 1200.0 762.0 : 70.0 128.0 150.0 208.0 230.0 288.0 358.0 416.0 438.0 496.0 566.0 624.0 646.0 704.0 726.0 784.0 854.0 912.0 934.0 992.0 1062.0 1120.0 1142.0 1200.0 832.0 : 58.0 80.0 138.0 160.0 218.0 288.0 346.0 368.0 426.0 496.0 554.0 576.0 634.0 656.0 714.0 784.0 842.0 864.0 922.0 992.0 1050.0 1072.0 1130.0 1200.0 890.0 : 22.0 80.0 102.0 160.0 230.0 288.0 310.0 368.0 438.0 496.0 518.0 576.0 598.0 656.0 726.0 784.0 806.0 864.0 934.0 992.0 1014.0 1072.0 1142.0 1200.0 912.0 : 58.0 80.0 138.0 208.0 266.0 288.0 346.0 416.0 474.0 496.0 554.0 576.0 634.0 704.0 762.0 784.0 842.0 912.0 970.0 992.0 1050.0 1120.0 1178.0 1200.0 970.0 : 22.0 80.0 150.0 208.0 230.0 288.0 358.0 416.0 438.0 496.0 518.0 576.0 646.0 704.0 726.0 784.0 854.0 912.0 934.0 992.0 1062.0 1120.0 1142.0 1200.0 992.0 : 58.0 128.0 186.0 208.0 266.0 336.0 394.0 416.0 474.0 496.0 554.0 624.0 682.0 704.0 762.0 832.0 890.0 912.0 970.0 1040.0 1098.0 1120.0 1178.0 1200.0 1050.0: 70.0 128.0 150.0 208.0 278.0 336.0 358.0 416.0 438.0 496.0 566.0 624.0 646.0 704.0 774.0 832.0 854.0 912.0 982.0 1040.0 1062.0 1120.0 1142.0 1200.0 1120.0: 58.0 80.0 138.0 208.0 266.0 288.0 346.0 368.0 426.0 496.0 554.0 576.0 634.0 704.0 762.0 784.0 842.0 912.0 970.0 992.0 1050.0 1072.0 1130.0 1200.0 1178.0: 22.0 80.0 150.0 208.0 230.0 288.0 310.0 368.0 438.0 496.0 518.0 576.0 646.0 704.0 726.0 784.0 854.0 912.0 934.0 992.0 1014.0 1072.0 1142.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.0000 .. 70.0000 cents 48.00000 cents 22.00000 cents 2: 80.0000 .. 128.0000 cents 48.00000 cents 10.00000 cents 3: 102.0000 .. 186.0000 cents 84.00000 cents -26.00000 cents 4: 160.0000 .. 208.0000 cents 48.00000 cents -26.00000 cents 5: 218.0000 .. 278.0000 cents 60.00000 cents 10.00000 cents 6: 288.0000 .. 336.0000 cents 48.00000 cents 10.00000 cents 7: 310.0000 .. 394.0000 cents 84.00000 cents -26.00000 cents 8: 368.0000 .. 416.0000 cents 48.00000 cents -26.00000 cents 9: 426.0000 .. 486.0000 cents 60.00000 cents 10.00000 cents 10: 496.0000 .. 544.0000 cents 48.00000 cents 10.00000 cents 11: 518.0000 .. 602.0000 cents 84.00000 cents -26.00000 cents 12: 576.0000 .. 624.0000 cents 48.00000 cents -26.00000 cents 13: 598.0000 .. 682.0000 cents 84.00000 cents -26.00000 cents 14: 656.0000 .. 704.0000 cents 48.00000 cents -26.00000 cents 15: 714.0000 .. 774.0000 cents 60.00000 cents 10.00000 cents 16: 784.0000 .. 832.0000 cents 48.00000 cents 10.00000 cents 17: 806.0000 .. 890.0000 cents 84.00000 cents -26.00000 cents 18: 864.0000 .. 912.0000 cents 48.00000 cents -26.00000 cents 19: 922.0000 .. 982.0000 cents 60.00000 cents 10.00000 cents 20: 992.0000 .. 1040.0000 cents 48.00000 cents 10.00000 cents 21: 1014.0000 .. 1098.0000 cents 84.00000 cents -26.00000 cents 22: 1072.0000 .. 1120.0000 cents 48.00000 cents -26.00000 cents 23: 1130.0000 .. 1178.0000 cents 48.00000 cents 10.00000 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 22.00000 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 70.00000 cents Average / Smallest step : 2.272727 Largest / Average step : 1.400000 Largest / Smallest step : 3.181818 Median interval of one step : 58.00000 cents, amount: 12 Most common interval of one step : 58.00000 cents, amount: 12 Least squares average step : 50.85388 cents, oct.: 1220.49306 cents Scale is not proper Scale is a mode of a 600-tone equal temperament with octave 2/1 degrees: 29 64 93 104 133 144 173 208 237 248 277 312 341 352 381 416 445 456 485 496 525 560 589 600 Least number of segments generator : 301 of 602.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 569 of 1138.000 cents and inv. generated superset size: 148 = 124 more = 616.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACACABACABACABACACABAC Step pattern size order : MLMSMSMLMSMLMSMLMSMSMLMS Scale is a Constant Structure, by a margin of 4.00000 cents Scale diversity : 1.265172 Lumma stability : 0.120000 Lumma impropriety factor : 0.256667 Number of different interval sizes : 68 = 2.95652 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 2.95652 = 68/23 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 4.00000 cents Most common intervals : 496.00000 cents & inv., amount: 22 Most common triad is 0.0 496.000 704.000 cents, amount: 20 Number of recognisable fifths : 23, average 704.4348 cents Scale contains two identical disjunct "tetrachords" of 11 notes Formal octave complements present : 7 = 29.1667% Limited inverse transpositions : 23 Inversional symmetry on intervals : 11-12 23-24 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
24: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 1 1 1 N T3 SD: 18.4436 c. M: 36.0000 c. 25: 1 2 1 0 2 0 1 2 1 0 2 1 1 1 1 1 2 0 1 1 1 1 2 0 N SD: 13.7356 c. M:-22.0000 c. 29: 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 P D3 SD: 12.9065 c. M: 21.0345 c. 30: 1 2 2 0 2 0 2 1 2 0 2 2 1 1 1 2 1 1 1 1 1 2 1 1 N SD: 11.2250 c. M: 18.0000 c. 32: 2 1 2 1 1 1 1 2 2 0 2 2 1 1 1 2 2 0 2 0 2 2 1 1 N SD: 10.6218 c. M:-17.0000 c. 39: 2 2 2 1 2 0 2 2 2 1 2 2 2 1 2 2 2 1 1 1 2 2 2 1 N SD: 8.3444 c. M: 16.1538 c. 40: 2 2 2 1 2 1 2 2 2 1 1 3 2 0 2 3 2 0 2 1 2 2 2 1 N SD: 8.9536 c. M:-14.0000 c. 41: 2 2 2 1 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 2 2 1 P D3 SD: 6.5051 c. M: 12.4878 c. 45: 2 3 2 1 2 1 2 3 2 1 2 2 3 0 3 2 2 1 2 1 2 3 2 1 N SD: 7.3585 c. M:-11.3333 c. 46: 2 3 2 1 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 1 2 3 2 1 N SD: 3.7554 c. M: 6.8696 c. 58: 3 3 3 1 3 1 3 3 3 1 3 3 3 1 3 3 3 1 3 1 3 3 3 1 N D3 SD: 2.8628 c. M:-5.7241 c. 63: 3 4 3 1 3 1 3 4 3 1 3 4 3 1 3 4 3 1 3 1 3 4 3 1 N G SD: 3.0464 c. M:-6.0952 c. 96: 5 5 5 2 4 2 5 5 5 2 4 6 5 1 5 6 4 2 5 1 5 6 4 2 N SD: 3.4701 c. M:-5.5000 c. 99: 5 6 4 2 5 2 5 5 5 2 5 5 5 2 5 6 4 2 5 2 5 5 5 2 N SD: 3.4222 c. M: 5.8182 c. 102: 5 6 5 2 5 1 5 6 5 2 5 6 5 2 5 6 5 2 4 2 5 6 5 2 N SD: 3.3036 c. M:-5.6471 c. 104: 5 6 5 2 5 2 5 6 5 2 5 6 5 2 5 6 5 2 5 2 5 6 5 2 N SD: 0.7718 c. M: 1.5385 c. 167: 8 10 8 3 8 3 8 10 8 3 8 10 8 3 8 10 8 3 8 3 8 10 8 3 N SD: 0.7436 c. M:-1.5329 c. 225: 11 13 11 4 11 4 11 13 11 4 11 13 11 4 11 13 11 4 11 4 11 13 11 4 N SD: 0.4714 c. M:-0.6667 c. 271: 13 16 13 5 13 5 13 16 13 5 13 16 13 5 13 16 13 5 13 5 13 16 13 5 N SD: 0.3064 c. M: 0.6125 c. 329: 16 19 16 6 16 6 16 19 16 6 16 19 16 6 16 19 16 6 16 6 16 19 16 6 N SD: 0.2523 c. M:-0.5046 c. 375: 18 22 18 7 18 7 18 22 18 7 18 22 18 7 18 22 18 7 18 7 18 22 18 7 N SD: 0.2828 c. M: 0.4000 c. 496: 24 29 24 9 24 9 24 29 24 9 24 29 24 9 24 29 24 9 24 9 24 29 24 9 N SD: 0.1618 c. M:-0.3226 c. 600: 29 35 29 11 29 11 29 35 29 11 29 35 29 11 29 35 29 11 29 11 29 35 29 11 N 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: 1.0225 cents 3 .. 6 match: 3 H SD: 2.0002 cents 4 .. 8 match: 4 H SD: 7.4449 cents 5 .. 10 match: 5 H SD: 10.1342 cents 6 .. 12 match: 6 H SD: 1.0718 cents 7 .. 14 match: 7 H SD: 6.8228 cents 8 .. 16 match: 8 H SD: 5.5767 cents 9 .. 18 match: 9 H SD: 2.7095 cents 10 .. 20 match: 10 H SD: 5.9377 cents 11 .. 22 match: 11 H SD: 4.7256 cents 12 .. 24 match: 12 H SD: 4.2841 cents 13 .. 26 match: 13 H SD: 3.3378 cents 14 .. 28 match: 14 H SD: 4.6727 cents 15 .. 30 match: 15 H SD: 4.9597 cents 16 .. 32 match: 15 SD: 3.5453 cents 17 .. 34 match: 16 S SD: 5.2559 cents 18 .. 36 match: 16 S SD: 2.8708 cents 19 .. 38 match: 18 S SD: 3.8235 cents 20 .. 40 match: 19 SD: 4.4664 cents 21 .. 42 match: 20 SD: 3.7541 cents 22 .. 44 match: 18 SD: 3.1355 cents 23 .. 46 match: 22 S SD: 2.7363 cents 24 .. 48 match: 20 SD: 2.6778 cents 25 .. 50 match: 20 S SD: 3.0587 cents 26 .. 52 match: 21 SD: 2.4393 cents 27 .. 54 match: 22 SD: 2.3903 cents 28 .. 56 match: 20 SD: 2.6576 cents 29 .. 58 match: 22 SD: 2.3918 cents 30 .. 60 match: 22 SD: 2.4218 cents 31 .. 62 match: 22 SD: 2.2919 cents 32 .. 64 match: 22 SD: 2.0395 cents 33 .. 66 match: 23 SD: 2.3454 cents 34 .. 68 match: 20 SD: 2.1362 cents 35 .. 70 match: 21 SD: 2.0285 cents 36 .. 72 match: 24 SD: 1.7797 cents 37 .. 74 match: 23 SD: 1.6567 cents 38 .. 76 match: 22 SD: 2.0834 cents 39 .. 78 match: 24 SD: 1.9118 cents 40 .. 80 match: 21 SD: 1.4789 cents 41 .. 82 match: 21 SD: 1.7963 cents 42 .. 84 match: 22 SD: 1.6473 cents 43 .. 86 match: 22 SD: 1.8037 cents 44 .. 88 match: 24 SD: 1.6759 cents 45 .. 90 match: 24 SD: 1.6441 cents 46 .. 92 match: 23 SD: 1.8231 cents 47 .. 94 match: 24 SD: 1.7412 cents 48 .. 96 match: 24 SD: 1.3804 cents 49 .. 98 match: 23 SD: 1.4129 cents 50 .. 100 match: 23 SD: 1.4503 cents 52 .. 104 match: 23 SD: 1.3471 cents 53 .. 106 match: 24 SD: 1.2826 cents 54 .. 108 match: 24 SD: 1.0423 cents 58 .. 116 match: 22 SD: 1.1966 cents 60 .. 120 match: 24 SD: 1.0324 cents 67 .. 134 match: 24 SD: 0.9848 cents 72 .. 144 match: 24 SD: 0.9795 cents 76 .. 152 match: 24 SD: 0.8798 cents 78 .. 156 match: 24 SD: 0.7518 cents 85 .. 170 match: 24 SD: 0.7283 cents 88 .. 176 match: 24 SD: 0.7051 cents 89 .. 178 match: 24 SD: 0.6861 cents 104 .. 208 match: 24 SD: 0.6716 cents 108 .. 216 match: 24 SD: 0.6063 cents 114 .. 228 match: 24 SD: 0.5265 cents 127 .. 254 match: 24 SD: 0.5247 cents 132 .. 264 match: 24 SD: 0.4862 cents 133 .. 266 match: 24 SD: 0.4575 cents 141 .. 282 match: 24 SD: 0.4526 cents 143 .. 286 match: 24 SD: 0.3942 cents 159 .. 318 match: 24 SD: 0.3893 cents 168 .. 336 match: 24 SD: 0.3860 cents 172 .. 344 match: 24 SD: 0.3848 cents 177 .. 354 match: 24 SD: 0.3670 cents 180 .. 360 match: 24 SD: 0.3418 cents 193 .. 386 match: 24 SD: 0.3245 cents 199 .. 398 match: 24 SD: 0.2915 cents 210 .. 420 match: 24 SD: 0.2913 cents 222 .. 444 match: 24 SD: 0.2867 cents 235 .. 470 match: 24 SD: 0.2276 cents 265 .. 530 match: 24 SD: 0.2076 cents 299 .. 598 match: 24 SD: 0.2035 cents 313 .. 626 match: 24 SD: 0.1883 cents 327 .. 654 match: 24 SD: 0.1837 cents 343 .. 686 match: 24 SD: 0.1790 cents 350 .. 700 match: 24 SD: 0.1752 cents 353 .. 706 match: 24 SD: 0.1309 cents 470 .. 940 match: 24 SD: 0.0892 cents 530 .. 1060 match: 24 SD: 0.0879 cents