Scala analysis: miracle24
Miracle[24] in 72-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.333 cents 33.333333 2: 83.333 cents 83.333333 3: 116.667 cents 116.666667 4: 150.000 cents 150.000000 5: 233.333 cents 233.333333 6: 266.667 cents 266.666667 7: 350.000 cents 350.000000 8: 383.333 cents 383.333333 9: 466.667 cents 466.666667 10: 500.000 cents 500.000000 11: 583.333 cents 583.333333 12: 616.667 cents 616.666667 13: 700.000 cents 700.000000 14: 733.333 cents 733.333333 15: 816.667 cents 816.666667 16: 850.000 cents 850.000000 17: 933.333 cents 933.333333 18: 966.667 cents 966.666667 19: 1000.000 cents 1000.000000 20: 1050.000 cents 1050.000000 21: 1083.333 cents 1083.333333 22: 1116.667 cents 1116.666667 23: 1166.667 cents 1166.666667 24: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 33.3333 cents 33.3333 1: 33.3333 cents 33.3333 2: 50.0000 cents 50.0000 3: 33.3333 cents 33.3333 4: 33.3333 cents 33.3333 5: 83.3333 cents 83.3333 6: 33.3333 cents 33.3333 7: 83.3333 cents 83.3333 8: 33.3333 cents 33.3333 9: 83.3333 cents 83.3333 10: 33.3333 cents 33.3333 11: 83.3333 cents 83.3333 12: 33.3333 cents 33.3333 13: 83.3333 cents 83.3333 14: 33.3333 cents 33.3333 15: 83.3333 cents 83.3333 16: 33.3333 cents 33.3333 17: 83.3333 cents 83.3333 18: 33.3333 cents 33.3333 19: 33.3333 cents 33.3333 20: 50.0000 cents 50.0000 21: 33.3333 cents 33.3333 22: 33.3333 cents 33.3333 23: 50.0000 cents 50.0000 24: 33.3333 cents 33.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 14 33.33333 cents 1: 3 50.00000 cents 1: 7 83.33333 cents 2: 4 66.66667 cents 2: 6 83.33333 cents 2: 14 116.66667 cents 3: 9 116.66667 cents 3: 9 150.00000 cents 3: 6 200.00000 cents 4: 6 150.00000 cents 4: 2 166.66667 cents 4: 2 183.33333 cents 4: 2 200.00000 cents 4: 12 233.33333 cents 5: 3 183.33333 cents 5: 4 200.00000 cents 5: 4 233.33333 cents 5: 8 266.66667 cents 5: 5 316.66667 cents 6: 6 233.33333 cents 6: 4 266.66667 cents 6: 2 300.00000 cents 6: 2 316.66667 cents 6: 10 350.00000 cents 7: 4 266.66667 cents 7: 1 283.33333 cents 7: 2 300.00000 cents 7: 2 316.66667 cents 7: 4 350.00000 cents 7: 7 383.33333 cents 7: 4 433.33333 cents 8: 2 300.00000 cents 8: 2 316.66667 cents 8: 4 350.00000 cents 8: 4 383.33333 cents 8: 2 416.66667 cents 8: 2 433.33333 cents 8: 8 466.66667 cents 9: 3 350.00000 cents 9: 4 383.33333 cents 9: 2 416.66667 cents 9: 2 433.33333 cents 9: 4 466.66667 cents 9: 6 500.00000 cents 9: 3 550.00000 cents 10: 2 383.33333 cents 10: 2 416.66667 cents 10: 2 433.33333 cents 10: 4 466.66667 cents 10: 4 500.00000 cents 10: 2 533.33333 cents 10: 2 550.00000 cents 10: 6 583.33333 cents 11: 1 416.66667 cents 11: 4 466.66667 cents 11: 4 500.00000 cents 11: 2 533.33333 cents 11: 2 550.00000 cents 11: 4 583.33333 cents 11: 5 616.66667 cents 11: 2 666.66667 cents 12: 4 500.00000 cents 12: 2 533.33333 cents 12: 2 550.00000 cents 12: 4 583.33333 cents 12: 4 616.66667 cents 12: 2 650.00000 cents 12: 2 666.66667 cents 12: 4 700.00000 cents 13: 2 533.33333 cents 13: 5 583.33333 cents 13: 4 616.66667 cents 13: 2 650.00000 cents 13: 2 666.66667 cents 13: 4 700.00000 cents 13: 4 733.33333 cents 13: 1 783.33333 cents 14: 6 616.66667 cents 14: 2 650.00000 cents 14: 2 666.66667 cents 14: 4 700.00000 cents 14: 4 733.33333 cents 14: 2 766.66667 cents 14: 2 783.33333 cents 14: 2 816.66667 cents 15: 3 650.00000 cents 15: 6 700.00000 cents 15: 4 733.33333 cents 15: 2 766.66667 cents 15: 2 783.33333 cents 15: 4 816.66667 cents 15: 3 850.00000 cents 16: 8 733.33333 cents 16: 2 766.66667 cents 16: 2 783.33333 cents 16: 4 816.66667 cents 16: 4 850.00000 cents 16: 2 883.33333 cents 16: 2 900.00000 cents 17: 4 766.66667 cents 17: 7 816.66667 cents 17: 4 850.00000 cents 17: 2 883.33333 cents 17: 2 900.00000 cents 17: 1 916.66667 cents 17: 4 933.33333 cents 18: 10 850.00000 cents 18: 2 883.33333 cents 18: 2 900.00000 cents 18: 4 933.33333 cents 18: 6 966.66667 cents 19: 5 883.33333 cents 19: 8 933.33333 cents 19: 4 966.66667 cents 19: 4 1000.00000 cents 19: 3 1016.66667 cents 20: 12 966.66667 cents 20: 2 1000.00000 cents 20: 2 1016.66667 cents 20: 2 1033.33333 cents 20: 6 1050.00000 cents 21: 6 1000.00000 cents 21: 9 1050.00000 cents 21: 9 1083.33333 cents 22: 14 1083.33333 cents 22: 6 1116.66667 cents 22: 4 1133.33333 cents 23: 7 1116.66667 cents 23: 3 1150.00000 cents 23: 14 1166.66667 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 5.65217 = 130/23
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 : 33.3 83.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1000.0 1050.0 1083.3 1116.7 1166.7 1200.0 33.3 : 50.0 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 966.7 1016.7 1050.0 1083.3 1133.3 1166.7 1200.0 83.3 : 33.3 66.7 150.0 183.3 266.7 300.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 916.7 966.7 1000.0 1033.3 1083.3 1116.7 1150.0 1200.0 116.7 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 883.3 933.3 966.7 1000.0 1050.0 1083.3 1116.7 1166.7 1200.0 150.0 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 850.0 900.0 933.3 966.7 1016.7 1050.0 1083.3 1133.3 1166.7 1200.0 233.3 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 766.7 816.7 850.0 883.3 933.3 966.7 1000.0 1050.0 1083.3 1116.7 1200.0 266.7 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 733.3 783.3 816.7 850.0 900.0 933.3 966.7 1016.7 1050.0 1083.3 1166.7 1200.0 350.0 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 650.0 700.0 733.3 766.7 816.7 850.0 883.3 933.3 966.7 1000.0 1083.3 1116.7 1200.0 383.3 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 616.7 666.7 700.0 733.3 783.3 816.7 850.0 900.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 466.7 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 533.3 583.3 616.7 650.0 700.0 733.3 766.7 816.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 500.0 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 500.0 550.0 583.3 616.7 666.7 700.0 733.3 783.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 583.3 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 416.7 466.7 500.0 533.3 583.3 616.7 650.0 700.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 616.7 : 83.3 116.7 200.0 233.3 316.7 350.0 383.3 433.3 466.7 500.0 550.0 583.3 616.7 666.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 700.0 : 33.3 116.7 150.0 233.3 266.7 300.0 350.0 383.3 416.7 466.7 500.0 533.3 583.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 733.3 : 83.3 116.7 200.0 233.3 266.7 316.7 350.0 383.3 433.3 466.7 500.0 550.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 816.7 : 33.3 116.7 150.0 183.3 233.3 266.7 300.0 350.0 383.3 416.7 466.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 850.0 : 83.3 116.7 150.0 200.0 233.3 266.7 316.7 350.0 383.3 433.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 933.3 : 33.3 66.7 116.7 150.0 183.3 233.3 266.7 300.0 350.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 966.7 : 33.3 83.3 116.7 150.0 200.0 233.3 266.7 316.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 1000.0: 50.0 83.3 116.7 166.7 200.0 233.3 283.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 1016.7 1050.0 1133.3 1166.7 1200.0 1050.0: 33.3 66.7 116.7 150.0 183.3 233.3 266.7 300.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1150.0 1200.0 1083.3: 33.3 83.3 116.7 150.0 200.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1116.7 1166.7 1200.0 1116.7: 50.0 83.3 116.7 166.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 1016.7 1050.0 1083.3 1133.3 1166.7 1200.0 1166.7: 33.3 66.7 116.7 150.0 183.3 266.7 300.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1033.3 1083.3 1116.7 1150.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 83.3333 cents 50.00000 cents 33.33333 cents 2: 66.6667 .. 116.6667 cents 50.00000 cents -16.66667 cents 3: 116.6667 .. 200.0000 cents 83.33333 cents 0.00000 cents 4: 150.0000 .. 233.3333 cents 83.33333 cents -50.00000 cents 5: 183.3333 .. 316.6667 cents 133.33333 cents -50.00000 cents 6: 233.3333 .. 350.0000 cents 116.66667 cents -83.33333 cents 7: 266.6667 .. 433.3333 cents 166.66667 cents -83.33333 cents 8: 300.0000 .. 466.6667 cents 166.66667 cents -133.33333 cents 9: 350.0000 .. 550.0000 cents 200.00000 cents -116.66667 cents 10: 383.3333 .. 583.3333 cents 200.00000 cents -166.66667 cents 11: 416.6667 .. 666.6667 cents 250.00000 cents -166.66667 cents 12: 500.0000 .. 700.0000 cents 200.00000 cents -166.66667 cents 13: 533.3333 .. 783.3333 cents 250.00000 cents -166.66667 cents 14: 616.6667 .. 816.6667 cents 200.00000 cents -166.66667 cents 15: 650.0000 .. 850.0000 cents 200.00000 cents -166.66667 cents 16: 733.3333 .. 900.0000 cents 166.66667 cents -116.66667 cents 17: 766.6667 .. 933.3333 cents 166.66667 cents -133.33333 cents 18: 850.0000 .. 966.6667 cents 116.66667 cents -83.33333 cents 19: 883.3333 .. 1016.6667 cents 133.33333 cents -83.33333 cents 20: 966.6667 .. 1050.0000 cents 83.33333 cents -50.00000 cents 21: 1000.0000 .. 1083.3333 cents 83.33333 cents -50.00000 cents 22: 1083.3333 .. 1133.3333 cents 50.00000 cents 0.00000 cents 23: 1116.6667 .. 1166.6667 cents 50.00000 cents -16.66667 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 83.33333 cents Average / Smallest step : 1.500000 Largest / Average step : 1.666667 Largest / Smallest step : 2.500000 Median interval of one step : 33.33333 cents, amount: 14 Most common interval of one step : 33.33333 cents, amount: 14 Least squares average step : 51.81293 cents, oct.: 1243.51020 cents Scale is not proper Scale is a mode of a 72-tone equal temperament with octave 1200.000 cents degrees: 2 5 7 9 14 16 21 23 28 30 35 37 42 44 49 51 56 58 60 63 65 67 70 72 Least number of segments generator : 65 of 1083.333 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 65 of 1083.333 cents and inv. generated superset size: 24 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 72-tone equal temperament Step pattern alph. order: ABAACACACACACACACAABAABA Step pattern size order : SMSSLSLSLSLSLSLSLSSMSSMS Interval vector is [ 0 14 3 4 13 0 23 0 15 2 5 12 0 22 0 16 1 6 11 0 21 0 17 0 7 10 0 20 0 18 0 8 9 0 19 0 ] Scale is not a Constant Structure Scale diversity : 1.179751 Lumma stability : 0.055556 Lumma impropriety factor : 0.777778 Rothenberg efficiency : 0.694444 redundancy: 0.305556 Efficiency x scale size : 16.666667 Number of different interval sizes : 46 = 2.00000 / class Number of one step interval sizes : 3 Highest interval variety : 8 Mean interval variety : 5.65217 = 130/23 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 16.66667 cents Most common intervals : 116.66667 cents & inv., amount: 23 Scale has Generated (pseudo-Myhill) property, generator: 1083.333 cents and inv. Scale is a chain of 12 triads 0.0 83.333 1083.333 cents Most common triad is 0.0 116.667 1083.333 cents, amount: 22 Number of recognisable fifths : 18, average 700.0000 cents Formal octave complements present : 23 = 95.8333% Limited inverse transpositions : 21 Inversional symmetry on intervals : 10-11 22-23 -- Rational properties --
FIT/MODE
24: 1 1 0 1 2 0 2 1 1 1 2 0 2 1 1 1 2 0 1 1 1 0 1 1 N SD: 13.6083 c. M: 16.6667 c. 25: 1 1 0 1 2 1 1 1 2 0 2 1 2 0 2 1 1 1 1 1 1 0 1 1 N SD: 13.5346 c. M: 21.3333 c. 28: 1 1 1 1 1 1 2 1 2 1 2 0 2 1 2 1 2 1 0 2 0 1 1 1 N SD: 12.2952 c. M:-21.4286 c. 29: 1 1 1 1 2 0 2 1 2 1 2 1 2 1 2 1 2 0 1 1 1 1 1 1 N SD: 11.4966 c. M: 18.9655 c. 31: 1 1 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 1 1 1 1 1 N SD: 3.7313 c. M:-6.4516 c. 41: 1 2 1 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 1 2 1 1 2 1 N SD: 2.8212 c. M: 4.8780 c. 72: 2 3 2 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 2 3 2 2 3 2 N G 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: 11.4714 cents 4 .. 8 match: 4 H SD: 1.0418 cents 5 .. 10 match: 5 H SD: 7.7452 cents 6 .. 12 match: 6 H SD: 5.7460 cents 7 .. 14 match: 7 H SD: 6.8602 cents 8 .. 16 match: 8 H SD: 5.6211 cents 9 .. 18 match: 9 H SD: 6.9352 cents 10 .. 20 match: 10 H SD: 4.6146 cents 11 .. 22 match: 11 H SD: 6.3534 cents 12 .. 24 match: 12 H SD: 3.7807 cents 13 .. 26 match: 13 H SD: 4.7593 cents 14 .. 28 match: 14 H SD: 4.4330 cents 15 .. 30 match: 15 H SD: 5.1161 cents 16 .. 32 match: 15 S SD: 4.6676 cents 17 .. 34 match: 17 H SD: 4.5305 cents 18 .. 36 match: 15 SD: 3.2804 cents 19 .. 38 match: 17 SD: 3.5770 cents 20 .. 40 match: 20 H SD: 3.3826 cents 21 .. 42 match: 17 SD: 3.4439 cents 22 .. 44 match: 18 SD: 2.5422 cents 23 .. 46 match: 22 SD: 2.5661 cents 24 .. 48 match: 21 SD: 2.8061 cents 25 .. 50 match: 19 SD: 2.6221 cents 26 .. 52 match: 18 SD: 2.9015 cents 27 .. 54 match: 21 SD: 2.8620 cents 28 .. 56 match: 22 SD: 2.3706 cents 29 .. 58 match: 21 SD: 2.6875 cents 30 .. 60 match: 22 SD: 2.1342 cents 31 .. 62 match: 22 SD: 2.4745 cents 32 .. 64 match: 22 SD: 1.8007 cents 33 .. 66 match: 22 SD: 2.1548 cents 34 .. 68 match: 21 SD: 2.5333 cents 35 .. 70 match: 23 SD: 1.8290 cents 36 .. 72 match: 23 SD: 1.6154 cents 37 .. 74 match: 23 SD: 2.1767 cents 38 .. 76 match: 22 SD: 1.9950 cents 39 .. 78 match: 23 SD: 2.1107 cents 40 .. 80 match: 24 SD: 1.5974 cents 42 .. 84 match: 24 SD: 1.3196 cents 53 .. 106 match: 24 SD: 1.2620 cents 54 .. 108 match: 24 SD: 1.1593 cents 55 .. 110 match: 24 SD: 1.0456 cents 68 .. 136 match: 24 SD: 0.9008 cents 77 .. 154 match: 24 SD: 0.8577 cents 84 .. 168 match: 24 SD: 0.6693 cents 98 .. 196 match: 24 SD: 0.5390 cents 120 .. 240 match: 24 SD: 0.5123 cents 138 .. 276 match: 24 SD: 0.4834 cents 140 .. 280 match: 24 SD: 0.4706 cents 143 .. 286 match: 24 SD: 0.4421 cents 144 .. 288 match: 24 SD: 0.4384 cents 146 .. 292 match: 24 SD: 0.4365 cents 155 .. 310 match: 24 SD: 0.4084 cents 158 .. 316 match: 24 SD: 0.3945 cents 161 .. 322 match: 24 SD: 0.3373 cents 187 .. 374 match: 24 SD: 0.3287 cents 197 .. 394 match: 24 SD: 0.3100 cents 199 .. 398 match: 24 SD: 0.3081 cents 201 .. 402 match: 24 SD: 0.2945 cents 210 .. 420 match: 24 SD: 0.2693 cents 241 .. 482 match: 24 SD: 0.2626 cents 242 .. 484 match: 24 SD: 0.2385 cents 245 .. 490 match: 24 SD: 0.2224 cents 262 .. 524 match: 24 SD: 0.2192 cents 287 .. 574 match: 24 SD: 0.2123 cents 290 .. 580 match: 24 SD: 0.2054 cents 299 .. 598 match: 24 SD: 0.1995 cents 307 .. 614 match: 24 SD: 0.1801 cents 343 .. 686 match: 24 SD: 0.1767 cents 361 .. 722 match: 24 SD: 0.1723 cents 362 .. 724 match: 24 SD: 0.1500 cents 407 .. 814 match: 24 SD: 0.1434 cents 421 .. 842 match: 24 SD: 0.1376 cents 445 .. 890 match: 24 SD: 0.1307 cents 463 .. 926 match: 24 SD: 0.1306 cents 469 .. 938 match: 24 SD: 0.1305 cents 472 .. 944 match: 24 SD: 0.1220 cents 500 .. 1000 match: 24 SD: 0.1185 cents 504 .. 1008 match: 24 SD: 0.1123 cents 554 .. 1108 match: 24 SD: 0.1119 cents 574 .. 1148 match: 24 SD: 0.1067 cents 576 .. 1152 match: 24 SD: 0.1011 cents