Scala analysis: blackjack_tuning_30510_30510
MOS of 11-limit "MIRACLE" temperament, Erlich & Keenan, TL 2-5-2001
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.333 cents 83.333330 2: 116.667 cents 116.666670 3: 200.000 cents 200.000000 4: 233.333 cents 233.333330 5: 316.667 cents 316.666670 6: 350.000 cents 350.000000 7: 383.333 cents 383.333330 8: 466.667 cents 466.666670 9: 500.000 cents 500.000000 10: 583.333 cents 583.333330 11: 616.667 cents 616.666670 12: 700.000 cents 700.000000 13: 733.333 cents 733.333330 14: 816.667 cents 816.666670 15: 850.000 cents 850.000000 16: 933.333 cents 933.333330 17: 966.667 cents 966.666670 18: 1050.000 cents 1050.000000 19: 1083.333 cents 1083.333330 20: 1166.667 cents 1166.666670 21: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 33.3333 cents 33.3333 1: 83.3333 cents 83.3333 2: 33.3333 cents 33.3333 3: 83.3333 cents 83.3333 4: 33.3333 cents 33.3333 5: 83.3333 cents 83.3333 6: 33.3333 cents 33.3333 7: 33.3333 cents 33.3333 8: 83.3333 cents 83.3333 9: 33.3333 cents 33.3333 10: 83.3333 cents 83.3333 11: 33.3333 cents 33.3333 12: 83.3333 cents 83.3333 13: 33.3333 cents 33.3333 14: 83.3333 cents 83.3333 15: 33.3333 cents 33.3333 16: 83.3333 cents 83.3333 17: 33.3333 cents 33.3333 18: 83.3333 cents 83.3333 19: 33.3333 cents 33.3333 20: 83.3333 cents 83.3333 21: 33.3333 cents 33.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 33.33334 cents 1: 10 83.33333 cents 2: 1 66.66666 cents 2: 20 116.66667 cents 3: 12 150.00000 cents 3: 9 200.00000 cents 4: 2 183.33333 cents 4: 19 233.33333 cents 5: 13 266.66667 cents 5: 8 316.66667 cents 6: 3 300.00000 cents 6: 18 350.00000 cents 7: 14 383.33333 cents 7: 7 433.33334 cents 8: 4 416.66667 cents 8: 17 466.66667 cents 9: 15 500.00000 cents 9: 6 550.00000 cents 10: 5 533.33334 cents 10: 16 583.33333 cents 11: 16 616.66667 cents 11: 5 666.66667 cents 12: 6 650.00000 cents 12: 15 700.00000 cents 13: 17 733.33333 cents 13: 4 783.33334 cents 14: 7 766.66667 cents 14: 14 816.66667 cents 15: 18 850.00000 cents 15: 3 900.00000 cents 16: 8 883.33334 cents 16: 13 933.33333 cents 17: 19 966.66667 cents 17: 2 1016.66667 cents 18: 9 1000.00000 cents 18: 12 1050.00000 cents 19: 20 1083.33333 cents 19: 1 1133.33334 cents 20: 10 1116.66667 cents 20: 11 1166.66667 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
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 0.0 : 83.3 116.7 200.0 233.3 316.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 83.3 : 33.3 116.7 150.0 233.3 266.7 300.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 116.7 : 83.3 116.7 200.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 200.0 : 33.3 116.7 150.0 183.3 266.7 300.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 233.3 : 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 1050.0 1083.3 1166.7 1200.0 316.7 : 33.3 66.7 150.0 183.3 266.7 300.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 350.0 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 383.3 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 1016.7 1050.0 1133.3 1166.7 1200.0 466.7 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1116.7 1200.0 500.0 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 1016.7 1050.0 1083.3 1166.7 1200.0 583.3 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1000.0 1083.3 1116.7 1200.0 616.7 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 700.0 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 733.3 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 816.7 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 850.0 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 933.3 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 966.7 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 1050.0: 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 1083.3: 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 1166.7: 33.3 116.7 150.0 233.3 266.7 350.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 83.3333 cents 49.99999 cents 33.33334 cents 2: 66.6667 .. 116.6667 cents 50.00001 cents -16.66667 cents 3: 150.0000 .. 200.0000 cents 50.00000 cents 33.33333 cents 4: 183.3333 .. 233.3333 cents 50.00000 cents -16.66667 cents 5: 266.6667 .. 316.6667 cents 50.00000 cents 33.33334 cents 6: 300.0000 .. 350.0000 cents 50.00000 cents -16.66667 cents 7: 383.3333 .. 433.3333 cents 50.00001 cents 33.33333 cents 8: 416.6667 .. 466.6667 cents 50.00000 cents -16.66667 cents 9: 500.0000 .. 550.0000 cents 50.00000 cents 33.33333 cents 10: 533.3333 .. 583.3333 cents 49.99999 cents -16.66666 cents 11: 616.6667 .. 666.6667 cents 50.00000 cents 33.33334 cents 12: 650.0000 .. 700.0000 cents 50.00000 cents -16.66667 cents 13: 733.3333 .. 783.3333 cents 50.00001 cents 33.33333 cents 14: 766.6667 .. 816.6667 cents 50.00000 cents -16.66667 cents 15: 850.0000 .. 900.0000 cents 50.00000 cents 33.33333 cents 16: 883.3333 .. 933.3333 cents 49.99999 cents -16.66666 cents 17: 966.6667 .. 1016.6667 cents 50.00000 cents 33.33334 cents 18: 1000.0000 .. 1050.0000 cents 50.00000 cents -16.66667 cents 19: 1083.3333 .. 1133.3333 cents 50.00001 cents 33.33333 cents 20: 1116.6667 .. 1166.6667 cents 50.00000 cents -16.66667 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 57.1429 cents Largest one step interval : 83.33333 cents Average / Smallest step : 1.714286 Largest / Average step : 1.458333 Largest / Smallest step : 2.500000 Median interval of one step : 33.33334 cents, amount: 11 Most common interval of one step : 33.33334 cents, amount: 11 Least squares average step : 57.55562 cents, oct.: 1208.66808 cents Scale is not proper Scale has Myhill's property chromas: 49.99999 cents and 16.66665 cents, ratio: 3.000002 generators: 2 of 116.66667 cents and 19 of 1083.33333 cents ET pair of linear temperament : 10&31 Scale is distributional even Scale is a mode of a 72-tone equal temperament with octave 2/1 degrees: 5 7 12 14 19 21 23 28 30 35 37 42 44 49 51 56 58 63 65 70 72 generators: 7 and 65 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABBABABABABABABAB Step pattern size order : LSLSLSSLSLSLSLSLSLSLS Interval vector is [ 0 11 0 1 10 0 20 0 12 0 2 9 0 19 0 13 0 3 8 0 18 0 14 0 4 7 0 17 0 15 0 5 6 0 16 0 ] Scale is a Constant Structure, by a margin of 16.66666 cents Scale diversity : 1.200678 Lumma stability : 0.305556 Lumma impropriety factor : 0.138889 Rothenberg efficiency : 0.698413 redundancy: 0.301587 Efficiency x scale size : 14.666667 Number of different interval sizes : 40 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16.66666 cents Most common intervals : 116.66667 cents & inv., amount: 20 Scale is a chain of 10 triads 0.0 116.667 233.333 cents Most common triad is 0.0 116.667 1083.333 cents, amount: 19 Number of recognisable fifths : 15, average 700.0000 cents Formal octave complements present : 15 = 71.4286% Limited inverse transpositions : 12 Inversional symmetry on degrees : 6 Inversional symmetry on intervals : 16-17 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
21: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 16.0898 c. M: 30.9524 c. 24: 2 0 2 1 1 1 1 1 1 2 0 2 1 1 1 2 0 2 1 1 1 N D3 S SD: 13.6083 c. M:-16.6667 c. 26: 2 1 1 1 2 1 0 2 1 2 0 2 1 2 0 2 1 2 0 2 1 N T3 SD: 13.0714 c. M:-21.7949 c. 29: 2 1 2 1 2 0 1 2 1 2 1 2 1 2 1 2 0 2 1 2 1 N T3 SD: 11.4112 c. M: 18.9655 c. 31: 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 P M ME S SD: 3.6332 c. M: 6.9893 c. 41: 3 1 3 1 3 1 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 N M DE S SD: 2.7470 c. M:-5.2845 c. 72: 5 2 5 2 5 2 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 N M DE 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: 11.4714 cents 4 .. 8 match: 4 H SD: 1.0418 cents 5 .. 10 match: 5 H SD: 6.5134 cents 6 .. 12 match: 6 H SD: 8.0162 cents 7 .. 14 match: 7 H SD: 6.8602 cents 8 .. 16 match: 8 H SD: 4.2788 cents 9 .. 18 match: 9 H SD: 7.0934 cents 10 .. 20 match: 10 H SD: 5.8622 cents 11 .. 22 match: 11 H SD: 7.9154 cents 12 .. 24 match: 11 S SD: 5.3313 cents 13 .. 26 match: 12 S SD: 5.1935 cents 14 .. 28 match: 13 S SD: 5.0442 cents 15 .. 30 match: 14 S SD: 4.7574 cents 16 .. 32 match: 15 S SD: 3.9254 cents 17 .. 34 match: 17 H SD: 4.3047 cents 18 .. 36 match: 14 SD: 3.8200 cents 19 .. 38 match: 16 SD: 4.1099 cents 20 .. 40 match: 18 SD: 3.5387 cents 21 .. 42 match: 15 SD: 3.2333 cents 22 .. 44 match: 16 SD: 3.6483 cents 23 .. 46 match: 19 SD: 3.0990 cents 24 .. 48 match: 18 SD: 2.7251 cents 25 .. 50 match: 19 SD: 2.6268 cents 26 .. 52 match: 18 SD: 2.8366 cents 27 .. 54 match: 20 SD: 2.9222 cents 28 .. 56 match: 19 SD: 2.4261 cents 29 .. 58 match: 18 SD: 2.8204 cents 30 .. 60 match: 19 SD: 2.2877 cents 31 .. 62 match: 18 SD: 2.4502 cents 32 .. 64 match: 20 SD: 2.0104 cents 33 .. 66 match: 19 SD: 2.2648 cents 34 .. 68 match: 18 SD: 2.6403 cents 35 .. 70 match: 20 SD: 1.8864 cents 37 .. 74 match: 20 SD: 2.5234 cents 38 .. 76 match: 19 SD: 2.0287 cents 39 .. 78 match: 21 SD: 2.0156 cents 40 .. 80 match: 21 SD: 1.4613 cents 45 .. 90 match: 20 SD: 1.5453 cents 48 .. 96 match: 21 SD: 1.4447 cents 54 .. 108 match: 21 SD: 1.4157 cents 55 .. 110 match: 21 SD: 1.2181 cents 60 .. 120 match: 21 SD: 1.0997 cents 68 .. 136 match: 21 SD: 0.9728 cents 74 .. 148 match: 21 SD: 0.9695 cents 75 .. 150 match: 21 SD: 0.9404 cents 80 .. 160 match: 21 SD: 0.8198 cents 84 .. 168 match: 21 SD: 0.6115 cents 98 .. 196 match: 21 SD: 0.5674 cents 120 .. 240 match: 21 SD: 0.5536 cents 125 .. 250 match: 21 SD: 0.5292 cents 129 .. 258 match: 21 SD: 0.4943 cents 138 .. 276 match: 21 SD: 0.4713 cents 140 .. 280 match: 21 SD: 0.4362 cents 158 .. 316 match: 21 SD: 0.4274 cents 161 .. 322 match: 21 SD: 0.3594 cents 197 .. 394 match: 21 SD: 0.3579 cents 199 .. 398 match: 21 SD: 0.3521 cents 201 .. 402 match: 21 SD: 0.3331 cents 203 .. 406 match: 21 SD: 0.3328 cents 210 .. 420 match: 21 SD: 0.3183 cents 214 .. 428 match: 21 SD: 0.3093 cents 227 .. 454 match: 21 SD: 0.2732 cents 229 .. 458 match: 21 SD: 0.2329 cents 245 .. 490 match: 21 SD: 0.2170 cents 285 .. 570 match: 21 SD: 0.2043 cents 320 .. 640 match: 21 SD: 0.2024 cents 343 .. 686 match: 21 SD: 0.1833 cents 360 .. 720 match: 21 SD: 0.1802 cents 374 .. 748 match: 21 SD: 0.1775 cents 385 .. 770 match: 21 SD: 0.1578 cents 423 .. 846 match: 21 SD: 0.1544 cents 424 .. 848 match: 21 SD: 0.1496 cents 459 .. 918 match: 21 SD: 0.1372 cents 472 .. 944 match: 21 SD: 0.1195 cents 504 .. 1008 match: 21 SD: 0.1145 cents 514 .. 1028 match: 21 SD: 0.1109 cents 549 .. 1098 match: 21 SD: 0.1089 cents 588 .. 1176 match: 21 SD: 0.1037 cents 589 .. 1178 match: 21 SD: 0.0981 cents