Scala analysis: blackjack
Paul Erlich, Tuning list ~5-May-2001, 7/72 octave generator
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: 116.667 cents 116.666667 3: 150.000 cents 150.000000 4: 233.333 cents 233.333333 5: 266.667 cents 266.666667 6: 350.000 cents 350.000000 7: 383.333 cents 383.333333 8: 466.667 cents 466.666667 9: 500.000 cents 500.000000 10: 583.333 cents 583.333333 11: 616.667 cents 616.666667 12: 700.000 cents 700.000000 13: 733.333 cents 733.333333 14: 816.667 cents 816.666667 15: 850.000 cents 850.000000 16: 933.333 cents 933.333333 17: 966.667 cents 966.666667 18: 1050.000 cents 1050.000000 19: 1083.333 cents 1083.333333 20: 1166.667 cents 1166.666667 21: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 33.3333 cents 33.3333 1: 33.3333 cents 33.3333 2: 83.3333 cents 83.3333 3: 33.3333 cents 33.3333 4: 83.3333 cents 83.3333 5: 33.3333 cents 33.3333 6: 83.3333 cents 83.3333 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 33.33333 cents 1: 10 83.33333 cents 2: 1 66.66667 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: 7 433.33333 cents 8: 4 416.66667 cents 8: 17 466.66667 cents 9: 15 500.00000 cents 9: 6 550.00000 cents 10: 5 533.33333 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: 4 783.33333 cents 14: 7 766.66667 cents 14: 14 816.66667 cents 15: 18 850.00000 cents 15: 3 900.00000 cents 16: 8 883.33333 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 1133.33333 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 : 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 33.3 : 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 1200.0 116.7 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1116.7 1200.0 150.0 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 1016.7 1050.0 1083.3 1166.7 1200.0 233.3 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1000.0 1083.3 1116.7 1200.0 266.7 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 350.0 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 383.3 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 466.7 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 500.0 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 583.3 : 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 1200.0 616.7 : 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 1200.0 700.0 : 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 1200.0 733.3 : 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 1200.0 816.7 : 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 1200.0 850.0 : 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 1200.0 933.3 : 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 1200.0 966.7 : 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 1050.0: 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 1083.3: 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 1166.7: 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 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: 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 33.33333 cents 6: 300.0000 .. 350.0000 cents 50.00000 cents -16.66667 cents 7: 383.3333 .. 433.3333 cents 50.00000 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 50.00000 cents -16.66667 cents 11: 616.6667 .. 666.6667 cents 50.00000 cents 33.33333 cents 12: 650.0000 .. 700.0000 cents 50.00000 cents -16.66667 cents 13: 733.3333 .. 783.3333 cents 50.00000 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 50.00000 cents -16.66667 cents 17: 966.6667 .. 1016.6667 cents 50.00000 cents 33.33333 cents 18: 1000.0000 .. 1050.0000 cents 50.00000 cents -16.66667 cents 19: 1083.3333 .. 1133.3333 cents 50.00000 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 : 33.33333 cents, amount: 11 Most common interval of one step : 33.33333 cents, amount: 11 Least squares average step : 57.41971 cents, oct.: 1205.81395 cents Scale is not proper Scale has Myhill's property chromas: 50.00000 cents and 16.66667 cents, ratio: 3.000000 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: 2 7 9 14 16 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 Scale is fully connected major-minor triadic in 72-tone equal temperament Step pattern alph. order: ABABABABABABABABABABA Step pattern size order : SLSLSLSLSLSLSLSLSLSLS 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 16.66667 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 : 16.66667 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 Scale contains two identical disjunct "tetrachords" of 10 notes Formal octave complements present : 21 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 10-11 -- 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: 14.4174 c. M: 23.8095 c. 24: 1 1 1 2 0 2 1 1 1 2 0 2 1 1 1 2 0 2 1 1 1 N D3 I SD: 13.6083 c. M: 16.6667 c. 27: 1 1 1 2 1 2 0 2 1 2 1 2 0 2 1 2 1 1 1 2 1 N D3 SD: 15.4303 c. M: 27.7778 c. 29: 1 2 1 2 0 2 1 2 1 2 1 2 1 2 1 2 0 2 1 2 1 N I SD: 12.1967 c. M: 18.9655 c. 31: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 P M ME I SD: 3.2555 c. M: 5.3763 c. 41: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 N M DE I SD: 2.4615 c. M: 4.0650 c. 72: 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 N M DE I 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: 9.4659 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: 7.7108 cents 10 .. 20 match: 10 H SD: 6.0137 cents 11 .. 22 match: 11 H SD: 7.1476 cents 12 .. 24 match: 11 S SD: 4.0299 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: 5.3526 cents 16 .. 32 match: 15 S SD: 4.6676 cents 17 .. 34 match: 17 H SD: 4.5570 cents 18 .. 36 match: 14 SD: 3.8480 cents 19 .. 38 match: 16 SD: 4.3371 cents 20 .. 40 match: 18 SD: 4.0341 cents 21 .. 42 match: 16 SD: 4.2957 cents 22 .. 44 match: 15 SD: 2.9571 cents 23 .. 46 match: 20 SD: 3.4208 cents 24 .. 48 match: 19 SD: 3.5392 cents 25 .. 50 match: 17 SD: 3.2051 cents 26 .. 52 match: 16 SD: 3.4459 cents 27 .. 54 match: 19 SD: 3.2511 cents 28 .. 56 match: 20 SD: 2.6475 cents 29 .. 58 match: 19 SD: 2.8957 cents 30 .. 60 match: 20 SD: 2.2117 cents 31 .. 62 match: 20 SD: 2.6937 cents 32 .. 64 match: 20 SD: 1.9805 cents 33 .. 66 match: 20 SD: 2.3476 cents 34 .. 68 match: 19 SD: 2.7502 cents 35 .. 70 match: 21 SD: 2.0561 cents 36 .. 72 match: 20 SD: 1.7077 cents 37 .. 74 match: 20 SD: 2.4006 cents 38 .. 76 match: 19 SD: 2.1926 cents 39 .. 78 match: 20 SD: 2.3104 cents 40 .. 80 match: 21 SD: 1.7784 cents 42 .. 84 match: 21 SD: 1.4903 cents 48 .. 96 match: 21 SD: 1.3137 cents 53 .. 106 match: 21 SD: 1.2685 cents 54 .. 108 match: 21 SD: 1.2157 cents 55 .. 110 match: 21 SD: 1.1145 cents 68 .. 136 match: 21 SD: 0.9047 cents 84 .. 168 match: 21 SD: 0.7292 cents 90 .. 180 match: 21 SD: 0.7260 cents 98 .. 196 match: 21 SD: 0.5658 cents 133 .. 266 match: 21 SD: 0.5104 cents 143 .. 286 match: 21 SD: 0.4822 cents 144 .. 288 match: 21 SD: 0.4584 cents 152 .. 304 match: 21 SD: 0.4284 cents 155 .. 310 match: 21 SD: 0.4097 cents 161 .. 322 match: 21 SD: 0.3808 cents 174 .. 348 match: 21 SD: 0.3771 cents 186 .. 372 match: 21 SD: 0.3745 cents 187 .. 374 match: 21 SD: 0.3471 cents 197 .. 394 match: 21 SD: 0.3183 cents 210 .. 420 match: 21 SD: 0.2693 cents 242 .. 484 match: 21 SD: 0.2652 cents 245 .. 490 match: 21 SD: 0.2375 cents 259 .. 518 match: 21 SD: 0.2348 cents 287 .. 574 match: 21 SD: 0.2311 cents 290 .. 580 match: 21 SD: 0.2121 cents 307 .. 614 match: 21 SD: 0.2017 cents 313 .. 626 match: 21 SD: 0.2006 cents 317 .. 634 match: 21 SD: 0.1972 cents 353 .. 706 match: 21 SD: 0.1921 cents 355 .. 710 match: 21 SD: 0.1726 cents 362 .. 724 match: 21 SD: 0.1684 cents 374 .. 748 match: 21 SD: 0.1684 cents 397 .. 794 match: 21 SD: 0.1611 cents 407 .. 814 match: 21 SD: 0.1596 cents 415 .. 830 match: 21 SD: 0.1527 cents 416 .. 832 match: 21 SD: 0.1487 cents 421 .. 842 match: 21 SD: 0.1434 cents 451 .. 902 match: 21 SD: 0.1404 cents 456 .. 912 match: 21 SD: 0.1346 cents 472 .. 944 match: 21 SD: 0.1274 cents 500 .. 1000 match: 21 SD: 0.1238 cents 504 .. 1008 match: 21 SD: 0.1222 cents 505 .. 1010 match: 21 SD: 0.1219 cents 554 .. 1108 match: 21 SD: 0.1191 cents 574 .. 1148 match: 21 SD: 0.1127 cents 576 .. 1152 match: 21 SD: 0.0978 cents