Scala analysis: xen18-keenan-blackjack-guitar
Fret tunings for a blackjack guitar fretboard
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.000 cents 33.000000 2: 117.000 cents 117.000000 3: 150.000 cents 150.000000 4: 233.000 cents 233.000000 5: 267.000 cents 267.000000 6: 350.000 cents 350.000000 7: 383.000 cents 383.000000 8: 467.000 cents 467.000000 9: 500.000 cents 500.000000 10: 583.000 cents 583.000000 11: 617.000 cents 617.000000 12: 700.000 cents 700.000000 13: 733.000 cents 733.000000 14: 817.000 cents 817.000000 15: 850.000 cents 850.000000 16: 883.000 cents 883.000000 17: 967.000 cents 967.000000 18: 1000.000 cents 1000.000000 19: 1083.000 cents 1083.000000 20: 1117.000 cents 1117.000000 21: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 83.0000 cents 83.0000 1: 33.0000 cents 33.0000 2: 84.0000 cents 84.0000 3: 33.0000 cents 33.0000 4: 83.0000 cents 83.0000 5: 34.0000 cents 34.0000 6: 83.0000 cents 83.0000 7: 33.0000 cents 33.0000 8: 84.0000 cents 84.0000 9: 33.0000 cents 33.0000 10: 83.0000 cents 83.0000 11: 34.0000 cents 34.0000 12: 83.0000 cents 83.0000 13: 33.0000 cents 33.0000 14: 84.0000 cents 84.0000 15: 33.0000 cents 33.0000 16: 33.0000 cents 33.0000 17: 84.0000 cents 84.0000 18: 33.0000 cents 33.0000 19: 83.0000 cents 83.0000 20: 34.0000 cents 34.0000 21: 83.0000 cents 83.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 33.00000 cents 1: 3 34.00000 cents 1: 6 83.00000 cents 1: 4 84.00000 cents 2: 1 66.00000 cents 2: 6 116.00000 cents 2: 14 117.00000 cents 3: 12 150.00000 cents 3: 9 200.00000 cents 4: 2 183.00000 cents 4: 12 233.00000 cents 4: 7 234.00000 cents 5: 5 266.00000 cents 5: 8 267.00000 cents 5: 2 316.00000 cents 5: 6 317.00000 cents 6: 3 300.00000 cents 6: 18 350.00000 cents 7: 10 383.00000 cents 7: 4 384.00000 cents 7: 4 433.00000 cents 7: 3 434.00000 cents 8: 2 416.00000 cents 8: 2 417.00000 cents 8: 5 466.00000 cents 8: 12 467.00000 cents 9: 15 500.00000 cents 9: 6 550.00000 cents 10: 4 533.00000 cents 10: 1 534.00000 cents 10: 10 583.00000 cents 10: 6 584.00000 cents 11: 6 616.00000 cents 11: 10 617.00000 cents 11: 1 666.00000 cents 11: 4 667.00000 cents 12: 6 650.00000 cents 12: 15 700.00000 cents 13: 12 733.00000 cents 13: 5 734.00000 cents 13: 2 783.00000 cents 13: 2 784.00000 cents 14: 3 766.00000 cents 14: 4 767.00000 cents 14: 4 816.00000 cents 14: 10 817.00000 cents 15: 18 850.00000 cents 15: 3 900.00000 cents 16: 6 883.00000 cents 16: 2 884.00000 cents 16: 8 933.00000 cents 16: 5 934.00000 cents 17: 7 966.00000 cents 17: 12 967.00000 cents 17: 2 1017.00000 cents 18: 9 1000.00000 cents 18: 12 1050.00000 cents 19: 14 1083.00000 cents 19: 6 1084.00000 cents 19: 1 1134.00000 cents 20: 4 1116.00000 cents 20: 6 1117.00000 cents 20: 3 1166.00000 cents 20: 8 1167.00000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.20000 = 16/5
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 : 33.0 117.0 150.0 233.0 267.0 350.0 383.0 467.0 500.0 583.0 617.0 700.0 733.0 817.0 850.0 883.0 967.0 1000.0 1083.0 1117.0 1200.0 33.0 : 84.0 117.0 200.0 234.0 317.0 350.0 434.0 467.0 550.0 584.0 667.0 700.0 784.0 817.0 850.0 934.0 967.0 1050.0 1084.0 1167.0 1200.0 117.0 : 33.0 116.0 150.0 233.0 266.0 350.0 383.0 466.0 500.0 583.0 616.0 700.0 733.0 766.0 850.0 883.0 966.0 1000.0 1083.0 1116.0 1200.0 150.0 : 83.0 117.0 200.0 233.0 317.0 350.0 433.0 467.0 550.0 583.0 667.0 700.0 733.0 817.0 850.0 933.0 967.0 1050.0 1083.0 1167.0 1200.0 233.0 : 34.0 117.0 150.0 234.0 267.0 350.0 384.0 467.0 500.0 584.0 617.0 650.0 734.0 767.0 850.0 884.0 967.0 1000.0 1084.0 1117.0 1200.0 267.0 : 83.0 116.0 200.0 233.0 316.0 350.0 433.0 466.0 550.0 583.0 616.0 700.0 733.0 816.0 850.0 933.0 966.0 1050.0 1083.0 1166.0 1200.0 350.0 : 33.0 117.0 150.0 233.0 267.0 350.0 383.0 467.0 500.0 533.0 617.0 650.0 733.0 767.0 850.0 883.0 967.0 1000.0 1083.0 1117.0 1200.0 383.0 : 84.0 117.0 200.0 234.0 317.0 350.0 434.0 467.0 500.0 584.0 617.0 700.0 734.0 817.0 850.0 934.0 967.0 1050.0 1084.0 1167.0 1200.0 467.0 : 33.0 116.0 150.0 233.0 266.0 350.0 383.0 416.0 500.0 533.0 616.0 650.0 733.0 766.0 850.0 883.0 966.0 1000.0 1083.0 1116.0 1200.0 500.0 : 83.0 117.0 200.0 233.0 317.0 350.0 383.0 467.0 500.0 583.0 617.0 700.0 733.0 817.0 850.0 933.0 967.0 1050.0 1083.0 1167.0 1200.0 583.0 : 34.0 117.0 150.0 234.0 267.0 300.0 384.0 417.0 500.0 534.0 617.0 650.0 734.0 767.0 850.0 884.0 967.0 1000.0 1084.0 1117.0 1200.0 617.0 : 83.0 116.0 200.0 233.0 266.0 350.0 383.0 466.0 500.0 583.0 616.0 700.0 733.0 816.0 850.0 933.0 966.0 1050.0 1083.0 1166.0 1200.0 700.0 : 33.0 117.0 150.0 183.0 267.0 300.0 383.0 417.0 500.0 533.0 617.0 650.0 733.0 767.0 850.0 883.0 967.0 1000.0 1083.0 1117.0 1200.0 733.0 : 84.0 117.0 150.0 234.0 267.0 350.0 384.0 467.0 500.0 584.0 617.0 700.0 734.0 817.0 850.0 934.0 967.0 1050.0 1084.0 1167.0 1200.0 817.0 : 33.0 66.0 150.0 183.0 266.0 300.0 383.0 416.0 500.0 533.0 616.0 650.0 733.0 766.0 850.0 883.0 966.0 1000.0 1083.0 1116.0 1200.0 850.0 : 33.0 117.0 150.0 233.0 267.0 350.0 383.0 467.0 500.0 583.0 617.0 700.0 733.0 817.0 850.0 933.0 967.0 1050.0 1083.0 1167.0 1200.0 883.0 : 84.0 117.0 200.0 234.0 317.0 350.0 434.0 467.0 550.0 584.0 667.0 700.0 784.0 817.0 900.0 934.0 1017.0 1050.0 1134.0 1167.0 1200.0 967.0 : 33.0 116.0 150.0 233.0 266.0 350.0 383.0 466.0 500.0 583.0 616.0 700.0 733.0 816.0 850.0 933.0 966.0 1050.0 1083.0 1116.0 1200.0 1000.0: 83.0 117.0 200.0 233.0 317.0 350.0 433.0 467.0 550.0 583.0 667.0 700.0 783.0 817.0 900.0 933.0 1017.0 1050.0 1083.0 1167.0 1200.0 1083.0: 34.0 117.0 150.0 234.0 267.0 350.0 384.0 467.0 500.0 584.0 617.0 700.0 734.0 817.0 850.0 934.0 967.0 1000.0 1084.0 1117.0 1200.0 1117.0: 83.0 116.0 200.0 233.0 316.0 350.0 433.0 466.0 550.0 583.0 666.0 700.0 783.0 816.0 900.0 933.0 966.0 1050.0 1083.0 1166.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.0000 .. 84.0000 cents 51.00000 cents 33.00000 cents 2: 66.0000 .. 117.0000 cents 51.00000 cents -18.00000 cents 3: 150.0000 .. 200.0000 cents 50.00000 cents 33.00000 cents 4: 183.0000 .. 234.0000 cents 51.00000 cents -17.00000 cents 5: 266.0000 .. 317.0000 cents 51.00000 cents 32.00000 cents 6: 300.0000 .. 350.0000 cents 50.00000 cents -17.00000 cents 7: 383.0000 .. 434.0000 cents 51.00000 cents 33.00000 cents 8: 416.0000 .. 467.0000 cents 51.00000 cents -18.00000 cents 9: 500.0000 .. 550.0000 cents 50.00000 cents 33.00000 cents 10: 533.0000 .. 584.0000 cents 51.00000 cents -17.00000 cents 11: 616.0000 .. 667.0000 cents 51.00000 cents 32.00000 cents 12: 650.0000 .. 700.0000 cents 50.00000 cents -17.00000 cents 13: 733.0000 .. 784.0000 cents 51.00000 cents 33.00000 cents 14: 766.0000 .. 817.0000 cents 51.00000 cents -18.00000 cents 15: 850.0000 .. 900.0000 cents 50.00000 cents 33.00000 cents 16: 883.0000 .. 934.0000 cents 51.00000 cents -17.00000 cents 17: 966.0000 .. 1017.0000 cents 51.00000 cents 32.00000 cents 18: 1000.0000 .. 1050.0000 cents 50.00000 cents -17.00000 cents 19: 1083.0000 .. 1134.0000 cents 51.00000 cents 33.00000 cents 20: 1116.0000 .. 1167.0000 cents 51.00000 cents -18.00000 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 33.00000 cents, class 1 Average step (divided formal octave): 57.1429 cents Largest one step interval : 84.00000 cents Average / Smallest step : 1.731602 Largest / Average step : 1.470000 Largest / Smallest step : 2.545455 Median interval of one step : 34.00000 cents, amount: 3 Most common interval of one step : 33.00000 cents, amount: 8 Least squares average step : 56.60495 cents, oct.: 1188.70402 cents Scale is not proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 33 117 150 233 267 350 383 467 500 583 617 700 733 817 850 883 967 1000 1083 1117 1200 Least number of segments generator : 611 of 611.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 761 of 761.000 cents and inv. generated superset size: 307 = 286 more = 1461.905% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACDCABACDCABAABACDC Step pattern size order : ADACBCADACBCADAADACBC Scale is a Constant Structure, by a margin of 16.00000 cents Scale diversity : 1.213842 Lumma stability : 0.300000 Lumma impropriety factor : 0.145000 Number of different interval sizes : 64 = 3.20000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.20000 = 16/5 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 1.00000 cents Most common intervals : 350.00000 cents & inv., amount: 18 Most common triad is 0.0 350.000 850.000 cents, amount: 15 Number of recognisable fifths : 15, average 700.0000 cents Formal octave complements present : 15 = 71.4286% Limited inverse transpositions : 9 Inversional symmetry on degrees : 15 Inversional symmetry on intervals : 4-5 -- Rational properties --
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: 16.1249 c. M:-31.2857 c. 22: 1 1 1 1 1 1 1 2 0 2 0 2 0 2 1 0 2 0 2 0 2 N D3 SD: 15.8663 c. M: 26.0909 c. 24: 1 1 1 2 0 2 1 1 1 2 0 2 1 1 1 1 1 1 2 0 2 N D3 S SD: 13.8804 c. M:-17.0000 c. 25: 1 1 1 2 1 1 1 2 0 2 1 2 0 2 1 0 2 1 2 0 2 N D3 SD: 13.6382 c. M:-21.0000 c. 26: 1 2 0 2 1 2 0 2 1 2 0 2 1 2 0 1 2 1 1 1 2 N T3 SD: 13.0400 c. M:-21.4615 c. 29: 1 2 1 2 0 2 1 2 1 2 1 2 1 2 1 0 2 1 2 1 2 N T3 SD: 11.4416 c. M: 18.9655 c. 31: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 P M ME S SD: 3.6760 c. M:-7.3226 c. 41: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 1 3 1 3 1 3 N M DE S SD: 2.7276 c. M: 4.9512 c. 72: 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 2 5 2 5 2 5 N M DE S SD: 0.2722 c. M: 0.3333 c. 624: 17 44 17 43 18 43 17 44 17 43 18 43 17 44 17 17 44 17 43 18 43 N S SD: 0.2512 c. M: 0.3077 c. 696: 19 49 19 48 20 48 19 49 19 48 20 48 19 49 19 19 49 19 48 20 48 N S SD: 0.1971 c. M: 0.2414 c. 768: 21 54 21 53 22 53 21 54 21 53 22 53 21 54 21 21 54 21 53 22 53 N S SD: 0.1531 c. M: 0.1875 c. 840: 23 59 23 58 24 58 23 59 23 58 24 58 23 59 23 23 59 23 58 24 58 N S SD: 0.1166 c. M:-0.1429 c. 912: 25 64 25 63 26 63 25 64 25 63 26 63 25 64 25 25 64 25 63 26 63 N S SD: 0.0859 c. M: 0.1053 c. 984: 27 69 27 68 28 68 27 69 27 68 28 68 27 69 27 27 69 27 68 28 68 N S SD: 0.0597 c. M:-0.0732 c. 1056: 29 74 29 73 30 73 29 74 29 73 30 73 29 74 29 29 74 29 73 30 73 N S SD: 0.0371 c. M:-0.0455 c. 1128: 31 79 31 78 32 78 31 79 31 78 32 78 31 79 31 31 79 31 78 32 78 N S SD: 0.0174 c. M: 0.0213 c. 1200: 33 84 33 83 34 83 33 84 33 83 34 83 33 84 33 33 84 33 83 34 83 N 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: 0.7936 cents 4 .. 8 match: 4 H SD: 1.0647 cents 5 .. 10 match: 5 H SD: 7.7495 cents 6 .. 12 match: 6 H SD: 5.6297 cents 7 .. 14 match: 7 H SD: 8.4369 cents 8 .. 16 match: 8 H SD: 5.5700 cents 9 .. 18 match: 9 H SD: 5.8115 cents 10 .. 20 match: 10 H SD: 5.6549 cents 11 .. 22 match: 11 H SD: 7.1292 cents 12 .. 24 match: 12 H SD: 3.7532 cents 13 .. 26 match: 13 H SD: 5.0908 cents 14 .. 28 match: 14 H SD: 5.0600 cents 15 .. 30 match: 15 H SD: 4.5793 cents 16 .. 32 match: 15 S SD: 4.8930 cents 17 .. 34 match: 14 S SD: 5.2962 cents 18 .. 36 match: 14 SD: 4.0513 cents 19 .. 38 match: 16 SD: 4.2728 cents 20 .. 40 match: 18 SD: 4.0803 cents 21 .. 42 match: 16 SD: 4.2445 cents 22 .. 44 match: 16 SD: 3.0216 cents 23 .. 46 match: 19 SD: 3.3700 cents 24 .. 48 match: 19 SD: 3.6132 cents 25 .. 50 match: 17 SD: 3.5206 cents 26 .. 52 match: 17 SD: 3.4740 cents 27 .. 54 match: 20 SD: 3.1534 cents 28 .. 56 match: 20 SD: 2.7355 cents 29 .. 58 match: 19 SD: 2.9778 cents 30 .. 60 match: 20 SD: 2.2374 cents 31 .. 62 match: 20 SD: 2.7642 cents 32 .. 64 match: 20 SD: 1.9748 cents 34 .. 68 match: 19 SD: 2.7980 cents 35 .. 70 match: 21 SD: 2.1314 cents 36 .. 72 match: 20 SD: 1.6759 cents 37 .. 74 match: 20 SD: 2.4079 cents 38 .. 76 match: 19 SD: 2.2111 cents 40 .. 80 match: 21 SD: 1.7107 cents 42 .. 84 match: 21 SD: 1.4597 cents 48 .. 96 match: 21 SD: 1.4189 cents 53 .. 106 match: 21 SD: 1.3208 cents 54 .. 108 match: 21 SD: 1.1618 cents 55 .. 110 match: 21 SD: 1.1470 cents 68 .. 136 match: 21 SD: 0.8536 cents 84 .. 168 match: 21 SD: 0.7495 cents 90 .. 180 match: 21 SD: 0.7294 cents 96 .. 192 match: 21 SD: 0.7272 cents 98 .. 196 match: 21 SD: 0.5907 cents 110 .. 220 match: 21 SD: 0.5505 cents 138 .. 276 match: 21 SD: 0.5198 cents 142 .. 284 match: 21 SD: 0.5128 cents 143 .. 286 match: 21 SD: 0.4722 cents 146 .. 292 match: 21 SD: 0.4700 cents 152 .. 304 match: 21 SD: 0.4089 cents 161 .. 322 match: 21 SD: 0.3715 cents 174 .. 348 match: 21 SD: 0.3691 cents 197 .. 394 match: 21 SD: 0.3008 cents 210 .. 420 match: 21 SD: 0.2731 cents 245 .. 490 match: 21 SD: 0.2311 cents 275 .. 550 match: 21 SD: 0.2150 cents 299 .. 598 match: 21 SD: 0.1894 cents 343 .. 686 match: 21 SD: 0.1890 cents 353 .. 706 match: 21 SD: 0.1592 cents 397 .. 794 match: 21 SD: 0.1503 cents 469 .. 938 match: 21 SD: 0.1410 cents 472 .. 944 match: 21 SD: 0.1029 cents