Scala analysis: 16-miracle-oct
21 out of 72 within 2/1 miracle scale, from 16-of-53 within 5/3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.333 cents 83.333333 2: 116.667 cents 116.666667 3: 200.000 cents 200.000000 4: 233.333 cents 233.333333 5: 316.667 cents 316.666667 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: 766.667 cents 766.666667 15: 850.000 cents 850.000000 16: 883.333 cents 883.333333 17: 966.667 cents 966.666667 18: 1000.000 cents 1000.000000 19: 1083.333 cents 1083.333333 20: 1116.667 cents 1116.666666 21: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 83.3333 cents 83.3333 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: 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: 83.3333 cents 83.3333 20: 33.3333 cents 33.3333 21: 83.3333 cents 83.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 33.33333 cents 1: 10 83.33333 cents 2: 2 66.66667 cents 2: 18 116.66667 cents 2: 1 166.66667 cents 3: 12 150.00000 cents 3: 9 200.00000 cents 4: 4 183.33333 cents 4: 15 233.33333 cents 4: 2 283.33333 cents 5: 13 266.66667 cents 5: 8 316.66667 cents 6: 6 300.00000 cents 6: 12 350.00000 cents 6: 3 400.00000 cents 7: 14 383.33333 cents 7: 7 433.33333 cents 8: 7 416.66667 cents 8: 11 466.66667 cents 8: 3 516.66667 cents 9: 1 450.00000 cents 9: 13 500.00000 cents 9: 7 550.00000 cents 10: 7 533.33333 cents 10: 12 583.33333 cents 10: 2 633.33333 cents 11: 2 566.66667 cents 11: 12 616.66667 cents 11: 7 666.66667 cents 12: 7 650.00000 cents 12: 13 700.00000 cents 12: 1 750.00000 cents 13: 3 683.33333 cents 13: 11 733.33333 cents 13: 7 783.33333 cents 14: 7 766.66667 cents 14: 14 816.66667 cents 15: 3 800.00000 cents 15: 12 850.00000 cents 15: 6 900.00000 cents 16: 8 883.33333 cents 16: 13 933.33333 cents 17: 2 916.66667 cents 17: 15 966.66667 cents 17: 4 1016.66667 cents 18: 9 1000.00000 cents 18: 12 1050.00000 cents 19: 1 1033.33333 cents 19: 18 1083.33333 cents 19: 2 1133.33333 cents 20: 10 1116.66667 cents 20: 11 1166.66667 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.60000 = 13/5
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 : 83.3 116.7 200.0 233.3 316.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 83.3 : 33.3 116.7 150.0 233.3 266.7 300.0 383.3 416.7 500.0 533.3 616.7 650.0 683.3 766.7 800.0 883.3 916.7 1000.0 1033.3 1116.7 1200.0 116.7 : 83.3 116.7 200.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1000.0 1083.3 1166.7 1200.0 200.0 : 33.3 116.7 150.0 183.3 266.7 300.0 383.3 416.7 500.0 533.3 566.7 650.0 683.3 766.7 800.0 883.3 916.7 1000.0 1083.3 1116.7 1200.0 233.3 : 83.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 883.3 966.7 1050.0 1083.3 1166.7 1200.0 316.7 : 33.3 66.7 150.0 183.3 266.7 300.0 383.3 416.7 450.0 533.3 566.7 650.0 683.3 766.7 800.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 350.0 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 766.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 383.3 : 83.3 116.7 200.0 233.3 316.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 900.0 933.3 1016.7 1050.0 1133.3 1166.7 1200.0 466.7 : 33.3 116.7 150.0 233.3 266.7 300.0 383.3 416.7 500.0 533.3 616.7 650.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1116.7 1200.0 500.0 : 83.3 116.7 200.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 616.7 700.0 783.3 816.7 900.0 933.3 1016.7 1050.0 1083.3 1166.7 1200.0 583.3 : 33.3 116.7 150.0 183.3 266.7 300.0 383.3 416.7 500.0 533.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1000.0 1083.3 1116.7 1200.0 616.7 : 83.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 500.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 700.0 : 33.3 66.7 150.0 183.3 266.7 300.0 383.3 416.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 733.3 : 33.3 116.7 150.0 233.3 266.7 350.0 383.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 766.7 : 83.3 116.7 200.0 233.3 316.7 350.0 433.3 516.7 550.0 633.3 666.7 750.0 783.3 816.7 900.0 933.3 1016.7 1050.0 1133.3 1166.7 1200.0 850.0 : 33.3 116.7 150.0 233.3 266.7 350.0 433.3 466.7 550.0 583.3 666.7 700.0 733.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1116.7 1200.0 883.3 : 83.3 116.7 200.0 233.3 316.7 400.0 433.3 516.7 550.0 633.3 666.7 700.0 783.3 816.7 900.0 933.3 1016.7 1050.0 1083.3 1166.7 1200.0 966.7 : 33.3 116.7 150.0 233.3 316.7 350.0 433.3 466.7 550.0 583.3 616.7 700.0 733.3 816.7 850.0 933.3 966.7 1000.0 1083.3 1116.7 1200.0 1000.0: 83.3 116.7 200.0 283.3 316.7 400.0 433.3 516.7 550.0 583.3 666.7 700.0 783.3 816.7 900.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 1083.3: 33.3 116.7 200.0 233.3 316.7 350.0 433.3 466.7 500.0 583.3 616.7 700.0 733.3 816.7 850.0 883.3 966.7 1000.0 1083.3 1116.7 1200.0 1116.7: 83.3 166.7 200.0 283.3 316.7 400.0 433.3 466.7 550.0 583.3 666.7 700.0 783.3 816.7 850.0 933.3 966.7 1050.0 1083.3 1166.7 1200.0 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 .. 166.6667 cents 100.00000 cents -16.66667 cents 3: 150.0000 .. 200.0000 cents 50.00000 cents -16.66667 cents 4: 183.3333 .. 283.3333 cents 100.00000 cents -16.66667 cents 5: 266.6667 .. 316.6667 cents 50.00000 cents -16.66667 cents 6: 300.0000 .. 400.0000 cents 100.00000 cents -16.66667 cents 7: 383.3333 .. 433.3333 cents 50.00000 cents -16.66667 cents 8: 416.6667 .. 516.6667 cents 100.00000 cents -16.66667 cents 9: 450.0000 .. 550.0000 cents 100.00000 cents -66.66667 cents 10: 533.3333 .. 633.3333 cents 100.00000 cents -16.66667 cents 11: 566.6667 .. 666.6667 cents 100.00000 cents -66.66667 cents 12: 650.0000 .. 750.0000 cents 100.00000 cents -16.66667 cents 13: 683.3333 .. 783.3333 cents 100.00000 cents -66.66667 cents 14: 766.6667 .. 816.6667 cents 50.00000 cents -16.66667 cents 15: 800.0000 .. 900.0000 cents 100.00000 cents -16.66667 cents 16: 883.3333 .. 933.3333 cents 50.00000 cents -16.66667 cents 17: 916.6667 .. 1016.6667 cents 100.00000 cents -16.66667 cents 18: 1000.0000 .. 1050.0000 cents 50.00000 cents -16.66667 cents 19: 1033.3333 .. 1133.3333 cents 100.00000 cents -16.66667 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 : 56.52874 cents, oct.: 1187.10359 cents Scale is not proper Scale is 3-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 46 51 53 58 60 65 67 72 Least number of segments generator : 49 of 816.667 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 65 of 1083.333 cents and inv. generated superset size: 28 = 7 more = 133.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABBABABABBABABABA Step pattern size order : LSLSLSSLSLSLSSLSLSLSL Interval vector is [ 0 11 0 2 10 0 18 0 12 1 4 9 0 15 0 13 2 6 8 0 12 0 14 3 7 7 1 11 0 13 3 7 7 2 12 0 ] Scale is a Constant Structure, by a margin of 16.66667 cents Scale diversity : 1.265503 Lumma stability : 0.055556 Lumma impropriety factor : 0.388889 Number of different interval sizes : 52 = 2.60000 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.60000 = 13/5 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16.66667 cents Most common intervals : 116.66667 cents & inv., amount: 18 Most common triad is 0.0 116.667 1083.333 cents, amount: 15 Number of recognisable fifths : 13, average 700.0000 cents Formal octave complements present : 19 = 90.4762% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
21: 1 1 1 1 1 1 0 2 0 2 0 2 0 1 1 1 1 1 1 1 2 N T3 SD: 32.3928 c. M: 54.7619 c. 22: 2 0 2 0 2 0 1 2 0 2 0 2 0 1 2 0 2 0 2 0 2 N SD: 16.5151 c. M:-25.7576 c. 23: 2 0 2 0 2 1 0 2 1 1 1 1 1 1 1 1 2 0 2 0 2 N SD: 15.0605 c. M:-24.6377 c. 24: 2 0 2 1 1 1 1 1 1 2 0 2 1 0 2 1 1 1 2 0 2 N SD: 13.6083 c. M:-16.6667 c. 25: 2 0 2 1 2 0 1 2 0 2 1 2 0 1 2 0 2 1 2 0 2 N SD: 13.4463 c. M:-20.6667 c. 26: 2 1 1 1 2 1 0 2 1 2 0 2 1 1 1 1 2 1 1 1 2 N SD: 13.2143 c. M:-21.7949 c. 28: 2 1 2 0 2 1 1 2 1 2 0 2 1 1 2 1 2 0 2 1 2 N SD: 12.1960 c. M:-19.0476 c. 29: 2 1 2 1 2 0 1 2 1 2 1 2 1 1 2 0 2 1 2 1 2 N SD: 11.1434 c. M:-19.5402 c. 30: 2 1 2 1 2 1 1 2 1 2 0 3 0 1 2 1 2 1 2 1 2 N SD: 10.6657 c. M:-20.0000 c. 31: 2 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 N D3 SD: 4.2219 c. M:-7.5269 c. 41: 3 1 3 1 3 1 1 3 1 3 1 3 1 1 3 1 3 1 3 1 3 N D3 SD: 3.1922 c. M: 5.6911 c. 72: 5 2 5 2 5 2 2 5 2 5 2 5 2 2 5 2 5 2 5 2 5 N D3 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: 0.7359 cents 4 .. 8 match: 4 H SD: 1.0418 cents 5 .. 10 match: 5 H SD: 8.0748 cents 6 .. 12 match: 6 H SD: 7.9712 cents 7 .. 14 match: 7 H SD: 7.1618 cents 8 .. 16 match: 8 H SD: 4.2788 cents 9 .. 18 match: 9 H SD: 3.4812 cents 10 .. 20 match: 10 H SD: 6.5500 cents 11 .. 22 match: 11 H SD: 7.7642 cents 12 .. 24 match: 12 H SD: 5.2012 cents 13 .. 26 match: 13 H SD: 5.2332 cents 14 .. 28 match: 14 H SD: 4.5507 cents 15 .. 30 match: 14 SD: 4.2387 cents 16 .. 32 match: 16 H SD: 3.9776 cents 17 .. 34 match: 13 S SD: 5.2150 cents 18 .. 36 match: 15 S SD: 4.0408 cents 19 .. 38 match: 16 SD: 3.9558 cents 20 .. 40 match: 17 SD: 3.5147 cents 21 .. 42 match: 16 SD: 3.1466 cents 22 .. 44 match: 16 SD: 3.6181 cents 23 .. 46 match: 18 SD: 3.0083 cents 24 .. 48 match: 17 SD: 2.6939 cents 25 .. 50 match: 19 SD: 2.9381 cents 26 .. 52 match: 19 SD: 2.9971 cents 27 .. 54 match: 21 SD: 2.7919 cents 28 .. 56 match: 19 SD: 2.6539 cents 29 .. 58 match: 18 SD: 2.7572 cents 30 .. 60 match: 19 SD: 2.3578 cents 31 .. 62 match: 18 SD: 2.5213 cents 32 .. 64 match: 20 SD: 1.9459 cents 33 .. 66 match: 19 SD: 2.1405 cents 34 .. 68 match: 18 SD: 2.5307 cents 35 .. 70 match: 20 SD: 2.1243 cents 36 .. 72 match: 21 SD: 1.9642 cents 37 .. 74 match: 20 SD: 2.5490 cents 38 .. 76 match: 19 SD: 2.0706 cents 39 .. 78 match: 21 SD: 1.9139 cents 40 .. 80 match: 21 SD: 1.4030 cents 45 .. 90 match: 20 SD: 1.4560 cents 54 .. 108 match: 21 SD: 1.3143 cents 55 .. 110 match: 21 SD: 1.2792 cents 57 .. 114 match: 21 SD: 1.2294 cents 60 .. 120 match: 21 SD: 1.1640 cents 63 .. 126 match: 21 SD: 1.1115 cents 68 .. 136 match: 21 SD: 0.9385 cents 75 .. 150 match: 21 SD: 0.8903 cents 81 .. 162 match: 21 SD: 0.8885 cents 84 .. 168 match: 21 SD: 0.6049 cents 116 .. 232 match: 21 SD: 0.5976 cents 117 .. 234 match: 21 SD: 0.5824 cents 120 .. 240 match: 21 SD: 0.5235 cents 129 .. 258 match: 21 SD: 0.4683 cents 138 .. 276 match: 21 SD: 0.4435 cents 140 .. 280 match: 21 SD: 0.4281 cents 161 .. 322 match: 21 SD: 0.3702 cents 185 .. 370 match: 21 SD: 0.3629 cents 188 .. 376 match: 21 SD: 0.3614 cents 197 .. 394 match: 21 SD: 0.3485 cents 201 .. 402 match: 21 SD: 0.3054 cents 215 .. 430 match: 21 SD: 0.3039 cents 227 .. 454 match: 21 SD: 0.2986 cents 229 .. 458 match: 21 SD: 0.2681 cents 243 .. 486 match: 21 SD: 0.2575 cents 245 .. 490 match: 21 SD: 0.2337 cents 269 .. 538 match: 21 SD: 0.2144 cents 285 .. 570 match: 21 SD: 0.1990 cents 320 .. 640 match: 21 SD: 0.1989 cents 343 .. 686 match: 21 SD: 0.1889 cents 344 .. 688 match: 21 SD: 0.1851 cents 359 .. 718 match: 21 SD: 0.1805 cents 362 .. 724 match: 21 SD: 0.1764 cents 384 .. 768 match: 21 SD: 0.1762 cents 385 .. 770 match: 21 SD: 0.1728 cents 388 .. 776 match: 21 SD: 0.1716 cents 400 .. 800 match: 21 SD: 0.1631 cents 404 .. 808 match: 21 SD: 0.1588 cents 407 .. 814 match: 21 SD: 0.1475 cents 449 .. 898 match: 21 SD: 0.1409 cents 459 .. 918 match: 21 SD: 0.1372 cents 472 .. 944 match: 21 SD: 0.1058 cents 588 .. 1176 match: 21 SD: 0.1049 cents 589 .. 1178 match: 21 SD: 0.1018 cents