Scala analysis: turquoise17
Turquoise 17, 1024-ED2: ~33:36:39:42:44 at steps 0, 7, 10
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 70.312 cents 70.312490 2: 151.172 cents 151.171870 3: 208.594 cents 208.593750 4: 289.453 cents 289.453130 5: 358.594 cents 358.593750 6: 416.016 cents 416.015630 7: 496.875 cents 496.875000 8: 566.016 cents 566.015620 9: 646.875 cents 646.875000 10: 704.297 cents 704.296880 11: 785.156 cents 785.156250 12: 854.297 cents 854.296870 13: 911.719 cents 911.718750 14: 992.578 cents 992.578120 15: 1061.719 cents 1061.718750 16: 1119.141 cents 1119.140630 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 80.8594 cents 80.8594 1: 70.3125 cents 70.3125 2: 80.8594 cents 80.8594 3: 57.4219 cents 57.4219 4: 80.8594 cents 80.8594 5: 69.1406 cents 69.1406 6: 57.4219 cents 57.4219 7: 80.8594 cents 80.8594 8: 69.1406 cents 69.1406 9: 80.8594 cents 80.8594 10: 57.4219 cents 57.4219 11: 80.8594 cents 80.8594 12: 69.1406 cents 69.1406 13: 57.4219 cents 57.4219 14: 80.8594 cents 80.8594 15: 69.1406 cents 69.1406 16: 57.4219 cents 57.4219 17: 80.8594 cents 80.8594
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 57.42188 cents 1: 4 69.14062 cents 1: 1 70.31249 cents 1: 7 80.85938 cents 2: 3 126.56250 cents 2: 7 138.28126 cents 2: 5 150.00000 cents 2: 2 151.17187 cents 3: 11 207.42188 cents 3: 2 208.59375 cents 3: 2 219.14064 cents 3: 1 230.85937 cents 3: 1 232.03124 cents 4: 3 264.84376 cents 4: 2 276.56249 cents 4: 1 277.73437 cents 4: 8 288.28126 cents 4: 3 289.45313 cents 5: 1 333.98438 cents 5: 6 345.70314 cents 5: 1 346.87500 cents 5: 4 357.42187 cents 5: 3 358.59375 cents 5: 1 369.14062 cents 5: 1 370.31250 cents 6: 6 414.84375 cents 6: 3 416.01563 cents 6: 3 426.56251 cents 6: 1 427.73438 cents 6: 2 438.28125 cents 6: 2 439.45312 cents 7: 1 472.26563 cents 7: 1 485.15624 cents 7: 9 495.70313 cents 7: 6 496.87500 cents 8: 4 553.12501 cents 8: 2 554.29688 cents 8: 2 564.84374 cents 8: 4 566.01562 cents 8: 3 576.56251 cents 8: 2 577.73438 cents 9: 2 622.26562 cents 9: 3 623.43749 cents 9: 4 633.98439 cents 9: 2 635.15626 cents 9: 2 645.70312 cents 9: 4 646.87500 cents 10: 6 703.12500 cents 10: 9 704.29688 cents 10: 1 714.84376 cents 10: 1 727.73437 cents 11: 2 760.54688 cents 11: 2 761.71875 cents 11: 1 772.26562 cents 11: 3 773.43749 cents 11: 3 783.98438 cents 11: 6 785.15625 cents 12: 1 829.68750 cents 12: 1 830.85938 cents 12: 3 841.40626 cents 12: 4 842.57813 cents 12: 1 853.12500 cents 12: 6 854.29687 cents 12: 1 866.01562 cents 13: 3 910.54688 cents 13: 8 911.71875 cents 13: 1 922.26563 cents 13: 2 923.43751 cents 13: 3 935.15624 cents 14: 1 967.96876 cents 14: 1 969.14063 cents 14: 2 980.85936 cents 14: 2 991.40626 cents 14: 11 992.57812 cents 15: 2 1048.82814 cents 15: 5 1050.00000 cents 15: 7 1061.71875 cents 15: 3 1073.43750 cents 16: 7 1119.14063 cents 16: 1 1129.68751 cents 16: 4 1130.85938 cents 16: 5 1142.57812 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.12500 = 41/8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 70.3 151.2 208.6 289.5 358.6 416.0 496.9 566.0 646.9 704.3 785.2 854.3 911.7 992.6 1061.7 1119.1 1200.0 70.3 : 80.9 138.3 219.1 288.3 345.7 426.6 495.7 576.6 634.0 714.8 784.0 841.4 922.3 991.4 1048.8 1129.7 1200.0 151.2 : 57.4 138.3 207.4 264.8 345.7 414.8 495.7 553.1 634.0 703.1 760.5 841.4 910.5 968.0 1048.8 1119.1 1200.0 208.6 : 80.9 150.0 207.4 288.3 357.4 438.3 495.7 576.6 645.7 703.1 784.0 853.1 910.5 991.4 1061.7 1142.6 1200.0 289.5 : 69.1 126.6 207.4 276.6 357.4 414.8 495.7 564.8 622.3 703.1 772.3 829.7 910.5 980.9 1061.7 1119.1 1200.0 358.6 : 57.4 138.3 207.4 288.3 345.7 426.6 495.7 553.1 634.0 703.1 760.5 841.4 911.7 992.6 1050.0 1130.9 1200.0 416.0 : 80.9 150.0 230.9 288.3 369.1 438.3 495.7 576.6 645.7 703.1 784.0 854.3 935.2 992.6 1073.4 1142.6 1200.0 496.9 : 69.1 150.0 207.4 288.3 357.4 414.8 495.7 564.8 622.3 703.1 773.4 854.3 911.7 992.6 1061.7 1119.1 1200.0 566.0 : 80.9 138.3 219.1 288.3 345.7 426.6 495.7 553.1 634.0 704.3 785.2 842.6 923.4 992.6 1050.0 1130.9 1200.0 646.9 : 57.4 138.3 207.4 264.8 345.7 414.8 472.3 553.1 623.4 704.3 761.7 842.6 911.7 969.1 1050.0 1119.1 1200.0 704.3 : 80.9 150.0 207.4 288.3 357.4 414.8 495.7 566.0 646.9 704.3 785.2 854.3 911.7 992.6 1061.7 1142.6 1200.0 785.2 : 69.1 126.6 207.4 276.6 334.0 414.8 485.2 566.0 623.4 704.3 773.4 830.9 911.7 980.9 1061.7 1119.1 1200.0 854.3 : 57.4 138.3 207.4 264.8 345.7 416.0 496.9 554.3 635.2 704.3 761.7 842.6 911.7 992.6 1050.0 1130.9 1200.0 911.7 : 80.9 150.0 207.4 288.3 358.6 439.5 496.9 577.7 646.9 704.3 785.2 854.3 935.2 992.6 1073.4 1142.6 1200.0 992.6 : 69.1 126.6 207.4 277.7 358.6 416.0 496.9 566.0 623.4 704.3 773.4 854.3 911.7 992.6 1061.7 1119.1 1200.0 1061.7: 57.4 138.3 208.6 289.5 346.9 427.7 496.9 554.3 635.2 704.3 785.2 842.6 923.4 992.6 1050.0 1130.9 1200.0 1119.1: 80.9 151.2 232.0 289.5 370.3 439.5 496.9 577.7 646.9 727.7 785.2 866.0 935.2 992.6 1073.4 1142.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.4219 .. 80.8594 cents 23.43750 cents 57.42188 cents 2: 126.5625 .. 151.1719 cents 24.60937 cents 45.70312 cents 3: 207.4219 .. 232.0312 cents 24.60936 cents 56.25001 cents 4: 264.8438 .. 289.4531 cents 24.60937 cents 32.81252 cents 5: 333.9844 .. 370.3125 cents 36.32812 cents 44.53125 cents 6: 414.8438 .. 439.4531 cents 24.60937 cents 44.53125 cents 7: 472.2656 .. 496.8750 cents 24.60937 cents 32.81251 cents 8: 553.1250 .. 577.7344 cents 24.60937 cents 56.25001 cents 9: 622.2656 .. 646.8750 cents 24.60938 cents 44.53124 cents 10: 703.1250 .. 727.7344 cents 24.60937 cents 56.25000 cents 11: 760.5469 .. 785.1563 cents 24.60937 cents 32.81251 cents 12: 829.6875 .. 866.0156 cents 36.32812 cents 44.53125 cents 13: 910.5469 .. 935.1562 cents 24.60936 cents 44.53126 cents 14: 967.9688 .. 992.5781 cents 24.60936 cents 32.81252 cents 15: 1048.8281 .. 1073.4375 cents 24.60936 cents 56.25002 cents 16: 1119.1406 .. 1142.5781 cents 23.43749 cents 45.70313 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 57.42188 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 80.85938 cents Average / Smallest step : 1.229292 Largest / Average step : 1.145508 Largest / Smallest step : 1.408163 Median interval of one step : 69.14062 cents, amount: 4 Most common interval of one step : 80.85938 cents, amount: 7 Least squares average step : 70.69196 cents, oct.: 1201.76339 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 60 129 178 247 306 355 424 483 552 601 670 729 778 847 906 955 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 831 of 973.828 cents and inv. generated superset size: 262 = 245 more = 1541.176% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBDCBDBCBDCBDCB Step pattern size order : CDADBADBDADBADBAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 32.81251 cents Scale diversity : 1.248453 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.654297 Number of different interval sizes : 82 = 5.12500 / class Number of one step interval sizes : 4 Highest interval variety : 7 Mean interval variety : 5.12500 = 41/8 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17186 cents Most common intervals : 207.42188 cents & inv., amount: 11 Most common triad is 0.0 207.422 992.578 cents, amount: 6 Number of recognisable fifths : 16, average 704.5166 cents Number of appreciable fifths : 15, average 703.8281 cents Best fifths form a closed circle Formal octave complements present : 1 = 5.8824% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.3733 c. M: 11.5809 c. 41: 2 3 2 3 2 2 3 2 3 2 3 2 2 3 2 2 3 SP D3 S SD: 5.8727 c. M: 11.7759 c. 46: 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 SP M ME S SD: 4.5835 c. M:-7.9484 c. 58: 3 4 3 4 3 3 4 3 4 3 4 3 3 4 3 3 4 SP D3 S SD: 4.4388 c. M: 8.2435 c. 63: 4 4 3 4 4 3 4 4 4 3 4 4 3 4 4 3 4 SP M ME S SD: 3.3150 c. M:-5.8780 c. 70: 4 5 3 5 4 3 5 4 5 3 5 4 3 5 4 3 5 SP SD: 2.7478 c. M: 4.8549 c. 87: 5 6 4 6 5 4 6 5 6 4 6 5 4 6 5 4 6 SP SD: 1.1056 c. M: 2.2225 c. 104: 6 7 5 7 6 5 7 6 7 5 7 6 5 7 6 5 7 SP SD: 0.6788 c. M: 1.1719 c. 191: 11 13 9 13 11 9 13 11 13 9 13 11 9 13 11 9 13 SP SD: 0.6773 c. M: 1.3559 c. 295: 17 20 14 20 17 14 20 17 20 14 20 17 14 20 17 14 20 SP SD: 0.6267 c. M: 1.1599 c. 341: 20 23 16 23 20 16 23 20 23 16 23 20 16 23 20 16 23 SP SD: 0.5915 c. M:-1.0378 c. 358: 21 24 17 24 21 17 24 21 24 17 24 21 17 24 21 17 24 SP SD: 0.5501 c. M: 1.1850 c. 399: 23 27 19 27 23 19 27 23 27 19 27 23 19 27 23 19 27 SP SD: 0.6220 c. M: 1.1396 c. 428: 25 29 20 29 25 20 29 25 29 20 29 25 20 29 25 20 29 SP SD: 0.6144 c. M: 1.1171 c. 445: 26 30 21 30 26 21 30 26 30 21 30 26 21 30 26 21 30 SP SD: 0.5087 c. M: 0.9533 c. 521: 31 35 25 35 30 25 35 30 35 25 35 30 25 35 30 25 35 SP SD: 0.6039 c. M:-1.0887 c. 530: 31 36 25 36 30 26 35 31 36 25 36 30 26 35 31 25 36 SP SD: 0.5759 c. M: 1.0259 c. 532: 31 36 25 36 31 25 36 31 36 25 36 31 25 36 31 25 36 SP SD: 0.5390 c. M: 1.0750 c. 545: 32 37 26 37 31 26 37 31 37 26 37 31 26 37 31 26 37 SP SD: 0.5377 c. M:-1.1891 c. 549: 32 37 26 37 32 26 37 32 37 26 37 32 26 37 32 26 37 SP SD: 0.4881 c. M: 0.9435 c. 562: 33 38 27 38 32 27 38 32 38 27 38 32 27 38 32 27 38 SP SD: 0.4241 c. M:-0.9383 c. 579: 34 39 28 39 33 28 39 33 39 28 39 33 28 39 33 28 39 SP SD: 0.3910 c. M:-0.7327 c. 608: 36 41 29 41 35 29 41 35 41 29 41 35 29 41 35 29 41 SP SD: 0.4645 c. M:-0.8018 c. 625: 37 42 30 42 36 30 42 36 42 30 42 36 30 42 36 30 42 SP SD: 0.3971 c. M:-0.7275 c. 649: 38 44 31 44 37 31 44 37 44 31 44 37 31 44 37 31 44 SP SD: 0.3785 c. M:-0.8396 c. 666: 39 45 32 45 38 32 45 38 45 32 45 38 32 45 38 32 45 SP SD: 0.2957 c. M:-0.6370 c. 683: 40 46 33 46 39 33 46 39 46 33 46 39 33 46 39 33 46 SP SD: 0.2953 c. M: 0.5182 c. 712: 42 48 34 48 41 34 48 41 48 34 48 41 34 48 41 34 48 SP SD: 0.2975 c. M:-0.5135 c. 729: 43 49 35 49 42 35 49 42 49 35 49 42 35 49 42 35 49 SP SD: 0.2536 c. M:-0.4694 c. 770: 45 52 37 52 44 37 52 44 52 37 52 44 37 52 44 37 52 SP SD: 0.2276 c. M: 0.4200 c. 816: 48 55 39 55 47 39 55 47 55 39 55 47 39 55 47 39 55 SP SD: 0.1730 c. M:-0.2987 c. 833: 49 56 40 56 48 40 56 48 56 40 56 48 40 56 48 40 56 SP SD: 0.1553 c. M:-0.3109 c. 920: 54 62 44 62 53 44 62 53 62 44 62 53 44 62 53 44 62 SP SD: 0.0767 c. M:-0.1325 c. 1024: 60 69 49 69 59 49 69 59 69 49 69 59 49 69 59 49 69 SP 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: 1.1709 cents 3 .. 6 match: 3 H SD: 9.1283 cents 4 .. 8 match: 4 H SD: 9.1448 cents 5 .. 10 match: 5 H SD: 9.7935 cents 6 .. 12 match: 6 H SD: 6.2762 cents 7 .. 14 match: 7 H SD: 6.8545 cents 8 .. 16 match: 8 H SD: 6.2130 cents 9 .. 18 match: 9 H SD: 5.4610 cents 10 .. 20 match: 10 H SD: 6.4535 cents 11 .. 22 match: 11 H SD: 5.5669 cents 12 .. 24 match: 12 H SD: 5.5509 cents 13 .. 26 match: 13 H SD: 5.7249 cents 14 .. 28 match: 14 H SD: 5.2020 cents 15 .. 30 match: 14 SD: 6.0599 cents 16 .. 32 match: 15 S SD: 4.9997 cents 17 .. 34 match: 16 S SD: 5.1642 cents 18 .. 36 match: 16 S SD: 4.2033 cents 19 .. 38 match: 16 S SD: 4.8181 cents 20 .. 40 match: 16 SD: 4.5541 cents 21 .. 42 match: 17 SD: 3.6488 cents 22 .. 44 match: 17 SD: 2.6921 cents 26 .. 52 match: 17 SD: 2.6825 cents 30 .. 60 match: 17 SD: 2.6050 cents 31 .. 62 match: 17 SD: 2.5403 cents 33 .. 66 match: 17 SD: 2.0974 cents 40 .. 80 match: 17 SD: 2.0423 cents 42 .. 84 match: 17 SD: 1.9784 cents 44 .. 88 match: 17 SD: 1.3905 cents 55 .. 110 match: 17 SD: 1.3174 cents 64 .. 128 match: 17 SD: 1.2750 cents 66 .. 132 match: 17 SD: 1.0058 cents 75 .. 150 match: 17 SD: 0.9754 cents 77 .. 154 match: 17 SD: 0.8448 cents 78 .. 156 match: 17 SD: 0.7049 cents 99 .. 198 match: 17 SD: 0.6107 cents 117 .. 234 match: 17 SD: 0.5617 cents 139 .. 278 match: 17 SD: 0.5480 cents 141 .. 282 match: 17 SD: 0.5310 cents 143 .. 286 match: 17 SD: 0.4323 cents 165 .. 330 match: 17 SD: 0.3412 cents 187 .. 374 match: 17 SD: 0.3290 cents 209 .. 418 match: 17 SD: 0.3281 cents 221 .. 442 match: 17 SD: 0.3083 cents 235 .. 470 match: 17 SD: 0.3013 cents 240 .. 480 match: 17 SD: 0.2978 cents 241 .. 482 match: 17 SD: 0.2887 cents 243 .. 486 match: 17 SD: 0.2309 cents 265 .. 530 match: 17 SD: 0.2019 cents 287 .. 574 match: 17 SD: 0.1915 cents 362 .. 724 match: 17 SD: 0.1869 cents 364 .. 728 match: 17 SD: 0.1784 cents 382 .. 764 match: 17 SD: 0.1773 cents 391 .. 782 match: 17 SD: 0.1713 cents 406 .. 812 match: 17 SD: 0.1518 cents 430 .. 860 match: 17 SD: 0.1314 cents 439 .. 878 match: 17 SD: 0.1312 cents 460 .. 920 match: 17 SD: 0.1218 cents 538 .. 1076 match: 17 SD: 0.1150 cents 556 .. 1112 match: 17 SD: 0.1102 cents