Scala analysis: turquoise17-104ed2
Turquoise 17 in 104-tET/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: 69.231 cents 69.230770 2: 150.000 cents 150.000000 3: 207.692 cents 207.692310 4: 288.462 cents 288.461540 5: 357.692 cents 357.692310 6: 415.385 cents 415.384620 7: 496.154 cents 496.153850 8: 565.385 cents 565.384620 9: 646.154 cents 646.153850 10: 703.846 cents 703.846160 11: 784.615 cents 784.615390 12: 853.846 cents 853.846160 13: 911.538 cents 911.538460 14: 992.308 cents 992.307690 15: 1061.538 cents 1061.538460 16: 1119.231 cents 1119.230770 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 80.7692 cents 80.7692 1: 69.2308 cents 69.2308 2: 80.7692 cents 80.7692 3: 57.6923 cents 57.6923 4: 80.7692 cents 80.7692 5: 69.2308 cents 69.2308 6: 57.6923 cents 57.6923 7: 80.7692 cents 80.7692 8: 69.2308 cents 69.2308 9: 80.7692 cents 80.7692 10: 57.6923 cents 57.6923 11: 80.7692 cents 80.7692 12: 69.2308 cents 69.2308 13: 57.6923 cents 57.6923 14: 80.7692 cents 80.7692 15: 69.2308 cents 69.2308 16: 57.6923 cents 57.6923 17: 80.7692 cents 80.7692
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 57.69231 cents 1: 5 69.23077 cents 1: 7 80.76923 cents 2: 3 126.92308 cents 2: 7 138.46154 cents 2: 7 150.00000 cents 3: 13 207.69231 cents 3: 2 219.23077 cents 3: 2 230.76923 cents 4: 3 265.38462 cents 4: 3 276.92308 cents 4: 11 288.46154 cents 5: 1 334.61538 cents 5: 7 346.15385 cents 5: 7 357.69231 cents 5: 2 369.23077 cents 6: 9 415.38462 cents 6: 4 426.92308 cents 6: 4 438.46154 cents 7: 1 473.07692 cents 7: 1 484.61538 cents 7: 15 496.15385 cents 8: 6 553.84616 cents 8: 6 565.38462 cents 8: 5 576.92308 cents 9: 5 623.07692 cents 9: 6 634.61539 cents 9: 6 646.15385 cents 10: 15 703.84616 cents 10: 1 715.38462 cents 10: 1 726.92308 cents 11: 4 761.53846 cents 11: 4 773.07692 cents 11: 9 784.61539 cents 12: 2 830.76923 cents 12: 7 842.30769 cents 12: 7 853.84616 cents 12: 1 865.38462 cents 13: 11 911.53846 cents 13: 3 923.07692 cents 13: 3 934.61538 cents 14: 2 969.23077 cents 14: 2 980.76923 cents 14: 13 992.30769 cents 15: 7 1050.00000 cents 15: 7 1061.53846 cents 15: 3 1073.07692 cents 16: 7 1119.23077 cents 16: 5 1130.76923 cents 16: 5 1142.30769 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.12500 = 25/8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 69.2 150.0 207.7 288.5 357.7 415.4 496.2 565.4 646.2 703.8 784.6 853.8 911.5 992.3 1061.5 1119.2 1200.0 69.2 : 80.8 138.5 219.2 288.5 346.2 426.9 496.2 576.9 634.6 715.4 784.6 842.3 923.1 992.3 1050.0 1130.8 1200.0 150.0 : 57.7 138.5 207.7 265.4 346.2 415.4 496.2 553.8 634.6 703.8 761.5 842.3 911.5 969.2 1050.0 1119.2 1200.0 207.7 : 80.8 150.0 207.7 288.5 357.7 438.5 496.2 576.9 646.2 703.8 784.6 853.8 911.5 992.3 1061.5 1142.3 1200.0 288.5 : 69.2 126.9 207.7 276.9 357.7 415.4 496.2 565.4 623.1 703.8 773.1 830.8 911.5 980.8 1061.5 1119.2 1200.0 357.7 : 57.7 138.5 207.7 288.5 346.2 426.9 496.2 553.8 634.6 703.8 761.5 842.3 911.5 992.3 1050.0 1130.8 1200.0 415.4 : 80.8 150.0 230.8 288.5 369.2 438.5 496.2 576.9 646.2 703.8 784.6 853.8 934.6 992.3 1073.1 1142.3 1200.0 496.2 : 69.2 150.0 207.7 288.5 357.7 415.4 496.2 565.4 623.1 703.8 773.1 853.8 911.5 992.3 1061.5 1119.2 1200.0 565.4 : 80.8 138.5 219.2 288.5 346.2 426.9 496.2 553.8 634.6 703.8 784.6 842.3 923.1 992.3 1050.0 1130.8 1200.0 646.2 : 57.7 138.5 207.7 265.4 346.2 415.4 473.1 553.8 623.1 703.8 761.5 842.3 911.5 969.2 1050.0 1119.2 1200.0 703.8 : 80.8 150.0 207.7 288.5 357.7 415.4 496.2 565.4 646.2 703.8 784.6 853.8 911.5 992.3 1061.5 1142.3 1200.0 784.6 : 69.2 126.9 207.7 276.9 334.6 415.4 484.6 565.4 623.1 703.8 773.1 830.8 911.5 980.8 1061.5 1119.2 1200.0 853.8 : 57.7 138.5 207.7 265.4 346.2 415.4 496.2 553.8 634.6 703.8 761.5 842.3 911.5 992.3 1050.0 1130.8 1200.0 911.5 : 80.8 150.0 207.7 288.5 357.7 438.5 496.2 576.9 646.2 703.8 784.6 853.8 934.6 992.3 1073.1 1142.3 1200.0 992.3 : 69.2 126.9 207.7 276.9 357.7 415.4 496.2 565.4 623.1 703.8 773.1 853.8 911.5 992.3 1061.5 1119.2 1200.0 1061.5: 57.7 138.5 207.7 288.5 346.2 426.9 496.2 553.8 634.6 703.8 784.6 842.3 923.1 992.3 1050.0 1130.8 1200.0 1119.2: 80.8 150.0 230.8 288.5 369.2 438.5 496.2 576.9 646.2 726.9 784.6 865.4 934.6 992.3 1073.1 1142.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.6923 .. 80.7692 cents 23.07692 cents 57.69231 cents 2: 126.9231 .. 150.0000 cents 23.07692 cents 46.15385 cents 3: 207.6923 .. 230.7692 cents 23.07692 cents 57.69231 cents 4: 265.3846 .. 288.4615 cents 23.07692 cents 34.61539 cents 5: 334.6154 .. 369.2308 cents 34.61539 cents 46.15384 cents 6: 415.3846 .. 438.4615 cents 23.07692 cents 46.15385 cents 7: 473.0769 .. 496.1538 cents 23.07693 cents 34.61538 cents 8: 553.8462 .. 576.9231 cents 23.07692 cents 57.69231 cents 9: 623.0769 .. 646.1539 cents 23.07693 cents 46.15384 cents 10: 703.8462 .. 726.9231 cents 23.07692 cents 57.69231 cents 11: 761.5385 .. 784.6154 cents 23.07693 cents 34.61538 cents 12: 830.7692 .. 865.3846 cents 34.61539 cents 46.15384 cents 13: 911.5385 .. 934.6154 cents 23.07692 cents 46.15384 cents 14: 969.2308 .. 992.3077 cents 23.07692 cents 34.61539 cents 15: 1050.0000 .. 1073.0769 cents 23.07692 cents 57.69231 cents 16: 1119.2308 .. 1142.3077 cents 23.07692 cents 46.15385 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 57.69230 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 80.76923 cents Average / Smallest step : 1.223530 Largest / Average step : 1.144231 Largest / Smallest step : 1.400000 Median interval of one step : 69.23077 cents, amount: 5 Most common interval of one step : 80.76923 cents, amount: 7 Least squares average step : 70.65934 cents, oct.: 1201.20879 cents Scale is strictly proper Scale is a mode of a 104-tone equal temperament with octave 2/1 degrees: 6 13 18 25 31 36 43 49 56 61 68 74 79 86 92 97 104 Least number of segments generator : 61 of 703.846 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 55 of 634.615 cents and inv. generated superset size: 32 = 15 more = 188.235% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBACBABCBACBACB Step pattern size order : MLSLMSLMLSLMSLMSL Interval vector is [ 0 0 0 0 5 5 7 0 0 0 3 7 7 0 0 0 0 13 2 2 0 0 3 3 11 0 0 0 1 7 7 2 0 0 0 9 4 4 0 0 1 1 15 0 0 0 0 6 6 5 0 0 ] Scale is a Constant Structure, by a margin of 34.61538 cents Scale diversity : 1.229574 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.673077 Number of different interval sizes : 50 = 3.12500 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.12500 = 25/8 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 11.53846 cents Most common intervals : 496.15385 cents & inv., amount: 15 Most common triad is 0.0 496.154 703.846 cents, amount: 13 Number of recognisable fifths : 16, average 704.5673 cents Number of appreciable fifths : 15, average 703.8462 cents Scale contains two identical conjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 9 = 52.9412% Limited transpositions with margin 23.0769 cents: 1 8 15 Limited inverse transpositions with margin 23.0769 cents: 4 7 8 10 11 14 -- 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: 6.0708 c. M: 10.8597 c. 41: 2 3 2 3 2 2 3 2 3 2 3 2 2 3 2 2 3 SP D3 S SD: 5.5148 c. M: 10.6942 c. 46: 3 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 SP M ME S SD: 4.9990 c. M:-9.0301 c. 58: 3 4 3 4 3 3 4 3 4 3 4 3 3 4 3 3 4 SP D3 S SD: 3.9647 c. M: 7.1618 c. 63: 4 4 3 4 4 3 4 4 4 3 4 4 3 4 4 3 4 SP M ME S SD: 3.5890 c. M:-6.9597 c. 70: 4 5 3 5 4 3 5 4 5 3 5 4 3 5 4 3 5 SP SD: 2.9487 c. M:-5.2747 c. 87: 5 6 4 6 5 4 6 5 6 4 6 5 4 6 5 4 6 SP SD: 1.1862 c. M:-2.1220 c. 104: 6 7 5 7 6 5 7 6 7 5 7 6 5 7 6 5 7 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: 0.9456 cents 3 .. 6 match: 3 H SD: 9.0818 cents 4 .. 8 match: 4 H SD: 9.2674 cents 5 .. 10 match: 5 H SD: 10.0334 cents 6 .. 12 match: 6 H SD: 6.1470 cents 7 .. 14 match: 7 H SD: 6.9034 cents 8 .. 16 match: 8 H SD: 6.2227 cents 9 .. 18 match: 9 H SD: 5.3421 cents 10 .. 20 match: 10 H SD: 6.6092 cents 11 .. 22 match: 11 H SD: 5.5202 cents 12 .. 24 match: 12 H SD: 5.5568 cents 13 .. 26 match: 13 H SD: 5.6825 cents 14 .. 28 match: 14 H SD: 5.1885 cents 15 .. 30 match: 14 SD: 6.0963 cents 16 .. 32 match: 15 S SD: 5.0074 cents 17 .. 34 match: 16 S SD: 5.2512 cents 18 .. 36 match: 16 S SD: 4.1502 cents 19 .. 38 match: 16 S SD: 4.8054 cents 20 .. 40 match: 16 SD: 4.6617 cents 21 .. 42 match: 17 SD: 3.7393 cents 22 .. 44 match: 17 SD: 2.7341 cents 26 .. 52 match: 17 SD: 2.6719 cents 30 .. 60 match: 17 SD: 2.6094 cents 31 .. 62 match: 17 SD: 2.5392 cents 33 .. 66 match: 17 SD: 2.1129 cents 40 .. 80 match: 17 SD: 2.0535 cents 42 .. 84 match: 17 SD: 2.0201 cents 44 .. 88 match: 17 SD: 1.4418 cents 54 .. 108 match: 17 SD: 1.4022 cents 55 .. 110 match: 17 SD: 1.3298 cents 56 .. 112 match: 17 SD: 1.2947 cents 66 .. 132 match: 17 SD: 1.0155 cents 70 .. 140 match: 17 SD: 1.0138 cents 77 .. 154 match: 17 SD: 0.9049 cents 78 .. 156 match: 17 SD: 0.6384 cents 117 .. 234 match: 17 SD: 0.6333 cents 121 .. 242 match: 17 SD: 0.5884 cents 132 .. 264 match: 17 SD: 0.5420 cents 143 .. 286 match: 17 SD: 0.4481 cents 165 .. 330 match: 17 SD: 0.4237 cents 166 .. 332 match: 17 SD: 0.3339 cents 199 .. 398 match: 17 SD: 0.2743 cents 221 .. 442 match: 17 SD: 0.2416 cents 243 .. 486 match: 17 SD: 0.2250 cents 265 .. 530 match: 17 SD: 0.1931 cents 365 .. 730 match: 17 SD: 0.1832 cents 375 .. 750 match: 17 SD: 0.1802 cents 391 .. 782 match: 17 SD: 0.1613 cents 398 .. 796 match: 17 SD: 0.1607 cents 440 .. 880 match: 17 SD: 0.1471 cents 464 .. 928 match: 17 SD: 0.1382 cents 495 .. 990 match: 17 SD: 0.1379 cents 518 .. 1036 match: 17 SD: 0.1136 cents