Scala analysis: myna23_makemicromusic_27704_27727
Myna[23] in 89et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40.449 cents 40.449440 2: 80.899 cents 80.898880 3: 121.348 cents 121.348310 4: 229.213 cents 229.213480 5: 269.663 cents 269.662920 6: 310.112 cents 310.112360 7: 350.562 cents 350.561800 8: 391.011 cents 391.011240 9: 431.461 cents 431.460670 10: 539.326 cents 539.325840 11: 579.775 cents 579.775280 12: 620.225 cents 620.224720 13: 660.674 cents 660.674160 14: 701.124 cents 701.123600 15: 741.573 cents 741.573030 16: 849.438 cents 849.438200 17: 889.888 cents 889.887640 18: 930.337 cents 930.337080 19: 970.787 cents 970.786520 20: 1011.236 cents 1011.235960 21: 1119.101 cents 1119.101120 22: 1159.551 cents 1159.550560 23: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40.4494 cents 40.4494 1: 40.4494 cents 40.4494 2: 40.4494 cents 40.4494 3: 40.4494 cents 40.4494 4: 107.8652 cents 107.8652 5: 40.4494 cents 40.4494 6: 40.4494 cents 40.4494 7: 40.4494 cents 40.4494 8: 40.4494 cents 40.4494 9: 40.4494 cents 40.4494 10: 107.8652 cents 107.8652 11: 40.4494 cents 40.4494 12: 40.4494 cents 40.4494 13: 40.4494 cents 40.4494 14: 40.4494 cents 40.4494 15: 40.4494 cents 40.4494 16: 107.8652 cents 107.8652 17: 40.4494 cents 40.4494 18: 40.4494 cents 40.4494 19: 40.4494 cents 40.4494 20: 40.4494 cents 40.4494 21: 107.8652 cents 107.8652 22: 40.4494 cents 40.4494 23: 40.4494 cents 40.4494
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 19 40.44944 cents 1: 4 107.86517 cents 2: 15 80.89888 cents 2: 8 148.31460 cents 3: 11 121.34831 cents 3: 12 188.76404 cents 4: 7 161.79776 cents 4: 16 229.21348 cents 5: 3 202.24719 cents 5: 20 269.66292 cents 6: 22 310.11236 cents 6: 1 377.52809 cents 7: 18 350.56180 cents 7: 5 417.97753 cents 8: 14 391.01124 cents 8: 9 458.42696 cents 9: 10 431.46067 cents 9: 13 498.87640 cents 10: 6 471.91012 cents 10: 17 539.32584 cents 11: 2 512.35955 cents 11: 21 579.77528 cents 12: 21 620.22472 cents 12: 2 687.64045 cents 13: 17 660.67416 cents 13: 6 728.08989 cents 14: 13 701.12360 cents 14: 10 768.53932 cents 15: 9 741.57303 cents 15: 14 808.98876 cents 16: 5 782.02248 cents 16: 18 849.43820 cents 17: 1 822.47191 cents 17: 22 889.88764 cents 18: 20 930.33708 cents 18: 3 997.75281 cents 19: 16 970.78652 cents 19: 7 1038.20224 cents 20: 12 1011.23596 cents 20: 11 1078.65168 cents 21: 8 1051.68540 cents 21: 15 1119.10112 cents 22: 4 1092.13483 cents 22: 19 1159.55056 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 22 23 0.0 : 40.4 80.9 121.3 229.2 269.7 310.1 350.6 391.0 431.5 539.3 579.8 620.2 660.7 701.1 741.6 849.4 889.9 930.3 970.8 1011.2 1119.1 1159.6 1200.0 40.4 : 40.4 80.9 188.8 229.2 269.7 310.1 350.6 391.0 498.9 539.3 579.8 620.2 660.7 701.1 809.0 849.4 889.9 930.3 970.8 1078.7 1119.1 1159.6 1200.0 80.9 : 40.4 148.3 188.8 229.2 269.7 310.1 350.6 458.4 498.9 539.3 579.8 620.2 660.7 768.5 809.0 849.4 889.9 930.3 1038.2 1078.7 1119.1 1159.6 1200.0 121.3 : 107.9 148.3 188.8 229.2 269.7 310.1 418.0 458.4 498.9 539.3 579.8 620.2 728.1 768.5 809.0 849.4 889.9 997.8 1038.2 1078.7 1119.1 1159.6 1200.0 229.2 : 40.4 80.9 121.3 161.8 202.2 310.1 350.6 391.0 431.5 471.9 512.4 620.2 660.7 701.1 741.6 782.0 889.9 930.3 970.8 1011.2 1051.7 1092.1 1200.0 269.7 : 40.4 80.9 121.3 161.8 269.7 310.1 350.6 391.0 431.5 471.9 579.8 620.2 660.7 701.1 741.6 849.4 889.9 930.3 970.8 1011.2 1051.7 1159.6 1200.0 310.1 : 40.4 80.9 121.3 229.2 269.7 310.1 350.6 391.0 431.5 539.3 579.8 620.2 660.7 701.1 809.0 849.4 889.9 930.3 970.8 1011.2 1119.1 1159.6 1200.0 350.6 : 40.4 80.9 188.8 229.2 269.7 310.1 350.6 391.0 498.9 539.3 579.8 620.2 660.7 768.5 809.0 849.4 889.9 930.3 970.8 1078.7 1119.1 1159.6 1200.0 391.0 : 40.4 148.3 188.8 229.2 269.7 310.1 350.6 458.4 498.9 539.3 579.8 620.2 728.1 768.5 809.0 849.4 889.9 930.3 1038.2 1078.7 1119.1 1159.6 1200.0 431.5 : 107.9 148.3 188.8 229.2 269.7 310.1 418.0 458.4 498.9 539.3 579.8 687.6 728.1 768.5 809.0 849.4 889.9 997.8 1038.2 1078.7 1119.1 1159.6 1200.0 539.3 : 40.4 80.9 121.3 161.8 202.2 310.1 350.6 391.0 431.5 471.9 579.8 620.2 660.7 701.1 741.6 782.0 889.9 930.3 970.8 1011.2 1051.7 1092.1 1200.0 579.8 : 40.4 80.9 121.3 161.8 269.7 310.1 350.6 391.0 431.5 539.3 579.8 620.2 660.7 701.1 741.6 849.4 889.9 930.3 970.8 1011.2 1051.7 1159.6 1200.0 620.2 : 40.4 80.9 121.3 229.2 269.7 310.1 350.6 391.0 498.9 539.3 579.8 620.2 660.7 701.1 809.0 849.4 889.9 930.3 970.8 1011.2 1119.1 1159.6 1200.0 660.7 : 40.4 80.9 188.8 229.2 269.7 310.1 350.6 458.4 498.9 539.3 579.8 620.2 660.7 768.5 809.0 849.4 889.9 930.3 970.8 1078.7 1119.1 1159.6 1200.0 701.1 : 40.4 148.3 188.8 229.2 269.7 310.1 418.0 458.4 498.9 539.3 579.8 620.2 728.1 768.5 809.0 849.4 889.9 930.3 1038.2 1078.7 1119.1 1159.6 1200.0 741.6 : 107.9 148.3 188.8 229.2 269.7 377.5 418.0 458.4 498.9 539.3 579.8 687.6 728.1 768.5 809.0 849.4 889.9 997.8 1038.2 1078.7 1119.1 1159.6 1200.0 849.4 : 40.4 80.9 121.3 161.8 269.7 310.1 350.6 391.0 431.5 471.9 579.8 620.2 660.7 701.1 741.6 782.0 889.9 930.3 970.8 1011.2 1051.7 1092.1 1200.0 889.9 : 40.4 80.9 121.3 229.2 269.7 310.1 350.6 391.0 431.5 539.3 579.8 620.2 660.7 701.1 741.6 849.4 889.9 930.3 970.8 1011.2 1051.7 1159.6 1200.0 930.3 : 40.4 80.9 188.8 229.2 269.7 310.1 350.6 391.0 498.9 539.3 579.8 620.2 660.7 701.1 809.0 849.4 889.9 930.3 970.8 1011.2 1119.1 1159.6 1200.0 970.8 : 40.4 148.3 188.8 229.2 269.7 310.1 350.6 458.4 498.9 539.3 579.8 620.2 660.7 768.5 809.0 849.4 889.9 930.3 970.8 1078.7 1119.1 1159.6 1200.0 1011.2: 107.9 148.3 188.8 229.2 269.7 310.1 418.0 458.4 498.9 539.3 579.8 620.2 728.1 768.5 809.0 849.4 889.9 930.3 1038.2 1078.7 1119.1 1159.6 1200.0 1119.1: 40.4 80.9 121.3 161.8 202.2 310.1 350.6 391.0 431.5 471.9 512.4 620.2 660.7 701.1 741.6 782.0 822.5 930.3 970.8 1011.2 1051.7 1092.1 1200.0 1159.6: 40.4 80.9 121.3 161.8 269.7 310.1 350.6 391.0 431.5 471.9 579.8 620.2 660.7 701.1 741.6 782.0 889.9 930.3 970.8 1011.2 1051.7 1159.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.4494 .. 107.8652 cents 67.41573 cents 40.44944 cents 2: 80.8989 .. 148.3146 cents 67.41572 cents -26.96629 cents 3: 121.3483 .. 188.7640 cents 67.41573 cents -26.96629 cents 4: 161.7978 .. 229.2135 cents 67.41572 cents -26.96628 cents 5: 202.2472 .. 269.6629 cents 67.41573 cents -26.96629 cents 6: 310.1124 .. 377.5281 cents 67.41573 cents 40.44944 cents 7: 350.5618 .. 417.9775 cents 67.41573 cents -26.96629 cents 8: 391.0112 .. 458.4270 cents 67.41572 cents -26.96629 cents 9: 431.4607 .. 498.8764 cents 67.41573 cents -26.96629 cents 10: 471.9101 .. 539.3258 cents 67.41572 cents -26.96628 cents 11: 512.3595 .. 579.7753 cents 67.41573 cents -26.96629 cents 12: 620.2247 .. 687.6405 cents 67.41573 cents 40.44944 cents 13: 660.6742 .. 728.0899 cents 67.41573 cents -26.96629 cents 14: 701.1236 .. 768.5393 cents 67.41572 cents -26.96629 cents 15: 741.5730 .. 808.9888 cents 67.41573 cents -26.96629 cents 16: 782.0225 .. 849.4382 cents 67.41572 cents -26.96628 cents 17: 822.4719 .. 889.8876 cents 67.41573 cents -26.96629 cents 18: 930.3371 .. 997.7528 cents 67.41573 cents 40.44944 cents 19: 970.7865 .. 1038.2022 cents 67.41572 cents -26.96629 cents 20: 1011.2360 .. 1078.6517 cents 67.41572 cents -26.96628 cents 21: 1051.6854 .. 1119.1011 cents 67.41572 cents -26.96628 cents 22: 1092.1348 .. 1159.5506 cents 67.41573 cents -26.96629 cents
SHOW DATA
Number of notes : 23 -- Interval properties -- Smallest interval : 40.44943 cents, class 1 Average step (divided formal octave): 52.1739 cents Largest one step interval : 107.86517 cents Average / Smallest step : 1.289855 Largest / Average step : 2.067416 Largest / Smallest step : 2.666667 Median interval of one step : 40.44944 cents, amount: 19 Most common interval of one step : 40.44944 cents, amount: 19 Least squares average step : 51.72177 cents, oct.: 1189.60077 cents Scale is not proper Scale has Myhill's property chromas: 67.41573 cents and 26.96629 cents, ratio: 2.500000 generators: 6 of 310.11236 cents and 17 of 889.88764 cents ET pair of linear temperament : 27&31 Scale is distributional even Scale is a mode of a 89-tone equal temperament with octave 2/1 degrees: 3 6 9 17 20 23 26 29 32 40 43 46 49 52 55 63 66 69 72 75 83 86 89 generators: 23 and 66 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 89-tone equal temperament Step pattern alph. order: AAABAAAAABAAAAABAAAABAA Step pattern size order : SSSLSSSSSLSSSSSLSSSSLSS Interval vector is [ 0 0 19 0 0 15 0 4 11 0 8 7 0 12 3 0 16 0 0 20 0 0 22 0 0 18 0 1 14 0 5 10 0 9 6 0 13 2 0 17 0 0 21 0 ] Scale is a Constant Structure, by a margin of 13.48314 cents Scale diversity : 1.168577 Lumma stability : 0.168539 Lumma impropriety factor : 0.404494 Rothenberg efficiency : 0.695652 redundancy: 0.304348 Efficiency x scale size : 16.000000 Number of different interval sizes : 44 = 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 : 13.48314 cents Most common intervals : 310.11236 cents & inv., amount: 22 Scale is a chain of 11 triads 0.0 310.112 620.225 cents Most common triad is 0.0 310.112 889.888 cents, amount: 21 Number of recognisable fifths : 15, average 699.3258 cents Number of appreciable fifths : 13, average 701.1236 cents Formal octave complements present : 17 = 73.9130% Limited inverse transpositions : 13 Inversional symmetry on degrees : 18 Inversional symmetry on intervals : 6-7 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
23: 0 1 1 2 1 1 0 1 1 2 1 1 0 1 1 2 1 1 0 1 2 1 1 N T3 SD: 20.9933 c. M: 40.4494 c. 26: 1 0 1 3 1 0 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 N SD: 18.4861 c. M: 34.7450 c. 27: 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 P M ME S SD: 7.2710 c. M:-13.9825 c. 31: 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 3 1 1 N M DE S SD: 3.1664 c. M: 6.0892 c. 58: 2 2 2 5 2 2 2 2 2 5 2 2 2 2 2 5 2 2 2 2 5 2 2 N M DE S SD: 1.6924 c. M:-3.2546 c. 89: 3 3 3 8 3 3 3 3 3 8 3 3 3 3 3 8 3 3 3 3 8 3 3 N M DE 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: 0.4157 cents 3 .. 6 match: 3 H SD: 13.8832 cents 4 .. 8 match: 4 H SD: 1.2894 cents 5 .. 10 match: 5 H SD: 7.3667 cents 6 .. 12 match: 6 H SD: 9.4234 cents 7 .. 14 match: 7 H SD: 8.9822 cents 8 .. 16 match: 8 H SD: 5.3629 cents 9 .. 18 match: 9 H SD: 8.0927 cents 10 .. 20 match: 10 H SD: 6.3089 cents 11 .. 22 match: 11 H SD: 4.5958 cents 12 .. 24 match: 11 S SD: 5.6541 cents 13 .. 26 match: 12 SD: 4.6133 cents 14 .. 28 match: 12 SD: 2.4085 cents 15 .. 30 match: 13 SD: 4.2685 cents 16 .. 32 match: 15 SD: 4.5681 cents 17 .. 34 match: 15 S SD: 4.2175 cents 18 .. 36 match: 15 SD: 3.3352 cents 19 .. 38 match: 15 SD: 2.8606 cents 20 .. 40 match: 17 SD: 2.8235 cents 21 .. 42 match: 18 SD: 3.0957 cents 22 .. 44 match: 18 S SD: 2.9325 cents 23 .. 46 match: 19 SD: 3.3148 cents 24 .. 48 match: 20 SD: 2.3804 cents 25 .. 50 match: 19 SD: 2.3980 cents 26 .. 52 match: 19 SD: 3.0125 cents 27 .. 54 match: 20 SD: 2.7482 cents 28 .. 56 match: 21 SD: 1.8703 cents 29 .. 58 match: 20 SD: 3.0686 cents 30 .. 60 match: 21 SD: 1.9510 cents 31 .. 62 match: 22 SD: 2.4868 cents 32 .. 64 match: 21 SD: 2.1753 cents 33 .. 66 match: 21 SD: 2.6045 cents 34 .. 68 match: 22 SD: 2.4339 cents 35 .. 70 match: 23 SD: 1.8600 cents 36 .. 72 match: 23 SD: 1.7536 cents 40 .. 80 match: 23 SD: 1.5512 cents 41 .. 82 match: 23 SD: 1.4756 cents 43 .. 86 match: 23 SD: 1.4487 cents 52 .. 104 match: 23 SD: 1.3482 cents 56 .. 112 match: 23 SD: 1.2901 cents 58 .. 116 match: 23 SD: 1.1078 cents 66 .. 132 match: 23 SD: 1.0512 cents 71 .. 142 match: 23 SD: 0.9238 cents 77 .. 154 match: 23 SD: 0.9006 cents 80 .. 160 match: 23 SD: 0.8907 cents 82 .. 164 match: 23 SD: 0.7279 cents 84 .. 168 match: 23 SD: 0.7170 cents 88 .. 176 match: 23 SD: 0.6865 cents 106 .. 212 match: 23 SD: 0.6059 cents 107 .. 214 match: 23 SD: 0.5915 cents 112 .. 224 match: 23 SD: 0.5565 cents 120 .. 240 match: 23 SD: 0.5499 cents 121 .. 242 match: 23 SD: 0.5259 cents 125 .. 250 match: 23 SD: 0.4930 cents 126 .. 252 match: 23 SD: 0.4858 cents 134 .. 268 match: 23 SD: 0.4792 cents 142 .. 284 match: 23 SD: 0.4175 cents 153 .. 306 match: 23 SD: 0.4136 cents 164 .. 328 match: 23 SD: 0.3953 cents 166 .. 332 match: 23 SD: 0.3921 cents 169 .. 338 match: 23 SD: 0.3870 cents 170 .. 340 match: 23 SD: 0.3394 cents 183 .. 366 match: 23 SD: 0.3297 cents 204 .. 408 match: 23 SD: 0.3064 cents 208 .. 416 match: 23 SD: 0.2953 cents 209 .. 418 match: 23 SD: 0.2799 cents 246 .. 492 match: 23 SD: 0.2781 cents 248 .. 496 match: 23 SD: 0.2744 cents 249 .. 498 match: 23 SD: 0.2381 cents 254 .. 508 match: 23 SD: 0.2353 cents 289 .. 578 match: 23 SD: 0.2350 cents 290 .. 580 match: 23 SD: 0.1884 cents 332 .. 664 match: 23 SD: 0.1817 cents 339 .. 678 match: 23 SD: 0.1789 cents 372 .. 744 match: 23 SD: 0.1690 cents 374 .. 748 match: 23 SD: 0.1358 cents 458 .. 916 match: 23 SD: 0.1310 cents 481 .. 962 match: 23 SD: 0.1285 cents 509 .. 1018 match: 23 SD: 0.1252 cents 540 .. 1080 match: 23 SD: 0.1161 cents 545 .. 1090 match: 23 SD: 0.1099 cents 561 .. 1122 match: 23 SD: 0.1098 cents 580 .. 1160 match: 23 SD: 0.1050 cents