Scala analysis: xen18-erlich-myna-27
4L 23s MOS for Myna, L=65.51, s=40.73
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40.730 cents 40.730000 2: 81.460 cents 81.460000 3: 122.190 cents 122.190000 4: 187.700 cents 187.700000 5: 228.430 cents 228.430000 6: 269.160 cents 269.160000 7: 309.890 cents 309.890000 8: 350.620 cents 350.620000 9: 391.350 cents 391.350000 10: 432.080 cents 432.080000 11: 497.590 cents 497.590000 12: 538.320 cents 538.320000 13: 579.050 cents 579.050000 14: 619.780 cents 619.780000 15: 660.510 cents 660.510000 16: 701.240 cents 701.240000 17: 766.750 cents 766.750000 18: 807.480 cents 807.480000 19: 848.210 cents 848.210000 20: 888.940 cents 888.940000 21: 929.670 cents 929.670000 22: 970.400 cents 970.400000 23: 1011.130 cents 1011.130000 24: 1076.640 cents 1076.640000 25: 1117.370 cents 1117.370000 26: 1158.100 cents 1158.100000 27: 1198.830 cents 1198.830000
SHOW/INTERVAL
0: 40.7300 cents 40.7300 1: 40.7300 cents 40.7300 2: 40.7300 cents 40.7300 3: 40.7300 cents 40.7300 4: 65.5100 cents 65.5100 5: 40.7300 cents 40.7300 6: 40.7300 cents 40.7300 7: 40.7300 cents 40.7300 8: 40.7300 cents 40.7300 9: 40.7300 cents 40.7300 10: 40.7300 cents 40.7300 11: 65.5100 cents 65.5100 12: 40.7300 cents 40.7300 13: 40.7300 cents 40.7300 14: 40.7300 cents 40.7300 15: 40.7300 cents 40.7300 16: 40.7300 cents 40.7300 17: 65.5100 cents 65.5100 18: 40.7300 cents 40.7300 19: 40.7300 cents 40.7300 20: 40.7300 cents 40.7300 21: 40.7300 cents 40.7300 22: 40.7300 cents 40.7300 23: 40.7300 cents 40.7300 24: 65.5100 cents 65.5100 25: 40.7300 cents 40.7300 26: 40.7300 cents 40.7300 27: 40.7300 cents 40.7300
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 23 40.73000 cents 1: 4 65.51000 cents 2: 19 81.46000 cents 2: 8 106.24000 cents 3: 15 122.19000 cents 3: 12 146.97000 cents 4: 11 162.92000 cents 4: 16 187.70000 cents 5: 7 203.65000 cents 5: 20 228.43000 cents 6: 3 244.38000 cents 6: 24 269.16000 cents 7: 26 309.89000 cents 7: 1 334.67000 cents 8: 22 350.62000 cents 8: 5 375.40000 cents 9: 18 391.35000 cents 9: 9 416.13000 cents 10: 14 432.08000 cents 10: 13 456.86000 cents 11: 10 472.81000 cents 11: 17 497.59000 cents 12: 6 513.54000 cents 12: 21 538.32000 cents 13: 2 554.27000 cents 13: 25 579.05000 cents 14: 25 619.78000 cents 14: 2 644.56000 cents 15: 21 660.51000 cents 15: 6 685.29000 cents 16: 17 701.24000 cents 16: 10 726.02000 cents 17: 13 741.97000 cents 17: 14 766.75000 cents 18: 9 782.70000 cents 18: 18 807.48000 cents 19: 5 823.43000 cents 19: 22 848.21000 cents 20: 1 864.16000 cents 20: 26 888.94000 cents 21: 24 929.67000 cents 21: 3 954.45000 cents 22: 20 970.40000 cents 22: 7 995.18000 cents 23: 16 1011.13000 cents 23: 11 1035.91000 cents 24: 12 1051.86000 cents 24: 15 1076.64000 cents 25: 8 1092.59000 cents 25: 19 1117.37000 cents 26: 4 1133.32000 cents 26: 23 1158.10000 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 24 25 26 27 0.0 : 40.7 81.5 122.2 187.7 228.4 269.2 309.9 350.6 391.4 432.1 497.6 538.3 579.0 619.8 660.5 701.2 766.8 807.5 848.2 888.9 929.7 970.4 1011.1 1076.6 1117.4 1158.1 1198.8 40.7 : 40.7 81.5 147.0 187.7 228.4 269.2 309.9 350.6 391.4 456.9 497.6 538.3 579.1 619.8 660.5 726.0 766.8 807.5 848.2 888.9 929.7 970.4 1035.9 1076.6 1117.4 1158.1 1198.8 81.5 : 40.7 106.2 147.0 187.7 228.4 269.2 309.9 350.6 416.1 456.9 497.6 538.3 579.0 619.8 685.3 726.0 766.8 807.5 848.2 888.9 929.7 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 122.2 : 65.5 106.2 147.0 187.7 228.4 269.2 309.9 375.4 416.1 456.9 497.6 538.3 579.1 644.6 685.3 726.0 766.8 807.5 848.2 888.9 954.5 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 187.7 : 40.7 81.5 122.2 162.9 203.7 244.4 309.9 350.6 391.4 432.1 472.8 513.5 579.1 619.8 660.5 701.2 742.0 782.7 823.4 888.9 929.7 970.4 1011.1 1051.9 1092.6 1133.3 1198.8 228.4 : 40.7 81.5 122.2 162.9 203.6 269.2 309.9 350.6 391.4 432.1 472.8 538.3 579.1 619.8 660.5 701.2 742.0 782.7 848.2 888.9 929.7 970.4 1011.1 1051.9 1092.6 1158.1 1198.8 269.2 : 40.7 81.5 122.2 162.9 228.4 269.2 309.9 350.6 391.4 432.1 497.6 538.3 579.1 619.8 660.5 701.2 742.0 807.5 848.2 888.9 929.7 970.4 1011.1 1051.9 1117.4 1158.1 1198.8 309.9 : 40.7 81.5 122.2 187.7 228.4 269.2 309.9 350.6 391.4 456.9 497.6 538.3 579.1 619.8 660.5 701.2 766.8 807.5 848.2 888.9 929.7 970.4 1011.1 1076.6 1117.4 1158.1 1198.8 350.6 : 40.7 81.5 147.0 187.7 228.4 269.2 309.9 350.6 416.1 456.9 497.6 538.3 579.0 619.8 660.5 726.0 766.7 807.5 848.2 888.9 929.7 970.4 1035.9 1076.6 1117.4 1158.1 1198.8 391.4 : 40.7 106.2 147.0 187.7 228.4 269.2 309.9 375.4 416.1 456.9 497.6 538.3 579.0 619.8 685.3 726.0 766.8 807.5 848.2 888.9 929.7 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 432.1 : 65.5 106.2 147.0 187.7 228.4 269.2 334.7 375.4 416.1 456.9 497.6 538.3 579.0 644.6 685.3 726.0 766.8 807.5 848.2 888.9 954.4 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 497.6 : 40.7 81.5 122.2 162.9 203.7 269.2 309.9 350.6 391.4 432.1 472.8 513.5 579.1 619.8 660.5 701.2 742.0 782.7 823.4 888.9 929.7 970.4 1011.1 1051.9 1092.6 1133.3 1198.8 538.3 : 40.7 81.5 122.2 162.9 228.4 269.2 309.9 350.6 391.3 432.1 472.8 538.3 579.0 619.8 660.5 701.2 742.0 782.7 848.2 888.9 929.7 970.4 1011.1 1051.9 1092.6 1158.1 1198.8 579.0 : 40.7 81.5 122.2 187.7 228.4 269.2 309.9 350.6 391.4 432.1 497.6 538.3 579.1 619.8 660.5 701.2 742.0 807.5 848.2 888.9 929.7 970.4 1011.1 1051.9 1117.4 1158.1 1198.8 619.8 : 40.7 81.5 147.0 187.7 228.4 269.2 309.9 350.6 391.4 456.9 497.6 538.3 579.0 619.8 660.5 701.2 766.7 807.5 848.2 888.9 929.7 970.4 1011.1 1076.6 1117.4 1158.1 1198.8 660.5 : 40.7 106.2 147.0 187.7 228.4 269.2 309.9 350.6 416.1 456.9 497.6 538.3 579.0 619.8 660.5 726.0 766.8 807.5 848.2 888.9 929.7 970.4 1035.9 1076.6 1117.4 1158.1 1198.8 701.2 : 65.5 106.2 147.0 187.7 228.4 269.2 309.9 375.4 416.1 456.9 497.6 538.3 579.0 619.8 685.3 726.0 766.7 807.5 848.2 888.9 929.7 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 766.8 : 40.7 81.5 122.2 162.9 203.7 244.4 309.9 350.6 391.4 432.1 472.8 513.5 554.3 619.8 660.5 701.2 742.0 782.7 823.4 864.2 929.7 970.4 1011.1 1051.9 1092.6 1133.3 1198.8 807.5 : 40.7 81.5 122.2 162.9 203.6 269.2 309.9 350.6 391.3 432.1 472.8 513.5 579.0 619.8 660.5 701.2 742.0 782.7 823.4 888.9 929.7 970.4 1011.1 1051.9 1092.6 1158.1 1198.8 848.2 : 40.7 81.5 122.2 162.9 228.4 269.2 309.9 350.6 391.3 432.1 472.8 538.3 579.0 619.8 660.5 701.2 742.0 782.7 848.2 888.9 929.7 970.4 1011.1 1051.9 1117.4 1158.1 1198.8 888.9 : 40.7 81.5 122.2 187.7 228.4 269.2 309.9 350.6 391.4 432.1 497.6 538.3 579.0 619.8 660.5 701.2 742.0 807.5 848.2 888.9 929.7 970.4 1011.1 1076.6 1117.4 1158.1 1198.8 929.7 : 40.7 81.5 147.0 187.7 228.4 269.2 309.9 350.6 391.3 456.9 497.6 538.3 579.0 619.8 660.5 701.2 766.7 807.5 848.2 888.9 929.7 970.4 1035.9 1076.6 1117.4 1158.1 1198.8 970.4 : 40.7 106.2 147.0 187.7 228.4 269.2 309.9 350.6 416.1 456.9 497.6 538.3 579.0 619.8 660.5 726.0 766.7 807.5 848.2 888.9 929.7 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 1011.1: 65.5 106.2 147.0 187.7 228.4 269.2 309.9 375.4 416.1 456.9 497.6 538.3 579.0 619.8 685.3 726.0 766.7 807.5 848.2 888.9 954.5 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 1076.6: 40.7 81.5 122.2 162.9 203.6 244.4 309.9 350.6 391.3 432.1 472.8 513.5 554.3 619.8 660.5 701.2 742.0 782.7 823.4 888.9 929.7 970.4 1011.1 1051.9 1092.6 1133.3 1198.8 1117.4: 40.7 81.5 122.2 162.9 203.7 269.2 309.9 350.6 391.4 432.1 472.8 513.5 579.1 619.8 660.5 701.2 742.0 782.7 848.2 888.9 929.7 970.4 1011.1 1051.9 1092.6 1158.1 1198.8 1158.1: 40.7 81.5 122.2 162.9 228.4 269.2 309.9 350.6 391.4 432.1 472.8 538.3 579.0 619.8 660.5 701.2 742.0 807.5 848.2 888.9 929.7 970.4 1011.1 1051.9 1117.4 1158.1 1198.8 1198.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.7300 .. 65.5100 cents 24.78000 cents 40.73000 cents 2: 81.4600 .. 106.2400 cents 24.78000 cents 15.95000 cents 3: 122.1900 .. 146.9700 cents 24.78000 cents 15.95000 cents 4: 162.9200 .. 187.7000 cents 24.78000 cents 15.95000 cents 5: 203.6500 .. 228.4300 cents 24.78000 cents 15.95000 cents 6: 244.3800 .. 269.1600 cents 24.78000 cents 15.95000 cents 7: 309.8900 .. 334.6700 cents 24.78000 cents 40.73000 cents 8: 350.6200 .. 375.4000 cents 24.78000 cents 15.95000 cents 9: 391.3500 .. 416.1300 cents 24.78000 cents 15.95000 cents 10: 432.0800 .. 456.8600 cents 24.78000 cents 15.95000 cents 11: 472.8100 .. 497.5900 cents 24.78000 cents 15.95000 cents 12: 513.5400 .. 538.3200 cents 24.78000 cents 15.95000 cents 13: 554.2700 .. 579.0500 cents 24.78000 cents 15.95000 cents 14: 619.7800 .. 644.5600 cents 24.78000 cents 40.73000 cents 15: 660.5100 .. 685.2900 cents 24.78000 cents 15.95000 cents 16: 701.2400 .. 726.0200 cents 24.78000 cents 15.95000 cents 17: 741.9700 .. 766.7500 cents 24.78000 cents 15.95000 cents 18: 782.7000 .. 807.4800 cents 24.78000 cents 15.95000 cents 19: 823.4300 .. 848.2100 cents 24.78000 cents 15.95000 cents 20: 864.1600 .. 888.9400 cents 24.78000 cents 15.95000 cents 21: 929.6700 .. 954.4500 cents 24.78000 cents 40.73000 cents 22: 970.4000 .. 995.1800 cents 24.78000 cents 15.95000 cents 23: 1011.1300 .. 1035.9100 cents 24.78000 cents 15.95000 cents 24: 1051.8600 .. 1076.6400 cents 24.78000 cents 15.95000 cents 25: 1092.5900 .. 1117.3700 cents 24.78000 cents 15.95000 cents 26: 1133.3200 .. 1158.1000 cents 24.78000 cents 15.95000 cents
SHOW DATA
Number of notes : 27 -- Interval properties -- Smallest interval : 40.73000 cents, class 1 Average step (divided formal octave): 44.4011 cents Largest one step interval : 65.51000 cents Average / Smallest step : 1.090133 Largest / Average step : 1.475414 Largest / Smallest step : 1.608397 Median interval of one step : 40.73000 cents, amount: 23 Most common interval of one step : 40.73000 cents, amount: 23 Least squares average step : 44.44521 cents, oct.: 1200.02073 cents Scale is strictly proper Scale has Myhill's property chromas: 24.78000 cents and 15.95000 cents, ratio: 1.553605 generators: 7 of 309.89000 cents and 20 of 888.94000 cents ET pair of linear temperament : 27&31 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 677-tone equal temperament with octave 1198.830 cents degrees: 23 46 69 106 129 152 175 198 221 244 281 304 327 350 373 396 433 456 479 502 525 548 571 608 631 654 677 generators: 175 and 502 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAAABAAAAABAAAAAABAAA Step pattern size order : SSSLSSSSSSLSSSSSLSSSSSSLSSS Scale is a Constant Structure, by a margin of 15.95000 cents Scale diversity : 1.176388 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.462576 Rothenberg efficiency : 0.691358 redundancy: 0.308642 Efficiency x scale size : 18.666667 Number of different interval sizes : 52 = 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 : 15.95000 cents Most common intervals : 309.89000 cents & inv., amount: 26 Scale is a chain of 13 triads 0.0 432.080 888.940 cents Most common triad is 0.0 309.890 888.940 cents, amount: 25 Number of recognisable fifths : 17, average 701.2400 cents Number of recognisable fourths : 23, average 501.7509 cents Number of appreciable fourths : 17, average 497.5900 cents Scale contains two identical disjunct "tetrachords" of 12 notes Best minor thirds form a closed circle Formal octave complements present : 27 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 13-14 -- Rational properties --
FIT/MODE
27: 1 1 1 1 1 1 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: 7.1485 c. M: 11.9311 c. 31: 1 1 1 2 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 P M ME I SD: 4.0075 c. M: 6.6887 c. 58: 2 2 2 3 2 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 3 2 2 2 SP M ME I SD: 1.1858 c. M: 1.9791 c. 89: 3 3 3 5 3 3 3 3 3 3 5 3 3 3 3 3 5 3 3 3 3 3 3 5 3 3 3 SP M DE I SD: 0.6231 c. M: 1.0400 c. 147: 5 5 5 8 5 5 5 5 5 5 8 5 5 5 5 5 8 5 5 5 5 5 5 8 5 5 5 SP M DE I SD: 0.0906 c. M: 0.1512 c. 383: 13 13 13 21 13 13 13 13 13 13 21 13 13 13 13 13 21 13 13 13 13 13 13 21 13 13 13 SP M DE I SD: 0.0752 c. M: 0.1256 c. 530: 18 18 18 29 18 18 18 18 18 18 29 18 18 18 18 18 29 18 18 18 18 18 18 29 18 18 18 SP M DE I SD: 0.0292 c. M: 0.0488 c. 677: 23 23 23 37 23 23 23 23 23 23 37 23 23 23 23 23 37 23 23 23 23 23 23 37 23 23 23 SP M DE I SD: 0.0032 c. M: 0.0054 c. 2178: 74 74 74 119 74 74 74 74 74 74 119 74 74 74 74 74 119 74 74 74 74 74 74 119 74 74 74 SP M DE I SD: 0.0031 c. M: 0.0052 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 1.1700 cents 2 .. 4 match: 2 H SD: 0.6856 cents 3 .. 6 match: 3 H SD: 1.5834 cents 4 .. 8 match: 4 H SD: 1.3629 cents 5 .. 10 match: 5 H SD: 2.2518 cents 6 .. 12 match: 6 H SD: 4.6319 cents 7 .. 14 match: 7 H SD: 2.5044 cents 8 .. 16 match: 8 H SD: 3.2008 cents 9 .. 18 match: 9 H SD: 3.2213 cents 10 .. 20 match: 10 H SD: 3.5944 cents 11 .. 22 match: 11 H SD: 4.6398 cents 12 .. 24 match: 12 H SD: 3.3044 cents 13 .. 26 match: 13 H SD: 4.6549 cents 14 .. 28 match: 14 H SD: 2.4589 cents 15 .. 30 match: 15 H SD: 3.0284 cents 16 .. 32 match: 16 H SD: 3.2648 cents 17 .. 34 match: 16 S SD: 3.6447 cents 18 .. 36 match: 17 S SD: 2.4033 cents 19 .. 38 match: 18 S SD: 3.0588 cents 20 .. 40 match: 20 H SD: 2.6058 cents 21 .. 42 match: 20 SD: 2.6545 cents 22 .. 44 match: 21 SD: 2.7154 cents 23 .. 46 match: 21 SD: 2.9642 cents 24 .. 48 match: 23 SD: 2.1299 cents 25 .. 50 match: 23 SD: 2.2137 cents 26 .. 52 match: 23 SD: 2.9463 cents 27 .. 54 match: 24 SD: 2.2359 cents 28 .. 56 match: 25 SD: 1.9507 cents 29 .. 58 match: 24 SD: 2.6660 cents 30 .. 60 match: 26 SD: 2.0474 cents 31 .. 62 match: 25 SD: 2.2915 cents 32 .. 64 match: 25 SD: 2.0844 cents 33 .. 66 match: 25 SD: 2.3653 cents 34 .. 68 match: 26 SD: 2.1568 cents 35 .. 70 match: 27 SD: 1.7291 cents 36 .. 72 match: 27 SD: 1.5348 cents 41 .. 82 match: 27 SD: 1.4778 cents 42 .. 84 match: 27 SD: 1.3453 cents 52 .. 104 match: 27 SD: 1.1812 cents 58 .. 116 match: 27 SD: 1.1292 cents 60 .. 120 match: 27 SD: 1.1117 cents 63 .. 126 match: 27 SD: 1.0166 cents 66 .. 132 match: 27 SD: 0.9513 cents 71 .. 142 match: 27 SD: 0.9020 cents 76 .. 152 match: 27 SD: 0.8625 cents 77 .. 154 match: 27 SD: 0.8300 cents 79 .. 158 match: 27 SD: 0.7722 cents 82 .. 164 match: 27 SD: 0.7394 cents 84 .. 168 match: 27 SD: 0.6751 cents 86 .. 172 match: 27 SD: 0.6677 cents 88 .. 176 match: 27 SD: 0.6575 cents 106 .. 212 match: 27 SD: 0.5246 cents 120 .. 240 match: 27 SD: 0.5191 cents 121 .. 242 match: 27 SD: 0.4701 cents 126 .. 252 match: 27 SD: 0.4697 cents 138 .. 276 match: 27 SD: 0.4264 cents 142 .. 284 match: 27 SD: 0.4203 cents 148 .. 296 match: 27 SD: 0.4189 cents 149 .. 298 match: 27 SD: 0.4160 cents 161 .. 322 match: 27 SD: 0.4154 cents 162 .. 324 match: 27 SD: 0.3726 cents 165 .. 330 match: 27 SD: 0.3225 cents 204 .. 408 match: 27 SD: 0.2527 cents 244 .. 488 match: 27 SD: 0.2332 cents 246 .. 492 match: 27 SD: 0.2269 cents 271 .. 542 match: 27 SD: 0.2254 cents 285 .. 570 match: 27 SD: 0.2100 cents 286 .. 572 match: 27 SD: 0.2043 cents 290 .. 580 match: 27 SD: 0.1965 cents 291 .. 582 match: 27 SD: 0.1881 cents 332 .. 664 match: 27 SD: 0.1651 cents 370 .. 740 match: 27 SD: 0.1551 cents 409 .. 817 match: 27 SD: 0.1531 cents 411 .. 821 match: 27 SD: 0.1373 cents 453 .. 905 match: 27 SD: 0.1311 cents 454 .. 907 match: 27 SD: 0.1267 cents 463 .. 925 match: 27 SD: 0.1129 cents 504 .. 1007 match: 27 SD: 0.1026 cents 547 .. 1093 match: 27 SD: 0.1005 cents 560 .. 1119 match: 27 SD: 0.0950 cents 587 .. 1173 match: 27 SD: 0.0935 cents