Scala analysis: myna23_tuning_66272_66321
23 notes of myna temperament, 7-limit TOP tuning (Paul Erlich).
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: 187.700 cents 187.700000 4: 228.430 cents 228.430000 5: 269.160 cents 269.160000 6: 309.890 cents 309.890000 7: 350.620 cents 350.620000 8: 391.350 cents 391.350000 9: 497.590 cents 497.590000 10: 538.320 cents 538.320000 11: 579.050 cents 579.050000 12: 619.780 cents 619.780000 13: 660.510 cents 660.510000 14: 701.240 cents 701.240000 15: 807.480 cents 807.480000 16: 848.210 cents 848.210000 17: 888.940 cents 888.940000 18: 929.670 cents 929.670000 19: 970.400 cents 970.400000 20: 1011.130 cents 1011.130000 21: 1117.370 cents 1117.370000 22: 1158.100 cents 1158.100000 23: 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: 106.2400 cents 106.2400 4: 40.7300 cents 40.7300 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: 106.2400 cents 106.2400 10: 40.7300 cents 40.7300 11: 40.7300 cents 40.7300 12: 40.7300 cents 40.7300 13: 40.7300 cents 40.7300 14: 40.7300 cents 40.7300 15: 106.2400 cents 106.2400 16: 40.7300 cents 40.7300 17: 40.7300 cents 40.7300 18: 40.7300 cents 40.7300 19: 40.7300 cents 40.7300 20: 40.7300 cents 40.7300 21: 106.2400 cents 106.2400 22: 40.7300 cents 40.7300 23: 40.7300 cents 40.7300
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 19 40.73000 cents 1: 4 106.24000 cents 2: 15 81.46000 cents 2: 8 146.97000 cents 3: 11 122.19000 cents 3: 12 187.70000 cents 4: 7 162.92000 cents 4: 16 228.43000 cents 5: 3 203.65000 cents 5: 20 269.16000 cents 6: 22 309.89000 cents 6: 1 375.40000 cents 7: 18 350.62000 cents 7: 5 416.13000 cents 8: 14 391.35000 cents 8: 9 456.86000 cents 9: 10 432.08000 cents 9: 13 497.59000 cents 10: 6 472.81000 cents 10: 17 538.32000 cents 11: 2 513.54000 cents 11: 21 579.05000 cents 12: 21 619.78000 cents 12: 2 685.29000 cents 13: 17 660.51000 cents 13: 6 726.02000 cents 14: 13 701.24000 cents 14: 10 766.75000 cents 15: 9 741.97000 cents 15: 14 807.48000 cents 16: 5 782.70000 cents 16: 18 848.21000 cents 17: 1 823.43000 cents 17: 22 888.94000 cents 18: 20 929.67000 cents 18: 3 995.18000 cents 19: 16 970.40000 cents 19: 7 1035.91000 cents 20: 12 1011.13000 cents 20: 11 1076.64000 cents 21: 8 1051.86000 cents 21: 15 1117.37000 cents 22: 4 1092.59000 cents 22: 19 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 0.0 : 40.7 81.5 187.7 228.4 269.2 309.9 350.6 391.4 497.6 538.3 579.0 619.8 660.5 701.2 807.5 848.2 888.9 929.7 970.4 1011.1 1117.4 1158.1 1198.8 40.7 : 40.7 147.0 187.7 228.4 269.2 309.9 350.6 456.9 497.6 538.3 579.1 619.8 660.5 766.8 807.5 848.2 888.9 929.7 970.4 1076.6 1117.4 1158.1 1198.8 81.5 : 106.2 147.0 187.7 228.4 269.2 309.9 416.1 456.9 497.6 538.3 579.0 619.8 726.0 766.8 807.5 848.2 888.9 929.7 1035.9 1076.6 1117.4 1158.1 1198.8 187.7 : 40.7 81.5 122.2 162.9 203.7 309.9 350.6 391.4 432.1 472.8 513.5 619.8 660.5 701.2 742.0 782.7 823.4 929.7 970.4 1011.1 1051.9 1092.6 1198.8 228.4 : 40.7 81.5 122.2 162.9 269.2 309.9 350.6 391.4 432.1 472.8 579.1 619.8 660.5 701.2 742.0 782.7 888.9 929.7 970.4 1011.1 1051.9 1158.1 1198.8 269.2 : 40.7 81.5 122.2 228.4 269.2 309.9 350.6 391.4 432.1 538.3 579.1 619.8 660.5 701.2 742.0 848.2 888.9 929.7 970.4 1011.1 1117.4 1158.1 1198.8 309.9 : 40.7 81.5 187.7 228.4 269.2 309.9 350.6 391.4 497.6 538.3 579.1 619.8 660.5 701.2 807.5 848.2 888.9 929.7 970.4 1076.6 1117.4 1158.1 1198.8 350.6 : 40.7 147.0 187.7 228.4 269.2 309.9 350.6 456.9 497.6 538.3 579.0 619.8 660.5 766.7 807.5 848.2 888.9 929.7 1035.9 1076.6 1117.4 1158.1 1198.8 391.4 : 106.2 147.0 187.7 228.4 269.2 309.9 416.1 456.9 497.6 538.3 579.0 619.8 726.0 766.8 807.5 848.2 888.9 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 497.6 : 40.7 81.5 122.2 162.9 203.7 309.9 350.6 391.4 432.1 472.8 513.5 619.8 660.5 701.2 742.0 782.7 888.9 929.7 970.4 1011.1 1051.9 1092.6 1198.8 538.3 : 40.7 81.5 122.2 162.9 269.2 309.9 350.6 391.3 432.1 472.8 579.0 619.8 660.5 701.2 742.0 848.2 888.9 929.7 970.4 1011.1 1051.9 1158.1 1198.8 579.0 : 40.7 81.5 122.2 228.4 269.2 309.9 350.6 391.4 432.1 538.3 579.1 619.8 660.5 701.2 807.5 848.2 888.9 929.7 970.4 1011.1 1117.4 1158.1 1198.8 619.8 : 40.7 81.5 187.7 228.4 269.2 309.9 350.6 391.4 497.6 538.3 579.0 619.8 660.5 766.7 807.5 848.2 888.9 929.7 970.4 1076.6 1117.4 1158.1 1198.8 660.5 : 40.7 147.0 187.7 228.4 269.2 309.9 350.6 456.9 497.6 538.3 579.0 619.8 726.0 766.8 807.5 848.2 888.9 929.7 1035.9 1076.6 1117.4 1158.1 1198.8 701.2 : 106.2 147.0 187.7 228.4 269.2 309.9 416.1 456.9 497.6 538.3 579.0 685.3 726.0 766.7 807.5 848.2 888.9 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 807.5 : 40.7 81.5 122.2 162.9 203.6 309.9 350.6 391.3 432.1 472.8 579.0 619.8 660.5 701.2 742.0 782.7 888.9 929.7 970.4 1011.1 1051.9 1092.6 1198.8 848.2 : 40.7 81.5 122.2 162.9 269.2 309.9 350.6 391.3 432.1 538.3 579.0 619.8 660.5 701.2 742.0 848.2 888.9 929.7 970.4 1011.1 1051.9 1158.1 1198.8 888.9 : 40.7 81.5 122.2 228.4 269.2 309.9 350.6 391.4 497.6 538.3 579.0 619.8 660.5 701.2 807.5 848.2 888.9 929.7 970.4 1011.1 1117.4 1158.1 1198.8 929.7 : 40.7 81.5 187.7 228.4 269.2 309.9 350.6 456.9 497.6 538.3 579.0 619.8 660.5 766.7 807.5 848.2 888.9 929.7 970.4 1076.6 1117.4 1158.1 1198.8 970.4 : 40.7 147.0 187.7 228.4 269.2 309.9 416.1 456.9 497.6 538.3 579.0 619.8 726.0 766.7 807.5 848.2 888.9 929.7 1035.9 1076.6 1117.4 1158.1 1198.8 1011.1: 106.2 147.0 187.7 228.4 269.2 375.4 416.1 456.9 497.6 538.3 579.0 685.3 726.0 766.7 807.5 848.2 888.9 995.2 1035.9 1076.6 1117.4 1158.1 1198.8 1117.4: 40.7 81.5 122.2 162.9 269.2 309.9 350.6 391.4 432.1 472.8 579.1 619.8 660.5 701.2 742.0 782.7 888.9 929.7 970.4 1011.1 1051.9 1092.6 1198.8 1158.1: 40.7 81.5 122.2 228.4 269.2 309.9 350.6 391.4 432.1 538.3 579.0 619.8 660.5 701.2 742.0 848.2 888.9 929.7 970.4 1011.1 1051.9 1158.1 1198.8 1198.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.7300 .. 106.2400 cents 65.51000 cents 40.73000 cents 2: 81.4600 .. 146.9700 cents 65.51000 cents -24.78000 cents 3: 122.1900 .. 187.7000 cents 65.51000 cents -24.78000 cents 4: 162.9200 .. 228.4300 cents 65.51000 cents -24.78000 cents 5: 203.6500 .. 269.1600 cents 65.51000 cents -24.78000 cents 6: 309.8900 .. 375.4000 cents 65.51000 cents 40.73000 cents 7: 350.6200 .. 416.1300 cents 65.51000 cents -24.78000 cents 8: 391.3500 .. 456.8600 cents 65.51000 cents -24.78000 cents 9: 432.0800 .. 497.5900 cents 65.51000 cents -24.78000 cents 10: 472.8100 .. 538.3200 cents 65.51000 cents -24.78000 cents 11: 513.5400 .. 579.0500 cents 65.51000 cents -24.78000 cents 12: 619.7800 .. 685.2900 cents 65.51000 cents 40.73000 cents 13: 660.5100 .. 726.0200 cents 65.51000 cents -24.78000 cents 14: 701.2400 .. 766.7500 cents 65.51000 cents -24.78000 cents 15: 741.9700 .. 807.4800 cents 65.51000 cents -24.78000 cents 16: 782.7000 .. 848.2100 cents 65.51000 cents -24.78000 cents 17: 823.4300 .. 888.9400 cents 65.51000 cents -24.78000 cents 18: 929.6700 .. 995.1800 cents 65.51000 cents 40.73000 cents 19: 970.4000 .. 1035.9100 cents 65.51000 cents -24.78000 cents 20: 1011.1300 .. 1076.6400 cents 65.51000 cents -24.78000 cents 21: 1051.8600 .. 1117.3700 cents 65.51000 cents -24.78000 cents 22: 1092.5900 .. 1158.1000 cents 65.51000 cents -24.78000 cents
SHOW DATA
Number of notes : 23 -- Interval properties -- Smallest interval : 40.73000 cents, class 1 Average step (divided formal octave): 52.1230 cents Largest one step interval : 106.24000 cents Average / Smallest step : 1.279721 Largest / Average step : 2.038254 Largest / Smallest step : 2.608397 Median interval of one step : 40.73000 cents, amount: 19 Most common interval of one step : 40.73000 cents, amount: 19 Least squares average step : 52.09274 cents, oct.: 1198.13309 cents Scale is not proper Scale has Myhill's property chromas: 65.51000 cents and 24.78000 cents, ratio: 2.643664 generators: 6 of 309.89000 cents and 17 of 888.94000 cents ET pair of linear temperament : 27&31 Scale is distributional even Scale is a mode of a 677-tone equal temperament with octave 1198.830 cents degrees: 23 46 106 129 152 175 198 221 281 304 327 350 373 396 456 479 502 525 548 571 631 654 677 generators: 175 and 502 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAAABAAAAABAAAAABAA Step pattern size order : SSLSSSSSLSSSSSLSSSSSLSS Scale is a Constant Structure, by a margin of 15.95000 cents Scale diversity : 1.175100 Lumma stability : 0.169874 Lumma impropriety factor : 0.372063 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 : 15.95000 cents Most common intervals : 309.89000 cents & inv., amount: 22 Scale is a chain of 11 triads 0.0 309.890 619.780 cents Most common triad is 0.0 309.890 888.940 cents, amount: 21 Number of recognisable fifths : 13, average 701.2400 cents Number of recognisable fourths : 15, average 499.7167 cents Number of appreciable fourths : 13, average 497.5900 cents Scale contains two identical disjunct "tetrachords" of 10 notes Formal octave complements present : 23 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 11-12 -- Rational properties --
FIT/MODE
23: 0 1 2 1 1 1 0 1 2 1 1 1 0 1 2 1 1 0 1 1 2 1 1 N T3 SD: 24.6323 c. M: 43.5783 c. 24: 1 1 2 1 0 1 1 1 2 1 1 0 1 1 2 1 1 1 0 1 2 1 1 N I SD: 13.5725 c. M: 21.3263 c. 25: 1 1 2 1 1 0 1 1 2 1 1 1 1 1 2 1 1 0 1 1 2 1 1 N T3 I SD: 13.1278 c. M:-22.1708 c. 26: 1 1 2 1 1 1 1 0 3 1 1 0 1 1 3 0 1 1 1 1 2 1 1 N I SD: 13.0272 c. M: 22.4792 c. 27: 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 P M ME I SD: 6.0878 c. M: 10.0956 c. 31: 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3 1 1 1 1 1 3 1 1 N M DE I SD: 3.4129 c. M:-5.6597 c. 58: 2 2 5 2 2 2 2 2 5 2 2 2 2 2 5 2 2 2 2 2 5 2 2 N M DE I SD: 1.0099 c. M: 1.6747 c. 89: 3 3 8 3 3 3 3 3 8 3 3 3 3 3 8 3 3 3 3 3 8 3 3 N M DE I SD: 0.5307 c. M:-0.8800 c. 147: 5 5 13 5 5 5 5 5 13 5 5 5 5 5 13 5 5 5 5 5 13 5 5 N M DE I SD: 0.0772 c. M: 0.1280 c. 383: 13 13 34 13 13 13 13 13 34 13 13 13 13 13 34 13 13 13 13 13 34 13 13 N M DE I SD: 0.0641 c. M:-0.1063 c. 530: 18 18 47 18 18 18 18 18 47 18 18 18 18 18 47 18 18 18 18 18 47 18 18 N M DE I SD: 0.0249 c. M: 0.0413 c. 677: 23 23 60 23 23 23 23 23 60 23 23 23 23 23 60 23 23 23 23 23 60 23 23 N M DE I SD: 0.0027 c. M: 0.0045 c. 2178: 74 74 193 74 74 74 74 74 193 74 74 74 74 74 193 74 74 74 74 74 193 74 74 N M DE I SD: 0.0026 c. M: 0.0044 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: 6.4336 cents 7 .. 14 match: 7 H SD: 9.7403 cents 8 .. 16 match: 8 H SD: 4.6222 cents 9 .. 18 match: 9 H SD: 5.7185 cents 10 .. 20 match: 10 H SD: 5.1803 cents 11 .. 22 match: 11 H SD: 7.1667 cents 12 .. 24 match: 12 H SD: 5.5498 cents 13 .. 26 match: 11 SD: 6.5561 cents 14 .. 28 match: 13 SD: 5.3714 cents 15 .. 30 match: 13 SD: 3.5584 cents 16 .. 32 match: 14 SD: 3.7891 cents 17 .. 34 match: 14 SD: 3.4878 cents 18 .. 36 match: 16 SD: 3.2453 cents 19 .. 38 match: 17 S SD: 3.0394 cents 20 .. 40 match: 17 SD: 2.6484 cents 21 .. 42 match: 18 SD: 3.1239 cents 22 .. 44 match: 18 SD: 2.9086 cents 23 .. 46 match: 17 SD: 2.9306 cents 24 .. 48 match: 19 SD: 2.0880 cents 25 .. 50 match: 19 SD: 2.4544 cents 26 .. 52 match: 20 SD: 3.1496 cents 27 .. 54 match: 20 SD: 2.4904 cents 28 .. 56 match: 21 SD: 2.1767 cents 29 .. 58 match: 20 SD: 3.1244 cents 30 .. 60 match: 22 SD: 2.0874 cents 31 .. 62 match: 21 SD: 2.5393 cents 32 .. 64 match: 22 SD: 2.4016 cents 33 .. 66 match: 22 SD: 2.4672 cents 34 .. 68 match: 23 SD: 2.3247 cents 35 .. 70 match: 23 SD: 1.6789 cents 36 .. 72 match: 23 SD: 1.6177 cents 41 .. 82 match: 23 SD: 1.6003 cents 42 .. 84 match: 23 SD: 1.4834 cents 44 .. 88 match: 23 SD: 1.4406 cents 52 .. 104 match: 23 SD: 1.3239 cents 58 .. 116 match: 23 SD: 1.1832 cents 60 .. 120 match: 23 SD: 1.1599 cents 63 .. 126 match: 23 SD: 1.0791 cents 66 .. 132 match: 23 SD: 1.0573 cents 71 .. 142 match: 23 SD: 0.9836 cents 72 .. 144 match: 23 SD: 0.9779 cents 76 .. 152 match: 23 SD: 0.7935 cents 84 .. 168 match: 23 SD: 0.7335 cents 86 .. 172 match: 23 SD: 0.6949 cents 88 .. 176 match: 23 SD: 0.6862 cents 106 .. 212 match: 23 SD: 0.5702 cents 120 .. 240 match: 23 SD: 0.5687 cents 121 .. 242 match: 23 SD: 0.4825 cents 142 .. 284 match: 23 SD: 0.4204 cents 162 .. 324 match: 23 SD: 0.4181 cents 164 .. 328 match: 23 SD: 0.4100 cents 165 .. 330 match: 23 SD: 0.3610 cents 183 .. 366 match: 23 SD: 0.3454 cents 204 .. 408 match: 23 SD: 0.2803 cents 209 .. 418 match: 23 SD: 0.2794 cents 244 .. 488 match: 23 SD: 0.2568 cents 249 .. 498 match: 23 SD: 0.2349 cents 286 .. 572 match: 23 SD: 0.2254 cents 290 .. 580 match: 23 SD: 0.2097 cents 291 .. 582 match: 23 SD: 0.1834 cents 332 .. 664 match: 23 SD: 0.1789 cents 367 .. 734 match: 23 SD: 0.1768 cents 374 .. 747 match: 23 SD: 0.1741 cents 375 .. 749 match: 23 SD: 0.1632 cents 411 .. 821 match: 23 SD: 0.1376 cents 453 .. 905 match: 23 SD: 0.1328 cents 463 .. 925 match: 23 SD: 0.1238 cents 504 .. 1007 match: 23 SD: 0.1138 cents 516 .. 1031 match: 23 SD: 0.1087 cents 560 .. 1119 match: 23 SD: 0.1082 cents 587 .. 1173 match: 23 SD: 0.0999 cents