Scala analysis: magic16terzbirat
Magic[16] in regular Terzbirat tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 59.047 cents 59.047465 2: 203.175 cents 203.175117 3: 262.223 cents 262.222582 4: 321.270 cents 321.270047 5: 380.318 cents 380.317512 6: 439.365 cents 439.364977 7: 498.412 cents 498.412441 8: 642.540 cents 642.540094 9: 701.588 cents 701.587559 10: 760.635 cents 760.635023 11: 819.682 cents 819.682488 12: 878.730 cents 878.729953 13: 1022.858 cents 1022.857606 14: 1081.905 cents 1081.905070 15: 1140.953 cents 1140.952535 16: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 59.0475 cents 59.0475 1: 59.0475 cents 59.0475 2: 144.1277 cents 144.1277 3: 59.0475 cents 59.0475 4: 59.0475 cents 59.0475 5: 59.0475 cents 59.0475 6: 59.0475 cents 59.0475 7: 59.0475 cents 59.0475 8: 144.1277 cents 144.1277 9: 59.0475 cents 59.0475 10: 59.0475 cents 59.0475 11: 59.0475 cents 59.0475 12: 59.0475 cents 59.0475 13: 144.1277 cents 144.1277 14: 59.0475 cents 59.0475 15: 59.0475 cents 59.0475 16: 59.0475 cents 59.0475
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 59.04746 cents 1: 3 144.12765 cents 2: 10 118.09493 cents 2: 6 203.17512 cents 3: 7 177.14239 cents 3: 9 262.22258 cents 4: 4 236.18986 cents 4: 12 321.27005 cents 5: 1 295.23732 cents 5: 15 380.31751 cents 6: 14 439.36498 cents 6: 2 524.44516 cents 7: 11 498.41244 cents 7: 5 583.49263 cents 8: 8 557.45991 cents 8: 8 642.54009 cents 9: 5 616.50737 cents 9: 11 701.58756 cents 10: 2 675.55484 cents 10: 14 760.63502 cents 11: 15 819.68249 cents 11: 1 904.76268 cents 12: 12 878.72995 cents 12: 4 963.81014 cents 13: 9 937.77742 cents 13: 7 1022.85761 cents 14: 6 996.82488 cents 14: 10 1081.90507 cents 15: 3 1055.87235 cents 15: 13 1140.95254 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 0.0 : 59.0 203.2 262.2 321.3 380.3 439.4 498.4 642.5 701.6 760.6 819.7 878.7 1022.9 1081.9 1141.0 1200.0 59.0 : 144.1 203.2 262.2 321.3 380.3 439.4 583.5 642.5 701.6 760.6 819.7 963.8 1022.9 1081.9 1141.0 1200.0 203.2 : 59.0 118.1 177.1 236.2 295.2 439.4 498.4 557.5 616.5 675.6 819.7 878.7 937.8 996.8 1055.9 1200.0 262.2 : 59.0 118.1 177.1 236.2 380.3 439.4 498.4 557.5 616.5 760.6 819.7 878.7 937.8 996.8 1141.0 1200.0 321.3 : 59.0 118.1 177.1 321.3 380.3 439.4 498.4 557.5 701.6 760.6 819.7 878.7 937.8 1081.9 1141.0 1200.0 380.3 : 59.0 118.1 262.2 321.3 380.3 439.4 498.4 642.5 701.6 760.6 819.7 878.7 1022.9 1081.9 1141.0 1200.0 439.4 : 59.0 203.2 262.2 321.3 380.3 439.4 583.5 642.5 701.6 760.6 819.7 963.8 1022.9 1081.9 1141.0 1200.0 498.4 : 144.1 203.2 262.2 321.3 380.3 524.4 583.5 642.5 701.6 760.6 904.8 963.8 1022.9 1081.9 1141.0 1200.0 642.5 : 59.0 118.1 177.1 236.2 380.3 439.4 498.4 557.5 616.5 760.6 819.7 878.7 937.8 996.8 1055.9 1200.0 701.6 : 59.0 118.1 177.1 321.3 380.3 439.4 498.4 557.5 701.6 760.6 819.7 878.7 937.8 996.8 1141.0 1200.0 760.6 : 59.0 118.1 262.2 321.3 380.3 439.4 498.4 642.5 701.6 760.6 819.7 878.7 937.8 1081.9 1141.0 1200.0 819.7 : 59.0 203.2 262.2 321.3 380.3 439.4 583.5 642.5 701.6 760.6 819.7 878.7 1022.9 1081.9 1141.0 1200.0 878.7 : 144.1 203.2 262.2 321.3 380.3 524.4 583.5 642.5 701.6 760.6 819.7 963.8 1022.9 1081.9 1141.0 1200.0 1022.9: 59.0 118.1 177.1 236.2 380.3 439.4 498.4 557.5 616.5 675.6 819.7 878.7 937.8 996.8 1055.9 1200.0 1081.9: 59.0 118.1 177.1 321.3 380.3 439.4 498.4 557.5 616.5 760.6 819.7 878.7 937.8 996.8 1141.0 1200.0 1141.0: 59.0 118.1 262.2 321.3 380.3 439.4 498.4 557.5 701.6 760.6 819.7 878.7 937.8 1081.9 1141.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 59.0475 .. 144.1277 cents 85.08019 cents 59.04746 cents 2: 118.0949 .. 203.1751 cents 85.08019 cents -26.03272 cents 3: 177.1424 .. 262.2226 cents 85.08019 cents -26.03272 cents 4: 236.1899 .. 321.2700 cents 85.08019 cents -26.03272 cents 5: 295.2373 .. 380.3175 cents 85.08019 cents -26.03272 cents 6: 439.3650 .. 524.4452 cents 85.08019 cents 59.04746 cents 7: 498.4124 .. 583.4926 cents 85.08019 cents -26.03272 cents 8: 557.4599 .. 642.5401 cents 85.08019 cents -26.03272 cents 9: 616.5074 .. 701.5876 cents 85.08019 cents -26.03272 cents 10: 675.5548 .. 760.6350 cents 85.08019 cents -26.03272 cents 11: 819.6825 .. 904.7627 cents 85.08019 cents 59.04746 cents 12: 878.7300 .. 963.8101 cents 85.08019 cents -26.03272 cents 13: 937.7774 .. 1022.8576 cents 85.08019 cents -26.03272 cents 14: 996.8249 .. 1081.9051 cents 85.08019 cents -26.03272 cents 15: 1055.8723 .. 1140.9525 cents 85.08019 cents -26.03272 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 59.04746 cents, class 1 Average step (divided formal octave): 75.0000 cents Largest one step interval : 144.12765 cents Average / Smallest step : 1.270165 Largest / Average step : 1.921702 Largest / Smallest step : 2.440878 Median interval of one step : 59.04746 cents, amount: 13 Most common interval of one step : 59.04746 cents, amount: 13 Least squares average step : 76.16587 cents, oct.: 1218.65394 cents Scale is not proper Scale has Myhill's property chromas: 85.08019 cents and 26.03272 cents, ratio: 3.268202 generators: 5 of 380.31751 cents and 11 of 819.68249 cents ET pair of linear temperament : 19&41 Scale is distributional even Scale is a mode of a 1199-tone equal temperament with octave 1200.000 cents degrees: 59 203 262 321 380 439 498 642 701 760 819 878 1022 1081 1140 1199 generators: 380 and 819 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAAAABAAAABAAA Step pattern size order : SLSSSSSLSSSSLSSS Scale is a Constant Structure, by a margin of 26.03272 cents Scale diversity : 1.192291 Lumma stability : 0.196825 Lumma impropriety factor : 0.260327 Rothenberg efficiency : 0.708333 redundancy: 0.291667 Efficiency x scale size : 11.333333 Number of different interval sizes : 30 = 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 : 26.03272 cents Most common intervals : 380.31751 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 557.460 819.682 cents Most common triad is 0.0 380.318 819.682 cents, amount: 14 Number of recognisable fifths : 11, average 701.5876 cents Formal octave complements present : 11 = 68.7500% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 12-13 -- Rational properties --
FIT/MODE
16: 0 2 1 1 1 0 1 2 1 1 0 1 2 1 1 1 N T3 SD: 42.2803 c. M: 69.6825 c. 17: 1 2 0 1 1 1 1 2 1 1 0 1 2 1 1 1 N D3 SD: 25.4250 c. M: 50.4579 c. 18: 1 2 1 1 0 1 1 2 1 1 1 1 2 1 1 1 N T3 SD: 25.1477 c. M: 46.9842 c. 19: 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 P M ME SD: 7.1851 c. M: 13.7014 c. 40: 2 5 2 2 2 2 2 4 2 2 2 2 5 2 2 2 N SD: 8.3389 c. M: 12.5401 c. 41: 2 5 2 2 2 2 2 5 2 2 2 2 5 2 2 2 N M DE SD: 0.8930 c. M:-1.7029 c. 101: 5 12 5 5 5 5 5 12 5 5 5 5 12 5 5 5 N M DE SD: 0.6266 c. M: 1.1949 c. 142: 7 17 7 7 7 7 7 17 7 7 7 7 17 7 7 7 N M DE SD: 0.1878 c. M: 0.3582 c. 183: 9 22 9 9 9 9 9 22 9 9 9 9 22 9 9 9 N M DE SD: 0.0543 c. M:-0.1036 c. 325: 16 39 16 16 16 16 16 39 16 16 16 16 39 16 16 16 N M DE SD: 0.0515 c. M: 0.0982 c. 508: 25 61 25 25 25 25 25 61 25 25 25 25 61 25 25 25 N M DE SD: 0.0134 c. M: 0.0255 c. 691: 34 83 34 34 34 34 34 83 34 34 34 34 83 34 34 34 N M DE SD: 0.0045 c. M:-0.0087 c. 1199: 59 144 59 59 59 59 59 144 59 59 59 59 144 59 59 59 N M DE SD: 0.0030 c. M: 0.0058 c. 1890: 93 227 93 93 93 93 93 227 93 93 93 93 227 93 93 93 N M DE SD: 0.0003 c. M: 0.0005 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.1837 cents 3 .. 6 match: 3 H SD: 1.8802 cents 4 .. 8 match: 4 H SD: 13.5912 cents 5 .. 10 match: 5 H SD: 12.1633 cents 6 .. 12 match: 6 H SD: 4.5829 cents 7 .. 14 match: 7 H SD: 10.0722 cents 8 .. 16 match: 8 H SD: 9.8663 cents 9 .. 18 match: 9 H SD: 5.3086 cents 10 .. 20 match: 9 SD: 7.2214 cents 11 .. 22 match: 10 S SD: 8.2647 cents 12 .. 24 match: 10 S SD: 5.6139 cents 13 .. 26 match: 12 SD: 8.0654 cents 14 .. 28 match: 13 SD: 6.6826 cents 15 .. 30 match: 13 SD: 5.3128 cents 16 .. 32 match: 14 SD: 5.0973 cents 17 .. 34 match: 14 SD: 5.2037 cents 18 .. 36 match: 15 S SD: 4.1371 cents 19 .. 38 match: 14 SD: 5.9940 cents 20 .. 40 match: 16 SD: 3.9387 cents 21 .. 42 match: 15 SD: 4.3547 cents 22 .. 44 match: 15 SD: 4.3476 cents 23 .. 46 match: 16 SD: 3.9875 cents 24 .. 48 match: 16 SD: 2.3260 cents 36 .. 72 match: 16 SD: 2.2576 cents 38 .. 76 match: 16 SD: 1.9568 cents 45 .. 90 match: 16 SD: 1.9060 cents 48 .. 96 match: 16 SD: 1.5608 cents 54 .. 108 match: 16 SD: 1.3793 cents 56 .. 112 match: 16 SD: 1.1270 cents 62 .. 124 match: 16 SD: 1.1098 cents 73 .. 146 match: 16 SD: 1.0978 cents 74 .. 148 match: 16 SD: 1.0438 cents 78 .. 156 match: 16 SD: 0.9584 cents 80 .. 160 match: 16 SD: 0.9579 cents 86 .. 172 match: 16 SD: 0.9057 cents 87 .. 174 match: 16 SD: 0.8838 cents 89 .. 178 match: 16 SD: 0.8192 cents 94 .. 188 match: 16 SD: 0.8065 cents 98 .. 196 match: 16 SD: 0.7101 cents 114 .. 228 match: 16 SD: 0.5186 cents 122 .. 244 match: 16 SD: 0.4950 cents 138 .. 276 match: 16 SD: 0.4820 cents 152 .. 304 match: 16 SD: 0.4651 cents 167 .. 334 match: 16 SD: 0.4503 cents 170 .. 340 match: 16 SD: 0.4411 cents 176 .. 352 match: 16 SD: 0.3521 cents 200 .. 400 match: 16 SD: 0.3268 cents 207 .. 414 match: 16 SD: 0.3140 cents 225 .. 450 match: 16 SD: 0.2695 cents 256 .. 512 match: 16 SD: 0.2155 cents 294 .. 588 match: 16 SD: 0.2151 cents 312 .. 624 match: 16 SD: 0.2044 cents 314 .. 628 match: 16 SD: 0.2030 cents 342 .. 684 match: 16 SD: 0.2021 cents 354 .. 708 match: 16 SD: 0.1719 cents 378 .. 756 match: 16 SD: 0.1565 cents 402 .. 804 match: 16 SD: 0.1443 cents 464 .. 928 match: 16 SD: 0.1383 cents 489 .. 978 match: 16 SD: 0.1347 cents 520 .. 1040 match: 16 SD: 0.1303 cents 525 .. 1050 match: 16 SD: 0.1296 cents 540 .. 1080 match: 16 SD: 0.1221 cents 570 .. 1140 match: 16 SD: 0.1136 cents 578 .. 1156 match: 16 SD: 0.1111 cents