Scala analysis: mavsynch16
Mavilla[16] in synch (brat=-1) tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65.640 cents 65.639925 2: 152.674 cents 152.674307 3: 218.314 cents 218.314232 4: 305.349 cents 305.348614 5: 370.989 cents 370.988539 6: 458.023 cents 458.022921 7: 523.663 cents 523.662846 8: 610.697 cents 610.697228 9: 676.337 cents 676.337154 10: 741.977 cents 741.977079 11: 829.011 cents 829.011461 12: 894.651 cents 894.651386 13: 981.686 cents 981.685768 14: 1047.326 cents 1047.325693 15: 1134.360 cents 1134.360075 16: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 65.6399 cents 65.6399 1: 65.6399 cents 65.6399 2: 87.0344 cents 87.0344 3: 65.6399 cents 65.6399 4: 87.0344 cents 87.0344 5: 65.6399 cents 65.6399 6: 87.0344 cents 87.0344 7: 65.6399 cents 65.6399 8: 87.0344 cents 87.0344 9: 65.6399 cents 65.6399 10: 65.6399 cents 65.6399 11: 87.0344 cents 87.0344 12: 65.6399 cents 65.6399 13: 87.0344 cents 87.0344 14: 65.6399 cents 65.6399 15: 87.0344 cents 87.0344 16: 65.6399 cents 65.6399
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 65.63992 cents 1: 7 87.03438 cents 2: 2 131.27985 cents 2: 14 152.67431 cents 3: 11 218.31423 cents 3: 5 239.70869 cents 4: 4 283.95416 cents 4: 12 305.34861 cents 5: 13 370.98854 cents 5: 3 392.38300 cents 6: 6 436.62846 cents 6: 10 458.02292 cents 7: 15 523.66285 cents 7: 1 545.05730 cents 8: 8 589.30277 cents 8: 8 610.69723 cents 9: 1 654.94270 cents 9: 15 676.33715 cents 10: 10 741.97708 cents 10: 6 763.37154 cents 11: 3 807.61700 cents 11: 13 829.01146 cents 12: 12 894.65139 cents 12: 4 916.04584 cents 13: 5 960.29131 cents 13: 11 981.68577 cents 14: 14 1047.32569 cents 14: 2 1068.72015 cents 15: 7 1112.96562 cents 15: 9 1134.36007 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 : 65.6 152.7 218.3 305.3 371.0 458.0 523.7 610.7 676.3 742.0 829.0 894.7 981.7 1047.3 1134.4 1200.0 65.6 : 87.0 152.7 239.7 305.3 392.4 458.0 545.1 610.7 676.3 763.4 829.0 916.0 981.7 1068.7 1134.4 1200.0 152.7 : 65.6 152.7 218.3 305.3 371.0 458.0 523.7 589.3 676.3 742.0 829.0 894.7 981.7 1047.3 1113.0 1200.0 218.3 : 87.0 152.7 239.7 305.3 392.4 458.0 523.7 610.7 676.3 763.4 829.0 916.0 981.7 1047.3 1134.4 1200.0 305.3 : 65.6 152.7 218.3 305.3 371.0 436.6 523.7 589.3 676.3 742.0 829.0 894.7 960.3 1047.3 1113.0 1200.0 371.0 : 87.0 152.7 239.7 305.3 371.0 458.0 523.7 610.7 676.3 763.4 829.0 894.7 981.7 1047.3 1134.4 1200.0 458.0 : 65.6 152.7 218.3 284.0 371.0 436.6 523.7 589.3 676.3 742.0 807.6 894.7 960.3 1047.3 1113.0 1200.0 523.7 : 87.0 152.7 218.3 305.3 371.0 458.0 523.7 610.7 676.3 742.0 829.0 894.7 981.7 1047.3 1134.4 1200.0 610.7 : 65.6 131.3 218.3 284.0 371.0 436.6 523.7 589.3 654.9 742.0 807.6 894.7 960.3 1047.3 1113.0 1200.0 676.3 : 65.6 152.7 218.3 305.3 371.0 458.0 523.7 589.3 676.3 742.0 829.0 894.7 981.7 1047.3 1134.4 1200.0 742.0 : 87.0 152.7 239.7 305.3 392.4 458.0 523.7 610.7 676.3 763.4 829.0 916.0 981.7 1068.7 1134.4 1200.0 829.0 : 65.6 152.7 218.3 305.3 371.0 436.6 523.7 589.3 676.3 742.0 829.0 894.7 981.7 1047.3 1113.0 1200.0 894.7 : 87.0 152.7 239.7 305.3 371.0 458.0 523.7 610.7 676.3 763.4 829.0 916.0 981.7 1047.3 1134.4 1200.0 981.7 : 65.6 152.7 218.3 284.0 371.0 436.6 523.7 589.3 676.3 742.0 829.0 894.7 960.3 1047.3 1113.0 1200.0 1047.3: 87.0 152.7 218.3 305.3 371.0 458.0 523.7 610.7 676.3 763.4 829.0 894.7 981.7 1047.3 1134.4 1200.0 1134.4: 65.6 131.3 218.3 284.0 371.0 436.6 523.7 589.3 676.3 742.0 807.6 894.7 960.3 1047.3 1113.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.6399 .. 87.0344 cents 21.39446 cents 65.63992 cents 2: 131.2799 .. 152.6743 cents 21.39446 cents 44.24547 cents 3: 218.3142 .. 239.7087 cents 21.39446 cents 65.63992 cents 4: 283.9542 .. 305.3486 cents 21.39446 cents 44.24547 cents 5: 370.9885 .. 392.3830 cents 21.39446 cents 65.63992 cents 6: 436.6285 .. 458.0229 cents 21.39446 cents 44.24547 cents 7: 523.6628 .. 545.0573 cents 21.39446 cents 65.63992 cents 8: 589.3028 .. 610.6972 cents 21.39446 cents 44.24547 cents 9: 654.9427 .. 676.3372 cents 21.39446 cents 44.24547 cents 10: 741.9771 .. 763.3715 cents 21.39446 cents 65.63992 cents 11: 807.6170 .. 829.0115 cents 21.39446 cents 44.24547 cents 12: 894.6514 .. 916.0458 cents 21.39446 cents 65.63992 cents 13: 960.2913 .. 981.6858 cents 21.39446 cents 44.24547 cents 14: 1047.3257 .. 1068.7202 cents 21.39446 cents 65.63992 cents 15: 1112.9656 .. 1134.3601 cents 21.39446 cents 44.24547 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 65.63992 cents, class 1 Average step (divided formal octave): 75.0000 cents Largest one step interval : 87.03438 cents Average / Smallest step : 1.142597 Largest / Average step : 1.160458 Largest / Smallest step : 1.325937 Median interval of one step : 65.63992 cents, amount: 9 Most common interval of one step : 65.63992 cents, amount: 9 Least squares average step : 75.13586 cents, oct.: 1202.17377 cents Scale is strictly proper Scale has Myhill's property chromas: 21.39446 cents and 44.24547 cents, ratio: 2.068081 generators: 7 of 523.66285 cents and 9 of 676.33715 cents ET pair of linear temperament : 16&55 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 841-tone equal temperament with octave 1200.000 cents degrees: 46 107 153 214 260 321 367 428 474 520 581 627 688 734 795 841 generators: 367 and 474 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABAABABABA Step pattern size order : SLSLSLSLSSLSLSLS Scale is a Constant Structure, by a margin of 44.24547 cents Scale diversity : 1.164767 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.732569 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 : 21.39446 cents Most common intervals : 523.66285 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 65.640 676.337 cents Most common triad is 0.0 523.663 676.337 cents, amount: 14 Number of recognisable fifths : 0 Scale contains two identical disjunct "tetrachords" of 8 notes Best major thirds form a closed circle Formal octave complements present : 15 = 93.7500% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 12-13 -- Rational properties --
FIT/MODE
16: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.2001 c. M: 10.6972 c. 39: 2 3 2 3 2 3 2 3 2 2 3 2 3 2 3 2 SP M ME SD: 2.7168 c. M:-4.6874 c. 55: 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 SP M ME SD: 0.1228 c. M:-0.2119 c. 456: 25 33 25 33 25 33 25 33 25 25 33 25 33 25 33 25 SP M DE SD: 0.0991 c. M: 0.1709 c. 511: 28 37 28 37 28 37 28 37 28 28 37 28 37 28 37 28 SP M DE SD: 0.0752 c. M: 0.1297 c. 566: 31 41 31 41 31 41 31 41 31 31 41 31 41 31 41 31 SP M DE SD: 0.0559 c. M: 0.0965 c. 621: 34 45 34 45 34 45 34 45 34 34 45 34 45 34 45 34 SP M DE SD: 0.0401 c. M: 0.0692 c. 676: 37 49 37 49 37 49 37 49 37 37 49 37 49 37 49 37 SP M DE SD: 0.0269 c. M: 0.0463 c. 731: 40 53 40 53 40 53 40 53 40 40 53 40 53 40 53 40 SP M DE SD: 0.0156 c. M: 0.0269 c. 786: 43 57 43 57 43 57 43 57 43 43 57 43 57 43 57 43 SP M DE SD: 0.0059 c. M: 0.0102 c. 841: 46 61 46 61 46 61 46 61 46 46 61 46 61 46 61 46 SP M DE SD: 0.0025 c. M:-0.0043 c. 1627: 89 118 89 118 89 118 89 118 89 89 118 89 118 89 118 89 SP M DE SD: 0.0016 c. M: 0.0027 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 12.8089 cents 3 .. 6 match: 3 H SD: 9.2027 cents 4 .. 8 match: 4 H SD: 8.1260 cents 5 .. 10 match: 5 H SD: 8.9867 cents 6 .. 12 match: 6 H SD: 8.9802 cents 7 .. 14 match: 7 H SD: 9.5339 cents 8 .. 16 match: 8 H SD: 7.7437 cents 9 .. 18 match: 9 H SD: 7.6316 cents 10 .. 20 match: 10 H SD: 6.2879 cents 11 .. 22 match: 11 H SD: 6.5385 cents 12 .. 24 match: 12 H SD: 5.7405 cents 13 .. 26 match: 13 H SD: 4.9274 cents 14 .. 28 match: 12 SD: 6.1734 cents 15 .. 30 match: 14 SD: 5.9840 cents 16 .. 32 match: 15 SD: 5.0484 cents 17 .. 34 match: 15 SD: 4.5962 cents 18 .. 36 match: 15 SD: 5.9476 cents 19 .. 38 match: 16 SD: 4.9739 cents 20 .. 40 match: 16 SD: 4.3900 cents 21 .. 42 match: 16 SD: 3.2670 cents 25 .. 50 match: 16 SD: 3.2107 cents 26 .. 52 match: 16 SD: 3.1861 cents 28 .. 56 match: 16 SD: 3.1821 cents 29 .. 58 match: 16 SD: 2.6620 cents 30 .. 60 match: 16 SD: 2.3830 cents 31 .. 62 match: 16 SD: 2.3415 cents 37 .. 74 match: 16 SD: 2.2223 cents 42 .. 84 match: 16 SD: 1.8603 cents 43 .. 86 match: 16 SD: 1.7691 cents 46 .. 92 match: 16 SD: 1.5481 cents 52 .. 104 match: 16 SD: 1.2404 cents 67 .. 134 match: 16 SD: 1.0794 cents 73 .. 146 match: 16 SD: 1.0208 cents 76 .. 152 match: 16 SD: 0.9017 cents 83 .. 166 match: 16 SD: 0.8487 cents 88 .. 176 match: 16 SD: 0.8088 cents 96 .. 192 match: 16 SD: 0.7622 cents 99 .. 198 match: 16 SD: 0.6860 cents 105 .. 210 match: 16 SD: 0.6695 cents 109 .. 218 match: 16 SD: 0.6400 cents 119 .. 238 match: 16 SD: 0.6383 cents 125 .. 250 match: 16 SD: 0.6064 cents 130 .. 260 match: 16 SD: 0.5320 cents 142 .. 284 match: 16 SD: 0.5269 cents 151 .. 302 match: 16 SD: 0.4497 cents 155 .. 310 match: 16 SD: 0.4132 cents 172 .. 344 match: 16 SD: 0.3932 cents 185 .. 370 match: 16 SD: 0.3780 cents 207 .. 414 match: 16 SD: 0.3382 cents 230 .. 460 match: 16 SD: 0.3201 cents 238 .. 476 match: 16 SD: 0.2448 cents 260 .. 520 match: 16 SD: 0.2078 cents 337 .. 674 match: 16 SD: 0.1965 cents 379 .. 758 match: 16 SD: 0.1950 cents 380 .. 760 match: 16 SD: 0.1918 cents 389 .. 778 match: 16 SD: 0.1673 cents 393 .. 786 match: 16 SD: 0.1617 cents 439 .. 878 match: 16 SD: 0.1594 cents 445 .. 890 match: 16 SD: 0.1537 cents 456 .. 912 match: 16 SD: 0.1299 cents 498 .. 996 match: 16 SD: 0.1101 cents 544 .. 1088 match: 16 SD: 0.0820 cents