Scala analysis: xen07-chalmers-19-50-equal
19 of 50 Equal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 72.000 cents 72.000000 2: 120.000 cents 120.000000 3: 192.000 cents 192.000000 4: 264.000 cents 264.000000 5: 312.000 cents 312.000000 6: 384.000 cents 384.000000 7: 456.000 cents 456.000000 8: 504.000 cents 504.000000 9: 576.000 cents 576.000000 10: 624.000 cents 624.000000 11: 696.000 cents 696.000000 12: 768.000 cents 768.000000 13: 816.000 cents 816.000000 14: 888.000 cents 888.000000 15: 960.000 cents 960.000000 16: 1008.000 cents 1008.000000 17: 1080.000 cents 1080.000000 18: 1152.000 cents 1152.000000 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 48.0000 cents 48.0000 1: 72.0000 cents 72.0000 2: 48.0000 cents 48.0000 3: 72.0000 cents 72.0000 4: 72.0000 cents 72.0000 5: 48.0000 cents 48.0000 6: 72.0000 cents 72.0000 7: 72.0000 cents 72.0000 8: 48.0000 cents 48.0000 9: 72.0000 cents 72.0000 10: 48.0000 cents 48.0000 11: 72.0000 cents 72.0000 12: 72.0000 cents 72.0000 13: 48.0000 cents 48.0000 14: 72.0000 cents 72.0000 15: 72.0000 cents 72.0000 16: 48.0000 cents 48.0000 17: 72.0000 cents 72.0000 18: 72.0000 cents 72.0000 19: 48.0000 cents 48.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 48.00000 cents 1: 12 72.00000 cents 2: 14 120.00000 cents 2: 5 144.00000 cents 3: 2 168.00000 cents 3: 17 192.00000 cents 4: 9 240.00000 cents 4: 10 264.00000 cents 5: 16 312.00000 cents 5: 3 336.00000 cents 6: 4 360.00000 cents 6: 15 384.00000 cents 7: 11 432.00000 cents 7: 8 456.00000 cents 8: 18 504.00000 cents 8: 1 528.00000 cents 9: 6 552.00000 cents 9: 13 576.00000 cents 10: 13 624.00000 cents 10: 6 648.00000 cents 11: 1 672.00000 cents 11: 18 696.00000 cents 12: 8 744.00000 cents 12: 11 768.00000 cents 13: 15 816.00000 cents 13: 4 840.00000 cents 14: 3 864.00000 cents 14: 16 888.00000 cents 15: 10 936.00000 cents 15: 9 960.00000 cents 16: 17 1008.00000 cents 16: 2 1032.00000 cents 17: 5 1056.00000 cents 17: 14 1080.00000 cents 18: 12 1128.00000 cents 18: 7 1152.00000 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 0.0 : 72.0 120.0 192.0 264.0 312.0 384.0 456.0 504.0 576.0 624.0 696.0 768.0 816.0 888.0 960.0 1008.0 1080.0 1152.0 1200.0 72.0 : 48.0 120.0 192.0 240.0 312.0 384.0 432.0 504.0 552.0 624.0 696.0 744.0 816.0 888.0 936.0 1008.0 1080.0 1128.0 1200.0 120.0 : 72.0 144.0 192.0 264.0 336.0 384.0 456.0 504.0 576.0 648.0 696.0 768.0 840.0 888.0 960.0 1032.0 1080.0 1152.0 1200.0 192.0 : 72.0 120.0 192.0 264.0 312.0 384.0 432.0 504.0 576.0 624.0 696.0 768.0 816.0 888.0 960.0 1008.0 1080.0 1128.0 1200.0 264.0 : 48.0 120.0 192.0 240.0 312.0 360.0 432.0 504.0 552.0 624.0 696.0 744.0 816.0 888.0 936.0 1008.0 1056.0 1128.0 1200.0 312.0 : 72.0 144.0 192.0 264.0 312.0 384.0 456.0 504.0 576.0 648.0 696.0 768.0 840.0 888.0 960.0 1008.0 1080.0 1152.0 1200.0 384.0 : 72.0 120.0 192.0 240.0 312.0 384.0 432.0 504.0 576.0 624.0 696.0 768.0 816.0 888.0 936.0 1008.0 1080.0 1128.0 1200.0 456.0 : 48.0 120.0 168.0 240.0 312.0 360.0 432.0 504.0 552.0 624.0 696.0 744.0 816.0 864.0 936.0 1008.0 1056.0 1128.0 1200.0 504.0 : 72.0 120.0 192.0 264.0 312.0 384.0 456.0 504.0 576.0 648.0 696.0 768.0 816.0 888.0 960.0 1008.0 1080.0 1152.0 1200.0 576.0 : 48.0 120.0 192.0 240.0 312.0 384.0 432.0 504.0 576.0 624.0 696.0 744.0 816.0 888.0 936.0 1008.0 1080.0 1128.0 1200.0 624.0 : 72.0 144.0 192.0 264.0 336.0 384.0 456.0 528.0 576.0 648.0 696.0 768.0 840.0 888.0 960.0 1032.0 1080.0 1152.0 1200.0 696.0 : 72.0 120.0 192.0 264.0 312.0 384.0 456.0 504.0 576.0 624.0 696.0 768.0 816.0 888.0 960.0 1008.0 1080.0 1128.0 1200.0 768.0 : 48.0 120.0 192.0 240.0 312.0 384.0 432.0 504.0 552.0 624.0 696.0 744.0 816.0 888.0 936.0 1008.0 1056.0 1128.0 1200.0 816.0 : 72.0 144.0 192.0 264.0 336.0 384.0 456.0 504.0 576.0 648.0 696.0 768.0 840.0 888.0 960.0 1008.0 1080.0 1152.0 1200.0 888.0 : 72.0 120.0 192.0 264.0 312.0 384.0 432.0 504.0 576.0 624.0 696.0 768.0 816.0 888.0 936.0 1008.0 1080.0 1128.0 1200.0 960.0 : 48.0 120.0 192.0 240.0 312.0 360.0 432.0 504.0 552.0 624.0 696.0 744.0 816.0 864.0 936.0 1008.0 1056.0 1128.0 1200.0 1008.0: 72.0 144.0 192.0 264.0 312.0 384.0 456.0 504.0 576.0 648.0 696.0 768.0 816.0 888.0 960.0 1008.0 1080.0 1152.0 1200.0 1080.0: 72.0 120.0 192.0 240.0 312.0 384.0 432.0 504.0 576.0 624.0 696.0 744.0 816.0 888.0 936.0 1008.0 1080.0 1128.0 1200.0 1152.0: 48.0 120.0 168.0 240.0 312.0 360.0 432.0 504.0 552.0 624.0 672.0 744.0 816.0 864.0 936.0 1008.0 1056.0 1128.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.0000 .. 72.0000 cents 24.00000 cents 48.00000 cents 2: 120.0000 .. 144.0000 cents 24.00000 cents 48.00000 cents 3: 168.0000 .. 192.0000 cents 24.00000 cents 24.00000 cents 4: 240.0000 .. 264.0000 cents 24.00000 cents 48.00000 cents 5: 312.0000 .. 336.0000 cents 24.00000 cents 48.00000 cents 6: 360.0000 .. 384.0000 cents 24.00000 cents 24.00000 cents 7: 432.0000 .. 456.0000 cents 24.00000 cents 48.00000 cents 8: 504.0000 .. 528.0000 cents 24.00000 cents 48.00000 cents 9: 552.0000 .. 576.0000 cents 24.00000 cents 24.00000 cents 10: 624.0000 .. 648.0000 cents 24.00000 cents 48.00000 cents 11: 672.0000 .. 696.0000 cents 24.00000 cents 24.00000 cents 12: 744.0000 .. 768.0000 cents 24.00000 cents 48.00000 cents 13: 816.0000 .. 840.0000 cents 24.00000 cents 48.00000 cents 14: 864.0000 .. 888.0000 cents 24.00000 cents 24.00000 cents 15: 936.0000 .. 960.0000 cents 24.00000 cents 48.00000 cents 16: 1008.0000 .. 1032.0000 cents 24.00000 cents 48.00000 cents 17: 1056.0000 .. 1080.0000 cents 24.00000 cents 24.00000 cents 18: 1128.0000 .. 1152.0000 cents 24.00000 cents 48.00000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 48.00000 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 72.00000 cents Average / Smallest step : 1.315789 Largest / Average step : 1.140000 Largest / Smallest step : 1.500000 Median interval of one step : 72.00000 cents, amount: 12 Most common interval of one step : 72.00000 cents, amount: 12 Least squares average step : 63.47854 cents, oct.: 1206.09231 cents Scale is strictly proper Scale has Myhill's property chromas: 24.00000 cents and 24.00000 cents, ratio: 1.000000 generators: 8 of 504.00000 cents and 11 of 696.00000 cents Scale is maximally even in 50-tone equal temperament ET pair of linear temperament : 12&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 50-tone equal temperament with octave 1200.000 cents degrees: 3 5 8 11 13 16 19 21 24 26 29 32 34 37 40 42 45 48 50 generators: 21 and 29 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 50-tone equal temperament Step pattern alph. order: ABAABAABABAABAABAAB Step pattern size order : LSLLSLLSLSLLSLLSLLS Interval vector is [ 0 7 12 0 14 5 2 17 0 9 10 0 16 3 4 15 0 11 8 0 18 1 6 13 0 ] Scale is a Constant Structure, by a margin of 24.00000 cents Ratio Whole / Half tone : 1.600000 ( 8/5 ) Scale diversity : 1.186410 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.640000 Rothenberg efficiency : 0.701754 redundancy: 0.298246 Efficiency x scale size : 13.333333 Number of different interval sizes : 36 = 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 : 24.00000 cents Most common intervals : 504.00000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 504.000 1008.000 cents Most common triad is 0.0 504.000 696.000 cents, amount: 17 Number of recognisable fifths : 18, average 696.0000 cents Scale contains two identical disjunct "tetrachords" of 9 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 13 = 68.4211% Limited inverse transpositions : 9 Inversional symmetry on degrees : 14 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.8884 c. M: 15.1579 c. 31: 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 P M ME S SD: 4.8348 c. M:-9.2903 c. 50: 3 2 3 3 2 3 3 2 3 2 3 3 2 3 3 2 3 3 2 SP M ME 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: 2.9775 cents 3 .. 6 match: 3 H SD: 2.3267 cents 4 .. 8 match: 4 H SD: 2.7239 cents 5 .. 10 match: 5 H SD: 2.4747 cents 6 .. 12 match: 6 H SD: 5.3517 cents 7 .. 14 match: 7 H SD: 7.2257 cents 8 .. 16 match: 8 H SD: 4.9049 cents 9 .. 18 match: 9 H SD: 5.1496 cents 10 .. 20 match: 10 H SD: 5.3224 cents 11 .. 22 match: 11 H SD: 7.9844 cents 12 .. 24 match: 12 H SD: 4.5473 cents 13 .. 26 match: 13 H SD: 5.2287 cents 14 .. 28 match: 14 H SD: 4.9706 cents 15 .. 30 match: 15 H SD: 3.9782 cents 16 .. 32 match: 16 H SD: 3.4615 cents 17 .. 34 match: 15 S SD: 4.9123 cents 18 .. 36 match: 17 S SD: 3.7952 cents 19 .. 38 match: 15 SD: 4.2040 cents 20 .. 40 match: 18 SD: 3.0571 cents 21 .. 42 match: 18 SD: 4.0701 cents 22 .. 44 match: 17 SD: 4.4445 cents 23 .. 46 match: 19 SD: 3.1148 cents 24 .. 48 match: 19 SD: 2.9275 cents 25 .. 50 match: 18 SD: 2.6267 cents 30 .. 60 match: 19 SD: 2.2680 cents 36 .. 72 match: 19 SD: 2.1111 cents 40 .. 80 match: 19 SD: 1.9597 cents 41 .. 82 match: 19 SD: 1.7705 cents 42 .. 84 match: 19 SD: 1.7663 cents 43 .. 86 match: 19 SD: 1.5899 cents 50 .. 100 match: 19 SD: 1.4957 cents 51 .. 102 match: 19 SD: 1.4652 cents 53 .. 106 match: 19 SD: 1.3013 cents 60 .. 120 match: 19 SD: 1.2812 cents 61 .. 122 match: 19 SD: 1.2592 cents 65 .. 130 match: 19 SD: 1.2445 cents 66 .. 132 match: 19 SD: 1.0197 cents 71 .. 142 match: 19 SD: 1.0191 cents 73 .. 146 match: 19 SD: 0.9320 cents 85 .. 170 match: 19 SD: 0.8383 cents 86 .. 172 match: 19 SD: 0.8006 cents 93 .. 186 match: 19 SD: 0.7951 cents 95 .. 190 match: 19 SD: 0.7832 cents 96 .. 192 match: 19 SD: 0.7065 cents 97 .. 194 match: 19 SD: 0.5959 cents 113 .. 226 match: 19 SD: 0.5549 cents 127 .. 254 match: 19 SD: 0.5160 cents 136 .. 272 match: 19 SD: 0.4797 cents 152 .. 304 match: 19 SD: 0.4608 cents 162 .. 324 match: 19 SD: 0.4416 cents 163 .. 326 match: 19 SD: 0.3991 cents 170 .. 340 match: 19 SD: 0.3961 cents 182 .. 364 match: 19 SD: 0.3705 cents 186 .. 372 match: 19 SD: 0.3562 cents 196 .. 392 match: 19 SD: 0.3556 cents 206 .. 412 match: 19 SD: 0.3281 cents 212 .. 424 match: 19 SD: 0.3212 cents 213 .. 426 match: 19 SD: 0.2891 cents 233 .. 466 match: 19 SD: 0.2788 cents 237 .. 474 match: 19 SD: 0.2724 cents 238 .. 476 match: 19 SD: 0.2586 cents 254 .. 508 match: 19 SD: 0.2524 cents 263 .. 526 match: 19 SD: 0.2294 cents 279 .. 558 match: 19 SD: 0.1947 cents 309 .. 618 match: 19 SD: 0.1871 cents 334 .. 668 match: 19 SD: 0.1766 cents 375 .. 750 match: 19 SD: 0.1601 cents 418 .. 836 match: 19 SD: 0.1550 cents 444 .. 888 match: 19 SD: 0.1507 cents 471 .. 942 match: 19 SD: 0.1267 cents 491 .. 982 match: 19 SD: 0.1067 cents 588 .. 1176 match: 19 SD: 0.0844 cents