Scala analysis: miller19
Herman Miller circulating based on {225/224, 1029/1000}
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 62.005 cents 62.004635 2: 124.009 cents 124.009271 3: 186.014 cents 186.013906 4: 248.019 cents 248.018542 5: 322.429 cents 322.429409 6: 384.434 cents 384.434045 7: 446.439 cents 446.438680 8: 508.443 cents 508.443315 9: 570.448 cents 570.447951 10: 632.453 cents 632.452586 11: 694.457 cents 694.457222 12: 756.462 cents 756.461857 13: 818.466 cents 818.466492 14: 880.471 cents 880.471128 15: 954.882 cents 954.881995 16: 1016.887 cents 1016.886631 17: 1078.891 cents 1078.891266 18: 1140.896 cents 1140.895902 19: 1202.901 cents 1202.900537
SHOW/INTERVAL
0: 62.0046 cents 62.0046 1: 62.0046 cents 62.0046 2: 62.0046 cents 62.0046 3: 62.0046 cents 62.0046 4: 62.0046 cents 62.0046 5: 74.4109 cents 74.4109 6: 62.0046 cents 62.0046 7: 62.0046 cents 62.0046 8: 62.0046 cents 62.0046 9: 62.0046 cents 62.0046 10: 62.0046 cents 62.0046 11: 62.0046 cents 62.0046 12: 62.0046 cents 62.0046 13: 62.0046 cents 62.0046 14: 62.0046 cents 62.0046 15: 74.4109 cents 74.4109 16: 62.0046 cents 62.0046 17: 62.0046 cents 62.0046 18: 62.0046 cents 62.0046 19: 62.0046 cents 62.0046
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 17 62.00464 cents 1: 2 74.41087 cents 2: 15 124.00927 cents 2: 4 136.41550 cents 3: 13 186.01391 cents 3: 6 198.42014 cents 4: 11 248.01854 cents 4: 8 260.42477 cents 5: 9 310.02318 cents 5: 10 322.42941 cents 6: 7 372.02781 cents 6: 12 384.43404 cents 7: 5 434.03245 cents 7: 14 446.43868 cents 8: 3 496.03708 cents 8: 16 508.44332 cents 9: 1 558.04172 cents 9: 18 570.44795 cents 10: 18 632.45259 cents 10: 1 644.85882 cents 11: 16 694.45722 cents 11: 3 706.86345 cents 12: 14 756.46186 cents 12: 5 768.86809 cents 13: 12 818.46649 cents 13: 7 830.87272 cents 14: 10 880.47113 cents 14: 9 892.87736 cents 15: 8 942.47576 cents 15: 11 954.88199 cents 16: 6 1004.48040 cents 16: 13 1016.88663 cents 17: 4 1066.48503 cents 17: 15 1078.89127 cents 18: 2 1128.48967 cents 18: 17 1140.89590 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 : 62.0 124.0 186.0 248.0 322.4 384.4 446.4 508.4 570.4 632.5 694.5 756.5 818.5 880.5 954.9 1016.9 1078.9 1140.9 1202.9 62.0 : 62.0 124.0 186.0 260.4 322.4 384.4 446.4 508.4 570.4 632.5 694.5 756.5 818.5 892.9 954.9 1016.9 1078.9 1140.9 1202.9 124.0 : 62.0 124.0 198.4 260.4 322.4 384.4 446.4 508.4 570.4 632.5 694.5 756.5 830.9 892.9 954.9 1016.9 1078.9 1140.9 1202.9 186.0 : 62.0 136.4 198.4 260.4 322.4 384.4 446.4 508.4 570.4 632.5 694.5 768.9 830.9 892.9 954.9 1016.9 1078.9 1140.9 1202.9 248.0 : 74.4 136.4 198.4 260.4 322.4 384.4 446.4 508.4 570.4 632.5 706.9 768.9 830.9 892.9 954.9 1016.9 1078.9 1140.9 1202.9 322.4 : 62.0 124.0 186.0 248.0 310.0 372.0 434.0 496.0 558.0 632.5 694.5 756.5 818.5 880.5 942.5 1004.5 1066.5 1128.5 1202.9 384.4 : 62.0 124.0 186.0 248.0 310.0 372.0 434.0 496.0 570.4 632.5 694.5 756.5 818.5 880.5 942.5 1004.5 1066.5 1140.9 1202.9 446.4 : 62.0 124.0 186.0 248.0 310.0 372.0 434.0 508.4 570.4 632.5 694.5 756.5 818.5 880.5 942.5 1004.5 1078.9 1140.9 1202.9 508.4 : 62.0 124.0 186.0 248.0 310.0 372.0 446.4 508.4 570.4 632.5 694.5 756.5 818.5 880.5 942.5 1016.9 1078.9 1140.9 1202.9 570.4 : 62.0 124.0 186.0 248.0 310.0 384.4 446.4 508.4 570.4 632.5 694.5 756.5 818.5 880.5 954.9 1016.9 1078.9 1140.9 1202.9 632.5 : 62.0 124.0 186.0 248.0 322.4 384.4 446.4 508.4 570.4 632.5 694.5 756.5 818.5 892.9 954.9 1016.9 1078.9 1140.9 1202.9 694.5 : 62.0 124.0 186.0 260.4 322.4 384.4 446.4 508.4 570.4 632.5 694.5 756.5 830.9 892.9 954.9 1016.9 1078.9 1140.9 1202.9 756.5 : 62.0 124.0 198.4 260.4 322.4 384.4 446.4 508.4 570.4 632.5 694.5 768.9 830.9 892.9 954.9 1016.9 1078.9 1140.9 1202.9 818.5 : 62.0 136.4 198.4 260.4 322.4 384.4 446.4 508.4 570.4 632.5 706.9 768.9 830.9 892.9 954.9 1016.9 1078.9 1140.9 1202.9 880.5 : 74.4 136.4 198.4 260.4 322.4 384.4 446.4 508.4 570.4 644.9 706.9 768.9 830.9 892.9 954.9 1016.9 1078.9 1140.9 1202.9 954.9 : 62.0 124.0 186.0 248.0 310.0 372.0 434.0 496.0 570.4 632.5 694.5 756.5 818.5 880.5 942.5 1004.5 1066.5 1128.5 1202.9 1016.9: 62.0 124.0 186.0 248.0 310.0 372.0 434.0 508.4 570.4 632.5 694.5 756.5 818.5 880.5 942.5 1004.5 1066.5 1140.9 1202.9 1078.9: 62.0 124.0 186.0 248.0 310.0 372.0 446.4 508.4 570.4 632.5 694.5 756.5 818.5 880.5 942.5 1004.5 1078.9 1140.9 1202.9 1140.9: 62.0 124.0 186.0 248.0 310.0 384.4 446.4 508.4 570.4 632.5 694.5 756.5 818.5 880.5 942.5 1016.9 1078.9 1140.9 1202.9 1202.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.0046 .. 74.4109 cents 12.40623 cents 62.00464 cents 2: 124.0093 .. 136.4155 cents 12.40623 cents 49.59840 cents 3: 186.0139 .. 198.4201 cents 12.40623 cents 49.59840 cents 4: 248.0185 .. 260.4248 cents 12.40623 cents 49.59840 cents 5: 310.0232 .. 322.4294 cents 12.40623 cents 49.59840 cents 6: 372.0278 .. 384.4340 cents 12.40623 cents 49.59840 cents 7: 434.0324 .. 446.4387 cents 12.40623 cents 49.59840 cents 8: 496.0371 .. 508.4433 cents 12.40623 cents 49.59840 cents 9: 558.0417 .. 570.4480 cents 12.40623 cents 49.59840 cents 10: 632.4526 .. 644.8588 cents 12.40623 cents 62.00464 cents 11: 694.4572 .. 706.8635 cents 12.40623 cents 49.59840 cents 12: 756.4619 .. 768.8681 cents 12.40623 cents 49.59840 cents 13: 818.4665 .. 830.8727 cents 12.40623 cents 49.59840 cents 14: 880.4711 .. 892.8774 cents 12.40623 cents 49.59840 cents 15: 942.4758 .. 954.8820 cents 12.40623 cents 49.59840 cents 16: 1004.4804 .. 1016.8866 cents 12.40623 cents 49.59840 cents 17: 1066.4850 .. 1078.8913 cents 12.40623 cents 49.59840 cents 18: 1128.4897 .. 1140.8959 cents 12.40623 cents 49.59840 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 62.00464 cents, class 1 Average step (divided formal octave): 63.3106 cents Largest one step interval : 74.41087 cents Average / Smallest step : 1.021062 Largest / Average step : 1.175331 Largest / Smallest step : 1.200086 Median interval of one step : 62.00464 cents, amount: 17 Most common interval of one step : 62.00464 cents, amount: 17 Least squares average step : 63.33567 cents, oct.: 1203.37770 cents Scale is strictly proper Scale has Myhill's property chromas: 12.40623 cents and 49.59840 cents, ratio: 3.997862 generators: 9 of 570.44795 cents and 10 of 632.45259 cents Scale is maximally even in 97-tone equal temperament ET pair of linear temperament : 19&78 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 97-tone equal temperament with octave 1202.901 cents degrees: 5 10 15 20 26 31 36 41 46 51 56 61 66 71 77 82 87 92 97 generators: 46 and 51 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAAABAAAAAAAAABAAAA Step pattern size order : SSSSLSSSSSSSSSLSSSS Interval vector is [ 0 0 0 0 17 2 0 0 0 15 4 0 0 0 13 6 0 0 0 11 8 0 0 0 9 10 0 0 0 7 12 0 0 0 5 14 0 0 0 3 16 0 0 0 1 18 0 0 ] Scale is a Constant Structure, by a margin of 49.59840 cents Scale diversity : 1.116555 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.814355 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 : 12.40623 cents Most common intervals : 570.44795 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 570.448 1140.896 cents Most common triad is 0.0 570.448 632.453 cents, amount: 17 Number of recognisable fifths : 19, average 696.4161 cents Number of recognisable fourths : 19, average 506.4844 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 : 19 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- 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: 3.5764 c. M:-5.8766 c. 59: 3 3 3 3 4 3 3 3 3 3 3 3 3 3 4 3 3 3 3 SP M ME I SD: 2.3010 c. M:-3.7809 c. 78: 4 4 4 4 5 4 4 4 4 4 4 4 4 4 5 4 4 4 4 SP M ME I SD: 0.8693 c. M:-1.4284 c. 97: 5 5 5 5 6 5 5 5 5 5 5 5 5 5 6 5 5 5 5 SP M ME I SD: 0.0015 c. M: 0.0025 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 2.9005 cents 2 .. 4 match: 2 H SD: 4.0196 cents 3 .. 6 match: 3 H SD: 3.8246 cents 4 .. 8 match: 4 H SD: 4.0512 cents 5 .. 10 match: 5 H SD: 2.9893 cents 6 .. 12 match: 6 H SD: 6.2699 cents 7 .. 14 match: 7 H SD: 6.1403 cents 8 .. 16 match: 8 H SD: 4.8789 cents 9 .. 18 match: 9 H SD: 4.6888 cents 10 .. 20 match: 10 H SD: 5.4559 cents 11 .. 22 match: 11 H SD: 6.6693 cents 12 .. 24 match: 12 H SD: 4.8805 cents 13 .. 26 match: 13 H SD: 4.8827 cents 14 .. 28 match: 14 H SD: 4.0090 cents 15 .. 30 match: 15 H SD: 3.8126 cents 16 .. 32 match: 16 H SD: 4.0513 cents 17 .. 34 match: 16 S SD: 5.0246 cents 18 .. 36 match: 17 S SD: 3.6994 cents 19 .. 38 match: 17 SD: 4.7936 cents 20 .. 40 match: 18 SD: 2.7069 cents 21 .. 42 match: 18 SD: 3.9114 cents 22 .. 44 match: 17 SD: 4.7208 cents 23 .. 46 match: 19 SD: 3.5238 cents 24 .. 48 match: 19 SD: 2.9179 cents 25 .. 50 match: 19 SD: 2.8498 cents 26 .. 52 match: 19 SD: 2.7575 cents 27 .. 54 match: 19 SD: 2.5785 cents 28 .. 56 match: 19 SD: 2.5374 cents 30 .. 60 match: 19 SD: 2.5020 cents 33 .. 66 match: 19 SD: 2.3582 cents 35 .. 70 match: 19 SD: 2.2611 cents 38 .. 76 match: 19 SD: 1.9312 cents 44 .. 88 match: 19 SD: 1.4960 cents 52 .. 104 match: 19 SD: 1.4881 cents 53 .. 106 match: 19 SD: 1.1050 cents 64 .. 128 match: 19 SD: 1.0643 cents 77 .. 154 match: 19 SD: 0.9292 cents 79 .. 158 match: 19 SD: 0.7390 cents 104 .. 208 match: 19 SD: 0.7358 cents 105 .. 210 match: 19 SD: 0.6977 cents 106 .. 212 match: 19 SD: 0.6443 cents 109 .. 218 match: 19 SD: 0.6157 cents 131 .. 262 match: 19 SD: 0.6062 cents 132 .. 264 match: 19 SD: 0.5514 cents 133 .. 266 match: 19 SD: 0.5470 cents 136 .. 272 match: 19 SD: 0.4995 cents 160 .. 321 match: 19 SD: 0.4829 cents 161 .. 323 match: 19 SD: 0.4265 cents 164 .. 329 match: 19 SD: 0.4239 cents 170 .. 341 match: 19 SD: 0.4009 cents 184 .. 369 match: 19 SD: 0.3936 cents 190 .. 381 match: 19 SD: 0.3260 cents 213 .. 427 match: 19 SD: 0.3139 cents 220 .. 441 match: 19 SD: 0.2832 cents 241 .. 483 match: 19 SD: 0.2797 cents 245 .. 491 match: 19 SD: 0.2632 cents 254 .. 509 match: 19 SD: 0.2508 cents 272 .. 545 match: 19 SD: 0.2301 cents 298 .. 597 match: 19 SD: 0.2149 cents 299 .. 599 match: 19 SD: 0.1961 cents 326 .. 653 match: 19 SD: 0.1710 cents 377 .. 755 match: 19 SD: 0.1702 cents 387 .. 775 match: 19 SD: 0.1673 cents 415 .. 831 match: 19 SD: 0.1354 cents 513 .. 1028 match: 19 SD: 0.1250 cents 527 .. 1056 match: 19 SD: 0.1232 cents 551 .. 1104 match: 19 SD: 0.1157 cents 571 .. 1144 match: 19 SD: 0.1091 cents 592 .. 1186 match: 19 SD: 0.1089 cents