Scala analysis: xen18-erlich-flattone-19
7L 12s MOS for Flattone, L=72.98, s=57.64
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57.640 cents 57.640000 2: 130.620 cents 130.620000 3: 188.260 cents 188.260000 4: 245.900 cents 245.900000 5: 318.880 cents 318.880000 6: 376.520 cents 376.520000 7: 449.500 cents 449.500000 8: 507.140 cents 507.140000 9: 564.780 cents 564.780000 10: 637.760 cents 637.760000 11: 695.400 cents 695.400000 12: 753.040 cents 753.040000 13: 826.020 cents 826.020000 14: 883.660 cents 883.660000 15: 956.640 cents 956.640000 16: 1014.280 cents 1014.280000 17: 1071.920 cents 1071.920000 18: 1144.900 cents 1144.900000 19: 1202.540 cents 1202.540000
SHOW/INTERVAL
0: 57.6400 cents 57.6400 1: 57.6400 cents 57.6400 2: 72.9800 cents 72.9800 3: 57.6400 cents 57.6400 4: 57.6400 cents 57.6400 5: 72.9800 cents 72.9800 6: 57.6400 cents 57.6400 7: 72.9800 cents 72.9800 8: 57.6400 cents 57.6400 9: 57.6400 cents 57.6400 10: 72.9800 cents 72.9800 11: 57.6400 cents 57.6400 12: 57.6400 cents 57.6400 13: 72.9800 cents 72.9800 14: 57.6400 cents 57.6400 15: 72.9800 cents 72.9800 16: 57.6400 cents 57.6400 17: 57.6400 cents 57.6400 18: 72.9800 cents 72.9800 19: 57.6400 cents 57.6400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 57.64000 cents 1: 7 72.98000 cents 2: 5 115.28000 cents 2: 14 130.62000 cents 3: 17 188.26000 cents 3: 2 203.60000 cents 4: 10 245.90000 cents 4: 9 261.24000 cents 5: 3 303.54000 cents 5: 16 318.88000 cents 6: 15 376.52000 cents 6: 4 391.86000 cents 7: 8 434.16000 cents 7: 11 449.50000 cents 8: 1 491.80000 cents 8: 18 507.14000 cents 9: 13 564.78000 cents 9: 6 580.12000 cents 10: 6 622.42000 cents 10: 13 637.76000 cents 11: 18 695.40000 cents 11: 1 710.74000 cents 12: 11 753.04000 cents 12: 8 768.38000 cents 13: 4 810.68000 cents 13: 15 826.02000 cents 14: 16 883.66000 cents 14: 3 899.00000 cents 15: 9 941.30000 cents 15: 10 956.64000 cents 16: 2 998.94000 cents 16: 17 1014.28000 cents 17: 14 1071.92000 cents 17: 5 1087.26000 cents 18: 7 1129.56000 cents 18: 12 1144.90000 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 : 57.6 130.6 188.3 245.9 318.9 376.5 449.5 507.1 564.8 637.8 695.4 753.0 826.0 883.7 956.6 1014.3 1071.9 1144.9 1202.5 57.6 : 73.0 130.6 188.3 261.2 318.9 391.9 449.5 507.1 580.1 637.8 695.4 768.4 826.0 899.0 956.6 1014.3 1087.3 1144.9 1202.5 130.6 : 57.6 115.3 188.3 245.9 318.9 376.5 434.2 507.1 564.8 622.4 695.4 753.0 826.0 883.7 941.3 1014.3 1071.9 1129.6 1202.5 188.3 : 57.6 130.6 188.3 261.2 318.9 376.5 449.5 507.1 564.8 637.8 695.4 768.4 826.0 883.7 956.6 1014.3 1071.9 1144.9 1202.5 245.9 : 73.0 130.6 203.6 261.2 318.9 391.9 449.5 507.1 580.1 637.8 710.7 768.4 826.0 899.0 956.6 1014.3 1087.3 1144.9 1202.5 318.9 : 57.6 130.6 188.3 245.9 318.9 376.5 434.2 507.1 564.8 637.8 695.4 753.0 826.0 883.7 941.3 1014.3 1071.9 1129.6 1202.5 376.5 : 73.0 130.6 188.3 261.2 318.9 376.5 449.5 507.1 580.1 637.8 695.4 768.4 826.0 883.7 956.6 1014.3 1071.9 1144.9 1202.5 449.5 : 57.6 115.3 188.3 245.9 303.5 376.5 434.2 507.1 564.8 622.4 695.4 753.0 810.7 883.7 941.3 998.9 1071.9 1129.6 1202.5 507.1 : 57.6 130.6 188.3 245.9 318.9 376.5 449.5 507.1 564.8 637.8 695.4 753.0 826.0 883.7 941.3 1014.3 1071.9 1144.9 1202.5 564.8 : 73.0 130.6 188.3 261.2 318.9 391.9 449.5 507.1 580.1 637.8 695.4 768.4 826.0 883.7 956.6 1014.3 1087.3 1144.9 1202.5 637.8 : 57.6 115.3 188.3 245.9 318.9 376.5 434.2 507.1 564.8 622.4 695.4 753.0 810.7 883.7 941.3 1014.3 1071.9 1129.6 1202.5 695.4 : 57.6 130.6 188.3 261.2 318.9 376.5 449.5 507.1 564.8 637.8 695.4 753.0 826.0 883.7 956.6 1014.3 1071.9 1144.9 1202.5 753.0 : 73.0 130.6 203.6 261.2 318.9 391.9 449.5 507.1 580.1 637.8 695.4 768.4 826.0 899.0 956.6 1014.3 1087.3 1144.9 1202.5 826.0 : 57.6 130.6 188.3 245.9 318.9 376.5 434.2 507.1 564.8 622.4 695.4 753.0 826.0 883.7 941.3 1014.3 1071.9 1129.6 1202.5 883.7 : 73.0 130.6 188.3 261.2 318.9 376.5 449.5 507.1 564.8 637.8 695.4 768.4 826.0 883.7 956.6 1014.3 1071.9 1144.9 1202.5 956.6 : 57.6 115.3 188.3 245.9 303.5 376.5 434.2 491.8 564.8 622.4 695.4 753.0 810.7 883.7 941.3 998.9 1071.9 1129.6 1202.5 1014.3: 57.6 130.6 188.3 245.9 318.9 376.5 434.2 507.1 564.8 637.8 695.4 753.0 826.0 883.7 941.3 1014.3 1071.9 1144.9 1202.5 1071.9: 73.0 130.6 188.3 261.2 318.9 376.5 449.5 507.1 580.1 637.8 695.4 768.4 826.0 883.7 956.6 1014.3 1087.3 1144.9 1202.5 1144.9: 57.6 115.3 188.3 245.9 303.5 376.5 434.2 507.1 564.8 622.4 695.4 753.0 810.7 883.7 941.3 1014.3 1071.9 1129.6 1202.5 1202.5
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.6400 .. 72.9800 cents 15.34000 cents 57.64000 cents 2: 115.2800 .. 130.6200 cents 15.34000 cents 42.30000 cents 3: 188.2600 .. 203.6000 cents 15.34000 cents 57.64000 cents 4: 245.9000 .. 261.2400 cents 15.34000 cents 42.30000 cents 5: 303.5400 .. 318.8800 cents 15.34000 cents 42.30000 cents 6: 376.5200 .. 391.8600 cents 15.34000 cents 57.64000 cents 7: 434.1600 .. 449.5000 cents 15.34000 cents 42.30000 cents 8: 491.8000 .. 507.1400 cents 15.34000 cents 42.30000 cents 9: 564.7800 .. 580.1200 cents 15.34000 cents 57.64000 cents 10: 622.4200 .. 637.7600 cents 15.34000 cents 42.30000 cents 11: 695.4000 .. 710.7400 cents 15.34000 cents 57.64000 cents 12: 753.0400 .. 768.3800 cents 15.34000 cents 42.30000 cents 13: 810.6800 .. 826.0200 cents 15.34000 cents 42.30000 cents 14: 883.6600 .. 899.0000 cents 15.34000 cents 57.64000 cents 15: 941.3000 .. 956.6400 cents 15.34000 cents 42.30000 cents 16: 998.9400 .. 1014.2800 cents 15.34000 cents 42.30000 cents 17: 1071.9200 .. 1087.2600 cents 15.34000 cents 57.64000 cents 18: 1129.5600 .. 1144.9000 cents 15.34000 cents 42.30000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 57.64000 cents, class 1 Average step (divided formal octave): 63.2916 cents Largest one step interval : 72.98000 cents Average / Smallest step : 1.098050 Largest / Average step : 1.153076 Largest / Smallest step : 1.266135 Median interval of one step : 57.64000 cents, amount: 12 Most common interval of one step : 57.64000 cents, amount: 12 Least squares average step : 63.33505 cents, oct.: 1203.36600 cents Scale is strictly proper Scale has Myhill's property chromas: 15.34000 cents and 42.30000 cents, ratio: 2.757497 generators: 8 of 507.14000 cents and 11 of 695.40000 cents ET pair of linear temperament : 19&64 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1961-tone equal temperament with octave 1202.540 cents degrees: 94 213 307 401 520 614 733 827 921 1040 1134 1228 1347 1441 1560 1654 1748 1867 1961 generators: 827 and 1134 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABAABABAABA Step pattern size order : SLSSLSLSSLSSLSLSSLS Scale is a Constant Structure, by a margin of 42.30000 cents Scale diversity : 1.137329 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.770386 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 : 15.34000 cents Most common intervals : 507.14000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 507.140 1014.280 cents Most common triad is 0.0 507.140 695.400 cents, amount: 17 Number of recognisable fifths : 19, average 696.2074 cents Number of recognisable fourths : 19, average 506.3326 cents Scale contains two identical conjunct "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: 4.4221 c. M:-7.2663 c. 45: 2 3 2 2 3 2 3 2 2 3 2 2 3 2 3 2 2 3 2 SP M ME I SD: 3.2815 c. M:-5.3920 c. 64: 3 4 3 3 4 3 4 3 3 4 3 3 4 3 4 3 3 4 3 SP M ME I SD: 0.9945 c. M:-1.6341 c. 83: 4 5 4 4 5 4 5 4 4 5 4 4 5 4 5 4 4 5 4 SP M ME I SD: 0.2455 c. M:-0.4034 c. 230: 11 14 11 11 14 11 14 11 11 14 11 11 14 11 14 11 11 14 11 SP M DE I SD: 0.0995 c. M:-0.1636 c. 313: 15 19 15 15 19 15 19 15 15 19 15 15 19 15 19 15 15 19 15 SP M DE I SD: 0.0080 c. M:-0.0132 c. 1335: 64 81 64 64 81 64 81 64 64 81 64 64 81 64 81 64 64 81 64 SP M DE I SD: 0.0077 c. M:-0.0127 c. 1648: 79 100 79 79 100 79 100 79 79 100 79 79 100 79 100 79 79 100 79 SP M DE I SD: 0.0047 c. M:-0.0078 c. 1961: 94 119 94 94 119 94 119 94 94 119 94 94 119 94 119 94 94 119 94 SP M DE I SD: 0.0027 c. M:-0.0044 c. 2274: 109 138 109 109 138 109 138 109 109 138 109 109 138 109 138 109 109 138 109 SP M DE I SD: 0.0012 c. M:-0.0020 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 2.5400 cents 2 .. 4 match: 2 H SD: 3.5150 cents 3 .. 6 match: 3 H SD: 3.1563 cents 4 .. 8 match: 4 H SD: 4.2854 cents 5 .. 10 match: 5 H SD: 4.4474 cents 6 .. 12 match: 6 H SD: 5.4803 cents 7 .. 14 match: 7 H SD: 6.7948 cents 8 .. 16 match: 8 H SD: 4.3260 cents 9 .. 18 match: 9 H SD: 5.2814 cents 10 .. 20 match: 10 H SD: 5.8821 cents 11 .. 22 match: 11 H SD: 6.4899 cents 12 .. 24 match: 12 H SD: 5.1843 cents 13 .. 26 match: 13 H SD: 3.9858 cents 14 .. 28 match: 14 H SD: 4.4891 cents 15 .. 30 match: 15 H SD: 4.0713 cents 16 .. 32 match: 16 H SD: 3.9363 cents 17 .. 34 match: 16 S SD: 5.4945 cents 18 .. 36 match: 17 SD: 4.0000 cents 19 .. 38 match: 17 SD: 4.6870 cents 20 .. 40 match: 18 SD: 2.9134 cents 21 .. 42 match: 18 SD: 3.7316 cents 22 .. 44 match: 17 SD: 4.5864 cents 23 .. 46 match: 19 SD: 3.7991 cents 24 .. 48 match: 19 SD: 2.7298 cents 26 .. 52 match: 19 SD: 2.3141 cents 33 .. 66 match: 19 SD: 2.0608 cents 34 .. 68 match: 19 SD: 1.9280 cents 41 .. 82 match: 19 SD: 1.8037 cents 49 .. 98 match: 19 SD: 1.6182 cents 50 .. 100 match: 19 SD: 1.3636 cents 53 .. 106 match: 19 SD: 1.3214 cents 54 .. 108 match: 19 SD: 1.1450 cents 64 .. 128 match: 19 SD: 1.1443 cents 65 .. 130 match: 19 SD: 1.0019 cents 77 .. 154 match: 19 SD: 0.9343 cents 79 .. 158 match: 19 SD: 0.8646 cents 85 .. 170 match: 19 SD: 0.7743 cents 98 .. 196 match: 19 SD: 0.7645 cents 99 .. 198 match: 19 SD: 0.6935 cents 111 .. 222 match: 19 SD: 0.6754 cents 112 .. 224 match: 19 SD: 0.6167 cents 114 .. 228 match: 19 SD: 0.5351 cents 138 .. 276 match: 19 SD: 0.5328 cents 139 .. 278 match: 19 SD: 0.5180 cents 148 .. 296 match: 19 SD: 0.5054 cents 149 .. 298 match: 19 SD: 0.4957 cents 152 .. 304 match: 19 SD: 0.4728 cents 156 .. 312 match: 19 SD: 0.4674 cents 164 .. 328 match: 19 SD: 0.4556 cents 168 .. 336 match: 19 SD: 0.4323 cents 176 .. 353 match: 19 SD: 0.3678 cents 182 .. 365 match: 19 SD: 0.3133 cents 202 .. 405 match: 19 SD: 0.2987 cents 242 .. 485 match: 19 SD: 0.2831 cents 243 .. 487 match: 19 SD: 0.2641 cents 267 .. 535 match: 19 SD: 0.2109 cents 296 .. 593 match: 19 SD: 0.1942 cents 321 .. 643 match: 19 SD: 0.1492 cents 435 .. 871 match: 19 SD: 0.1422 cents 485 .. 971 match: 19 SD: 0.1418 cents 499 .. 999 match: 19 SD: 0.1395 cents 506 .. 1013 match: 19 SD: 0.1368 cents 523 .. 1048 match: 19 SD: 0.1248 cents 563 .. 1128 match: 19 SD: 0.1189 cents 564 .. 1130 match: 19 SD: 0.1141 cents 584 .. 1170 match: 19 SD: 0.0983 cents