Scala analysis: xen18-erlich-injera-26
12L 14s MOS for Injera, L=54.38, s=39.23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39.230 cents 39.230000 2: 93.610 cents 93.610000 3: 132.840 cents 132.840000 4: 187.220 cents 187.220000 5: 226.450 cents 226.450000 6: 280.830 cents 280.830000 7: 320.060 cents 320.060000 8: 374.440 cents 374.440000 9: 413.670 cents 413.670000 10: 468.050 cents 468.050000 11: 507.280 cents 507.280000 12: 561.660 cents 561.660000 13: 600.890 cents 600.890000 14: 640.120 cents 640.120000 15: 694.500 cents 694.500000 16: 733.730 cents 733.730000 17: 788.110 cents 788.110000 18: 827.340 cents 827.340000 19: 881.720 cents 881.720000 20: 920.950 cents 920.950000 21: 975.330 cents 975.330000 22: 1014.560 cents 1014.560000 23: 1068.940 cents 1068.940000 24: 1108.170 cents 1108.170000 25: 1162.550 cents 1162.550000 26: 1201.780 cents 1201.780000
SHOW/INTERVAL
0: 39.2300 cents 39.2300 1: 39.2300 cents 39.2300 2: 54.3800 cents 54.3800 3: 39.2300 cents 39.2300 4: 54.3800 cents 54.3800 5: 39.2300 cents 39.2300 6: 54.3800 cents 54.3800 7: 39.2300 cents 39.2300 8: 54.3800 cents 54.3800 9: 39.2300 cents 39.2300 10: 54.3800 cents 54.3800 11: 39.2300 cents 39.2300 12: 54.3800 cents 54.3800 13: 39.2300 cents 39.2300 14: 39.2300 cents 39.2300 15: 54.3800 cents 54.3800 16: 39.2300 cents 39.2300 17: 54.3800 cents 54.3800 18: 39.2300 cents 39.2300 19: 54.3800 cents 54.3800 20: 39.2300 cents 39.2300 21: 54.3800 cents 54.3800 22: 39.2300 cents 39.2300 23: 54.3800 cents 54.3800 24: 39.2300 cents 39.2300 25: 54.3800 cents 54.3800 26: 39.2300 cents 39.2300
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 14 39.23000 cents 1: 12 54.38000 cents 2: 2 78.46000 cents 2: 24 93.61000 cents 3: 16 132.84000 cents 3: 10 147.99000 cents 4: 4 172.07000 cents 4: 22 187.22000 cents 5: 18 226.45000 cents 5: 8 241.60000 cents 6: 6 265.68000 cents 6: 20 280.83000 cents 7: 20 320.06000 cents 7: 6 335.21000 cents 8: 8 359.29000 cents 8: 18 374.44000 cents 9: 22 413.67000 cents 9: 4 428.82000 cents 10: 10 452.90000 cents 10: 16 468.05000 cents 11: 24 507.28000 cents 11: 2 522.43000 cents 12: 12 546.51000 cents 12: 14 561.66000 cents 13: 26 600.89000 cents 14: 14 640.12000 cents 14: 12 655.27000 cents 15: 2 679.35000 cents 15: 24 694.50000 cents 16: 16 733.73000 cents 16: 10 748.88000 cents 17: 4 772.96000 cents 17: 22 788.11000 cents 18: 18 827.34000 cents 18: 8 842.49000 cents 19: 6 866.57000 cents 19: 20 881.72000 cents 20: 20 920.95000 cents 20: 6 936.10000 cents 21: 8 960.18000 cents 21: 18 975.33000 cents 22: 22 1014.56000 cents 22: 4 1029.71000 cents 23: 10 1053.79000 cents 23: 16 1068.94000 cents 24: 24 1108.17000 cents 24: 2 1123.32000 cents 25: 12 1147.40000 cents 25: 14 1162.55000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.96000 = 49/25
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0.0 : 39.2 93.6 132.8 187.2 226.5 280.8 320.1 374.4 413.7 468.0 507.3 561.7 600.9 640.1 694.5 733.7 788.1 827.3 881.7 921.0 975.3 1014.6 1068.9 1108.2 1162.5 1201.8 39.2 : 54.4 93.6 148.0 187.2 241.6 280.8 335.2 374.4 428.8 468.0 522.4 561.7 600.9 655.3 694.5 748.9 788.1 842.5 881.7 936.1 975.3 1029.7 1068.9 1123.3 1162.5 1201.8 93.6 : 39.2 93.6 132.8 187.2 226.5 280.8 320.1 374.4 413.7 468.0 507.3 546.5 600.9 640.1 694.5 733.7 788.1 827.3 881.7 921.0 975.3 1014.6 1068.9 1108.2 1147.4 1201.8 132.8 : 54.4 93.6 148.0 187.2 241.6 280.8 335.2 374.4 428.8 468.1 507.3 561.7 600.9 655.3 694.5 748.9 788.1 842.5 881.7 936.1 975.3 1029.7 1068.9 1108.2 1162.6 1201.8 187.2 : 39.2 93.6 132.8 187.2 226.5 280.8 320.1 374.4 413.7 452.9 507.3 546.5 600.9 640.1 694.5 733.7 788.1 827.3 881.7 921.0 975.3 1014.6 1053.8 1108.2 1147.4 1201.8 226.5 : 54.4 93.6 148.0 187.2 241.6 280.8 335.2 374.4 413.7 468.0 507.3 561.7 600.9 655.3 694.5 748.9 788.1 842.5 881.7 936.1 975.3 1014.6 1068.9 1108.2 1162.5 1201.8 280.8 : 39.2 93.6 132.8 187.2 226.5 280.8 320.1 359.3 413.7 452.9 507.3 546.5 600.9 640.1 694.5 733.7 788.1 827.3 881.7 921.0 960.2 1014.6 1053.8 1108.2 1147.4 1201.8 320.1 : 54.4 93.6 148.0 187.2 241.6 280.8 320.1 374.4 413.7 468.0 507.3 561.7 600.9 655.3 694.5 748.9 788.1 842.5 881.7 921.0 975.3 1014.6 1068.9 1108.2 1162.5 1201.8 374.4 : 39.2 93.6 132.8 187.2 226.5 265.7 320.1 359.3 413.7 452.9 507.3 546.5 600.9 640.1 694.5 733.7 788.1 827.3 866.6 921.0 960.2 1014.6 1053.8 1108.2 1147.4 1201.8 413.7 : 54.4 93.6 148.0 187.2 226.5 280.8 320.1 374.4 413.7 468.0 507.3 561.7 600.9 655.3 694.5 748.9 788.1 827.3 881.7 921.0 975.3 1014.6 1068.9 1108.2 1162.5 1201.8 468.0 : 39.2 93.6 132.8 172.1 226.5 265.7 320.1 359.3 413.7 452.9 507.3 546.5 600.9 640.1 694.5 733.7 773.0 827.3 866.6 921.0 960.2 1014.6 1053.8 1108.2 1147.4 1201.8 507.3 : 54.4 93.6 132.8 187.2 226.5 280.8 320.1 374.4 413.7 468.1 507.3 561.7 600.9 655.3 694.5 733.7 788.1 827.3 881.7 921.0 975.3 1014.6 1068.9 1108.2 1162.5 1201.8 561.7 : 39.2 78.5 132.8 172.1 226.5 265.7 320.1 359.3 413.7 452.9 507.3 546.5 600.9 640.1 679.4 733.7 773.0 827.3 866.6 920.9 960.2 1014.6 1053.8 1108.2 1147.4 1201.8 600.9 : 39.2 93.6 132.8 187.2 226.5 280.8 320.1 374.4 413.7 468.0 507.3 561.7 600.9 640.1 694.5 733.7 788.1 827.3 881.7 921.0 975.3 1014.6 1068.9 1108.2 1162.5 1201.8 640.1 : 54.4 93.6 148.0 187.2 241.6 280.8 335.2 374.4 428.8 468.0 522.4 561.7 600.9 655.3 694.5 748.9 788.1 842.5 881.7 936.1 975.3 1029.7 1068.9 1123.3 1162.6 1201.8 694.5 : 39.2 93.6 132.8 187.2 226.5 280.8 320.1 374.4 413.7 468.0 507.3 546.5 600.9 640.1 694.5 733.7 788.1 827.3 881.7 921.0 975.3 1014.6 1068.9 1108.2 1147.4 1201.8 733.7 : 54.4 93.6 148.0 187.2 241.6 280.8 335.2 374.4 428.8 468.1 507.3 561.7 600.9 655.3 694.5 748.9 788.1 842.5 881.7 936.1 975.3 1029.7 1068.9 1108.2 1162.5 1201.8 788.1 : 39.2 93.6 132.8 187.2 226.5 280.8 320.1 374.4 413.7 452.9 507.3 546.5 600.9 640.1 694.5 733.7 788.1 827.3 881.7 921.0 975.3 1014.6 1053.8 1108.2 1147.4 1201.8 827.3 : 54.4 93.6 148.0 187.2 241.6 280.8 335.2 374.4 413.7 468.0 507.3 561.7 600.9 655.3 694.5 748.9 788.1 842.5 881.7 936.1 975.3 1014.6 1068.9 1108.2 1162.5 1201.8 881.7 : 39.2 93.6 132.8 187.2 226.5 280.8 320.1 359.3 413.7 452.9 507.3 546.5 600.9 640.1 694.5 733.7 788.1 827.3 881.7 921.0 960.2 1014.6 1053.8 1108.2 1147.4 1201.8 921.0 : 54.4 93.6 148.0 187.2 241.6 280.8 320.1 374.4 413.7 468.1 507.3 561.7 600.9 655.3 694.5 748.9 788.1 842.5 881.7 921.0 975.3 1014.6 1068.9 1108.2 1162.5 1201.8 975.3 : 39.2 93.6 132.8 187.2 226.5 265.7 320.1 359.3 413.7 452.9 507.3 546.5 600.9 640.1 694.5 733.7 788.1 827.3 866.6 920.9 960.2 1014.6 1053.8 1108.2 1147.4 1201.8 1014.6: 54.4 93.6 148.0 187.2 226.5 280.8 320.1 374.4 413.7 468.0 507.3 561.7 600.9 655.3 694.5 748.9 788.1 827.3 881.7 921.0 975.3 1014.6 1068.9 1108.2 1162.6 1201.8 1068.9: 39.2 93.6 132.8 172.1 226.5 265.7 320.1 359.3 413.7 452.9 507.3 546.5 600.9 640.1 694.5 733.7 773.0 827.3 866.6 921.0 960.2 1014.6 1053.8 1108.2 1147.4 1201.8 1108.2: 54.4 93.6 132.8 187.2 226.5 280.8 320.1 374.4 413.7 468.1 507.3 561.7 600.9 655.3 694.5 733.7 788.1 827.3 881.7 921.0 975.3 1014.6 1068.9 1108.2 1162.6 1201.8 1162.5: 39.2 78.5 132.8 172.1 226.5 265.7 320.1 359.3 413.7 452.9 507.3 546.5 600.9 640.1 679.4 733.7 773.0 827.3 866.6 921.0 960.2 1014.6 1053.8 1108.2 1147.4 1201.8 1201.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 39.2300 .. 54.3800 cents 15.15000 cents 39.23000 cents 2: 78.4600 .. 93.6100 cents 15.15000 cents 24.08000 cents 3: 132.8400 .. 147.9900 cents 15.15000 cents 39.23000 cents 4: 172.0700 .. 187.2200 cents 15.15000 cents 24.08000 cents 5: 226.4500 .. 241.6000 cents 15.15000 cents 39.23000 cents 6: 265.6800 .. 280.8300 cents 15.15000 cents 24.08000 cents 7: 320.0600 .. 335.2100 cents 15.15000 cents 39.23000 cents 8: 359.2900 .. 374.4400 cents 15.15000 cents 24.08000 cents 9: 413.6700 .. 428.8200 cents 15.15000 cents 39.23000 cents 10: 452.9000 .. 468.0500 cents 15.15000 cents 24.08000 cents 11: 507.2800 .. 522.4300 cents 15.15000 cents 39.23000 cents 12: 546.5100 .. 561.6600 cents 15.15000 cents 24.08000 cents 13: 600.8900 .. 600.8900 cents 1/1, 0.0000 cents 39.23000 cents 14: 640.1200 .. 655.2700 cents 15.15000 cents 39.23000 cents 15: 679.3500 .. 694.5000 cents 15.15000 cents 24.08000 cents 16: 733.7300 .. 748.8800 cents 15.15000 cents 39.23000 cents 17: 772.9600 .. 788.1100 cents 15.15000 cents 24.08000 cents 18: 827.3400 .. 842.4900 cents 15.15000 cents 39.23000 cents 19: 866.5700 .. 881.7200 cents 15.15000 cents 24.08000 cents 20: 920.9500 .. 936.1000 cents 15.15000 cents 39.23000 cents 21: 960.1800 .. 975.3300 cents 15.15000 cents 24.08000 cents 22: 1014.5600 .. 1029.7100 cents 15.15000 cents 39.23000 cents 23: 1053.7900 .. 1068.9400 cents 15.15000 cents 24.08000 cents 24: 1108.1700 .. 1123.3200 cents 15.15000 cents 39.23000 cents 25: 1147.4000 .. 1162.5500 cents 15.15000 cents 24.08000 cents
SHOW DATA
Number of notes : 26 -- Interval properties -- Smallest interval : 39.23000 cents, class 1 Average step (divided formal octave): 46.2223 cents Largest one step interval : 54.38000 cents Average / Smallest step : 1.178239 Largest / Average step : 1.176488 Largest / Smallest step : 1.386184 Median interval of one step : 39.23000 cents, amount: 14 Most common interval of one step : 39.23000 cents, amount: 14 Least squares average step : 46.25651 cents, oct.: 1202.66931 cents Scale is strictly proper Scale has 2 repeating blocks of 13 notes Blocks have Myhill's property chromas: 15.15000 cents and 24.08000 cents, ratio: 1.589439 generators: 2 of 93.61000 cents and 11 of 507.28000 cents ET pair of linear temperament : 26&64 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1348-tone equal temperament with octave 1201.780 cents degrees: 44 105 149 210 254 315 359 420 464 525 569 630 674 718 779 823 884 928 989 1033 1094 1138 1199 1243 1304 1348 Least number of segments generator : 675 of 601.782 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 779 of 694.500 cents and inv. generated superset size: 687 = 661 more = 2642.308% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABAABABABABABABA Step pattern size order : SLSLSLSLSLSLSSLSLSLSLSLSLS Scale is a Constant Structure, by a margin of 24.08000 cents Scale diversity : 1.149271 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.697449 Number of different interval sizes : 49 = 1.96000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.96000 = 49/25 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 15.15000 cents Most common intervals : 600.89000 cents & inv., amount: 26 Number of recognisable fifths : 24, average 694.5000 cents Number of recognisable fourths : 24, average 507.2800 cents Scale contains two identical disjunct "tetrachords" of 12 notes Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 26 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 13 Limited inverse transpositions : 13 Inversional symmetry on degrees : 0 13 Inversional symmetry on intervals : 6-7 19-20 -- Rational properties --
FIT/MODE
26: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 4.3605 c. M:-6.9923 c. 64: 2 3 2 3 2 3 2 3 2 3 2 3 2 2 3 2 3 2 3 2 3 2 3 2 3 2 SP B ME I SD: 1.0442 c. M:-1.6744 c. 90: 3 4 3 4 3 4 3 4 3 4 3 4 3 3 4 3 4 3 4 3 4 3 4 3 4 3 SP B ME I SD: 0.5172 c. M:-0.8293 c. 154: 5 7 5 7 5 7 5 7 5 7 5 7 5 5 7 5 7 5 7 5 7 5 7 5 7 5 SP B DE I SD: 0.1317 c. M:-0.2112 c. 244: 8 11 8 11 8 11 8 11 8 11 8 11 8 8 11 8 11 8 11 8 11 8 11 8 11 8 SP B DE I SD: 0.1076 c. M:-0.1726 c. 398: 13 18 13 18 13 18 13 18 13 18 13 18 13 13 18 13 18 13 18 13 18 13 18 13 18 13 SP B DE I SD: 0.0150 c. M:-0.0241 c. 950: 31 43 31 43 31 43 31 43 31 43 31 43 31 31 43 31 43 31 43 31 43 31 43 31 43 31 SP B DE I SD: 0.0087 c. M:-0.0140 c. 1348: 44 61 44 61 44 61 44 61 44 61 44 61 44 44 61 44 61 44 61 44 61 44 61 44 61 44 SP B DE I SD: 0.0017 c. M:-0.0028 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 1.7800 cents 2 .. 4 match: 2 H SD: 3.8323 cents 3 .. 6 match: 3 H SD: 3.2560 cents 4 .. 8 match: 4 H SD: 3.8894 cents 5 .. 10 match: 5 H SD: 4.7163 cents 6 .. 12 match: 6 H SD: 4.5003 cents 7 .. 14 match: 7 H SD: 4.3963 cents 8 .. 16 match: 8 H SD: 4.2849 cents 9 .. 18 match: 9 H SD: 4.7029 cents 10 .. 20 match: 10 H SD: 3.6210 cents 11 .. 22 match: 11 H SD: 5.2264 cents 12 .. 24 match: 12 H SD: 3.0443 cents 13 .. 26 match: 13 H SD: 3.4760 cents 14 .. 28 match: 14 H SD: 4.0160 cents 15 .. 30 match: 15 H SD: 3.5120 cents 16 .. 32 match: 16 H SD: 3.2652 cents 17 .. 34 match: 17 H SD: 3.3205 cents 18 .. 36 match: 18 H SD: 3.1068 cents 19 .. 38 match: 19 H SD: 3.1318 cents 20 .. 40 match: 20 H SD: 2.6821 cents 21 .. 42 match: 21 H SD: 2.5665 cents 22 .. 44 match: 20 SD: 3.1051 cents 23 .. 46 match: 22 SD: 2.6726 cents 24 .. 48 match: 23 SD: 2.5981 cents 25 .. 50 match: 23 SD: 2.9503 cents 26 .. 52 match: 24 SD: 2.2690 cents 27 .. 54 match: 23 SD: 2.6084 cents 28 .. 56 match: 25 SD: 2.5120 cents 29 .. 58 match: 25 SD: 1.7994 cents 30 .. 60 match: 24 SD: 2.3656 cents 31 .. 62 match: 24 SD: 2.6418 cents 32 .. 64 match: 25 SD: 2.5213 cents 33 .. 66 match: 26 SD: 1.9398 cents 34 .. 68 match: 26 SD: 1.7478 cents 36 .. 72 match: 26 SD: 1.4617 cents 41 .. 82 match: 26 SD: 1.4280 cents 45 .. 90 match: 26 SD: 1.4183 cents 49 .. 98 match: 26 SD: 1.1785 cents 51 .. 102 match: 26 SD: 1.1769 cents 62 .. 124 match: 26 SD: 1.1260 cents 63 .. 126 match: 26 SD: 1.1187 cents 67 .. 134 match: 26 SD: 1.0713 cents 70 .. 140 match: 26 SD: 0.8937 cents 74 .. 148 match: 26 SD: 0.7919 cents 78 .. 156 match: 26 SD: 0.7435 cents 85 .. 170 match: 26 SD: 0.7353 cents 87 .. 174 match: 26 SD: 0.6248 cents 103 .. 206 match: 26 SD: 0.6245 cents 108 .. 216 match: 26 SD: 0.6123 cents 114 .. 228 match: 26 SD: 0.5454 cents 123 .. 246 match: 26 SD: 0.4051 cents 164 .. 328 match: 26 SD: 0.3600 cents 177 .. 354 match: 26 SD: 0.3427 cents 178 .. 356 match: 26 SD: 0.3177 cents 203 .. 406 match: 26 SD: 0.3062 cents 212 .. 424 match: 26 SD: 0.2533 cents 251 .. 503 match: 26 SD: 0.2456 cents 255 .. 511 match: 26 SD: 0.2330 cents 271 .. 543 match: 26 SD: 0.2215 cents 290 .. 581 match: 26 SD: 0.2125 cents 300 .. 601 match: 26 SD: 0.1818 cents 340 .. 681 match: 26 SD: 0.1806 cents 349 .. 699 match: 26 SD: 0.1622 cents 385 .. 771 match: 26 SD: 0.1613 cents 393 .. 787 match: 26 SD: 0.1344 cents 438 .. 877 match: 26 SD: 0.1172 cents 522 .. 1045 match: 26 SD: 0.1140 cents 523 .. 1047 match: 26 SD: 0.1114 cents 527 .. 1055 match: 26 SD: 0.1099 cents 561 .. 1123 match: 26 SD: 0.1068 cents 563 .. 1127 match: 26 SD: 0.1014 cents