Scala analysis: xen18-erlich-tetracot-20
7L 13s MOS for Tetracot, L=108.63, s=33.74
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.740 cents 33.740000 2: 142.370 cents 142.370000 3: 176.110 cents 176.110000 4: 209.850 cents 209.850000 5: 318.480 cents 318.480000 6: 352.220 cents 352.220000 7: 385.960 cents 385.960000 8: 494.590 cents 494.590000 9: 528.330 cents 528.330000 10: 636.960 cents 636.960000 11: 670.700 cents 670.700000 12: 704.440 cents 704.440000 13: 813.070 cents 813.070000 14: 846.810 cents 846.810000 15: 880.550 cents 880.550000 16: 989.180 cents 989.180000 17: 1022.920 cents 1022.920000 18: 1056.660 cents 1056.660000 19: 1165.290 cents 1165.290000 20: 1199.030 cents 1199.030000
SHOW/INTERVAL
0: 33.7400 cents 33.7400 1: 33.7400 cents 33.7400 2: 108.6300 cents 108.6300 3: 33.7400 cents 33.7400 4: 33.7400 cents 33.7400 5: 108.6300 cents 108.6300 6: 33.7400 cents 33.7400 7: 33.7400 cents 33.7400 8: 108.6300 cents 108.6300 9: 33.7400 cents 33.7400 10: 108.6300 cents 108.6300 11: 33.7400 cents 33.7400 12: 33.7400 cents 33.7400 13: 108.6300 cents 108.6300 14: 33.7400 cents 33.7400 15: 33.7400 cents 33.7400 16: 108.6300 cents 108.6300 17: 33.7400 cents 33.7400 18: 33.7400 cents 33.7400 19: 108.6300 cents 108.6300 20: 33.7400 cents 33.7400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 33.74000 cents 1: 7 108.63000 cents 2: 6 67.48000 cents 2: 14 142.37000 cents 3: 19 176.11000 cents 3: 1 251.00000 cents 4: 12 209.85000 cents 4: 8 284.74000 cents 5: 5 243.59000 cents 5: 15 318.48000 cents 6: 18 352.22000 cents 6: 2 427.11000 cents 7: 11 385.96000 cents 7: 9 460.85000 cents 8: 4 419.70000 cents 8: 16 494.59000 cents 9: 17 528.33000 cents 9: 3 603.22000 cents 10: 10 562.07000 cents 10: 10 636.96000 cents 11: 3 595.81000 cents 11: 17 670.70000 cents 12: 16 704.44000 cents 12: 4 779.33000 cents 13: 9 738.18000 cents 13: 11 813.07000 cents 14: 2 771.92000 cents 14: 18 846.81000 cents 15: 15 880.55000 cents 15: 5 955.44000 cents 16: 8 914.29000 cents 16: 12 989.18000 cents 17: 1 948.03000 cents 17: 19 1022.92000 cents 18: 14 1056.66000 cents 18: 6 1131.55000 cents 19: 7 1090.40000 cents 19: 13 1165.29000 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 20 0.0 : 33.7 142.4 176.1 209.9 318.5 352.2 386.0 494.6 528.3 637.0 670.7 704.4 813.1 846.8 880.5 989.2 1022.9 1056.7 1165.3 1199.0 33.7 : 108.6 142.4 176.1 284.7 318.5 352.2 460.9 494.6 603.2 637.0 670.7 779.3 813.1 846.8 955.4 989.2 1022.9 1131.5 1165.3 1199.0 142.4 : 33.7 67.5 176.1 209.9 243.6 352.2 386.0 494.6 528.3 562.1 670.7 704.4 738.2 846.8 880.5 914.3 1022.9 1056.7 1090.4 1199.0 176.1 : 33.7 142.4 176.1 209.9 318.5 352.2 460.9 494.6 528.3 637.0 670.7 704.4 813.1 846.8 880.6 989.2 1022.9 1056.7 1165.3 1199.0 209.9 : 108.6 142.4 176.1 284.7 318.5 427.1 460.9 494.6 603.2 637.0 670.7 779.3 813.1 846.8 955.4 989.2 1022.9 1131.5 1165.3 1199.0 318.5 : 33.7 67.5 176.1 209.9 318.5 352.2 386.0 494.6 528.3 562.1 670.7 704.4 738.2 846.8 880.5 914.3 1022.9 1056.7 1090.4 1199.0 352.2 : 33.7 142.4 176.1 284.7 318.5 352.2 460.9 494.6 528.3 637.0 670.7 704.4 813.1 846.8 880.5 989.2 1022.9 1056.7 1165.3 1199.0 386.0 : 108.6 142.4 251.0 284.7 318.5 427.1 460.9 494.6 603.2 637.0 670.7 779.3 813.1 846.8 955.4 989.2 1022.9 1131.5 1165.3 1199.0 494.6 : 33.7 142.4 176.1 209.9 318.5 352.2 386.0 494.6 528.3 562.1 670.7 704.4 738.2 846.8 880.5 914.3 1022.9 1056.7 1090.4 1199.0 528.3 : 108.6 142.4 176.1 284.7 318.5 352.2 460.9 494.6 528.3 637.0 670.7 704.4 813.1 846.8 880.6 989.2 1022.9 1056.7 1165.3 1199.0 637.0 : 33.7 67.5 176.1 209.9 243.6 352.2 386.0 419.7 528.3 562.1 595.8 704.4 738.2 771.9 880.5 914.3 948.0 1056.7 1090.4 1199.0 670.7 : 33.7 142.4 176.1 209.8 318.5 352.2 386.0 494.6 528.3 562.1 670.7 704.4 738.2 846.8 880.5 914.3 1022.9 1056.7 1165.3 1199.0 704.4 : 108.6 142.4 176.1 284.7 318.5 352.2 460.9 494.6 528.3 637.0 670.7 704.4 813.1 846.8 880.5 989.2 1022.9 1131.5 1165.3 1199.0 813.1 : 33.7 67.5 176.1 209.8 243.6 352.2 386.0 419.7 528.3 562.1 595.8 704.4 738.2 771.9 880.5 914.3 1022.9 1056.7 1090.4 1199.0 846.8 : 33.7 142.4 176.1 209.9 318.5 352.2 386.0 494.6 528.3 562.1 670.7 704.4 738.2 846.8 880.5 989.2 1022.9 1056.7 1165.3 1199.0 880.5 : 108.6 142.4 176.1 284.7 318.5 352.2 460.9 494.6 528.3 637.0 670.7 704.4 813.1 846.8 955.4 989.2 1022.9 1131.5 1165.3 1199.0 989.2 : 33.7 67.5 176.1 209.9 243.6 352.2 386.0 419.7 528.3 562.1 595.8 704.4 738.2 846.8 880.6 914.3 1022.9 1056.7 1090.4 1199.0 1022.9: 33.7 142.4 176.1 209.9 318.5 352.2 386.0 494.6 528.3 562.1 670.7 704.4 813.1 846.8 880.6 989.2 1022.9 1056.7 1165.3 1199.0 1056.7: 108.6 142.4 176.1 284.7 318.5 352.2 460.8 494.6 528.3 637.0 670.7 779.3 813.1 846.8 955.4 989.2 1022.9 1131.5 1165.3 1199.0 1165.3: 33.7 67.5 176.1 209.9 243.6 352.2 386.0 419.7 528.3 562.1 670.7 704.4 738.2 846.8 880.5 914.3 1022.9 1056.7 1090.4 1199.0 1199.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.7400 .. 108.6300 cents 74.89000 cents 33.74000 cents 2: 67.4800 .. 142.3700 cents 74.89000 cents -41.15000 cents 3: 176.1100 .. 251.0000 cents 74.89000 cents 33.74000 cents 4: 209.8500 .. 284.7400 cents 74.89000 cents -41.15000 cents 5: 243.5900 .. 318.4800 cents 74.89000 cents -41.15000 cents 6: 352.2200 .. 427.1100 cents 74.89000 cents 33.74000 cents 7: 385.9600 .. 460.8500 cents 74.89000 cents -41.15000 cents 8: 419.7000 .. 494.5900 cents 74.89000 cents -41.15000 cents 9: 528.3300 .. 603.2200 cents 74.89000 cents 33.74000 cents 10: 562.0700 .. 636.9600 cents 74.89000 cents -41.15000 cents 11: 595.8100 .. 670.7000 cents 74.89000 cents -41.15000 cents 12: 704.4400 .. 779.3300 cents 74.89000 cents 33.74000 cents 13: 738.1800 .. 813.0700 cents 74.89000 cents -41.15000 cents 14: 771.9200 .. 846.8100 cents 74.89000 cents -41.15000 cents 15: 880.5500 .. 955.4400 cents 74.89000 cents 33.74000 cents 16: 914.2900 .. 989.1800 cents 74.89000 cents -41.15000 cents 17: 948.0300 .. 1022.9200 cents 74.89000 cents -41.15000 cents 18: 1056.6600 .. 1131.5500 cents 74.89000 cents 33.74000 cents 19: 1090.4000 .. 1165.2900 cents 74.89000 cents -41.15000 cents
SHOW DATA
Number of notes : 20 -- Interval properties -- Smallest interval : 33.74000 cents, class 1 Average step (divided formal octave): 59.9515 cents Largest one step interval : 108.63000 cents Average / Smallest step : 1.776867 Largest / Average step : 1.811965 Largest / Smallest step : 3.219621 Median interval of one step : 33.74000 cents, amount: 13 Most common interval of one step : 33.74000 cents, amount: 13 Least squares average step : 60.27768 cents, oct.: 1205.55352 cents Scale is not proper Scale has Myhill's property chromas: 74.89000 cents and 41.15000 cents, ratio: 1.819927 generators: 3 of 176.11000 cents and 17 of 1022.92000 cents ET pair of linear temperament : 34&143 Scale is distributional even Scale is a mode of a 1457-tone equal temperament with octave 1199.030 cents degrees: 41 173 214 255 387 428 469 601 642 774 815 856 988 1029 1070 1202 1243 1284 1416 1457 generators: 214 and 1243 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABABAABAABAABA Step pattern size order : SLSSLSSLSLSSLSSLSSLS Scale is a Constant Structure, by a margin of 7.41000 cents Scale diversity : 1.195459 Lumma stability : 0.225115 Lumma impropriety factor : 0.380933 Rothenberg efficiency : 0.700000 redundancy: 0.300000 Efficiency x scale size : 14.000000 Number of different interval sizes : 38 = 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 : 7.41000 cents Most common intervals : 176.11000 cents & inv., amount: 19 Scale is a chain of 10 triads 0.0 385.960 1022.920 cents Most common triad is 0.0 176.110 1022.920 cents, amount: 18 Number of recognisable fifths : 16, average 704.4400 cents Number of recognisable fourths : 16, average 494.5900 cents Scale contains two identical disjunct "tetrachords" of 9 notes Formal octave complements present : 19 = 95.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 17 Inversional symmetry on intervals : 8-9 18-19 -- Rational properties --
FIT/MODE
20: 0 2 0 1 2 0 1 2 0 2 1 0 2 1 0 2 1 0 2 1 N T3 SD: 32.8161 c. M: 56.2070 c. 21: 0 2 1 0 2 1 0 2 1 2 0 1 2 0 1 2 1 0 2 1 N SD: 27.5533 c. M: 47.4567 c. 22: 1 2 0 1 2 0 1 2 1 2 0 1 2 1 0 2 1 0 2 1 N SD: 15.0722 c. M: 25.2118 c. 25: 1 2 1 0 3 0 1 2 1 2 1 1 2 1 0 3 0 1 2 1 N SD: 12.9093 c. M:-18.0052 c. 27: 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 1 2 1 P M ME SD: 8.8212 c. M: 15.2407 c. 34: 1 3 1 1 3 1 1 3 1 3 1 1 3 1 1 3 1 1 3 1 N M DE SD: 1.2614 c. M: 2.1794 c. 109: 3 10 3 3 10 3 3 10 3 10 3 3 10 3 3 10 3 3 10 3 N M DE SD: 0.6112 c. M:-1.0560 c. 143: 4 13 4 4 13 4 4 13 4 13 4 4 13 4 4 13 4 4 13 4 N M DE SD: 0.1659 c. M:-0.2867 c. 177: 5 16 5 5 16 5 5 16 5 16 5 5 16 5 5 16 5 5 16 5 N M DE SD: 0.1082 c. M: 0.1870 c. 320: 9 29 9 9 29 9 9 29 9 29 9 9 29 9 9 29 9 9 29 9 N M DE SD: 0.0143 c. M:-0.0247 c. 817: 23 74 23 23 74 23 23 74 23 74 23 23 74 23 23 74 23 23 74 23 N M DE SD: 0.0123 c. M: 0.0212 c. 1137: 32 103 32 32 103 32 32 103 32 103 32 32 103 32 32 103 32 32 103 32 N M DE SD: 0.0048 c. M: 0.0083 c. 1457: 41 132 41 41 132 41 41 132 41 132 41 41 132 41 41 132 41 41 132 41 N M DE SD: 0.0006 c. M: 0.0010 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.9700 cents 2 .. 4 match: 2 H SD: 1.3338 cents 3 .. 6 match: 3 H SD: 1.7443 cents 4 .. 8 match: 4 H SD: 5.1328 cents 5 .. 10 match: 5 H SD: 10.9058 cents 6 .. 12 match: 6 H SD: 8.7406 cents 7 .. 14 match: 7 H SD: 12.0998 cents 8 .. 16 match: 8 H SD: 5.6234 cents 9 .. 18 match: 9 H SD: 7.3928 cents 10 .. 20 match: 9 S SD: 8.7377 cents 11 .. 22 match: 10 S SD: 8.1120 cents 12 .. 24 match: 11 S SD: 6.1919 cents 13 .. 26 match: 13 H SD: 6.8966 cents 14 .. 28 match: 13 SD: 6.1403 cents 15 .. 30 match: 13 SD: 4.9023 cents 16 .. 32 match: 14 SD: 4.8455 cents 17 .. 34 match: 13 SD: 5.8312 cents 18 .. 36 match: 12 SD: 3.7534 cents 19 .. 38 match: 15 SD: 4.2320 cents 20 .. 40 match: 15 SD: 4.5415 cents 21 .. 42 match: 16 SD: 4.4061 cents 22 .. 44 match: 17 SD: 3.9607 cents 23 .. 46 match: 15 SD: 3.8685 cents 24 .. 48 match: 17 SD: 3.3882 cents 25 .. 50 match: 18 SD: 2.9900 cents 26 .. 52 match: 15 SD: 3.2597 cents 27 .. 54 match: 19 SD: 2.9252 cents 28 .. 56 match: 19 SD: 3.2369 cents 29 .. 58 match: 18 SD: 3.1902 cents 30 .. 60 match: 18 SD: 2.0767 cents 31 .. 62 match: 19 SD: 2.5326 cents 32 .. 64 match: 18 SD: 2.3867 cents 33 .. 66 match: 18 SD: 2.4884 cents 34 .. 68 match: 18 SD: 2.3726 cents 35 .. 70 match: 19 SD: 2.4253 cents 36 .. 72 match: 20 SD: 1.6753 cents 38 .. 76 match: 19 SD: 2.0192 cents 39 .. 78 match: 20 SD: 1.9073 cents 40 .. 80 match: 20 SD: 1.6738 cents 41 .. 82 match: 19 SD: 2.1801 cents 42 .. 84 match: 19 SD: 2.2368 cents 43 .. 86 match: 20 SD: 1.9976 cents 44 .. 88 match: 20 SD: 1.6029 cents 45 .. 90 match: 20 SD: 1.2249 cents 48 .. 96 match: 20 SD: 1.1399 cents 68 .. 136 match: 20 SD: 1.0869 cents 70 .. 140 match: 20 SD: 1.0393 cents 79 .. 158 match: 20 SD: 1.0239 cents 81 .. 162 match: 20 SD: 1.0191 cents 83 .. 166 match: 20 SD: 0.9023 cents 84 .. 168 match: 20 SD: 0.7402 cents 92 .. 184 match: 20 SD: 0.7111 cents 93 .. 186 match: 20 SD: 0.6141 cents 103 .. 206 match: 20 SD: 0.5737 cents 124 .. 248 match: 20 SD: 0.5715 cents 133 .. 266 match: 20 SD: 0.5416 cents 139 .. 278 match: 20 SD: 0.4559 cents 140 .. 280 match: 20 SD: 0.4478 cents 148 .. 296 match: 20 SD: 0.4104 cents 160 .. 320 match: 20 SD: 0.3996 cents 187 .. 374 match: 20 SD: 0.3379 cents 196 .. 392 match: 20 SD: 0.3359 cents 207 .. 414 match: 20 SD: 0.3342 cents 209 .. 418 match: 20 SD: 0.2980 cents 241 .. 482 match: 20 SD: 0.2959 cents 243 .. 486 match: 20 SD: 0.2704 cents 247 .. 494 match: 20 SD: 0.2629 cents 252 .. 504 match: 20 SD: 0.2576 cents 257 .. 514 match: 20 SD: 0.2373 cents 288 .. 576 match: 20 SD: 0.2291 cents 297 .. 594 match: 20 SD: 0.2219 cents 302 .. 604 match: 20 SD: 0.2137 cents 317 .. 634 match: 20 SD: 0.1951 cents 364 .. 728 match: 20 SD: 0.1937 cents 365 .. 730 match: 20 SD: 0.1922 cents 372 .. 744 match: 20 SD: 0.1658 cents 412 .. 824 match: 20 SD: 0.1419 cents 456 .. 911 match: 20 SD: 0.1410 cents 457 .. 913 match: 20 SD: 0.1278 cents 504 .. 1007 match: 20 SD: 0.1157 cents 549 .. 1097 match: 20 SD: 0.1118 cents 560 .. 1119 match: 20 SD: 0.0961 cents