Scala analysis: xen18-schulter-archytan-1-2-17
1/2-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22.065 cents 22.064766 2: 209.109 cents 209.109327 3: 231.174 cents 231.174094 4: 253.239 cents 253.238860 5: 440.283 cents 440.283421 6: 462.348 cents 462.348187 7: 484.413 cents 484.412953 8: 506.478 cents 506.477719 9: 693.522 cents 693.522281 10: 715.587 cents 715.587047 11: 737.652 cents 737.651813 12: 924.696 cents 924.696374 13: 946.761 cents 946.761140 14: 968.826 cents 968.825906 15: 1155.870 cents 1155.870468 16: 1177.935 cents 1177.935234 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 22.0648 cents 22.0648 1: 22.0648 cents 22.0648 2: 187.0446 cents 187.0446 3: 22.0648 cents 22.0648 4: 22.0648 cents 22.0648 5: 187.0446 cents 187.0446 6: 22.0648 cents 22.0648 7: 22.0648 cents 22.0648 8: 22.0648 cents 22.0648 9: 187.0446 cents 187.0446 10: 22.0648 cents 22.0648 11: 22.0648 cents 22.0648 12: 187.0446 cents 187.0446 13: 22.0648 cents 22.0648 14: 22.0648 cents 22.0648 15: 187.0446 cents 187.0446 16: 22.0648 cents 22.0648 17: 22.0648 cents 22.0648
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 22.06477 cents 1: 5 187.04456 cents 2: 7 44.12953 cents 2: 10 209.10933 cents 3: 2 66.19430 cents 3: 15 231.17409 cents 4: 14 253.23886 cents 4: 3 418.21865 cents 5: 9 275.30363 cents 5: 8 440.28342 cents 6: 4 297.36839 cents 6: 13 462.34819 cents 7: 16 484.41295 cents 7: 1 649.39275 cents 8: 11 506.47772 cents 8: 6 671.45752 cents 9: 6 528.54249 cents 9: 11 693.52228 cents 10: 1 550.60725 cents 10: 16 715.58705 cents 11: 13 737.65181 cents 11: 4 902.63161 cents 12: 8 759.71658 cents 12: 9 924.69637 cents 13: 3 781.78135 cents 13: 14 946.76114 cents 14: 15 968.82591 cents 14: 2 1133.80570 cents 15: 10 990.89067 cents 15: 7 1155.87047 cents 16: 5 1012.95544 cents 16: 12 1177.93523 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 0.0 : 22.1 209.1 231.2 253.2 440.3 462.3 484.4 506.5 693.5 715.6 737.7 924.7 946.8 968.8 1155.9 1177.9 1200.0 22.1 : 187.0 209.1 231.2 418.2 440.3 462.3 484.4 671.5 693.5 715.6 902.6 924.7 946.8 1133.8 1155.9 1177.9 1200.0 209.1 : 22.1 44.1 231.2 253.2 275.3 297.4 484.4 506.5 528.5 715.6 737.7 759.7 946.8 968.8 990.9 1013.0 1200.0 231.2 : 22.1 209.1 231.2 253.2 275.3 462.3 484.4 506.5 693.5 715.6 737.7 924.7 946.8 968.8 990.9 1177.9 1200.0 253.2 : 187.0 209.1 231.2 253.2 440.3 462.3 484.4 671.5 693.5 715.6 902.6 924.7 946.8 968.8 1155.9 1177.9 1200.0 440.3 : 22.1 44.1 66.2 253.2 275.3 297.4 484.4 506.5 528.5 715.6 737.7 759.7 781.8 968.8 990.9 1013.0 1200.0 462.3 : 22.1 44.1 231.2 253.2 275.3 462.3 484.4 506.5 693.5 715.6 737.7 759.7 946.8 968.8 990.9 1177.9 1200.0 484.4 : 22.1 209.1 231.2 253.2 440.3 462.3 484.4 671.5 693.5 715.6 737.7 924.7 946.8 968.8 1155.9 1177.9 1200.0 506.5 : 187.0 209.1 231.2 418.2 440.3 462.3 649.4 671.5 693.5 715.6 902.6 924.7 946.8 1133.8 1155.9 1177.9 1200.0 693.5 : 22.1 44.1 231.2 253.2 275.3 462.3 484.4 506.5 528.5 715.6 737.7 759.7 946.8 968.8 990.9 1013.0 1200.0 715.6 : 22.1 209.1 231.2 253.2 440.3 462.3 484.4 506.5 693.5 715.6 737.7 924.7 946.8 968.8 990.9 1177.9 1200.0 737.7 : 187.0 209.1 231.2 418.2 440.3 462.3 484.4 671.5 693.5 715.6 902.6 924.7 946.8 968.8 1155.9 1177.9 1200.0 924.7 : 22.1 44.1 231.2 253.2 275.3 297.4 484.4 506.5 528.5 715.6 737.7 759.7 781.8 968.8 990.9 1013.0 1200.0 946.8 : 22.1 209.1 231.2 253.2 275.3 462.3 484.4 506.5 693.5 715.6 737.7 759.7 946.8 968.8 990.9 1177.9 1200.0 968.8 : 187.0 209.1 231.2 253.2 440.3 462.3 484.4 671.5 693.5 715.6 737.7 924.7 946.8 968.8 1155.9 1177.9 1200.0 1155.9: 22.1 44.1 66.2 253.2 275.3 297.4 484.4 506.5 528.5 550.6 737.7 759.7 781.8 968.8 990.9 1013.0 1200.0 1177.9: 22.1 44.1 231.2 253.2 275.3 462.3 484.4 506.5 528.5 715.6 737.7 759.7 946.8 968.8 990.9 1177.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.0648 .. 187.0446 cents 164.97979 cents 22.06477 cents 2: 44.1295 .. 209.1093 cents 164.97979 cents -142.91503 cents 3: 66.1943 .. 231.1741 cents 164.97980 cents -142.91503 cents 4: 253.2389 .. 418.2187 cents 164.97980 cents 22.06477 cents 5: 275.3036 .. 440.2834 cents 164.97979 cents -142.91503 cents 6: 297.3684 .. 462.3482 cents 164.97980 cents -142.91503 cents 7: 484.4130 .. 649.3927 cents 164.97980 cents 22.06477 cents 8: 506.4777 .. 671.4575 cents 164.97980 cents -142.91503 cents 9: 528.5425 .. 693.5223 cents 164.97980 cents -142.91503 cents 10: 550.6073 .. 715.5870 cents 164.97980 cents -142.91503 cents 11: 737.6518 .. 902.6316 cents 164.97980 cents 22.06477 cents 12: 759.7166 .. 924.6964 cents 164.97979 cents -142.91503 cents 13: 781.7813 .. 946.7611 cents 164.97979 cents -142.91503 cents 14: 968.8259 .. 1133.8057 cents 164.97980 cents 22.06477 cents 15: 990.8907 .. 1155.8705 cents 164.97980 cents -142.91503 cents 16: 1012.9554 .. 1177.9352 cents 164.97979 cents -142.91503 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 22.06477 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 187.04456 cents Average / Smallest step : 3.199138 Largest / Average step : 2.649798 Largest / Smallest step : 8.477070 Median interval of one step : 22.06477 cents, amount: 12 Most common interval of one step : 22.06477 cents, amount: 12 Least squares average step : 72.62160 cents, oct.: 1234.56720 cents Scale is not proper Scale has Myhill's property chromas: 164.97979 cents and 142.91503 cents, ratio: 1.154391 generators: 7 of 484.41295 cents and 10 of 715.58705 cents ET pair of linear temperament : 52&109 Scale is distributional even Scale is a mode of a 1142-tone equal temperament with octave 1200.000 cents degrees: 21 199 220 241 419 440 461 482 660 681 702 880 901 922 1100 1121 1142 generators: 461 and 681 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABAABAABAA Step pattern size order : SLSSLSSSLSSLSSLSS Scale is a Constant Structure, by a margin of 22.06476 cents Ratio Whole / Half tone : 10.477070 Scale diversity : 1.012279 Lumma stability : 0.110324 Lumma impropriety factor : 0.705803 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 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 : 22.06476 cents Most common intervals : 484.41295 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 484.413 968.826 cents Most common triad is 0.0 484.413 715.587 cents, amount: 15 Number of recognisable fifths : 27, average 706.5977 cents Number of appreciable fifths : 11, average 693.5223 cents Formal octave complements present : 13 = 76.4706% Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 Inversional symmetry on intervals : 11-12 -- Rational properties --
FIT/MODE
17: 0 3 0 0 3 0 1 0 3 0 0 3 0 0 3 0 1 N S SD: 27.0650 c. M: 51.1788 c. 19: 0 3 1 0 3 0 1 0 3 0 1 3 0 0 3 1 0 N SD: 16.8945 c. M:-22.6720 c. 21: 0 4 0 0 4 0 0 1 3 1 0 3 1 0 3 1 0 N SD: 16.8181 c. M:-27.2701 c. 23: 0 4 0 1 3 1 0 1 3 1 0 4 0 1 3 1 0 N SD: 15.1636 c. M: 22.8921 c. 24: 0 4 1 0 4 0 1 0 4 0 1 3 1 0 4 1 0 N SD: 14.1423 c. M: 24.6964 c. 28: 1 4 0 1 4 1 0 1 4 1 0 5 0 1 4 1 0 N SD: 12.4606 c. M:-22.0648 c. 30: 0 5 1 0 5 0 1 0 5 1 0 5 0 1 5 0 1 N T3 SD: 14.7764 c. M: 26.7611 c. 31: 0 5 1 0 5 1 0 1 5 0 1 5 0 1 5 0 1 N T3 SD: 12.8361 c. M: 22.0648 c. 33: 1 5 0 1 5 1 0 1 5 1 0 5 1 1 5 0 1 N SD: 9.8628 c. M: 15.6055 c. 38: 1 6 0 1 6 1 0 1 6 1 0 6 1 1 6 0 1 N SD: 8.6080 c. M:-12.5506 c. 42: 1 6 1 1 6 1 1 1 6 1 1 6 1 1 6 1 1 N M DE S SD: 6.8860 c. M: 13.0133 c. 47: 1 7 1 1 7 1 1 1 7 1 1 7 1 1 7 1 1 N M DE S SD: 3.6693 c. M: 6.9343 c. 52: 1 8 1 1 8 1 1 1 8 1 1 8 1 1 8 1 1 N M DE S SD: 1.0712 c. M: 2.0243 c. 57: 1 9 1 1 9 1 1 1 9 1 1 9 1 1 9 1 1 N M DE S SD: 1.0711 c. M:-2.0243 c. 109: 2 17 2 2 17 2 2 2 17 2 2 17 2 2 17 2 2 N M DE S SD: 0.0491 c. M:-0.0928 c. 597: 11 93 11 11 93 11 11 11 93 11 11 93 11 11 93 11 11 N M DE S SD: 0.0485 c. M: 0.0916 c. 706: 13 110 13 13 110 13 13 13 110 13 13 110 13 13 110 13 13 N M DE S SD: 0.0334 c. M: 0.0631 c. 815: 15 127 15 15 127 15 15 15 127 15 15 127 15 15 127 15 15 N M DE S SD: 0.0224 c. M: 0.0422 c. 924: 17 144 17 17 144 17 17 17 144 17 17 144 17 17 144 17 17 N M DE S SD: 0.0139 c. M: 0.0263 c. 1033: 19 161 19 19 161 19 19 19 161 19 19 161 19 19 161 19 19 N M DE S SD: 0.0073 c. M: 0.0137 c. 1142: 21 178 21 21 178 21 21 21 178 21 21 178 21 21 178 21 21 N M DE S SD: 0.0019 c. M: 0.0036 c. 2393: 44 373 44 44 373 44 44 44 373 44 44 373 44 44 373 44 44 N M DE S SD: 0.0004 c. M:-0.0008 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 4.2164 cents 3 .. 6 match: 3 H SD: 13.7366 cents 4 .. 8 match: 4 H SD: 13.6561 cents 5 .. 10 match: 5 H SD: 26.7096 cents 6 .. 12 match: 6 H SD: 15.3128 cents 7 .. 14 match: 6 S SD: 14.8043 cents 8 .. 16 match: 6 S SD: 11.8104 cents 9 .. 18 match: 7 S SD: 12.0680 cents 10 .. 20 match: 7 SD: 13.0867 cents 11 .. 22 match: 9 SD: 10.9726 cents 12 .. 24 match: 8 SD: 9.4713 cents 13 .. 26 match: 8 SD: 6.3148 cents 14 .. 28 match: 8 SD: 5.9166 cents 15 .. 30 match: 9 SD: 11.2812 cents 16 .. 32 match: 10 SD: 10.3420 cents 17 .. 34 match: 11 SD: 8.2506 cents 18 .. 36 match: 11 SD: 8.1069 cents 19 .. 38 match: 10 SD: 8.3234 cents 20 .. 40 match: 10 SD: 6.9277 cents 21 .. 42 match: 10 SD: 6.4608 cents 22 .. 44 match: 10 SD: 6.7169 cents 23 .. 46 match: 11 SD: 5.7795 cents 24 .. 48 match: 11 SD: 4.9193 cents 25 .. 50 match: 11 SD: 4.9884 cents 26 .. 52 match: 12 SD: 4.7018 cents 27 .. 54 match: 11 SD: 5.0008 cents 28 .. 56 match: 11 SD: 4.3327 cents 29 .. 58 match: 13 SD: 4.1440 cents 30 .. 60 match: 13 SD: 3.6561 cents 31 .. 62 match: 13 SD: 3.3460 cents 32 .. 64 match: 13 SD: 3.0048 cents 33 .. 66 match: 14 SD: 2.9999 cents 34 .. 68 match: 14 SD: 3.0616 cents 35 .. 70 match: 15 SD: 3.1156 cents 36 .. 72 match: 14 SD: 2.7411 cents 37 .. 74 match: 15 SD: 2.4064 cents 38 .. 76 match: 14 SD: 2.2832 cents 39 .. 78 match: 14 SD: 2.1793 cents 40 .. 80 match: 14 SD: 2.2386 cents 41 .. 82 match: 15 SD: 1.7842 cents 42 .. 84 match: 15 SD: 2.4253 cents 43 .. 86 match: 16 SD: 1.9606 cents 44 .. 88 match: 14 SD: 1.8611 cents 45 .. 90 match: 15 SD: 1.6130 cents 46 .. 92 match: 15 SD: 2.2015 cents 47 .. 94 match: 15 SD: 1.6024 cents 48 .. 96 match: 16 SD: 1.9415 cents 49 .. 98 match: 17 SD: 1.5628 cents 51 .. 102 match: 15 SD: 1.5570 cents 52 .. 104 match: 16 SD: 1.6070 cents 53 .. 106 match: 16 SD: 1.5184 cents 54 .. 108 match: 16 SD: 1.9372 cents 55 .. 110 match: 17 SD: 1.1875 cents 57 .. 114 match: 16 SD: 1.5664 cents 58 .. 116 match: 17 SD: 1.5099 cents 59 .. 118 match: 16 SD: 1.2556 cents 60 .. 120 match: 16 SD: 1.6704 cents 61 .. 122 match: 17 SD: 1.3874 cents 62 .. 124 match: 17 SD: 1.0158 cents 69 .. 138 match: 17 SD: 0.9994 cents 71 .. 142 match: 17 SD: 0.9434 cents 76 .. 152 match: 17 SD: 0.9287 cents 77 .. 154 match: 17 SD: 0.7941 cents 96 .. 192 match: 17 SD: 0.7699 cents 100 .. 200 match: 17 SD: 0.7390 cents 115 .. 230 match: 17 SD: 0.7124 cents 118 .. 236 match: 17 SD: 0.7044 cents 120 .. 240 match: 17 SD: 0.7004 cents 121 .. 242 match: 17 SD: 0.6678 cents 124 .. 248 match: 17 SD: 0.6538 cents 127 .. 254 match: 17 SD: 0.6353 cents 132 .. 264 match: 17 SD: 0.5620 cents 139 .. 278 match: 17 SD: 0.5211 cents 140 .. 280 match: 17 SD: 0.5045 cents 147 .. 294 match: 17 SD: 0.4851 cents 153 .. 306 match: 17 SD: 0.4813 cents 154 .. 308 match: 17 SD: 0.4550 cents 156 .. 312 match: 17 SD: 0.4318 cents 170 .. 340 match: 17 SD: 0.4115 cents 173 .. 346 match: 17 SD: 0.3899 cents 180 .. 360 match: 17 SD: 0.3845 cents 203 .. 406 match: 17 SD: 0.3254 cents 217 .. 434 match: 17 SD: 0.2913 cents 232 .. 464 match: 17 SD: 0.2767 cents 235 .. 470 match: 17 SD: 0.2318 cents 297 .. 594 match: 17 SD: 0.2262 cents 303 .. 606 match: 17 SD: 0.2157 cents 320 .. 640 match: 17 SD: 0.2117 cents 356 .. 712 match: 17 SD: 0.1858 cents 391 .. 782 match: 17 SD: 0.1851 cents 400 .. 800 match: 17 SD: 0.1773 cents 405 .. 810 match: 17 SD: 0.1734 cents 412 .. 824 match: 17 SD: 0.1284 cents 477 .. 954 match: 17 SD: 0.1050 cents