Scala analysis: xen18-schulter-archytan-1-3-17
1/3-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44.785 cents 44.784843 2: 177.301 cents 177.301220 3: 222.086 cents 222.086063 4: 266.871 cents 266.870906 5: 399.387 cents 399.387283 6: 444.172 cents 444.172126 7: 488.957 cents 488.956969 8: 533.742 cents 533.741811 9: 666.258 cents 666.258189 10: 711.043 cents 711.043031 11: 755.828 cents 755.827874 12: 888.344 cents 888.344252 13: 933.129 cents 933.129094 14: 977.914 cents 977.913937 15: 1110.430 cents 1110.430315 16: 1155.215 cents 1155.215157 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 44.7848 cents 44.7848 1: 44.7848 cents 44.7848 2: 132.5164 cents 132.5164 3: 44.7848 cents 44.7848 4: 44.7848 cents 44.7848 5: 132.5164 cents 132.5164 6: 44.7848 cents 44.7848 7: 44.7848 cents 44.7848 8: 44.7848 cents 44.7848 9: 132.5164 cents 132.5164 10: 44.7848 cents 44.7848 11: 44.7848 cents 44.7848 12: 132.5164 cents 132.5164 13: 44.7848 cents 44.7848 14: 44.7848 cents 44.7848 15: 132.5164 cents 132.5164 16: 44.7848 cents 44.7848 17: 44.7848 cents 44.7848
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 44.78484 cents 1: 5 132.51638 cents 2: 7 89.56969 cents 2: 10 177.30122 cents 3: 2 134.35453 cents 3: 15 222.08606 cents 4: 14 266.87091 cents 4: 3 354.60244 cents 5: 9 311.65575 cents 5: 8 399.38728 cents 6: 4 356.44059 cents 6: 13 444.17213 cents 7: 16 488.95697 cents 7: 1 576.68850 cents 8: 11 533.74181 cents 8: 6 621.47335 cents 9: 6 578.52665 cents 9: 11 666.25819 cents 10: 1 623.31150 cents 10: 16 711.04303 cents 11: 13 755.82787 cents 11: 4 843.55941 cents 12: 8 800.61272 cents 12: 9 888.34425 cents 13: 3 845.39756 cents 13: 14 933.12909 cents 14: 15 977.91394 cents 14: 2 1065.64547 cents 15: 10 1022.69878 cents 15: 7 1110.43032 cents 16: 5 1067.48362 cents 16: 12 1155.21516 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 : 44.8 177.3 222.1 266.9 399.4 444.2 489.0 533.7 666.3 711.0 755.8 888.3 933.1 977.9 1110.4 1155.2 1200.0 44.8 : 132.5 177.3 222.1 354.6 399.4 444.2 489.0 621.5 666.3 711.0 843.6 888.3 933.1 1065.6 1110.4 1155.2 1200.0 177.3 : 44.8 89.6 222.1 266.9 311.7 356.4 489.0 533.7 578.5 711.0 755.8 800.6 933.1 977.9 1022.7 1067.5 1200.0 222.1 : 44.8 177.3 222.1 266.9 311.7 444.2 489.0 533.7 666.3 711.0 755.8 888.3 933.1 977.9 1022.7 1155.2 1200.0 266.9 : 132.5 177.3 222.1 266.9 399.4 444.2 489.0 621.5 666.3 711.0 843.6 888.3 933.1 977.9 1110.4 1155.2 1200.0 399.4 : 44.8 89.6 134.4 266.9 311.7 356.4 489.0 533.7 578.5 711.0 755.8 800.6 845.4 977.9 1022.7 1067.5 1200.0 444.2 : 44.8 89.6 222.1 266.9 311.7 444.2 489.0 533.7 666.3 711.0 755.8 800.6 933.1 977.9 1022.7 1155.2 1200.0 489.0 : 44.8 177.3 222.1 266.9 399.4 444.2 489.0 621.5 666.3 711.0 755.8 888.3 933.1 977.9 1110.4 1155.2 1200.0 533.7 : 132.5 177.3 222.1 354.6 399.4 444.2 576.7 621.5 666.3 711.0 843.6 888.3 933.1 1065.6 1110.4 1155.2 1200.0 666.3 : 44.8 89.6 222.1 266.9 311.7 444.2 489.0 533.7 578.5 711.0 755.8 800.6 933.1 977.9 1022.7 1067.5 1200.0 711.0 : 44.8 177.3 222.1 266.9 399.4 444.2 489.0 533.7 666.3 711.0 755.8 888.3 933.1 977.9 1022.7 1155.2 1200.0 755.8 : 132.5 177.3 222.1 354.6 399.4 444.2 489.0 621.5 666.3 711.0 843.6 888.3 933.1 977.9 1110.4 1155.2 1200.0 888.3 : 44.8 89.6 222.1 266.9 311.7 356.4 489.0 533.7 578.5 711.0 755.8 800.6 845.4 977.9 1022.7 1067.5 1200.0 933.1 : 44.8 177.3 222.1 266.9 311.7 444.2 489.0 533.7 666.3 711.0 755.8 800.6 933.1 977.9 1022.7 1155.2 1200.0 977.9 : 132.5 177.3 222.1 266.9 399.4 444.2 489.0 621.5 666.3 711.0 755.8 888.3 933.1 977.9 1110.4 1155.2 1200.0 1110.4: 44.8 89.6 134.4 266.9 311.7 356.4 489.0 533.7 578.5 623.3 755.8 800.6 845.4 977.9 1022.7 1067.5 1200.0 1155.2: 44.8 89.6 222.1 266.9 311.7 444.2 489.0 533.7 578.5 711.0 755.8 800.6 933.1 977.9 1022.7 1155.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.7848 .. 132.5164 cents 87.73153 cents 44.78484 cents 2: 89.5697 .. 177.3012 cents 87.73153 cents -42.94669 cents 3: 134.3545 .. 222.0861 cents 87.73154 cents -42.94669 cents 4: 266.8709 .. 354.6024 cents 87.73153 cents 44.78484 cents 5: 311.6557 .. 399.3873 cents 87.73153 cents -42.94669 cents 6: 356.4406 .. 444.1721 cents 87.73154 cents -42.94669 cents 7: 488.9570 .. 576.6885 cents 87.73154 cents 44.78484 cents 8: 533.7418 .. 621.4733 cents 87.73154 cents -42.94669 cents 9: 578.5267 .. 666.2582 cents 87.73154 cents -42.94669 cents 10: 623.3115 .. 711.0430 cents 87.73154 cents -42.94669 cents 11: 755.8279 .. 843.5594 cents 87.73154 cents 44.78484 cents 12: 800.6127 .. 888.3443 cents 87.73153 cents -42.94669 cents 13: 845.3976 .. 933.1291 cents 87.73153 cents -42.94669 cents 14: 977.9139 .. 1065.6455 cents 87.73154 cents 44.78484 cents 15: 1022.6988 .. 1110.4303 cents 87.73154 cents -42.94669 cents 16: 1067.4836 .. 1155.2152 cents 87.73153 cents -42.94669 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 44.78484 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 132.51638 cents Average / Smallest step : 1.576164 Largest / Average step : 1.877315 Largest / Smallest step : 2.958956 Median interval of one step : 44.78484 cents, amount: 12 Most common interval of one step : 44.78484 cents, amount: 12 Least squares average step : 71.66952 cents, oct.: 1218.38185 cents Scale is not proper Scale has Myhill's property chromas: 87.73153 cents and 42.94669 cents, ratio: 2.042801 generators: 7 of 488.95697 cents and 10 of 711.04303 cents ET pair of linear temperament : 22&27 Scale is distributional even Scale is a mode of a 1313-tone equal temperament with octave 1200.000 cents degrees: 49 194 243 292 437 486 535 584 729 778 827 972 1021 1070 1215 1264 1313 generators: 535 and 778 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 1.83815 cents Ratio Whole / Half tone : 4.958956 Scale diversity : 1.169519 Lumma stability : 0.223924 Lumma impropriety factor : 0.393678 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 : 1.83815 cents Most common intervals : 488.95697 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 488.957 977.914 cents Most common triad is 0.0 488.957 711.043 cents, amount: 15 Number of recognisable fifths : 16, average 711.0430 cents Scale contains two identical disjunct "tetrachords" of 8 notes 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 2 1 0 2 1 0 1 2 1 0 2 1 0 2 1 1 N T3 SD: 40.0539 c. M: 65.4276 c. 18: 1 2 0 1 2 1 0 1 2 1 0 2 1 1 2 0 1 N T3 SD: 17.9040 c. M:-22.9030 c. 21: 1 2 1 0 3 1 0 1 2 1 1 2 1 1 2 1 1 N SD: 21.1712 c. M: 38.2995 c. 22: 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 1 1 P M ME S SD: 10.3297 c. M: 19.5212 c. 27: 1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1 1 N M DE S SD: 0.3602 c. M:-0.6808 c. 346: 13 38 13 13 38 13 13 13 38 13 13 38 13 13 38 13 13 N M DE S SD: 0.3195 c. M: 0.6037 c. 373: 14 41 14 14 41 14 14 14 41 14 14 41 14 14 41 14 14 N M DE S SD: 0.2703 c. M: 0.5107 c. 400: 15 44 15 15 44 15 15 15 44 15 15 44 15 15 44 15 15 N M DE S SD: 0.2277 c. M: 0.4303 c. 427: 16 47 16 16 47 16 16 16 47 16 16 47 16 16 47 16 16 N M DE S SD: 0.1905 c. M: 0.3601 c. 454: 17 50 17 17 50 17 17 17 50 17 17 50 17 17 50 17 17 N M DE S SD: 0.1578 c. M: 0.2982 c. 481: 18 53 18 18 53 18 18 18 53 18 18 53 18 18 53 18 18 N M DE S SD: 0.1287 c. M: 0.2432 c. 508: 19 56 19 19 56 19 19 19 56 19 19 56 19 19 56 19 19 N M DE S SD: 0.1027 c. M: 0.1941 c. 535: 20 59 20 20 59 20 20 20 59 20 20 59 20 20 59 20 20 N M DE S SD: 0.0793 c. M: 0.1499 c. 562: 21 62 21 21 62 21 21 21 62 21 21 62 21 21 62 21 21 N M DE S SD: 0.0582 c. M: 0.1100 c. 589: 22 65 22 22 65 22 22 22 65 22 22 65 22 22 65 22 22 N M DE S SD: 0.0390 c. M: 0.0738 c. 616: 23 68 23 23 68 23 23 23 68 23 23 68 23 23 68 23 23 N M DE S SD: 0.0215 c. M: 0.0407 c. 643: 24 71 24 24 71 24 24 24 71 24 24 71 24 24 71 24 24 N M DE S SD: 0.0055 c. M: 0.0104 c. 1313: 49 145 49 49 145 49 49 49 145 49 49 145 49 49 145 49 49 N M DE S SD: 0.0020 c. M:-0.0038 c. 1956: 73 216 73 73 216 73 73 73 216 73 73 216 73 73 216 73 73 N M DE S SD: 0.0005 c. M: 0.0009 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 4.5440 cents 3 .. 6 match: 3 H SD: 3.3078 cents 4 .. 8 match: 4 H SD: 4.5833 cents 5 .. 10 match: 5 H SD: 19.6768 cents 6 .. 12 match: 6 H SD: 10.4221 cents 7 .. 14 match: 7 H SD: 9.8505 cents 8 .. 16 match: 8 H SD: 7.6577 cents 9 .. 18 match: 9 H SD: 7.2059 cents 10 .. 20 match: 9 SD: 9.2141 cents 11 .. 22 match: 10 SD: 5.8249 cents 12 .. 24 match: 10 SD: 6.1363 cents 13 .. 26 match: 11 SD: 7.5522 cents 14 .. 28 match: 10 SD: 5.3102 cents 15 .. 30 match: 11 SD: 5.9722 cents 16 .. 32 match: 13 SD: 6.4584 cents 17 .. 34 match: 14 SD: 5.5392 cents 18 .. 36 match: 15 SD: 5.0179 cents 19 .. 38 match: 13 SD: 4.6179 cents 20 .. 40 match: 15 SD: 4.1979 cents 21 .. 42 match: 16 SD: 4.4636 cents 22 .. 44 match: 16 SD: 3.7936 cents 23 .. 46 match: 16 SD: 4.3067 cents 24 .. 48 match: 16 SD: 3.0077 cents 25 .. 50 match: 16 SD: 3.5072 cents 26 .. 52 match: 15 SD: 3.7265 cents 27 .. 54 match: 17 SD: 3.0978 cents 28 .. 56 match: 17 SD: 2.3745 cents 29 .. 58 match: 16 SD: 3.2179 cents 30 .. 60 match: 17 SD: 2.2560 cents 34 .. 68 match: 17 SD: 2.2427 cents 36 .. 72 match: 17 SD: 1.8991 cents 37 .. 74 match: 17 SD: 1.8013 cents 38 .. 76 match: 17 SD: 1.7975 cents 42 .. 84 match: 17 SD: 1.6735 cents 49 .. 98 match: 17 SD: 1.4743 cents 55 .. 110 match: 17 SD: 1.4176 cents 58 .. 116 match: 17 SD: 1.3344 cents 64 .. 128 match: 17 SD: 1.2920 cents 66 .. 132 match: 17 SD: 1.0824 cents 73 .. 146 match: 17 SD: 0.8402 cents 100 .. 200 match: 17 SD: 0.7698 cents 102 .. 204 match: 17 SD: 0.7148 cents 108 .. 216 match: 17 SD: 0.6629 cents 113 .. 226 match: 17 SD: 0.6435 cents 119 .. 238 match: 17 SD: 0.4898 cents 150 .. 300 match: 17 SD: 0.4490 cents 161 .. 322 match: 17 SD: 0.4482 cents 174 .. 348 match: 17 SD: 0.4476 cents 175 .. 350 match: 17 SD: 0.3975 cents 185 .. 370 match: 17 SD: 0.3634 cents 196 .. 392 match: 17 SD: 0.3516 cents 197 .. 394 match: 17 SD: 0.3512 cents 221 .. 442 match: 17 SD: 0.3097 cents 232 .. 464 match: 17 SD: 0.2829 cents 258 .. 516 match: 17 SD: 0.2468 cents 269 .. 538 match: 17 SD: 0.2357 cents 270 .. 540 match: 17 SD: 0.1898 cents 307 .. 614 match: 17 SD: 0.1614 cents 416 .. 832 match: 17 SD: 0.1487 cents 462 .. 924 match: 17 SD: 0.1280 cents 490 .. 980 match: 17 SD: 0.1244 cents 528 .. 1056 match: 17 SD: 0.1168 cents 577 .. 1154 match: 17 SD: 0.1098 cents