Scala analysis: xen18-schulter-archytan-5-26-17
5/26-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64.010 cents 64.009523 2: 150.387 cents 150.386668 3: 214.396 cents 214.396191 4: 278.406 cents 278.405714 5: 364.783 cents 364.782859 6: 428.792 cents 428.792382 7: 492.802 cents 492.801905 8: 556.811 cents 556.811427 9: 643.189 cents 643.188573 10: 707.198 cents 707.198095 11: 771.208 cents 771.207618 12: 857.585 cents 857.584764 13: 921.594 cents 921.594286 14: 985.604 cents 985.603809 15: 1071.981 cents 1071.980954 16: 1135.990 cents 1135.990477 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 64.0095 cents 64.0095 1: 64.0095 cents 64.0095 2: 86.3771 cents 86.3771 3: 64.0095 cents 64.0095 4: 64.0095 cents 64.0095 5: 86.3771 cents 86.3771 6: 64.0095 cents 64.0095 7: 64.0095 cents 64.0095 8: 64.0095 cents 64.0095 9: 86.3771 cents 86.3771 10: 64.0095 cents 64.0095 11: 64.0095 cents 64.0095 12: 86.3771 cents 86.3771 13: 64.0095 cents 64.0095 14: 64.0095 cents 64.0095 15: 86.3771 cents 86.3771 16: 64.0095 cents 64.0095 17: 64.0095 cents 64.0095
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 64.00952 cents 1: 5 86.37715 cents 2: 7 128.01905 cents 2: 10 150.38667 cents 3: 2 192.02857 cents 3: 15 214.39619 cents 4: 14 278.40571 cents 4: 3 300.77334 cents 5: 9 342.41524 cents 5: 8 364.78286 cents 6: 4 406.42476 cents 6: 13 428.79238 cents 7: 16 492.80190 cents 7: 1 515.16953 cents 8: 11 556.81143 cents 8: 6 579.17905 cents 9: 6 620.82095 cents 9: 11 643.18857 cents 10: 1 684.83047 cents 10: 16 707.19809 cents 11: 13 771.20762 cents 11: 4 793.57524 cents 12: 8 835.21714 cents 12: 9 857.58476 cents 13: 3 899.22666 cents 13: 14 921.59429 cents 14: 15 985.60381 cents 14: 2 1007.97143 cents 15: 10 1049.61333 cents 15: 7 1071.98095 cents 16: 5 1113.62285 cents 16: 12 1135.99048 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 : 64.0 150.4 214.4 278.4 364.8 428.8 492.8 556.8 643.2 707.2 771.2 857.6 921.6 985.6 1072.0 1136.0 1200.0 64.0 : 86.4 150.4 214.4 300.8 364.8 428.8 492.8 579.2 643.2 707.2 793.6 857.6 921.6 1008.0 1072.0 1136.0 1200.0 150.4 : 64.0 128.0 214.4 278.4 342.4 406.4 492.8 556.8 620.8 707.2 771.2 835.2 921.6 985.6 1049.6 1113.6 1200.0 214.4 : 64.0 150.4 214.4 278.4 342.4 428.8 492.8 556.8 643.2 707.2 771.2 857.6 921.6 985.6 1049.6 1136.0 1200.0 278.4 : 86.4 150.4 214.4 278.4 364.8 428.8 492.8 579.2 643.2 707.2 793.6 857.6 921.6 985.6 1072.0 1136.0 1200.0 364.8 : 64.0 128.0 192.0 278.4 342.4 406.4 492.8 556.8 620.8 707.2 771.2 835.2 899.2 985.6 1049.6 1113.6 1200.0 428.8 : 64.0 128.0 214.4 278.4 342.4 428.8 492.8 556.8 643.2 707.2 771.2 835.2 921.6 985.6 1049.6 1136.0 1200.0 492.8 : 64.0 150.4 214.4 278.4 364.8 428.8 492.8 579.2 643.2 707.2 771.2 857.6 921.6 985.6 1072.0 1136.0 1200.0 556.8 : 86.4 150.4 214.4 300.8 364.8 428.8 515.2 579.2 643.2 707.2 793.6 857.6 921.6 1008.0 1072.0 1136.0 1200.0 643.2 : 64.0 128.0 214.4 278.4 342.4 428.8 492.8 556.8 620.8 707.2 771.2 835.2 921.6 985.6 1049.6 1113.6 1200.0 707.2 : 64.0 150.4 214.4 278.4 364.8 428.8 492.8 556.8 643.2 707.2 771.2 857.6 921.6 985.6 1049.6 1136.0 1200.0 771.2 : 86.4 150.4 214.4 300.8 364.8 428.8 492.8 579.2 643.2 707.2 793.6 857.6 921.6 985.6 1072.0 1136.0 1200.0 857.6 : 64.0 128.0 214.4 278.4 342.4 406.4 492.8 556.8 620.8 707.2 771.2 835.2 899.2 985.6 1049.6 1113.6 1200.0 921.6 : 64.0 150.4 214.4 278.4 342.4 428.8 492.8 556.8 643.2 707.2 771.2 835.2 921.6 985.6 1049.6 1136.0 1200.0 985.6 : 86.4 150.4 214.4 278.4 364.8 428.8 492.8 579.2 643.2 707.2 771.2 857.6 921.6 985.6 1072.0 1136.0 1200.0 1072.0: 64.0 128.0 192.0 278.4 342.4 406.4 492.8 556.8 620.8 684.8 771.2 835.2 899.2 985.6 1049.6 1113.6 1200.0 1136.0: 64.0 128.0 214.4 278.4 342.4 428.8 492.8 556.8 620.8 707.2 771.2 835.2 921.6 985.6 1049.6 1136.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.0095 .. 86.3771 cents 22.36762 cents 64.00952 cents 2: 128.0190 .. 150.3867 cents 22.36762 cents 41.64190 cents 3: 192.0286 .. 214.3962 cents 22.36762 cents 41.64190 cents 4: 278.4057 .. 300.7733 cents 22.36762 cents 64.00952 cents 5: 342.4152 .. 364.7829 cents 22.36762 cents 41.64190 cents 6: 406.4248 .. 428.7924 cents 22.36762 cents 41.64190 cents 7: 492.8019 .. 515.1695 cents 22.36762 cents 64.00952 cents 8: 556.8114 .. 579.1791 cents 22.36762 cents 41.64190 cents 9: 620.8209 .. 643.1886 cents 22.36762 cents 41.64190 cents 10: 684.8305 .. 707.1981 cents 22.36762 cents 41.64190 cents 11: 771.2076 .. 793.5752 cents 22.36762 cents 64.00952 cents 12: 835.2171 .. 857.5848 cents 22.36762 cents 41.64190 cents 13: 899.2267 .. 921.5943 cents 22.36762 cents 41.64190 cents 14: 985.6038 .. 1007.9714 cents 22.36762 cents 64.00952 cents 15: 1049.6133 .. 1071.9810 cents 22.36762 cents 41.64190 cents 16: 1113.6229 .. 1135.9905 cents 22.36762 cents 41.64190 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 64.00952 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 86.37715 cents Average / Smallest step : 1.102777 Largest / Average step : 1.223676 Largest / Smallest step : 1.349442 Median interval of one step : 64.00952 cents, amount: 12 Most common interval of one step : 64.00952 cents, amount: 12 Least squares average step : 70.86391 cents, oct.: 1204.68655 cents Scale is strictly proper Scale has Myhill's property chromas: 22.36762 cents and 41.64190 cents, ratio: 1.861704 generators: 7 of 492.80190 cents and 10 of 707.19810 cents ET pair of linear temperament : 17&39 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1556-tone equal temperament with octave 1200.000 cents degrees: 83 195 278 361 473 556 639 722 834 917 1000 1112 1195 1278 1390 1473 1556 generators: 639 and 917 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 41.64190 cents Ratio Whole / Half tone : 3.349442 Scale diversity : 1.174518 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.701765 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 : 22.36762 cents Most common intervals : 492.80190 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 492.802 985.604 cents Most common triad is 0.0 492.802 707.198 cents, amount: 15 Number of recognisable fifths : 16, average 707.1981 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle 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: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.9623 c. M: 13.1574 c. 39: 2 3 2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 SP M ME S SD: 2.6151 c. M:-4.9421 c. 56: 3 4 3 3 4 3 3 3 4 3 3 4 3 3 4 3 3 SP M ME S SD: 0.2923 c. M: 0.5524 c. 207: 11 15 11 11 15 11 11 11 15 11 11 15 11 11 15 11 11 SP M DE S SD: 0.2555 c. M:-0.4828 c. 263: 14 19 14 14 19 14 14 14 19 14 14 19 14 14 19 14 14 SP M DE S SD: 0.1388 c. M:-0.2624 c. 319: 17 23 17 17 23 17 17 17 23 17 17 23 17 17 23 17 17 SP M DE S SD: 0.0632 c. M:-0.1194 c. 375: 20 27 20 20 27 20 20 20 27 20 20 27 20 20 27 20 20 SP M DE S SD: 0.0101 c. M:-0.0190 c. 1181: 63 85 63 63 85 63 63 63 85 63 63 85 63 63 85 63 63 SP M DE S SD: 0.0043 c. M: 0.0080 c. 1556: 83 112 83 83 112 83 83 83 112 83 83 112 83 83 112 83 83 SP M DE S SD: 0.0008 c. M: 0.0015 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.6215 cents 3 .. 6 match: 3 H SD: 9.0942 cents 4 .. 8 match: 4 H SD: 6.9488 cents 5 .. 10 match: 5 H SD: 13.9642 cents 6 .. 12 match: 6 H SD: 6.2726 cents 7 .. 14 match: 7 H SD: 5.0347 cents 8 .. 16 match: 8 H SD: 4.7908 cents 9 .. 18 match: 9 H SD: 6.1936 cents 10 .. 20 match: 10 H SD: 7.9911 cents 11 .. 22 match: 11 H SD: 5.1815 cents 12 .. 24 match: 12 H SD: 5.6536 cents 13 .. 26 match: 13 H SD: 4.9471 cents 14 .. 28 match: 14 H SD: 4.6152 cents 15 .. 30 match: 14 SD: 6.4312 cents 16 .. 32 match: 15 S SD: 4.4965 cents 17 .. 34 match: 15 SD: 5.1521 cents 18 .. 36 match: 16 SD: 4.2322 cents 19 .. 38 match: 16 SD: 5.3239 cents 20 .. 40 match: 16 SD: 4.3727 cents 21 .. 42 match: 17 SD: 3.5529 cents 22 .. 44 match: 17 SD: 2.8601 cents 29 .. 58 match: 17 SD: 2.5615 cents 30 .. 60 match: 17 SD: 2.4323 cents 34 .. 68 match: 17 SD: 2.2333 cents 42 .. 84 match: 17 SD: 2.0037 cents 43 .. 86 match: 17 SD: 1.9545 cents 44 .. 88 match: 17 SD: 1.9305 cents 45 .. 90 match: 17 SD: 1.7958 cents 46 .. 92 match: 17 SD: 1.6662 cents 47 .. 94 match: 17 SD: 1.5684 cents 51 .. 102 match: 17 SD: 1.4510 cents 52 .. 104 match: 17 SD: 1.4432 cents 53 .. 106 match: 17 SD: 1.3842 cents 55 .. 110 match: 17 SD: 1.2726 cents 64 .. 128 match: 17 SD: 1.1304 cents 69 .. 138 match: 17 SD: 1.0992 cents 75 .. 150 match: 17 SD: 1.0293 cents 76 .. 152 match: 17 SD: 0.9464 cents 78 .. 156 match: 17 SD: 0.9434 cents 82 .. 164 match: 17 SD: 0.8991 cents 85 .. 170 match: 17 SD: 0.7670 cents 97 .. 194 match: 17 SD: 0.7531 cents 98 .. 196 match: 17 SD: 0.6705 cents 107 .. 214 match: 17 SD: 0.6086 cents 121 .. 242 match: 17 SD: 0.6037 cents 131 .. 262 match: 17 SD: 0.5429 cents 142 .. 284 match: 17 SD: 0.5001 cents 153 .. 306 match: 17 SD: 0.4273 cents 166 .. 332 match: 17 SD: 0.4186 cents 167 .. 334 match: 17 SD: 0.3560 cents 189 .. 378 match: 17 SD: 0.2941 cents 218 .. 436 match: 17 SD: 0.2878 cents 242 .. 484 match: 17 SD: 0.2562 cents 264 .. 528 match: 17 SD: 0.2262 cents 287 .. 574 match: 17 SD: 0.2262 cents 317 .. 634 match: 17 SD: 0.2217 cents 321 .. 642 match: 17 SD: 0.2195 cents 340 .. 680 match: 17 SD: 0.2165 cents 342 .. 684 match: 17 SD: 0.2079 cents 343 .. 686 match: 17 SD: 0.2072 cents 349 .. 698 match: 17 SD: 0.1778 cents 371 .. 742 match: 17 SD: 0.1679 cents 374 .. 748 match: 17 SD: 0.1619 cents 395 .. 790 match: 17 SD: 0.1580 cents 440 .. 880 match: 17 SD: 0.1557 cents 476 .. 952 match: 17 SD: 0.1503 cents 477 .. 954 match: 17 SD: 0.1299 cents 498 .. 996 match: 17 SD: 0.1263 cents 529 .. 1058 match: 17 SD: 0.1215 cents 538 .. 1076 match: 17 SD: 0.1112 cents 562 .. 1124 match: 17 SD: 0.0983 cents 583 .. 1166 match: 17 SD: 0.0969 cents