Scala analysis: xen18-schulter-archytan-1-4-17
1/4-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56.145 cents 56.144881 2: 161.397 cents 161.397167 3: 217.542 cents 217.542048 4: 273.687 cents 273.686929 5: 378.939 cents 378.939214 6: 435.084 cents 435.084095 7: 491.229 cents 491.228976 8: 547.374 cents 547.373857 9: 652.626 cents 652.626143 10: 708.771 cents 708.771024 11: 764.916 cents 764.915905 12: 870.168 cents 870.168191 13: 926.313 cents 926.313071 14: 982.458 cents 982.457952 15: 1087.710 cents 1087.710238 16: 1143.855 cents 1143.855119 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 56.1449 cents 56.1449 1: 56.1449 cents 56.1449 2: 105.2523 cents 105.2523 3: 56.1449 cents 56.1449 4: 56.1449 cents 56.1449 5: 105.2523 cents 105.2523 6: 56.1449 cents 56.1449 7: 56.1449 cents 56.1449 8: 56.1449 cents 56.1449 9: 105.2523 cents 105.2523 10: 56.1449 cents 56.1449 11: 56.1449 cents 56.1449 12: 105.2523 cents 105.2523 13: 56.1449 cents 56.1449 14: 56.1449 cents 56.1449 15: 105.2523 cents 105.2523 16: 56.1449 cents 56.1449 17: 56.1449 cents 56.1449
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 56.14488 cents 1: 5 105.25229 cents 2: 7 112.28976 cents 2: 10 161.39717 cents 3: 2 168.43464 cents 3: 15 217.54205 cents 4: 14 273.68693 cents 4: 3 322.79433 cents 5: 9 329.83181 cents 5: 8 378.93921 cents 6: 4 385.97669 cents 6: 13 435.08410 cents 7: 16 491.22898 cents 7: 1 540.33638 cents 8: 11 547.37386 cents 8: 6 596.48126 cents 9: 6 603.51874 cents 9: 11 652.62614 cents 10: 1 659.66362 cents 10: 16 708.77102 cents 11: 13 764.91590 cents 11: 4 814.02331 cents 12: 8 821.06079 cents 12: 9 870.16819 cents 13: 3 877.20567 cents 13: 14 926.31307 cents 14: 15 982.45795 cents 14: 2 1031.56536 cents 15: 10 1038.60283 cents 15: 7 1087.71024 cents 16: 5 1094.74771 cents 16: 12 1143.85512 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 : 56.1 161.4 217.5 273.7 378.9 435.1 491.2 547.4 652.6 708.8 764.9 870.2 926.3 982.5 1087.7 1143.9 1200.0 56.1 : 105.3 161.4 217.5 322.8 378.9 435.1 491.2 596.5 652.6 708.8 814.0 870.2 926.3 1031.6 1087.7 1143.9 1200.0 161.4 : 56.1 112.3 217.5 273.7 329.8 386.0 491.2 547.4 603.5 708.8 764.9 821.1 926.3 982.5 1038.6 1094.7 1200.0 217.5 : 56.1 161.4 217.5 273.7 329.8 435.1 491.2 547.4 652.6 708.8 764.9 870.2 926.3 982.5 1038.6 1143.9 1200.0 273.7 : 105.3 161.4 217.5 273.7 378.9 435.1 491.2 596.5 652.6 708.8 814.0 870.2 926.3 982.5 1087.7 1143.9 1200.0 378.9 : 56.1 112.3 168.4 273.7 329.8 386.0 491.2 547.4 603.5 708.8 764.9 821.1 877.2 982.5 1038.6 1094.7 1200.0 435.1 : 56.1 112.3 217.5 273.7 329.8 435.1 491.2 547.4 652.6 708.8 764.9 821.1 926.3 982.5 1038.6 1143.9 1200.0 491.2 : 56.1 161.4 217.5 273.7 378.9 435.1 491.2 596.5 652.6 708.8 764.9 870.2 926.3 982.5 1087.7 1143.9 1200.0 547.4 : 105.3 161.4 217.5 322.8 378.9 435.1 540.3 596.5 652.6 708.8 814.0 870.2 926.3 1031.6 1087.7 1143.9 1200.0 652.6 : 56.1 112.3 217.5 273.7 329.8 435.1 491.2 547.4 603.5 708.8 764.9 821.1 926.3 982.5 1038.6 1094.7 1200.0 708.8 : 56.1 161.4 217.5 273.7 378.9 435.1 491.2 547.4 652.6 708.8 764.9 870.2 926.3 982.5 1038.6 1143.9 1200.0 764.9 : 105.3 161.4 217.5 322.8 378.9 435.1 491.2 596.5 652.6 708.8 814.0 870.2 926.3 982.5 1087.7 1143.9 1200.0 870.2 : 56.1 112.3 217.5 273.7 329.8 386.0 491.2 547.4 603.5 708.8 764.9 821.1 877.2 982.5 1038.6 1094.7 1200.0 926.3 : 56.1 161.4 217.5 273.7 329.8 435.1 491.2 547.4 652.6 708.8 764.9 821.1 926.3 982.5 1038.6 1143.9 1200.0 982.5 : 105.3 161.4 217.5 273.7 378.9 435.1 491.2 596.5 652.6 708.8 764.9 870.2 926.3 982.5 1087.7 1143.9 1200.0 1087.7: 56.1 112.3 168.4 273.7 329.8 386.0 491.2 547.4 603.5 659.7 764.9 821.1 877.2 982.5 1038.6 1094.7 1200.0 1143.9: 56.1 112.3 217.5 273.7 329.8 435.1 491.2 547.4 603.5 708.8 764.9 821.1 926.3 982.5 1038.6 1143.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 56.1449 .. 105.2523 cents 49.10740 cents 56.14488 cents 2: 112.2898 .. 161.3972 cents 49.10741 cents 7.03748 cents 3: 168.4346 .. 217.5420 cents 49.10741 cents 7.03748 cents 4: 273.6869 .. 322.7943 cents 49.10740 cents 56.14488 cents 5: 329.8318 .. 378.9392 cents 49.10741 cents 7.03748 cents 6: 385.9767 .. 435.0841 cents 49.10740 cents 7.03748 cents 7: 491.2290 .. 540.3364 cents 49.10741 cents 56.14488 cents 8: 547.3739 .. 596.4813 cents 49.10740 cents 7.03748 cents 9: 603.5187 .. 652.6261 cents 49.10741 cents 7.03748 cents 10: 659.6636 .. 708.7710 cents 49.10740 cents 7.03748 cents 11: 764.9159 .. 814.0233 cents 49.10741 cents 56.14488 cents 12: 821.0608 .. 870.1682 cents 49.10741 cents 7.03747 cents 13: 877.2057 .. 926.3131 cents 49.10740 cents 7.03748 cents 14: 982.4580 .. 1031.5654 cents 49.10740 cents 56.14488 cents 15: 1038.6028 .. 1087.7102 cents 49.10741 cents 7.03748 cents 16: 1094.7477 .. 1143.8551 cents 49.10740 cents 7.03748 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 56.14488 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 105.25229 cents Average / Smallest step : 1.257252 Largest / Average step : 1.491074 Largest / Smallest step : 1.874655 Median interval of one step : 56.14488 cents, amount: 12 Most common interval of one step : 56.14488 cents, amount: 12 Least squares average step : 71.19348 cents, oct.: 1210.28917 cents Scale is strictly proper Scale has Myhill's property chromas: 49.10740 cents and 7.03748 cents, ratio: 6.977985 generators: 7 of 491.22898 cents and 10 of 708.77102 cents ET pair of linear temperament : 17&22 Scale is maximally even for L / S <= 2 Scale is distributional even Step pattern alph. order: ABAABAAABAABAABAA Step pattern size order : SLSSLSSSLSSLSSLSS Scale is a Constant Structure, by a margin of 7.03748 cents Ratio Whole / Half tone : 3.874655 Scale diversity : 1.133419 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.345235 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 : 7.03747 cents Most common intervals : 491.22898 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 491.229 982.458 cents Most common triad is 0.0 491.229 708.771 cents, amount: 15 Number of recognisable fifths : 16, average 708.7710 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: 15.2854 c. M: 28.8867 c. 19: 1 2 0 1 2 1 1 1 1 1 1 2 1 1 1 1 1 N D3 SD: 17.3568 c. M:-28.0765 c. 20: 1 2 1 1 1 1 1 1 2 1 1 2 0 1 2 1 1 N D3 SD: 16.9659 c. M:-29.8318 c. 21: 1 2 1 1 2 1 1 1 1 1 1 2 1 1 2 1 1 N D3 S SD: 16.1720 c. M: 24.0547 c. 22: 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 1 1 P M ME S SD: 1.6927 c. M:-3.1989 c. 105: 5 9 5 5 9 5 5 5 9 5 5 9 5 5 9 5 5 SP M DE S SD: 1.0562 c. M: 1.9960 c. 127: 6 11 6 6 11 6 6 6 11 6 6 11 6 6 11 6 6 SP M DE S SD: 0.5800 c. M: 1.0961 c. 149: 7 13 7 7 13 7 7 7 13 7 7 13 7 7 13 7 7 SP M DE S SD: 0.2444 c. M: 0.4619 c. 171: 8 15 8 8 15 8 8 8 15 8 8 15 8 8 15 8 8 SP M DE S SD: 0.0048 c. M:-0.0091 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 3.4080 cents 3 .. 6 match: 3 H SD: 5.2475 cents 4 .. 8 match: 4 H SD: 4.2329 cents 5 .. 10 match: 5 H SD: 16.2581 cents 6 .. 12 match: 6 H SD: 7.0932 cents 7 .. 14 match: 7 H SD: 6.4400 cents 8 .. 16 match: 8 H SD: 4.6215 cents 9 .. 18 match: 9 H SD: 5.3325 cents 10 .. 20 match: 10 H SD: 8.7431 cents 11 .. 22 match: 10 SD: 4.7077 cents 12 .. 24 match: 11 S SD: 5.6179 cents 13 .. 26 match: 13 H SD: 6.0561 cents 14 .. 28 match: 14 H SD: 5.8194 cents 15 .. 30 match: 13 SD: 6.8101 cents 16 .. 32 match: 15 S SD: 5.0803 cents 17 .. 34 match: 14 SD: 4.7677 cents 18 .. 36 match: 16 S SD: 4.2590 cents 19 .. 38 match: 15 S SD: 5.2682 cents 20 .. 40 match: 15 SD: 4.0548 cents 21 .. 42 match: 17 SD: 3.6075 cents 22 .. 44 match: 17 SD: 3.3896 cents 24 .. 48 match: 17 SD: 2.7136 cents 26 .. 52 match: 16 SD: 4.0171 cents 27 .. 54 match: 17 SD: 3.3069 cents 28 .. 56 match: 17 SD: 2.6859 cents 29 .. 58 match: 17 SD: 2.4000 cents 30 .. 60 match: 17 SD: 2.2014 cents 37 .. 74 match: 17 SD: 2.1956 cents 40 .. 80 match: 17 SD: 2.0091 cents 42 .. 84 match: 17 SD: 2.0050 cents 45 .. 90 match: 17 SD: 1.9496 cents 46 .. 92 match: 17 SD: 1.8859 cents 48 .. 96 match: 17 SD: 1.8034 cents 49 .. 98 match: 17 SD: 1.7430 cents 51 .. 102 match: 17 SD: 1.6618 cents 52 .. 104 match: 17 SD: 1.2508 cents 59 .. 118 match: 17 SD: 1.1858 cents 61 .. 122 match: 17 SD: 1.1339 cents 70 .. 140 match: 17 SD: 1.0883 cents 81 .. 162 match: 17 SD: 0.7369 cents 110 .. 220 match: 17 SD: 0.6776 cents 112 .. 224 match: 17 SD: 0.6628 cents 113 .. 226 match: 17 SD: 0.6004 cents 122 .. 244 match: 17 SD: 0.5225 cents 140 .. 280 match: 17 SD: 0.5039 cents 144 .. 288 match: 17 SD: 0.4620 cents 151 .. 302 match: 17 SD: 0.4599 cents 158 .. 316 match: 17 SD: 0.4556 cents 164 .. 328 match: 17 SD: 0.3657 cents 204 .. 408 match: 17 SD: 0.3430 cents 216 .. 432 match: 17 SD: 0.2232 cents 245 .. 490 match: 17 SD: 0.2078 cents 326 .. 652 match: 17 SD: 0.1886 cents 360 .. 720 match: 17 SD: 0.1439 cents 461 .. 922 match: 17 SD: 0.1409 cents 479 .. 958 match: 17 SD: 0.1220 cents 524 .. 1048 match: 17 SD: 0.1219 cents 543 .. 1086 match: 17 SD: 0.1189 cents 573 .. 1146 match: 17 SD: 0.1176 cents