Scala analysis: xen18-schulter-archytan-1-5-17
1/5-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 62.961 cents 62.960904 2: 151.855 cents 151.854735 3: 214.816 cents 214.815638 4: 277.777 cents 277.776542 5: 366.670 cents 366.670373 6: 429.631 cents 429.631277 7: 492.592 cents 492.592181 8: 555.553 cents 555.553085 9: 644.447 cents 644.446915 10: 707.408 cents 707.407819 11: 770.369 cents 770.368723 12: 859.263 cents 859.262554 13: 922.223 cents 922.223458 14: 985.184 cents 985.184362 15: 1074.078 cents 1074.078192 16: 1137.039 cents 1137.039096 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 62.9609 cents 62.9609 1: 62.9609 cents 62.9609 2: 88.8938 cents 88.8938 3: 62.9609 cents 62.9609 4: 62.9609 cents 62.9609 5: 88.8938 cents 88.8938 6: 62.9609 cents 62.9609 7: 62.9609 cents 62.9609 8: 62.9609 cents 62.9609 9: 88.8938 cents 88.8938 10: 62.9609 cents 62.9609 11: 62.9609 cents 62.9609 12: 88.8938 cents 88.8938 13: 62.9609 cents 62.9609 14: 62.9609 cents 62.9609 15: 88.8938 cents 88.8938 16: 62.9609 cents 62.9609 17: 62.9609 cents 62.9609
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 62.96090 cents 1: 5 88.89383 cents 2: 7 125.92181 cents 2: 10 151.85474 cents 3: 2 188.88271 cents 3: 15 214.81564 cents 4: 14 277.77654 cents 4: 3 303.70947 cents 5: 9 340.73745 cents 5: 8 366.67037 cents 6: 4 403.69835 cents 6: 13 429.63128 cents 7: 16 492.59218 cents 7: 1 518.52511 cents 8: 11 555.55309 cents 8: 6 581.48601 cents 9: 6 618.51399 cents 9: 11 644.44691 cents 10: 1 681.47489 cents 10: 16 707.40782 cents 11: 13 770.36872 cents 11: 4 796.30165 cents 12: 8 833.32963 cents 12: 9 859.26255 cents 13: 3 896.29053 cents 13: 14 922.22346 cents 14: 15 985.18436 cents 14: 2 1011.11729 cents 15: 10 1048.14526 cents 15: 7 1074.07819 cents 16: 5 1111.10617 cents 16: 12 1137.03910 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 : 63.0 151.9 214.8 277.8 366.7 429.6 492.6 555.6 644.4 707.4 770.4 859.3 922.2 985.2 1074.1 1137.0 1200.0 63.0 : 88.9 151.9 214.8 303.7 366.7 429.6 492.6 581.5 644.4 707.4 796.3 859.3 922.2 1011.1 1074.1 1137.0 1200.0 151.9 : 63.0 125.9 214.8 277.8 340.7 403.7 492.6 555.6 618.5 707.4 770.4 833.3 922.2 985.2 1048.1 1111.1 1200.0 214.8 : 63.0 151.9 214.8 277.8 340.7 429.6 492.6 555.6 644.4 707.4 770.4 859.3 922.2 985.2 1048.1 1137.0 1200.0 277.8 : 88.9 151.9 214.8 277.8 366.7 429.6 492.6 581.5 644.4 707.4 796.3 859.3 922.2 985.2 1074.1 1137.0 1200.0 366.7 : 63.0 125.9 188.9 277.8 340.7 403.7 492.6 555.6 618.5 707.4 770.4 833.3 896.3 985.2 1048.1 1111.1 1200.0 429.6 : 63.0 125.9 214.8 277.8 340.7 429.6 492.6 555.6 644.4 707.4 770.4 833.3 922.2 985.2 1048.1 1137.0 1200.0 492.6 : 63.0 151.9 214.8 277.8 366.7 429.6 492.6 581.5 644.4 707.4 770.4 859.3 922.2 985.2 1074.1 1137.0 1200.0 555.6 : 88.9 151.9 214.8 303.7 366.7 429.6 518.5 581.5 644.4 707.4 796.3 859.3 922.2 1011.1 1074.1 1137.0 1200.0 644.4 : 63.0 125.9 214.8 277.8 340.7 429.6 492.6 555.6 618.5 707.4 770.4 833.3 922.2 985.2 1048.1 1111.1 1200.0 707.4 : 63.0 151.9 214.8 277.8 366.7 429.6 492.6 555.6 644.4 707.4 770.4 859.3 922.2 985.2 1048.1 1137.0 1200.0 770.4 : 88.9 151.9 214.8 303.7 366.7 429.6 492.6 581.5 644.4 707.4 796.3 859.3 922.2 985.2 1074.1 1137.0 1200.0 859.3 : 63.0 125.9 214.8 277.8 340.7 403.7 492.6 555.6 618.5 707.4 770.4 833.3 896.3 985.2 1048.1 1111.1 1200.0 922.2 : 63.0 151.9 214.8 277.8 340.7 429.6 492.6 555.6 644.4 707.4 770.4 833.3 922.2 985.2 1048.1 1137.0 1200.0 985.2 : 88.9 151.9 214.8 277.8 366.7 429.6 492.6 581.5 644.4 707.4 770.4 859.3 922.2 985.2 1074.1 1137.0 1200.0 1074.1: 63.0 125.9 188.9 277.8 340.7 403.7 492.6 555.6 618.5 681.5 770.4 833.3 896.3 985.2 1048.1 1111.1 1200.0 1137.0: 63.0 125.9 214.8 277.8 340.7 429.6 492.6 555.6 618.5 707.4 770.4 833.3 922.2 985.2 1048.1 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 88.8938 cents 25.93293 cents 62.96090 cents 2: 125.9218 .. 151.8547 cents 25.93293 cents 37.02798 cents 3: 188.8827 .. 214.8156 cents 25.93293 cents 37.02798 cents 4: 277.7765 .. 303.7095 cents 25.93293 cents 62.96090 cents 5: 340.7374 .. 366.6704 cents 25.93293 cents 37.02798 cents 6: 403.6983 .. 429.6313 cents 25.93293 cents 37.02798 cents 7: 492.5922 .. 518.5251 cents 25.93293 cents 62.96090 cents 8: 555.5531 .. 581.4860 cents 25.93293 cents 37.02798 cents 9: 618.5140 .. 644.4469 cents 25.93293 cents 37.02798 cents 10: 681.4749 .. 707.4078 cents 25.93293 cents 37.02798 cents 11: 770.3687 .. 796.3017 cents 25.93293 cents 62.96090 cents 12: 833.3296 .. 859.2626 cents 25.93293 cents 37.02798 cents 13: 896.2905 .. 922.2235 cents 25.93293 cents 37.02798 cents 14: 985.1844 .. 1011.1173 cents 25.93293 cents 62.96090 cents 15: 1048.1453 .. 1074.0782 cents 25.93293 cents 37.02798 cents 16: 1111.1062 .. 1137.0391 cents 25.93293 cents 37.02798 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 62.96090 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 88.89383 cents Average / Smallest step : 1.121144 Largest / Average step : 1.259329 Largest / Smallest step : 1.411889 Median interval of one step : 62.96090 cents, amount: 12 Most common interval of one step : 62.96090 cents, amount: 12 Least squares average step : 70.90786 cents, oct.: 1205.43357 cents Scale is strictly proper Scale has Myhill's property chromas: 25.93293 cents and 37.02798 cents, ratio: 1.427836 generators: 7 of 492.59218 cents and 10 of 707.40782 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 324-tone equal temperament with octave 1200.000 cents degrees: 17 41 58 75 99 116 133 150 174 191 208 232 249 266 290 307 324 generators: 133 and 191 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 37.02798 cents Ratio Whole / Half tone : 3.411889 Scale diversity : 1.188712 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.654228 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 : 25.93293 cents Most common intervals : 492.59218 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 492.592 985.184 cents Most common triad is 0.0 492.592 707.408 cents, amount: 15 Number of recognisable fifths : 16, average 707.4078 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: 8.0720 c. M: 15.2547 c. 36: 2 3 1 2 3 2 2 2 2 2 2 3 2 2 2 2 2 P D3 SD: 9.1609 c. M: 14.8156 c. 37: 2 3 2 2 2 2 2 2 3 2 2 2 2 2 3 2 2 P D3 SD: 9.1323 c. M: 16.0193 c. 38: 2 3 2 2 3 2 2 2 2 2 2 3 2 2 3 2 2 P D3 S SD: 8.9294 c. M:-12.8680 c. 39: 2 3 2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 SP M ME S SD: 1.5054 c. M:-2.8449 c. 56: 3 4 3 3 4 3 3 3 4 3 3 4 3 3 4 3 3 SP M ME S SD: 1.4020 c. M: 2.6496 c. 95: 5 7 5 5 7 5 5 5 7 5 5 7 5 5 7 5 5 SP M DE S SD: 0.2085 c. M: 0.3940 c. 229: 12 17 12 12 17 12 12 12 17 12 12 17 12 12 17 12 12 SP M DE S SD: 0.0834 c. M:-0.1576 c. 324: 17 24 17 17 24 17 17 17 24 17 17 24 17 17 24 17 17 SP M DE S SD: 0.0022 c. M: 0.0041 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.7264 cents 3 .. 6 match: 3 H SD: 8.5606 cents 4 .. 8 match: 4 H SD: 6.5345 cents 5 .. 10 match: 5 H SD: 14.2653 cents 6 .. 12 match: 6 H SD: 6.2784 cents 7 .. 14 match: 7 H SD: 5.1422 cents 8 .. 16 match: 8 H SD: 4.6308 cents 9 .. 18 match: 9 H SD: 5.9846 cents 10 .. 20 match: 10 H SD: 8.1086 cents 11 .. 22 match: 11 H SD: 5.2841 cents 12 .. 24 match: 12 H SD: 5.7229 cents 13 .. 26 match: 13 H SD: 5.0372 cents 14 .. 28 match: 14 H SD: 4.7257 cents 15 .. 30 match: 14 SD: 6.4404 cents 16 .. 32 match: 15 S SD: 4.5213 cents 17 .. 34 match: 15 SD: 5.1170 cents 18 .. 36 match: 16 SD: 4.2536 cents 19 .. 38 match: 16 SD: 5.3794 cents 20 .. 40 match: 16 SD: 4.3167 cents 21 .. 42 match: 17 SD: 3.6467 cents 22 .. 44 match: 17 SD: 2.9048 cents 29 .. 58 match: 17 SD: 2.4511 cents 30 .. 60 match: 17 SD: 2.3555 cents 34 .. 68 match: 17 SD: 2.2237 cents 42 .. 84 match: 17 SD: 1.9792 cents 43 .. 86 match: 17 SD: 1.9364 cents 45 .. 90 match: 17 SD: 1.7232 cents 46 .. 92 match: 17 SD: 1.6111 cents 51 .. 102 match: 17 SD: 1.3931 cents 55 .. 110 match: 17 SD: 1.3481 cents 64 .. 128 match: 17 SD: 1.0875 cents 75 .. 150 match: 17 SD: 0.9675 cents 82 .. 164 match: 17 SD: 0.9388 cents 84 .. 168 match: 17 SD: 0.8837 cents 85 .. 170 match: 17 SD: 0.6918 cents 98 .. 196 match: 17 SD: 0.6712 cents 107 .. 214 match: 17 SD: 0.6478 cents 109 .. 218 match: 17 SD: 0.6084 cents 127 .. 254 match: 17 SD: 0.5625 cents 128 .. 256 match: 17 SD: 0.5553 cents 131 .. 262 match: 17 SD: 0.5392 cents 137 .. 274 match: 17 SD: 0.5305 cents 143 .. 286 match: 17 SD: 0.4863 cents 161 .. 322 match: 17 SD: 0.4863 cents 162 .. 324 match: 17 SD: 0.4534 cents 164 .. 328 match: 17 SD: 0.4450 cents 166 .. 332 match: 17 SD: 0.3642 cents 188 .. 376 match: 17 SD: 0.3582 cents 195 .. 390 match: 17 SD: 0.3443 cents 212 .. 424 match: 17 SD: 0.3406 cents 219 .. 438 match: 17 SD: 0.2983 cents 241 .. 482 match: 17 SD: 0.2526 cents 264 .. 528 match: 17 SD: 0.2399 cents 294 .. 588 match: 17 SD: 0.2353 cents 317 .. 634 match: 17 SD: 0.2084 cents 327 .. 654 match: 17 SD: 0.1980 cents 355 .. 710 match: 17 SD: 0.1920 cents 373 .. 746 match: 17 SD: 0.1685 cents 380 .. 760 match: 17 SD: 0.1683 cents 402 .. 804 match: 17 SD: 0.1553 cents 437 .. 874 match: 17 SD: 0.1448 cents 459 .. 918 match: 17 SD: 0.1434 cents 462 .. 924 match: 17 SD: 0.1342 cents 483 .. 966 match: 17 SD: 0.1333 cents 492 .. 984 match: 17 SD: 0.1302 cents 523 .. 1046 match: 17 SD: 0.1240 cents 547 .. 1094 match: 17 SD: 0.1229 cents 568 .. 1136 match: 17 SD: 0.1022 cents 590 .. 1180 match: 17 SD: 0.0983 cents