Scala analysis: 17-tET
17-EDO
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 70.588 cents 70.588240 2: 141.176 cents 141.176470 3: 211.765 cents 211.764710 4: 282.353 cents 282.352940 5: 352.941 cents 352.941180 6: 423.529 cents 423.529410 7: 494.118 cents 494.117650 8: 564.706 cents 564.705880 9: 635.294 cents 635.294120 10: 705.882 cents 705.882350 11: 776.471 cents 776.470590 12: 847.059 cents 847.058820 13: 917.647 cents 917.647060 14: 988.235 cents 988.235290 15: 1058.824 cents 1058.823530 16: 1129.412 cents 1129.411760 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 70.5882 cents 70.5882 1: 70.5882 cents 70.5882 2: 70.5882 cents 70.5882 3: 70.5882 cents 70.5882 4: 70.5882 cents 70.5882 5: 70.5882 cents 70.5882 6: 70.5882 cents 70.5882 7: 70.5882 cents 70.5882 8: 70.5882 cents 70.5882 9: 70.5882 cents 70.5882 10: 70.5882 cents 70.5882 11: 70.5882 cents 70.5882 12: 70.5882 cents 70.5882 13: 70.5882 cents 70.5882 14: 70.5882 cents 70.5882 15: 70.5882 cents 70.5882 16: 70.5882 cents 70.5882 17: 70.5882 cents 70.5882
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 17 70.58824 cents 2: 17 141.17647 cents 3: 17 211.76471 cents 4: 17 282.35294 cents 5: 17 352.94118 cents 6: 17 423.52941 cents 7: 17 494.11765 cents 8: 17 564.70588 cents 9: 17 635.29412 cents 10: 17 705.88235 cents 11: 17 776.47059 cents 12: 17 847.05882 cents 13: 17 917.64706 cents 14: 17 988.23529 cents 15: 17 1058.82353 cents 16: 17 1129.41176 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 70.6 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 141.2 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 211.8 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 282.4 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 352.9 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 423.5 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 494.1 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 564.7 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 635.3 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 705.9 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 776.5 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 847.1 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 917.6 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 988.2 : 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 1058.8: 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 1129.4: 70.6 141.2 211.8 282.4 352.9 423.5 494.1 564.7 635.3 705.9 776.5 847.1 917.6 988.2 1058.8 1129.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.5882 .. 70.5882 cents 1/1, 0.0000 cents 70.58824 cents 2: 141.1765 .. 141.1765 cents 1/1, 0.0000 cents 70.58823 cents 3: 211.7647 .. 211.7647 cents 1/1, 0.0000 cents 70.58824 cents 4: 282.3529 .. 282.3529 cents 1/1, 0.0000 cents 70.58823 cents 5: 352.9412 .. 352.9412 cents 1/1, 0.0000 cents 70.58824 cents 6: 423.5294 .. 423.5294 cents 1/1, 0.0000 cents 70.58823 cents 7: 494.1176 .. 494.1176 cents 1/1, 0.0000 cents 70.58824 cents 8: 564.7059 .. 564.7059 cents 1/1, 0.0000 cents 70.58823 cents 9: 635.2941 .. 635.2941 cents 1/1, 0.0000 cents 70.58824 cents 10: 705.8823 .. 705.8823 cents 1/1, 0.0000 cents 70.58823 cents 11: 776.4706 .. 776.4706 cents 1/1, 0.0000 cents 70.58824 cents 12: 847.0588 .. 847.0588 cents 1/1, 0.0000 cents 70.58823 cents 13: 917.6471 .. 917.6471 cents 1/1, 0.0000 cents 70.58824 cents 14: 988.2353 .. 988.2353 cents 1/1, 0.0000 cents 70.58823 cents 15: 1058.8235 .. 1058.8235 cents 1/1, 0.0000 cents 70.58824 cents 16: 1129.4118 .. 1129.4118 cents 1/1, 0.0000 cents 70.58823 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 70.58823 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 70.58824 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 70.58824 cents, amount: 17 Most common interval of one step : 70.58824 cents, amount: 17 Least squares average step : 70.58824 cents, oct.: 1200.00000 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 70.58824 cents Ratio Whole / Half tone : 3.000000 ( 3 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.058824 redundancy: 0.941176 Efficiency x scale size : 1.000000 Number of different interval sizes : 16 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 17, average 705.8823 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties -- Prime limit : 2 (not all pitches rational)
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: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.9637 cents 3 .. 6 match: 3 H SD: 11.1731 cents 4 .. 8 match: 4 H SD: 9.7014 cents 5 .. 10 match: 5 H SD: 11.6636 cents 6 .. 12 match: 6 H SD: 6.3861 cents 7 .. 14 match: 7 H SD: 5.0892 cents 8 .. 16 match: 8 H SD: 6.4426 cents 9 .. 18 match: 9 H SD: 6.1039 cents 10 .. 20 match: 10 H SD: 7.2515 cents 11 .. 22 match: 11 H SD: 5.1072 cents 12 .. 24 match: 12 H SD: 5.5165 cents 13 .. 26 match: 13 H SD: 4.8926 cents 14 .. 28 match: 14 H SD: 4.3381 cents 15 .. 30 match: 14 SD: 6.4557 cents 16 .. 32 match: 15 SD: 4.7363 cents 17 .. 34 match: 16 SD: 5.3578 cents 18 .. 36 match: 16 SD: 3.6875 cents 19 .. 38 match: 16 SD: 5.0813 cents 20 .. 40 match: 17 SD: 5.0387 cents 21 .. 42 match: 17 SD: 3.3839 cents 22 .. 44 match: 17 SD: 3.1412 cents 23 .. 46 match: 17 SD: 3.0944 cents 26 .. 52 match: 17 SD: 3.0882 cents 30 .. 60 match: 17 SD: 2.6760 cents 32 .. 64 match: 17 SD: 2.5992 cents 34 .. 68 match: 17 SD: 2.5399 cents 36 .. 72 match: 17 SD: 2.2157 cents 39 .. 78 match: 17 SD: 1.7817 cents 44 .. 88 match: 17 SD: 1.7372 cents 46 .. 92 match: 17 SD: 1.4384 cents 57 .. 114 match: 17 SD: 1.2836 cents 67 .. 134 match: 17 SD: 1.2044 cents 69 .. 138 match: 17 SD: 1.1149 cents 70 .. 140 match: 17 SD: 0.9318 cents 79 .. 158 match: 17 SD: 0.9185 cents 83 .. 166 match: 17 SD: 0.9175 cents 90 .. 180 match: 17 SD: 0.8041 cents 94 .. 188 match: 17 SD: 0.7869 cents 97 .. 194 match: 17 SD: 0.6632 cents 115 .. 230 match: 17 SD: 0.6086 cents 129 .. 258 match: 17 SD: 0.5660 cents 140 .. 280 match: 17 SD: 0.4865 cents 163 .. 326 match: 17 SD: 0.3786 cents 187 .. 374 match: 17 SD: 0.3178 cents 236 .. 472 match: 17 SD: 0.3123 cents 238 .. 476 match: 17 SD: 0.2908 cents 239 .. 478 match: 17 SD: 0.2592 cents 260 .. 520 match: 17 SD: 0.1987 cents 339 .. 678 match: 17 SD: 0.1578 cents 412 .. 824 match: 17 SD: 0.1575 cents 415 .. 830 match: 17 SD: 0.1549 cents 433 .. 866 match: 17 SD: 0.1385 cents 451 .. 902 match: 17 SD: 0.1375 cents 505 .. 1010 match: 17 SD: 0.1329 cents 508 .. 1016 match: 17 SD: 0.1299 cents 509 .. 1018 match: 17 SD: 0.1263 cents 530 .. 1060 match: 17 SD: 0.1134 cents 578 .. 1156 match: 17 SD: 0.1082 cents