Scala analysis: 696_S5
Semi-tempered tetrachord (4/3)**(3/20) * (4/3)**(7/60) * (4/3)**(11/15)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 74.707 cents 74.706750 2: 132.812 cents 132.812000 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 365.2330 cents 365.2330 1: 74.7068 cents 74.7068 2: 58.1053 cents 58.1053 3: 365.2330 cents 365.2330
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 58.10525 cents 1: 1 74.70675 cents 1: 1 365.23300 cents 2: 1 132.81200 cents 2: 1 423.33825 cents 2: 1 439.93975 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 74.7 132.8 498.0 74.7 : 58.1 423.3 498.0 132.8: 365.2 439.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.1053 .. 365.2330 cents 307.12775 cents 58.10525 cents 2: 132.8120 .. 439.9397 cents 307.12775 cents -232.42100 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 58.10525 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 365.23300 cents Average / Smallest step : 2.857143 Largest / Average step : 2.200000 Largest / Smallest step : 6.285714 Median interval of one step : 74.70675 cents, amount: 1 Least squares average step : 131.03327 cents, oct.: 393.09980 cents Scale is not proper Scale has trivalence property Scale is a mode of a 60-tone equal temperament with octave 4/3 degrees: 9 16 60 Least number of segments generator : 31 of 257.323 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 43 of 356.932 cents and inv. generated superset size: 12 = 9 more = 400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Interval vector is [ 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 58.10525 cents Scale diversity : 0.667833 Lumma stability : 0.233333 Lumma impropriety factor : 0.466667 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 16.60150 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 307.1277 cents: 2 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
3: 0 1 2 N G T3 SD: 47.2001 c. M: 74.7068 c. 4: 1 0 3 N G T3 SD: 29.1513 c. M:-49.8045 c. 5: 1 0 4 N G T3 SD: 23.9622 c. M: 33.2030 c. 6: 1 1 4 N M DE S SD: 19.7597 c. M:-33.2030 c. 7: 1 1 5 N M DE S SD: 5.8495 c. M:-9.4866 c. 12: 2 1 9 N T3 SD: 6.7775 c. M: 8.3008 c. 15: 2 2 11 N M DE S SD: 4.7924 c. M: 8.3008 c. 18: 3 2 13 N T3 SD: 5.7598 c. M:-8.3007 c. 19: 3 2 14 N T3 SD: 2.4842 c. M:-3.9319 c. 26: 4 3 19 N T3 SD: 1.3292 c. M:-1.9156 c. 34: 5 4 25 N T3 SD: 1.0164 c. M: 1.4648 c. 53: 8 6 39 N T3 SD: 0.7726 c. M: 1.2529 c. 60: 9 7 44 N T3 SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x x 7 SD: 84.4672 cents 6 x 7:8 S SD: 67.0295 cents 7 x 8:9 S SD: 58.3934 cents 8 x 9:11 SD: 44.4211 cents 9 x 10:12 S SD: 24.7959 cents 10 x 11:13 SD: 27.1915 cents 11 x 12:15 S SD: 21.3974 cents 12 x 13:16 SD: 2.8803 cents 13 x 14:17 SD: 16.9595 cents 14 x 15:19 SD: 16.7158 cents 15 x 16:20 S SD: 10.5404 cents 16 x 17:21 SD: 19.4892 cents 17:18 x 23 SD: 17.5124 cents 18:19 x 24 SD: 9.4481 cents 21:22:23:28 SD: 8.4536 cents 23:24:25:31 SD: 7.3375 cents 24:25:26:32 SD: 2.3443 cents 63:66:68:84 SD: 1.9534 cents 87:91:94:116 SD: 1.1082 cents 90:94:97:120 SD: 1.0642 cents 111:116:120:148 SD: 0.8897 cents 114:119:123:152 SD: 0.4408 cents 138:144:149:184 SD: 0.3423 cents 225:235:243:300 SD: 0.2388 cents 339:354:366:452 SD: 0.0959 cents 363:379:392:484 SD: 0.0837 cents 477:498:515:636 SD: 0.0545 cents