Scala analysis: 683_T90
Tempered tetrachord in cents 212.5 + 62.5 + 225, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 212.500 cents 212.500000 2: 275.000 cents 275.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 225.0000 cents 225.0000 1: 212.5000 cents 212.5000 2: 62.5000 cents 62.5000 3: 225.0000 cents 225.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 62.50000 cents 1: 1 212.50000 cents 1: 1 225.00000 cents 2: 1 275.00000 cents 2: 1 287.50000 cents 2: 1 437.50000 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 : 212.5 275.0 500.0 212.5: 62.5 287.5 500.0 275.0: 225.0 437.5 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.5000 .. 225.0000 cents 162.50000 cents 62.50000 cents 2: 275.0000 .. 437.5000 cents 162.50000 cents 50.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 62.50000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 225.00000 cents Average / Smallest step : 2.666667 Largest / Average step : 1.350000 Largest / Smallest step : 3.600000 Median interval of one step : 212.50000 cents, amount: 1 Least squares average step : 161.60714 cents, oct.: 484.82143 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 40-tone equal temperament with octave 500.000 cents degrees: 17 22 40 Least number of segments generator : 21 of 262.500 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 23 of 287.500 cents and inv. generated superset size: 7 = 4 more = 233.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Interval vector is [ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 0.796279 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.350000 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 : 12.50000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 42.8310 c. M:-58.3333 c. 4: 2 0 2 P M DE I SD: 26.0208 c. M:-37.5000 c. 5: 2 1 2 SP M ME I SD: 16.1374 c. M:-25.0000 c. 7: 3 1 3 SP M DE I SD: 6.2712 c. M:-10.7143 c. 9: 4 1 4 SP M DE I SD: 5.8377 c. M:-9.7222 c. 16: 7 2 7 SP M DE I SD: 5.1031 c. M:-6.2500 c. 22: 9 3 10 SP T3 SD: 4.7763 c. M: 7.9545 c. 24: 10 3 11 SP T3 SD: 3.4021 c. M: 4.1667 c. 26: 11 3 12 SP T3 SD: 3.3768 c. M: 5.7692 c. 29: 12 4 13 SP T3 SD: 3.2732 c. M: 5.6034 c. 31: 13 4 14 SP T3 SD: 1.6948 c. M: 2.8226 c. 33: 14 4 15 SP T3 SD: 1.3303 c. M: 2.2727 c. 38: 16 5 17 SP T3 SD: 1.3695 c. M: 1.9737 c. 40: 17 5 18 SP T3 SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 700.0000 cents 2 x x 3 S SD: 201.9550 cents 3 x x 4 S SD: 1.9550 cents 4 x 5 x S SD: 111.3137 cents 5 x 6:7 S SD: 45.9891 cents 6 x 7:8 S SD: 4.1804 cents 7:8 x 9 S SD: 33.7742 cents 8:9 x 11 SD: 26.0160 cents 10:11:12:13 H SD: 25.8283 cents 11:12:13:15 SD: 24.4820 cents 12 x 14:16 S SD: 4.1804 cents 13 x 15:17 SD: 22.4078 cents 14:16 x 19 SD: 17.1148 cents 15:17:18:20 SD: 13.6344 cents 16:18:19:21 SD: 12.6244 cents 17:19:20:23 SD: 10.4451 cents 18:20:21:24 S SD: 10.4120 cents 20:23 x 27 SD: 17.6790 cents 21:24:25:28 SD: 10.9203 cents 22:25:26:29 SD: 9.1420 cents 23:26:27:31 SD: 5.6540 cents 24:27:28:32 S SD: 3.9957 cents 30:34:35:40 SD: 3.1168 cents 47:53:55:63 SD: 2.9962 cents 53:60:62:71 SD: 2.4833 cents 63:71:74:84 SD: 2.2980 cents 69:78:81:92 SD: 1.0850 cents 93:105:109:124 SD: 1.0323 cents 99:112:116:132 SD: 0.7782 cents 122:138:143:163 SD: 0.6000 cents 191:216:224:255 SD: 0.3542 cents 215:243:252:287 SD: 0.1891 cents 406:459:476:542 SD: 0.1417 cents 436:493:511:582 SD: 0.0988 cents