Scala analysis: 675_T82
Tempered tetrachord in cents 225 + 25 + 250, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 225.000 cents 225.000000 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 225.0000 cents 225.0000 2: 25.0000 cents 25.0000 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25.00000 cents 1: 1 225.00000 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 275.00000 cents 2: 1 475.00000 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 : 225.0 250.0 500.0 225.0: 25.0 275.0 500.0 250.0: 250.0 475.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.0000 .. 250.0000 cents 225.00000 cents 25.00000 cents 2: 250.0000 .. 475.0000 cents 225.00000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 25.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 6.666667 Largest / Average step : 1.500000 Largest / Smallest step : 10.000000 Median interval of one step : 225.00000 cents, amount: 1 Least squares average step : 158.92857 cents, oct.: 476.78571 cents Scale is proper Scale has trivalence property Scale is a mode of a 20-tone equal temperament with octave 500.000 cents degrees: 9 10 20 Least number of segments generator : 11 of 275.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 11 of 275.000 cents and inv. generated superset size: 11 = 8 more = 366.667% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABC Step pattern size order : MSL Interval vector is [ 1 0 0 0 0 0 0 0 1 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 0.447031 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.100000 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 2.333333 Number of different interval sizes : 5 = 2.50000 / 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 : 25.00000 cents Most common intervals : 250.00000 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 2 = 66.6667% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 1 0 2 N G T3 SD: 58.7288 c. M: 83.3333 c. 4: 2 0 2 P M DE I SD: 14.4338 c. M:-25.0000 c. 10: 4 1 5 P T3 SD: 14.4338 c. M: 25.0000 c. 11: 5 0 6 N G T3 SD: 13.1870 c. M: 22.7273 c. 12: 5 1 6 P T3 SD: 9.6225 c. M: 16.6667 c. 14: 6 1 7 P T3 SD: 6.1859 c. M: 10.7143 c. 16: 7 1 8 P T3 SD: 3.6084 c. M: 6.2500 c. 18: 8 1 9 P T3 SD: 1.6038 c. M: 2.7778 c. 20: 9 1 10 P 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 x 5 S SD: 113.6863 cents 5 x 6:7 S SD: 52.7187 cents 6 x 7:8 S SD: 8.4919 cents 7:8 x 9 S SD: 32.6044 cents 8:9 x 11 SD: 27.7413 cents 9:10 x 12 S SD: 21.3206 cents 11 x 13:15 SD: 26.9386 cents 12 x 14:16 S SD: 8.4919 cents 13 x 15:17 SD: 17.8220 cents 14:16 x 19 SD: 14.6720 cents 15:17 x 20 SD: 4.2700 cents 16:18 x 21 S SD: 18.0177 cents 17:19:20:23 SD: 16.9300 cents 18 x 21:24 S SD: 8.4919 cents 19 x 22:25 SD: 12.5874 cents 20 x 23:27 SD: 10.5698 cents 21:24 x 28 S SD: 3.2381 cents 22:25 x 29 SD: 11.0259 cents 24:27:28:32 S SD: 9.0261 cents 26 x 30:35 SD: 7.3928 cents 27 x 31:36 SD: 5.5022 cents 28:32 x 37 SD: 9.2700 cents 30:34:35:40 SD: 6.3031 cents 33 x 38:44 SD: 3.0413 cents 34 x 39:45 SD: 9.6513 cents 35:40 x 47 SD: 6.0331 cents 36:41:42:48 SD: 5.6615 cents 38:43:44:51 SD: 4.9854 cents 40 x 46:53 SD: 7.5615 cents 41:47 x 55 SD: 7.1485 cents 42:48:49:56 S SD: 6.0237 cents 43:49:50:57 SD: 5.4763 cents 44:50:51:59 SD: 3.4412 cents 45:51:52:60 SD: 2.8485 cents 47 x 54:63 SD: 6.0254 cents 48:55 x 64 SD: 5.4271 cents 50:57:58:67 SD: 3.2712 cents 51:58:59:68 SD: 1.2640 cents 108:123:125:144 SD: 1.2160 cents 116:132:134:155 SD: 0.7389 cents 122:139:141:163 SD: 0.6299 cents 167:190:193:223 SD: 0.6033 cents 173:197:200:231 SD: 0.4025 cents 245:279:283:327 SD: 0.1404 cents 418:476:483:558 SD: 0.0856 cents