Scala analysis: 672_T79
Tempered tetrachord in cents 55 + 170 + 275, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55.000 cents 55.000000 2: 225.000 cents 225.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 275.0000 cents 275.0000 1: 55.0000 cents 55.0000 2: 170.0000 cents 170.0000 3: 275.0000 cents 275.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55.00000 cents 1: 1 170.00000 cents 1: 1 275.00000 cents 2: 1 225.00000 cents 2: 1 330.00000 cents 2: 1 445.00000 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 : 55.0 225.0 500.0 55.0 : 170.0 445.0 500.0 225.0: 275.0 330.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 55.0000 .. 275.0000 cents 220.00000 cents 55.00000 cents 2: 225.0000 .. 445.0000 cents 220.00000 cents -50.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 275.00000 cents Average / Smallest step : 3.030303 Largest / Average step : 1.650000 Largest / Smallest step : 5.000000 Median interval of one step : 170.00000 cents, amount: 1 Least squares average step : 143.21429 cents, oct.: 429.64286 cents Scale is not proper Scale has trivalence property Scale is a mode of a 100-tone equal temperament with octave 500.000 cents degrees: 11 45 100 Least number of segments generator : 51 of 255.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 89 of 445.000 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 : SML Interval vector is [ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 0.890016 Lumma stability : 0.220000 Lumma impropriety factor : 0.100000 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 : 50.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 46.2881 c. M: 58.3333 c. 4: 0 2 2 P M DE S SD: 34.8807 c. M: 55.0000 c. 5: 0 2 3 N G T3 SD: 34.8807 c. M: 55.0000 c. 6: 1 2 3 P T3 SD: 21.8157 c. M:-28.3333 c. 7: 1 2 4 N T3 SD: 11.3239 c. M:-16.4286 c. 9: 1 3 5 N T3 SD: 1.6355 c. M: 2.7778 c. 29: 3 10 16 N T3 SD: 1.9557 c. M: 3.2759 c. 38: 4 13 21 N T3 SD: 1.5643 c. M: 2.3684 c. 44: 5 15 24 N T3 SD: 1.6804 c. M:-2.2727 c. 47: 5 16 26 N T3 SD: 1.3925 c. M: 1.8085 c. 53: 6 18 29 N T3 SD: 1.2349 c. M:-1.6038 c. 62: 7 21 34 N T3 SD: 0.9587 c. M:-1.4516 c. 64: 7 22 35 N T3 SD: 0.9200 c. M:-1.5625 c. 71: 8 24 39 N T3 SD: 0.7988 c. M:-1.3380 c. 73: 8 25 40 N T3 SD: 0.6049 c. M:-1.0274 c. 82: 9 28 45 N T3 SD: 0.3590 c. M:-0.6098 c. 91: 10 31 50 N T3 SD: 0.1618 c. M:-0.2747 c. 100: 11 34 55 N 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: 61.2864 cents 6 x 7:8 S SD: 20.9583 cents 7 x 8:9 S SD: 32.6044 cents 8 x 9:11 SD: 27.7413 cents 9 x 10:12 S SD: 21.3206 cents 10 x 11:13 SD: 37.7354 cents 11 x 13:15 SD: 37.0414 cents 12:13:14:16 S SD: 31.1651 cents 13:14:15:17 SD: 28.1961 cents 14:15:16:19 SD: 23.6031 cents 15:16:17:20 SD: 19.1235 cents 18:19:21:24 SD: 18.9947 cents 19:20:22:25 SD: 16.9689 cents 20:21:23:27 SD: 13.0734 cents 21:22:24:28 S SD: 8.7818 cents 27:28:31:36 SD: 5.4569 cents 29:30:33:39 SD: 4.4954 cents 30:31:34:40 SD: 2.9070 cents 36:37:41:48 SD: 2.6053 cents 57:59:65:76 SD: 1.8732 cents 65:67:74:87 SD: 1.7849 cents 66:68:75:88 SD: 1.7779 cents 87:90:99:116 SD: 1.4587 cents 93:96:106:124 SD: 0.8243 cents 122:126:139:163 SD: 0.6635 cents 152:157:173:203 SD: 0.5555 cents 158:163:180:211 SD: 0.4959 cents 188:194:214:251 SD: 0.3416 cents 245:253:279:327 SD: 0.2183 cents 281:290:320:375 SD: 0.1971 cents 403:416:459:538 SD: 0.1076 cents 526:543:599:702 SD: 0.1058 cents