Scala analysis: 685_T92
Tempered tetrachord in cents 225 + 175 + 100, 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: 400.000 cents 400.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 100.0000 cents 100.0000 1: 225.0000 cents 225.0000 2: 175.0000 cents 175.0000 3: 100.0000 cents 100.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100.00000 cents 1: 1 175.00000 cents 1: 1 225.00000 cents 2: 1 275.00000 cents 2: 1 325.00000 cents 2: 1 400.00000 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 : 225.0 400.0 500.0 225.0: 175.0 275.0 500.0 400.0: 100.0 325.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.0000 .. 225.0000 cents 125.00000 cents 100.00000 cents 2: 275.0000 .. 400.0000 cents 125.00000 cents 50.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 225.00000 cents Average / Smallest step : 1.666667 Largest / Average step : 1.350000 Largest / Smallest step : 2.250000 Median interval of one step : 175.00000 cents, amount: 1 Least squares average step : 180.35714 cents, oct.: 541.07143 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 20-tone equal temperament with octave 500.000 cents degrees: 9 16 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: 5 = 2 more = 166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LMS Interval vector is [ 0 0 0 1 0 0 1 0 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 1.219377 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.500000 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 fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly decreasing 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: 51.1443 c. M: 66.6667 c. 4: 2 1 1 P M ME S SD: 20.4124 c. M:-25.0000 c. 5: 2 2 1 SP M ME S SD: 14.4338 c. M: 25.0000 c. 9: 4 3 2 SP T3 SD: 6.6124 c. M: 11.1111 c. 11: 5 4 2 SP T3 SD: 5.4102 c. M:-9.0909 c. 15: 7 5 3 SP T3 SD: 4.8113 c. M:-8.3333 c. 16: 7 6 3 SP T3 SD: 5.1031 c. M:-6.2500 c. 20: 9 7 4 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: 13.6863 cents 5 x 6:7 S SD: 59.0014 cents 6:7 x 8 S SD: 20.9583 cents 7:8:9 x S SD: 17.8116 cents 10:11 x 13 SD: 37.7354 cents 11:13:14:15 SD: 25.3745 cents 12:14:15:16 S SD: 14.6981 cents 15:17:19:20 SD: 4.1951 cents 42:48:53:56 SD: 2.3419 cents 50:57:63:67 SD: 2.3098 cents 57:65:72:76 SD: 1.8008 cents 65:74:82:87 SD: 1.7379 cents 81:92:102:108 SD: 1.6770 cents 92:105:116:123 SD: 1.6267 cents 93:106:117:124 SD: 1.1847 cents 108:123:136:144 SD: 0.7205 cents 158:180:199:211 SD: 0.3984 cents 173:197:218:231 SD: 0.2046 cents 281:320:354:375 SD: 0.1516 cents 439:500:553:586 SD: 0.1378 cents 454:517:572:606 SD: 0.0204 cents