Scala analysis: 690_T97
Tempered tetrachord in cents 200 + 125 + 175, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 200.000 cents 200.000000 2: 325.000 cents 325.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 175.0000 cents 175.0000 1: 200.0000 cents 200.0000 2: 125.0000 cents 125.0000 3: 175.0000 cents 175.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 125.00000 cents 1: 1 175.00000 cents 1: 1 200.00000 cents 2: 1 300.00000 cents 2: 1 325.00000 cents 2: 1 375.00000 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 : 200.0 325.0 500.0 200.0: 125.0 300.0 500.0 325.0: 175.0 375.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 125.0000 .. 200.0000 cents 75.00000 cents 125.00000 cents 2: 300.0000 .. 375.0000 cents 75.00000 cents 100.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 125.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 200.00000 cents Average / Smallest step : 1.333333 Largest / Average step : 1.200000 Largest / Smallest step : 1.600000 Median interval of one step : 175.00000 cents, amount: 1 Least squares average step : 167.85714 cents, oct.: 503.57143 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: 8 13 20 Least number of segments generator : 11 of 275.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 13 of 325.000 cents and inv. generated superset size: 6 = 3 more = 200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Interval vector is [ 0 0 0 0 1 0 1 1 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 100.00000 cents Scale diversity : 1.304300 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.700000 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 : 25.00000 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 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: 19.8373 c. M: 33.3333 c. 5: 2 1 2 SP M ME I SD: 14.4338 c. M: 25.0000 c. 8: 3 2 3 SP M ME I SD: 10.2062 c. M: 12.5000 c. 12: 5 3 4 SP T3 SD: 6.8041 c. M:-8.3333 c. 15: 6 4 5 SP T3 SD: 4.8113 c. M:-8.3333 c. 17: 7 4 6 SP T3 SD: 3.5007 c. M:-5.8824 c. 20: 8 5 7 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: 61.3137 cents 5 x 6:7 S SD: 41.5206 cents 6 x 7:8 S SD: 29.0810 cents 7:8 x 9 S SD: 36.0066 cents 8:9:10:11 H SD: 26.6837 cents 9:10:11:12 H SD: 9.5194 cents 15:17:18:20 SD: 6.4105 cents 24:27:29:32 SD: 1.6992 cents 83:93:100:111 SD: 1.6922 cents 98:110:118:131 SD: 1.4198 cents 107:120:129:143 SD: 0.9563 cents 131:147:158:175 SD: 0.5150 cents 155:174:187:207 SD: 0.2861 cents 334:375:403:446 SD: 0.2625 cents 466:523:562:622 SD: 0.2508 cents 475:533:573:634 SD: 0.2093 cents 490:550:591:654 SD: 0.1935 cents 499:560:602:666 SD: 0.1410 cents 523:587:631:698 SD: 0.1107 cents