Scala analysis: 669_T76
Tempered tetrachord in cents 83.3 + 283.3 + 133.3, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.300 cents 83.300000 2: 366.600 cents 366.600000 3: 499.900 cents 499.900000
SHOW/INTERVAL
0: 133.3000 cents 133.3000 1: 83.3000 cents 83.3000 2: 283.3000 cents 283.3000 3: 133.3000 cents 133.3000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83.30000 cents 1: 1 133.30000 cents 1: 1 283.30000 cents 2: 1 216.60000 cents 2: 1 366.60000 cents 2: 1 416.60000 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 : 83.3 366.6 499.9 83.3 : 283.3 416.6 499.9 366.6: 133.3 216.6 499.9 499.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.3000 .. 283.3000 cents 200.00000 cents 83.30000 cents 2: 216.6000 .. 416.6000 cents 200.00000 cents -66.70000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 83.30000 cents, class 1 Average step (divided formal octave): 166.6333 cents Largest one step interval : 283.30000 cents Average / Smallest step : 2.000400 Largest / Average step : 1.700140 Largest / Smallest step : 3.400960 Median interval of one step : 133.30000 cents, amount: 1 Least squares average step : 165.44286 cents, oct.: 496.32857 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 66.70000 cents Scale diversity : 1.111760 Lumma stability : 0.333267 Lumma impropriety factor : 0.133427 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 2 1 N G T3 SD: 51.8009 c. M: 83.3000 c. 4: 1 2 1 P M ME I SD: 24.5364 c. M:-41.6750 c. 5: 1 3 1 N M DE I SD: 21.5131 c. M:-33.3200 c. 6: 1 3 2 P T3 SD: 19.2450 c. M: 33.3333 c. 7: 1 4 2 N T3 SD: 8.7951 c. M: 11.8857 c. 11: 2 6 3 N T3 SD: 4.7202 c. M:-7.5909 c. 12: 2 7 3 N T3 SD: 4.8065 c. M:-8.3250 c. 18: 3 10 5 N T3 SD: 3.2107 c. M: 5.5611 c. 19: 3 11 5 N T3 SD: 2.7164 c. M: 4.3684 c. 23: 4 13 6 N T3 SD: 2.6835 c. M:-3.6391 c. 30: 5 17 8 N T3 SD: 0.0104 c. M:-0.0167 c.
FIT/HARMONIC
1 x x 2 S SD: 700.1000 cents 2 x x 3 S SD: 202.0550 cents 3 x x 4 S SD: 1.8550 cents 4 x 5 x S SD: 19.7137 cents 5 x 6:7 S SD: 48.5324 cents 6 x 7:8 S SD: 49.8732 cents 7 x x 9 SD: 64.8159 cents 8:9:10:11 H SD: 44.1955 cents 9:10:11:12 H SD: 33.6540 cents 11:12:14:15 S SD: 30.7294 cents 12:13:15:16 SD: 19.5708 cents 13:14:16:17 S SD: 19.2467 cents 14:15:17:19 SD: 18.4495 cents 15:16:19:20 SD: 17.0955 cents 16:17:20:21 SD: 13.7659 cents 17:18:21:23 SD: 9.3933 cents 18:19:22:24 SD: 7.2872 cents 21:22:26:28 SD: 1.5267 cents 60:63:74:80 SD: 1.3835 cents 81:85:100:108 SD: 0.8613 cents 102:107:126:136 SD: 0.6867 cents 123:129:152:164 SD: 0.6803 cents 140:147:173:187 SD: 0.5695 cents 161:169:199:215 SD: 0.3624 cents 182:191:225:243 SD: 0.2751 cents 242:254:299:323 SD: 0.2183 cents 263:276:325:351 SD: 0.1142 cents 445:467:550:594 SD: 0.0993 cents 547:574:676:730 SD: 0.0987 cents