Scala analysis: 712_S21
Semi-tempered tetrachord (4/3)**(3/20) * (4/3)**(9/20) * (4/3)**(2/5)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 74.707 cents 74.706750 2: 298.827 cents 298.827000 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 199.2180 cents 199.2180 1: 74.7068 cents 74.7068 2: 224.1202 cents 224.1202 3: 199.2180 cents 199.2180
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 74.70675 cents 1: 1 199.21800 cents 1: 1 224.12025 cents 2: 1 273.92475 cents 2: 1 298.82700 cents 2: 1 423.33825 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 : 74.7 298.8 498.0 74.7 : 224.1 423.3 498.0 298.8: 199.2 273.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 74.7068 .. 224.1202 cents 149.41350 cents 74.70675 cents 2: 273.9247 .. 423.3382 cents 149.41350 cents 49.80450 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 74.70675 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 224.12025 cents Average / Smallest step : 2.222222 Largest / Average step : 1.350000 Largest / Smallest step : 3.000000 Median interval of one step : 199.21800 cents, amount: 1 Least squares average step : 154.74970 cents, oct.: 464.24909 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 20-tone equal temperament with octave 4/3 degrees: 3 12 20 Least number of segments generator : 11 of 273.925 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 17 of 423.338 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 : SLM Interval vector is [ 0 0 1 0 0 0 0 1 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 49.80450 cents Scale diversity : 0.951199 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.400000 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 : 24.90225 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% Limited inverse transpositions with margin 149.4135 cents: 1 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
3: 0 2 1 N G T3 SD: 47.2001 c. M: 74.7068 c. 4: 1 1 2 P M ME S SD: 40.6652 c. M: 49.8045 c. 5: 1 2 2 SP M ME S SD: 14.3773 c. M:-24.9022 c. 7: 1 3 3 SP M DE S SD: 8.4685 c. M: 14.2299 c. 8: 1 4 3 P T3 SD: 10.1663 c. M: 12.4511 c. 12: 2 5 5 SP M DE S SD: 6.7775 c. M: 8.3008 c. 13: 2 6 5 SP T3 SD: 4.5599 c. M:-7.6622 c. 20: 3 9 8 SP T3 SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x 5 x S SD: 87.4867 cents 5 x 6:7 S SD: 43.0622 cents 6 x 7:8 S SD: 15.9780 cents 7 x 8:9 S SD: 46.2087 cents 8 x 10:11 S SD: 51.2151 cents 9:10:11:12 H SD: 39.3824 cents 10:11:12:13 H SD: 33.9240 cents 11:12:13:15 SD: 28.6193 cents 12:13:14:16 S SD: 23.8049 cents 14:15:17:19 SD: 21.9386 cents 15:16:18:20 S SD: 13.5546 cents 17:18:20:23 SD: 13.0464 cents 18:19:21:24 SD: 12.3750 cents 20:21:24:27 S SD: 9.6638 cents 21:22:25:28 SD: 2.1886 cents 48:50:57:64 SD: 1.4143 cents 69:72:82:92 SD: 0.3420 cents 90:94:107:120 SD: 0.3047 cents 159:166:189:212 SD: 0.1405 cents