Scala analysis: 710_S19
Semi-tempered tetrachord (4/3)**(2/15) * (4/3)**(7/15) * (4/3)**(2/5)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.406 cents 66.406000 2: 298.827 cents 298.827000 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 199.2180 cents 199.2180 1: 66.4060 cents 66.4060 2: 232.4210 cents 232.4210 3: 199.2180 cents 199.2180
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66.40600 cents 1: 1 199.21800 cents 1: 1 232.42100 cents 2: 1 265.62400 cents 2: 1 298.82700 cents 2: 1 431.63900 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 : 66.4 298.8 498.0 66.4 : 232.4 431.6 498.0 298.8: 199.2 265.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.4060 .. 232.4210 cents 166.01500 cents 66.40600 cents 2: 265.6240 .. 431.6390 cents 166.01500 cents 33.20300 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66.40600 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 232.42100 cents Average / Smallest step : 2.500000 Largest / Average step : 1.400000 Largest / Smallest step : 3.500000 Median interval of one step : 199.21800 cents, amount: 1 Least squares average step : 154.15679 cents, oct.: 462.47036 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 15-tone equal temperament with octave 4/3 degrees: 2 9 15 Least number of segments generator : 8 of 265.624 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 8 of 265.624 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 1 0 0 0 1 1 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.20300 cents Scale diversity : 0.887218 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.333333 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 : 33.20300 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 -- Prime limit : 3 (not all pitches rational)
FIT/MODE
3: 0 2 1 N G T3 SD: 42.8649 c. M: 66.4060 c. 4: 0 2 2 P M DE S SD: 47.9244 c. M: 66.4060 c. 5: 1 2 2 SP M ME S SD: 19.1698 c. M:-33.2030 c. 6: 1 3 2 P T3 SD: 21.4324 c. M:-33.2030 c. 7: 1 3 3 SP M DE S SD: 8.6600 c. M: 14.2299 c. 8: 1 4 3 P T3 SD: 7.5775 c. M:-12.4511 c. 13: 2 6 5 SP T3 SD: 7.3730 c. M:-10.2163 c. 15: 2 7 6 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: 41.9200 cents 10:11:12:13 H SD: 36.4013 cents 11:12:13:15 SD: 31.0931 cents 12:13:14:16 S SD: 26.3085 cents 14:15:17:19 SD: 23.9056 cents 15:16:18:20 S SD: 16.1145 cents 16:17:19:21 SD: 15.7449 cents 17:18:20:23 SD: 14.9196 cents 18:19:21:24 SD: 13.9876 cents 20:21:24:27 S SD: 10.9110 cents 21:22:25:28 SD: 4.8167 cents 27:28:32:36 S SD: 1.9403 cents 48:50:57:64 SD: 1.4881 cents 75:78:89:100 SD: 0.9792 cents 132:137:157:176 SD: 0.8334 cents 153:159:182:204 SD: 0.5573 cents 180:187:214:240 SD: 0.2647 cents 207:215:246:276 SD: 0.2530 cents 228:237:271:304 SD: 0.2267 cents 255:265:303:340 SD: 0.1023 cents 435:452:517:580 SD: 0.0520 cents