Scala analysis: 701_S10
Semi-tempered tetrachord (4/3)**(2/15) * (4/3)**(4/15) * (4/3)**(3/5)
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: 199.218 cents 199.218000 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 298.8270 cents 298.8270 1: 66.4060 cents 66.4060 2: 132.8120 cents 132.8120 3: 298.8270 cents 298.8270
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66.40600 cents 1: 1 132.81200 cents 1: 1 298.82700 cents 2: 1 199.21800 cents 2: 1 365.23300 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 : 66.4 199.2 498.0 66.4 : 132.8 431.6 498.0 199.2: 298.8 365.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.4060 .. 298.8270 cents 232.42100 cents 66.40600 cents 2: 199.2180 .. 431.6390 cents 232.42100 cents -99.60900 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 : 298.82700 cents Average / Smallest step : 2.500000 Largest / Average step : 1.800000 Largest / Smallest step : 4.500000 Median interval of one step : 132.81200 cents, amount: 1 Least squares average step : 139.92693 cents, oct.: 419.78079 cents Scale is not proper Scale has trivalence property Scale is a mode of a 15-tone equal temperament with octave 4/3 degrees: 2 6 15 Least number of segments generator : 8 of 265.624 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 13 of 431.639 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 1 0 1 0 1 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 66.40600 cents Scale diversity : 1.001299 Lumma stability : 0.266667 Lumma impropriety factor : 0.200000 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 : 66.40600 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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 1 2 N G T3 SD: 42.8649 c. M: 66.4060 c. 5: 1 1 3 N M DE S SD: 19.1698 c. M:-33.2030 c. 7: 1 2 4 N T3 SD: 8.6600 c. M:-14.2299 c. 8: 1 2 5 N T3 SD: 7.5775 c. M: 12.4511 c. 13: 2 3 8 N T3 SD: 7.3730 c. M:-10.2163 c. 15: 2 4 9 N 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 71.9185 cents 6 x 7:8 S SD: 33.8265 cents 7 x 8:9 S SD: 35.3032 cents 8 x 9:11 SD: 26.7396 cents 9 x 10:12 S SD: 8.4071 cents 10 x 11:13 SD: 27.8017 cents 11 x 12:15 S SD: 31.1198 cents 12 x 13:16 SD: 30.3227 cents 13:14:15:17 SD: 28.5098 cents 14:15:16:19 SD: 23.0290 cents 15:16:17:20 SD: 16.1917 cents 16:17:18:21 S SD: 15.8163 cents 17:18:19:23 SD: 13.9146 cents 18:19:20:24 S SD: 10.6583 cents 22:23:25:29 SD: 10.4924 cents 23:24:26:31 SD: 7.9801 cents 24:25:27:32 SD: 2.1139 cents 74:77:83:99 SD: 2.1105 cents 75:78:84:100 SD: 1.1230 cents 99:103:111:132 SD: 0.8172 cents 132:137:148:176 SD: 0.7802 cents 156:162:175:208 SD: 0.3656 cents 180:187:202:240 SD: 0.1816 cents 435:452:488:580 SD: 0.0610 cents