Scala analysis: 698_S7
Semi-tempered tetrachord (4/3)**(1/5) * (4/3)**(1/10) * (4/3)**(7/10)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.609 cents 99.609000 2: 149.414 cents 149.413500 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 348.6315 cents 348.6315 1: 99.6090 cents 99.6090 2: 49.8045 cents 49.8045 3: 348.6315 cents 348.6315
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49.80450 cents 1: 1 99.60900 cents 1: 1 348.63150 cents 2: 1 149.41350 cents 2: 1 398.43600 cents 2: 1 448.24050 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 : 99.6 149.4 498.0 99.6 : 49.8 398.4 498.0 149.4: 348.6 448.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.8045 .. 348.6315 cents 298.82700 cents 49.80450 cents 2: 149.4135 .. 448.2405 cents 298.82700 cents -199.21800 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 49.80450 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 348.63150 cents Average / Smallest step : 3.333333 Largest / Average step : 2.100000 Largest / Smallest step : 7.000000 Median interval of one step : 99.60900 cents, amount: 1 Least squares average step : 135.18364 cents, oct.: 405.55093 cents Scale is not proper Scale has trivalence property Scale is a mode of a 10-tone equal temperament with octave 4/3 degrees: 2 3 10 Least number of segments generator : 7 of 348.631 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 9 of 448.240 cents and inv. generated superset size: 4 = 1 more = 133.333% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABC Step pattern size order : MSL Interval vector is [ 1 1 1 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 49.80450 cents Scale diversity : 0.736618 Lumma stability : 0.200000 Lumma impropriety factor : 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 : 49.80450 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: 1 0 2 N G T3 SD: 39.5195 c. M:-66.4060 c. 4: 1 0 3 N G T3 SD: 20.3326 c. M: 24.9023 c. 6: 1 1 4 N M DE S SD: 13.5551 c. M: 16.6015 c. 9: 2 1 6 N T3 SD: 11.5196 c. M:-16.6015 c. 10: 2 1 7 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: 93.2287 cents 6 x 7:8 S SD: 58.7287 cents 7 x 8:9 S SD: 51.5967 cents 8 x 9:11 SD: 38.1047 cents 9 x 10:12 S SD: 16.4951 cents 10 x 11:13 SD: 23.2607 cents 11 x 12:15 S SD: 19.4625 cents 12 x 13:16 SD: 5.4204 cents 13 x 14:17 SD: 19.8493 cents 14:15 x 19 SD: 18.2505 cents 15:16 x 20 S SD: 6.0611 cents 16:17 x 21 SD: 13.8917 cents 18:19:20:24 S SD: 11.1775 cents 20:21:22:27 SD: 10.1919 cents 21:22:23:28 SD: 6.9043 cents 26 x 28:35 S SD: 13.4194 cents 27:29 x 36 SD: 12.0516 cents 29:31:32:39 SD: 10.0743 cents 30:32:33:40 SD: 6.5830 cents 31:33:34:41 SD: 6.5093 cents 32:34:35:43 SD: 5.1949 cents 33:35:36:44 SD: 0.8560 cents 135:143:147:180 SD: 0.6621 cents 168:178:183:224 SD: 0.4802 cents 201:213:219:268 SD: 0.4050 cents 222:235:242:296 SD: 0.3635 cents 255:270:278:340 SD: 0.2203 cents 288:305:314:384 SD: 0.1298 cents 321:340:350:428 SD: 0.1097 cents 489:518:533:652 SD: 0.0949 cents