Scala analysis: 601_T8
Aristoxenian style tetrachord 4 + 3 + 23, Chapter 3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.667 cents 66.666670 2: 116.667 cents 116.666670 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 383.3333 cents 383.3333 1: 66.6667 cents 66.6667 2: 50.0000 cents 50.0000 3: 383.3333 cents 383.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50.00000 cents 1: 1 66.66667 cents 1: 1 383.33333 cents 2: 1 116.66667 cents 2: 1 433.33333 cents 2: 1 450.00000 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 : 66.7 116.7 500.0 66.7 : 50.0 433.3 500.0 116.7: 383.3 450.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.0000 .. 383.3333 cents 333.33333 cents 50.00000 cents 2: 116.6667 .. 450.0000 cents 333.33333 cents -266.66666 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 50.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 383.33333 cents Average / Smallest step : 3.333333 Largest / Average step : 2.300000 Largest / Smallest step : 7.666667 Median interval of one step : 66.66667 cents, amount: 1 Least squares average step : 128.57143 cents, oct.: 385.71429 cents Scale is not proper Scale has trivalence property Scale is a mode of a 30-tone equal temperament with octave 500.000 cents degrees: 4 7 30 Least number of segments generator : 19 of 316.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 29 of 483.333 cents and inv. generated superset size: 8 = 5 more = 266.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Interval vector is [ 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.00000 cents Scale diversity : 0.543715 Lumma stability : 0.200000 Lumma impropriety factor : 0.533333 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 : 16.66667 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 333.3333 cents: 2 -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 48.1125 c. M: 66.6667 c. 4: 1 0 3 N G T3 SD: 34.0207 c. M:-58.3333 c. 5: 1 0 4 N G T3 SD: 21.5166 c. M:-33.3333 c. 7: 1 1 5 N M DE S SD: 15.3690 c. M:-26.1905 c. 8: 1 1 6 N M DE S SD: 5.3791 c. M:-8.3333 c. 17: 2 2 13 N M DE S SD: 4.5635 c. M: 7.8431 c. 21: 3 2 16 N T3 SD: 3.0738 c. M:-4.7619 c. 22: 3 2 17 N T3 SD: 1.9561 c. M: 3.0303 c. 30: 4 3 23 N T3 SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 700.0000 cents 2 x x 3 S SD: 201.9550 cents 3 x x 4 S SD: 1.9550 cents 4 x x 5 S SD: 113.6863 cents 5 x x 7 SD: 82.5122 cents 6 x 7:8 S SD: 75.1085 cents 7 x 8:9 S SD: 65.8142 cents 8 x 9:11 SD: 50.6086 cents 9 x 10:12 S SD: 32.8831 cents 10 x 11:13 SD: 33.2899 cents 11 x 12:15 S SD: 25.0965 cents 12 x 13:16 SD: 10.9965 cents 13 x 14:17 SD: 18.7128 cents 14 x 15:19 SD: 14.4106 cents 15 x 16:20 S SD: 2.6542 cents 16 x 17:21 SD: 15.7394 cents 17 x 18:23 SD: 14.6415 cents 18 x 19:24 SD: 11.5732 cents 19:20 x 25 S SD: 16.6524 cents 20:21 x 27 SD: 13.2204 cents 21:22 x 28 SD: 7.0037 cents 26:27:28:35 S SD: 6.2412 cents 27:28:29:36 SD: 2.7324 cents 57:59:61:76 SD: 2.4237 cents 71:74:76:95 SD: 2.1906 cents 72:75:77:96 SD: 1.4928 cents 99:103:106:132 SD: 1.0566 cents 101:105:108:135 SD: 0.8276 cents 128:133:137:171 SD: 0.5847 cents 200:208:214:267 SD: 0.4450 cents 203:211:217:271 SD: 0.4154 cents 230:239:246:307 SD: 0.1095 cents