Scala analysis: 691_T98
Tempered tetrachord in cents 145 + 165 + 190, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 145.000 cents 145.000000 2: 310.000 cents 310.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 190.0000 cents 190.0000 1: 145.0000 cents 145.0000 2: 165.0000 cents 165.0000 3: 190.0000 cents 190.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 145.00000 cents 1: 1 165.00000 cents 1: 1 190.00000 cents 2: 1 310.00000 cents 2: 1 335.00000 cents 2: 1 355.00000 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 : 145.0 310.0 500.0 145.0: 165.0 355.0 500.0 310.0: 190.0 335.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 145.0000 .. 190.0000 cents 45.00000 cents 145.00000 cents 2: 310.0000 .. 355.0000 cents 45.00000 cents 120.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 145.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 190.00000 cents Average / Smallest step : 1.149425 Largest / Average step : 1.140000 Largest / Smallest step : 1.310345 Median interval of one step : 165.00000 cents, amount: 1 Least squares average step : 161.78571 cents, oct.: 485.35714 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 100-tone equal temperament with octave 500.000 cents degrees: 29 62 100 Least number of segments generator : 51 of 255.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 81 of 405.000 cents and inv. generated superset size: 10 = 7 more = 333.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 120.00000 cents Scale diversity : 1.314530 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.820000 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 : 20.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 25.0000 cents: 1 2 -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 18.3838 c. M:-23.3333 c. 7: 2 2 3 SP M ME S SD: 14.0758 c. M: 24.2857 c. 8: 2 3 3 SP M ME S SD: 11.6369 c. M: 20.0000 c. 10: 3 3 4 SP M ME S SD: 6.4550 c. M: 10.0000 c. 11: 3 4 4 SP M ME S SD: 6.8685 c. M: 8.6364 c. 13: 4 4 5 SP M ME S SD: 5.2783 c. M:-8.8462 c. 18: 5 6 7 SP T3 SD: 4.3627 c. M: 6.1111 c. 21: 6 7 8 SP T3 SD: 1.2674 c. M: 2.1429 c. 34: 10 11 13 SP T3 SD: 1.3690 c. M:-2.0588 c. 45: 13 15 17 SP T3 SD: 0.7172 c. M:-1.1111 c. 55: 16 18 21 SP T3 SD: 0.5868 c. M: 0.9091 c. 76: 22 25 29 SP T3 SD: 0.4805 c. M: 0.7895 c. 79: 23 26 30 SP T3 SD: 0.3369 c. M:-0.5696 c. 100: 29 33 38 SP 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 5 x S SD: 76.3137 cents 5 x 6:7 S SD: 41.3524 cents 6 x 7:8 S SD: 21.5867 cents 7 x 8:9 S SD: 51.0578 cents 8:9:10:11 H SD: 36.4047 cents 9:10:11:12 H SD: 17.6453 cents 10:11:12:13 H SD: 16.7609 cents 11:12:13:15 SD: 14.2571 cents 15:16:18:20 S SD: 11.2667 cents 20:22:24:27 S SD: 9.5117 cents 21:23:25:28 SD: 5.0154 cents 35:38:42:47 SD: 4.0304 cents 36:39:43:48 SD: 2.3771 cents 45:49:54:60 SD: 2.1484 cents 57:62:68:76 SD: 1.6502 cents 81:88:97:108 SD: 1.0742 cents 92:100:110:123 SD: 0.9636 cents 102:111:122:136 SD: 0.7994 cents 137:149:164:183 SD: 0.6327 cents 173:188:207:231 SD: 0.4461 cents 194:211:232:259 SD: 0.1989 cents 275:299:329:367 SD: 0.1875 cents 367:399:439:490 SD: 0.1670 cents 469:510:561:626 SD: 0.0573 cents