Scala analysis: 667_T74
Tempered tetrachord in cents 89 + 289 + 122, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 89.000 cents 89.000000 2: 378.000 cents 378.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 122.0000 cents 122.0000 1: 89.0000 cents 89.0000 2: 289.0000 cents 289.0000 3: 122.0000 cents 122.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 89.00000 cents 1: 1 122.00000 cents 1: 1 289.00000 cents 2: 1 211.00000 cents 2: 1 378.00000 cents 2: 1 411.00000 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 : 89.0 378.0 500.0 89.0 : 289.0 411.0 500.0 378.0: 122.0 211.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.0000 .. 289.0000 cents 200.00000 cents 89.00000 cents 2: 211.0000 .. 411.0000 cents 200.00000 cents -78.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 89.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 289.00000 cents Average / Smallest step : 1.872659 Largest / Average step : 1.734000 Largest / Smallest step : 3.247191 Median interval of one step : 122.00000 cents, amount: 1 Least squares average step : 167.50000 cents, oct.: 502.50000 cents Scale is not proper Scale has trivalence property Scale is a mode of a 500-tone equal temperament with octave 500.000 cents degrees: 89 378 500 Least number of segments generator : 251 of 251.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 313 of 313.000 cents and inv. generated superset size: 54 = 51 more = 1800.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 78.00000 cents Scale diversity : 1.119275 Lumma stability : 0.356000 Lumma impropriety factor : 0.156000 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 : 33.00000 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 --
FIT/MODE
3: 0 2 1 N G T3 SD: 57.4924 c. M: 89.0000 c. 4: 1 2 1 P M ME I SD: 20.8567 c. M:-36.0000 c. 5: 1 3 1 N M DE I SD: 14.2009 c. M:-22.0000 c. 7: 1 4 2 N T3 SD: 15.7456 c. M: 20.8571 c. 8: 1 5 2 N T3 SD: 15.3975 c. M: 26.5000 c. 9: 2 5 2 N M DE I SD: 14.2299 c. M:-22.1111 c. 11: 2 6 3 N T3 SD: 8.3658 c. M: 14.3636 c. 12: 2 7 3 N T3 SD: 3.7019 c. M: 5.6667 c. 16: 3 9 4 N T3 SD: 3.2436 c. M:-4.7500 c. 17: 3 10 4 N T3 SD: 2.5517 c. M:-4.3529 c. 28: 5 16 7 N T3 SD: 1.7399 c. M: 3.0000 c. 29: 5 17 7 N T3 SD: 1.7812 c. M: 2.7931 c. 33: 6 19 8 N T3 SD: 1.1924 c. M:-1.9091 c. 45: 8 26 11 N T3 SD: 0.1434 c. M: 0.2222 c. 197: 35 114 48 N T3 SD: 0.1389 c. M:-0.1726 c. 213: 38 123 52 N T3 SD: 0.1226 c. M:-0.2019 c. 242: 43 140 59 N T3 SD: 0.1072 c. M: 0.1570 c. 258: 46 149 63 N T3 SD: 0.1006 c. M:-0.1473 c. 275: 49 159 67 N T3 SD: 0.1174 c. M:-0.1818 c. 287: 51 166 70 N T3 SD: 0.0910 c. M: 0.1498 c. 303: 54 175 74 N T3 SD: 0.0903 c. M: 0.1122 c. 320: 57 185 78 N T3 SD: 0.0807 c. M:-0.1250 c. 365: 65 211 89 N T3 SD: 0.0531 c. M:-0.0822 c. 410: 73 237 100 N T3 SD: 0.0315 c. M:-0.0488 c. 455: 81 263 111 N T3 SD: 0.0142 c. M:-0.0220 c. 500: 89 289 122 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 5 x S SD: 8.3137 cents 5 x 6:7 S SD: 51.7128 cents 6 x 7:8 S SD: 55.5731 cents 7:8:9 x S SD: 76.6030 cents 8:9:10:11 H SD: 42.0409 cents 9:10:11:12 H SD: 32.7685 cents 11:12:14:15 S SD: 27.3361 cents 12:13:15:16 SD: 16.7677 cents 15:16:19:20 SD: 12.8959 cents 16:17:20:21 SD: 11.4380 cents 17:18:21:23 SD: 9.3754 cents 20:21:25:27 SD: 7.2412 cents 21:22:26:28 SD: 3.9939 cents 36:38:45:48 SD: 3.2340 cents 53:56:66:71 SD: 3.0079 cents 54:57:67:72 SD: 2.2555 cents 57:60:71:76 SD: 0.9904 cents 131:138:163:175 SD: 0.5966 cents 152:160:189:203 SD: 0.4093 cents 188:198:234:251 SD: 0.4091 cents 209:220:260:279 SD: 0.0767 cents