Scala analysis: 677_T84
Tempered tetrachord in cents 75 + 175 + 250, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75.000 cents 75.000000 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 75.0000 cents 75.0000 2: 175.0000 cents 175.0000 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 75.00000 cents 1: 1 175.00000 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 325.00000 cents 2: 1 425.00000 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 : 75.0 250.0 500.0 75.0 : 175.0 425.0 500.0 250.0: 250.0 325.0 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.0000 .. 250.0000 cents 175.00000 cents 75.00000 cents 2: 250.0000 .. 425.0000 cents 175.00000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 75.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 2.222222 Largest / Average step : 1.500000 Largest / Smallest step : 3.333333 Median interval of one step : 175.00000 cents, amount: 1 Least squares average step : 148.21429 cents, oct.: 444.64286 cents Scale is proper Scale has trivalence property Scale is a mode of a 20-tone equal temperament with octave 500.000 cents degrees: 3 10 20 Least number of segments generator : 11 of 275.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 11 of 275.000 cents and inv. generated superset size: 11 = 8 more = 366.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Interval vector is [ 0 0 1 0 0 0 1 0 0 1 ] Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 0.994706 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.300000 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 2.333333 Number of different interval sizes : 5 = 2.50000 / 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 : 75.00000 cents Most common intervals : 250.00000 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 2 = 66.6667% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 64.7288 c. M: 83.3333 c. 4: 1 1 2 P M ME S SD: 28.8675 c. M:-50.0000 c. 5: 1 2 2 SP M ME S SD: 32.2749 c. M:-50.0000 c. 6: 1 2 3 P T3 SD: 4.8113 c. M:-8.3333 c. 14: 2 5 7 P T3 SD: 2.0620 c. M: 3.5714 c. 20: 3 7 10 P 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 6:7 S SD: 52.7187 cents 6 x 7:8 S SD: 8.4919 cents 7 x 8:9 S SD: 33.7953 cents 8 x 9:11 SD: 34.4885 cents 9 x 10:12 S SD: 33.8123 cents 10 x 12:13 S SD: 40.0161 cents 11:12:13:15 SD: 30.9547 cents 12:13:14:16 S SD: 21.9341 cents 13:14:15:17 SD: 21.3729 cents 14:15:16:19 SD: 18.7158 cents 15:16:17:20 SD: 16.5422 cents 17:18:20:23 SD: 15.2787 cents 18:19:21:24 SD: 8.3966 cents 20:21:23:27 SD: 7.7209 cents 21:22:24:28 S SD: 6.5735 cents 24:25:28:32 SD: 5.8422 cents 27:28:31:36 SD: 5.4369 cents 39:41:45:52 SD: 3.9863 cents 44:46:51:59 SD: 3.2793 cents 45:47:52:60 SD: 0.6662 cents 155:162:179:207 SD: 0.6195 cents 161:168:186:215 SD: 0.5041 cents 200:209:231:267 SD: 0.4436 cents 206:215:238:275 SD: 0.3267 cents 251:262:290:335 SD: 0.2603 cents 296:309:342:395 SD: 0.2573 cents 361:377:417:482 SD: 0.1879 cents 406:424:469:542 SD: 0.1126 cents 451:471:521:602 SD: 0.0823 cents