Scala analysis: 676_T83
Tempered tetrachord in cents 66.7 + 183.3 + 250, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.700 cents 66.700000 2: 250.000 cents 250.000000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 250.0000 cents 250.0000 1: 66.7000 cents 66.7000 2: 183.3000 cents 183.3000 3: 250.0000 cents 250.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66.70000 cents 1: 1 183.30000 cents 1: 1 250.00000 cents 2: 1 250.00000 cents 2: 1 316.70000 cents 2: 1 433.30000 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 : 66.7 250.0 500.0 66.7 : 183.3 433.3 500.0 250.0: 250.0 316.7 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.7000 .. 250.0000 cents 183.30000 cents 66.70000 cents 2: 250.0000 .. 433.3000 cents 183.30000 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66.70000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 250.00000 cents Average / Smallest step : 2.498751 Largest / Average step : 1.500000 Largest / Smallest step : 3.748126 Median interval of one step : 183.30000 cents, amount: 1 Least squares average step : 147.62143 cents, oct.: 442.86429 cents Scale is proper Scale has trivalence property Scale is a mode of a 862-tone equal temperament with octave 500.000 cents degrees: 115 431 862 Least number of segments generator : 433 of 251.160 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 433 of 251.160 cents and inv. generated superset size: 432 = 429 more = 14400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is not a Constant Structure Scale diversity : 0.918412 Rothenberg stability : 0.666667 = 2/3 Lumma stability : 0.266800 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 : 66.70000 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: 61.6261 c. M: 83.3333 c. 4: 1 1 2 P M ME S SD: 33.6595 c. M:-58.3000 c. 5: 1 2 2 SP M ME S SD: 34.6838 c. M:-50.0000 c. 6: 1 2 3 P T3 SD: 9.6033 c. M:-16.6333 c. 8: 1 3 4 P T3 SD: 2.4249 c. M: 4.2000 c. 22: 3 8 11 P T3 SD: 0.8555 c. M:-1.4818 c. 30: 4 11 15 P T3 SD: 0.0192 c. M: 0.0333 c. 502: 67 184 251 P T3 SD: 0.0191 c. M:-0.0331 c. 532: 71 195 266 P T3 SD: 0.0169 c. M:-0.0293 c. 562: 75 206 281 P T3 SD: 0.0150 c. M:-0.0260 c. 592: 79 217 296 P T3 SD: 0.0133 c. M:-0.0230 c. 622: 83 228 311 P T3 SD: 0.0117 c. M:-0.0203 c. 652: 87 239 326 P T3 SD: 0.0103 c. M:-0.0178 c. 682: 91 250 341 P T3 SD: 0.0090 c. M:-0.0155 c. 712: 95 261 356 P T3 SD: 0.0078 c. M:-0.0135 c. 742: 99 272 371 P T3 SD: 0.0067 c. M:-0.0116 c. 772: 103 283 386 P T3 SD: 0.0057 c. M:-0.0098 c. 802: 107 294 401 P T3 SD: 0.0048 c. M:-0.0082 c. 832: 111 305 416 P T3 SD: 0.0039 c. M:-0.0067 c. 862: 115 316 431 P T3 SD: 0.0031 c. M:-0.0053 c. 892: 119 327 446 P T3 SD: 0.0023 c. M:-0.0040 c. 922: 123 338 461 P T3 SD: 0.0016 c. M:-0.0028 c. 952: 127 349 476 P T3 SD: 0.0010 c. M:-0.0017 c. 982: 131 360 491 P T3 SD: 0.0004 c. M:-0.0006 c. 1012: 135 371 506 P T3 SD: 0.0002 c. M: 0.0004 c. 1994: 266 731 997 P T3 SD: 0.0001 c. M:-0.0001 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: 33.2469 cents 12:13:14:16 S SD: 24.6174 cents 13:14:15:17 SD: 23.7225 cents 14:15:16:19 SD: 20.9740 cents 15:16:17:20 SD: 18.6828 cents 17:18:20:23 SD: 16.8901 cents 18:19:21:24 SD: 10.6051 cents 20:21:23:27 SD: 9.2048 cents 21:22:24:28 S SD: 7.8152 cents 24:25:28:32 SD: 5.8141 cents 26:27:30:35 S SD: 4.9494 cents 27:28:31:36 SD: 3.8741 cents 45:47:52:60 SD: 2.9360 cents 51:53:59:68 SD: 0.9970 cents 128:133:148:171 SD: 0.6635 cents 155:161:179:207 SD: 0.4935 cents 200:208:231:267 SD: 0.4426 cents 206:214:238:275 SD: 0.2515 cents 406:422:469:542 SD: 0.1293 cents 457:475:528:610 SD: 0.0636 cents