Scala analysis: 688_T95
Tempered tetrachord in cents 100 + 187.5 + 212.5, Chapter 5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 100.000 cents 100.000000 2: 287.500 cents 287.500000 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 212.5000 cents 212.5000 1: 100.0000 cents 100.0000 2: 187.5000 cents 187.5000 3: 212.5000 cents 212.5000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100.00000 cents 1: 1 187.50000 cents 1: 1 212.50000 cents 2: 1 287.50000 cents 2: 1 312.50000 cents 2: 1 400.00000 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 : 100.0 287.5 500.0 100.0: 187.5 400.0 500.0 287.5: 212.5 312.5 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 100.0000 .. 212.5000 cents 112.50000 cents 100.00000 cents 2: 287.5000 .. 400.0000 cents 112.50000 cents 75.00000 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100.00000 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 212.50000 cents Average / Smallest step : 1.666667 Largest / Average step : 1.275000 Largest / Smallest step : 2.125000 Median interval of one step : 187.50000 cents, amount: 1 Least squares average step : 155.35714 cents, oct.: 466.07143 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 40-tone equal temperament with octave 500.000 cents degrees: 8 23 40 Least number of segments generator : 21 of 262.500 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 21 of 262.500 cents and inv. generated superset size: 9 = 6 more = 300.000% 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 1 0 0 0 0 0 0 1 0 1 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 75.00000 cents Scale diversity : 1.172809 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.550000 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 : 25.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 87.5000 cents: 1 -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 46.7088 c. M:-66.6667 c. 4: 1 1 2 P M ME S SD: 26.0208 c. M: 37.5000 c. 5: 1 2 2 SP M ME S SD: 7.2169 c. M:-12.5000 c. 9: 2 3 4 SP T3 SD: 8.5241 c. M:-11.1111 c. 14: 3 5 6 SP T3 SD: 4.2509 c. M:-7.1429 c. 16: 3 6 7 SP T3 SD: 5.1031 c. M: 6.2500 c. 19: 4 7 8 SP T3 SD: 3.2453 c. M:-5.2632 c. 21: 4 8 9 SP T3 SD: 2.9362 c. M: 4.7619 c. 24: 5 9 10 SP T3 SD: 3.4021 c. M:-4.1667 c. 26: 5 10 11 SP T3 SD: 2.2889 c. M: 3.8462 c. 30: 6 11 13 SP T3 SD: 2.4056 c. M: 4.1667 c. 31: 6 12 13 SP T3 SD: 2.4747 c. M: 3.2258 c. 35: 7 13 15 SP T3 SD: 1.0310 c. M: 1.7857 c. 40: 8 15 17 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: 98.8137 cents 5 x 6:7 S SD: 43.5895 cents 6 x 7:8 S SD: 10.3608 cents 7 x 8:9 S SD: 42.9729 cents 8 x 9:11 SD: 49.0429 cents 9:10:11:12 H SD: 33.9659 cents 10:11:12:13 H SD: 28.1145 cents 11:12:13:15 SD: 20.9029 cents 12:13:14:16 S SD: 14.5954 cents 15:16:18:20 S SD: 10.1837 cents 17:18:20:23 SD: 8.0456 cents 18:19:21:24 SD: 7.2288 cents 32:34:38:43 SD: 5.3487 cents 33:35:39:44 SD: 1.0661 cents 116:123:137:155 SD: 0.7838 cents 149:158:176:199 SD: 0.6598 cents 167:177:197:223 SD: 0.5837 cents 188:199:222:251 SD: 0.5405 cents 200:212:236:267 SD: 0.4379 cents 221:234:261:295 SD: 0.3869 cents 254:269:300:339 SD: 0.3240 cents 337:357:398:450 SD: 0.2758 cents 370:392:437:494 SD: 0.2456 cents 388:411:458:518 SD: 0.1794 cents 421:446:497:562 SD: 0.0838 cents 454:481:536:606 SD: 0.0241 cents