Scala analysis: 661_T68
Aristoxenian style tetrachord 12 + 9 + 7, Tiby
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 211.714 cents 211.714290 2: 370.500 cents 370.500000 3: 494.000 cents 494.000000
SHOW/INTERVAL
0: 123.5000 cents 123.5000 1: 211.7143 cents 211.7143 2: 158.7857 cents 158.7857 3: 123.5000 cents 123.5000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 123.50000 cents 1: 1 158.78571 cents 1: 1 211.71429 cents 2: 1 282.28571 cents 2: 1 335.21429 cents 2: 1 370.50000 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 : 211.7 370.5 494.0 211.7: 158.8 282.3 494.0 370.5: 123.5 335.2 494.0 494.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 123.5000 .. 211.7143 cents 88.21429 cents 123.50000 cents 2: 282.2857 .. 370.5000 cents 88.21429 cents 70.57142 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 123.50000 cents, class 1 Average step (divided formal octave): 164.6667 cents Largest one step interval : 211.71429 cents Average / Smallest step : 1.333333 Largest / Average step : 1.285714 Largest / Smallest step : 1.714286 Median interval of one step : 158.78571 cents, amount: 1 Least squares average step : 173.90816 cents, oct.: 521.72449 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 28-tone equal temperament with octave 494.000 cents degrees: 12 21 28 Least number of segments generator : 15 of 264.643 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 25 of 441.071 cents and inv. generated superset size: 8 = 5 more = 266.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LMS Interval vector is [ 0 0 0 0 0 0 1 0 1 0 0 1 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 70.57142 cents Scale diversity : 1.335619 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.642857 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 : 35.28571 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 decreasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 36.0933 c. M: 47.0476 c. 4: 2 1 1 P M ME S SD: 20.3722 c. M:-35.2857 c. 5: 2 2 1 SP M ME S SD: 16.4246 c. M:-24.7000 c. 7: 3 2 2 SP M ME S SD: 10.1861 c. M: 17.6429 c. 9: 4 3 2 SP T3 SD: 9.1248 c. M:-13.7222 c. 11: 5 3 3 SP M DE S SD: 9.8436 c. M:-12.8312 c. 12: 5 4 3 SP T3 SD: 3.3954 c. M: 5.8810 c. 16: 7 5 4 SP T3 SD: 2.5465 c. M:-4.4107 c. 28: 12 9 7 SP T3 SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x 2 S SD: 706.0000 cents 2 x x 3 S SD: 207.9550 cents 3 x x 4 S SD: 4.0450 cents 4 x 5 x S SD: 15.8137 cents 5 x 6:7 S SD: 52.0670 cents 6:7 x 8 S SD: 27.6524 cents 7:8 x 9 S SD: 31.0232 cents 8:9:10:11 H SD: 19.9898 cents 9:10:11:12 H SD: 12.5110 cents 16:18:20:21 S SD: 9.7189 cents 21:24:26:28 S SD: 6.6300 cents 24:27:30:32 S SD: 6.0309 cents 30:34:37:40 SD: 3.2696 cents 46:52:57:61 SD: 1.8202 cents 54:61:67:72 SD: 1.6832 cents 76:86:94:101 SD: 1.2597 cents 100:113:124:133 SD: 0.6447 cents 130:147:161:173 SD: 0.4309 cents 176:199:218:234 SD: 0.4238 cents 230:260:285:306 SD: 0.3071 cents 239:270:296:318 SD: 0.2463 cents 285:322:353:379 SD: 0.2177 cents 339:383:420:451 SD: 0.2164 cents 369:417:457:491 SD: 0.1880 cents 415:469:514:552 SD: 0.0607 cents