Scala analysis: 627_T34
Aristoxenian style tetrachord 13/3 + 26/3 + 17, Chapter 4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 72.222 cents 72.222220 2: 216.667 cents 216.666670 3: 500.000 cents 500.000000
SHOW/INTERVAL
0: 283.3333 cents 283.3333 1: 72.2222 cents 72.2222 2: 144.4444 cents 144.4444 3: 283.3333 cents 283.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 72.22222 cents 1: 1 144.44445 cents 1: 1 283.33333 cents 2: 1 216.66667 cents 2: 1 355.55555 cents 2: 1 427.77778 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 : 72.2 216.7 500.0 72.2 : 144.4 427.8 500.0 216.7: 283.3 355.6 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 72.2222 .. 283.3333 cents 211.11111 cents 72.22222 cents 2: 216.6667 .. 427.7778 cents 211.11111 cents -66.66666 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 72.22222 cents, class 1 Average step (divided formal octave): 166.6667 cents Largest one step interval : 283.33333 cents Average / Smallest step : 2.307692 Largest / Average step : 1.700000 Largest / Smallest step : 3.923077 Median interval of one step : 144.44445 cents, amount: 1 Least squares average step : 143.25397 cents, oct.: 429.76191 cents Scale is not proper Scale has trivalence property Scale is a mode of a 90-tone equal temperament with octave 500.000 cents degrees: 13 39 90 Least number of segments generator : 47 of 261.111 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 77 of 427.778 cents and inv. generated superset size: 4 = 1 more = 133.333% 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 ] Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 66.66666 cents Scale diversity : 1.052296 Lumma stability : 0.288889 Lumma impropriety factor : 0.133333 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 : 66.66666 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
3: 0 1 2 N G T3 SD: 50.7151 c. M: 72.2222 c. 4: 1 1 2 P M ME S SD: 36.0398 c. M:-52.7778 c. 5: 1 1 3 N M DE S SD: 18.7028 c. M:-27.7778 c. 6: 1 2 3 P T3 SD: 20.2860 c. M:-33.3333 c. 7: 1 2 4 N T3 SD: 1.4490 c. M: 2.3810 c. 48: 7 14 27 N T3 SD: 1.2679 c. M:-2.0833 c. 55: 8 16 31 N T3 SD: 0.9221 c. M:-1.5151 c. 62: 9 18 35 N T3 SD: 0.6544 c. M:-1.0753 c. 69: 10 20 39 N T3 SD: 0.4410 c. M:-0.7246 c. 76: 11 22 43 N T3 SD: 0.2669 c. M:-0.4386 c. 83: 12 24 47 N T3 SD: 0.1222 c. M:-0.2008 c. 90: 13 26 51 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 x 5 S SD: 113.6863 cents 5 x 6:7 S SD: 64.4287 cents 6 x 7:8 S SD: 25.1211 cents 7 x 8:9 S SD: 33.2586 cents 8 x 9:11 SD: 26.4399 cents 9 x 10:12 S SD: 17.1593 cents 10 x 11:13 SD: 34.5158 cents 11 x 12:15 S SD: 37.8328 cents 12:13:14:16 S SD: 27.7422 cents 13:14:15:17 SD: 24.4393 cents 14:15:16:19 SD: 19.0415 cents 15:16:17:20 SD: 13.1858 cents 20:21:23:27 SD: 11.4114 cents 21:22:24:28 S SD: 5.6117 cents 24:25:27:32 SD: 4.3328 cents 44:46:50:59 SD: 3.4262 cents 45:47:51:60 SD: 1.2106 cents 113:118:128:151 SD: 1.1429 cents 119:124:135:159 SD: 0.8660 cents 120:125:136:160 SD: 0.8316 cents 143:149:162:191 SD: 0.5535 cents 164:171:186:219 SD: 0.4802 cents 188:196:213:251 SD: 0.2102 cents 352:367:399:470 SD: 0.1968 cents 397:414:450:530 SD: 0.1706 cents 472:492:535:630 SD: 0.1536 cents 517:539:586:690 SD: 0.1212 cents 585:610:663:781 SD: 0.1156 cents