Scala analysis: 715_S24
Semi-tempered tetrachord 1.09185 * 1.07803 * 1.13278
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 152.130 cents 152.129600 2: 282.206 cents 282.206400 3: 498.048 cents 498.047640
SHOW/INTERVAL
0: 215.8412 cents 215.8412 1: 152.1296 cents 152.1296 2: 130.0768 cents 130.0768 3: 215.8412 cents 215.8412
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 130.07680 cents 1: 1 152.12960 cents 1: 1 215.84124 cents 2: 1 282.20640 cents 2: 1 345.91804 cents 2: 1 367.97084 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 : 152.1 282.2 498.0 152.1: 130.1 345.9 498.0 282.2: 215.8 368.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 130.0768 .. 215.8412 cents 85.76444 cents 130.07680 cents 2: 282.2064 .. 367.9708 cents 85.76444 cents 66.36516 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 130.07680 cents, class 1 Average step (divided formal octave): 166.0159 cents Largest one step interval : 215.84124 cents Average / Smallest step : 1.276291 Largest / Average step : 1.300124 Largest / Smallest step : 1.659337 Median interval of one step : 152.12960 cents, amount: 1 Least squares average step : 157.90609 cents, oct.: 473.71828 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2056-tone equal temperament with octave 498.048 cents degrees: 628 1165 2056 Least number of segments generator : 1029 of 249.266 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1661 of 402.362 cents and inv. generated superset size: 56 = 53 more = 1866.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 66.36516 cents Scale diversity : 1.347885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.655597 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 : 22.05280 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 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 85.7644 cents: 2 -- Rational properties --
FIT/MODE
3: 1 1 1 SP B ME I SD: 29.8630 c. M:-49.8254 c. 4: 1 1 2 P M ME S SD: 24.9254 c. M: 33.1826 c. 6: 2 1 3 P T3 SD: 20.7679 c. M: 33.1826 c. 7: 2 2 3 SP M ME S SD: 5.8412 c. M: 9.8303 c. 16: 5 4 7 SP T3 SD: 2.3483 c. M:-3.5103 c. 23: 7 6 10 SP T3 SD: 0.5145 c. M: 0.7012 c. 111: 34 29 48 SP T3 SD: 0.3657 c. M:-0.4693 c. 118: 36 31 51 SP T3 SD: 0.3530 c. M:-0.5834 c. 134: 41 35 58 SP T3 SD: 0.2150 c. M:-0.2684 c. 157: 48 41 68 SP T3 SD: 0.1088 c. M:-0.1397 c. 180: 55 47 78 SP T3 SD: 0.0321 c. M:-0.0516 c. 383: 117 100 166 SP T3 SD: 0.0159 c. M: 0.0228 c. 563: 172 147 244 SP T3 SD: 0.0164 c. M:-0.0271 c. 946: 289 247 410 SP T3 SD: 0.0154 c. M:-0.0224 c. 1290: 394 337 559 SP T3 SD: 0.0140 c. M:-0.0206 c. 1313: 401 343 569 SP T3 SD: 0.0136 c. M: 0.0221 c. 1329: 406 347 576 SP T3 SD: 0.0153 c. M:-0.0204 c. 1470: 449 384 637 SP T3 SD: 0.0122 c. M:-0.0206 c. 1493: 456 390 647 SP T3 SD: 0.0094 c. M: 0.0132 c. 1673: 511 437 725 SP T3 SD: 0.0071 c. M:-0.0107 c. 1696: 518 443 735 SP T3 SD: 0.0079 c. M: 0.0136 c. 1853: 566 484 803 SP T3 SD: 0.0067 c. M:-0.0116 c. 1876: 573 490 813 SP T3 SD: 0.0046 c. M: 0.0074 c. 2056: 628 537 891 SP T3 SD: 0.0029 c. M:-0.0044 c. 2259: 690 590 979 SP T3 SD: 0.0022 c. M: 0.0035 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9524 cents 2 x x 3 S SD: 203.9074 cents 3 x x 4 S SD: 0.0026 cents 4 x 5 x S SD: 104.1073 cents 5 x 6:7 S SD: 45.4207 cents 6 x 7:8 S SD: 7.6677 cents 7 x 8:9 S SD: 40.5238 cents 8:9 x 11 SD: 37.1448 cents 9:10:11:12 H SD: 23.9624 cents 10:11:12:13 H SD: 18.8710 cents 11:12:13:15 SD: 13.1855 cents 12:13:14:16 S SD: 6.8229 cents 21:23:25:28 SD: 6.7865 cents 30:33:35:40 SD: 6.6744 cents 33:36:39:44 SD: 2.3869 cents 45:49:53:60 SD: 1.6076 cents 96:105:113:128 SD: 1.0035 cents 108:118:127:144 SD: 0.6755 cents 141:154:166:188 SD: 0.2234 cents 294:321:346:392 SD: 0.0867 cents 435:475:512:580 SD: 0.0577 cents