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