Scala analysis: 663_T70

Tempered tetrachord in cents 22.7 + 22.7 + 454.4, Chapter 5

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:         22.700 cents      22.700000
  2:         45.400 cents      45.400000
  3:        499.800 cents     499.800000
SHOW/INTERVAL
  0:        454.4000 cents    454.4000
  1:         22.7000 cents     22.7000
  2:         22.7000 cents     22.7000
  3:        454.4000 cents    454.4000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   2 22.70000 cents
  1:   1 454.40000 cents
  2:   1 45.40000 cents
  2:   2 477.10000 cents
Highest number of different intervals for one interval class: 2
Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
        1     2     3    
 0.0  : 22.7  45.4  499.8
 22.7 : 22.7  477.1 499.8
 45.4 : 454.4 477.1 499.8
 499.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  22.7000   .. 454.4000 cents      431.70000 cents                    22.70000 cents
  2:  45.4000   .. 477.1000 cents      431.70000 cents                   -409.00000 cents
SHOW DATA
Number of notes                     : 3
-- Interval properties --
Smallest interval                   : 22.70000 cents, class 1
Average step (divided formal octave): 166.6000 cents
Largest one step interval           : 454.40000 cents
Average / Smallest step             : 7.339207
Largest / Average step              : 2.727491
Largest / Smallest step             : 20.017621
Median interval of one step         : 22.70000 cents, amount: 2
Most common interval of one step    : 22.70000 cents, amount: 2
Least squares average step          : 115.20714 cents, oct.:  345.62143 cents
Scale is not proper
Scale has Myhill's property
  chromas: 431.70000 cents and 409.00000 cents, ratio: 1.055501
  generators: 1 of 22.70000 cents and 477.10000 cents
ET pair of linear temperament       : 44&2466
Scale is distributional even
Scale is a mode of a 1079-tone equal temperament with octave  499.800 cents
  degrees: 49 98 1079
  generators: 49 and 1030
Number of contiguous 1-step segments: 0
Step pattern alph. order: AAB
Step pattern size order : SSL
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 22.70000 cents
Scale diversity                     : 0.032071
Lumma stability                     : 0.090836
Lumma impropriety factor            : 0.818327
Rothenberg efficiency               : 0.888889   redundancy: 0.111111
Efficiency x scale size             : 2.666667
Number of different interval sizes  : 4 = 2.00000 / class
Number of one step interval sizes   : 2
Highest interval variety            : 2
Mean interval variety               : 2.00000 = 2
Median interval variety             : 2
Lowest interval variety             : 2
Smallest interval difference        : 22.70000 cents
Most common intervals               : 22.70000 cents & inv., amount: 2
Number of recognisable fifths       : 0
Number of recognisable fourths      : 0
Steps are increasing
Formal octave complements present   : 1 = 33.3333%
2/1 octave complements present      : 0 = 0.0000%
Limited inverse transpositions      :
 2
Inversional symmetry on degrees     :
 1
Inversional symmetry on intervals   :
 2-3
-- Rational properties --
FIT/MODE
  3:  0 0 3   N M DE S SD: 29.3056 c. M: 45.4000 c. 
  8:  0 1 7   N G T3   SD: 16.3997 c. M: 22.7000 c. 
  9:  0 1 8   N G T3   SD: 14.3524 c. M: 22.7000 c. 
 10:  0 1 9   N G T3   SD: 13.3699 c. M: 22.7000 c. 
 11:  0 1 10   N G T3   SD: 13.1059 c. M: 22.7000 c. 
 12:  0 1 11   N G T3   SD: 13.2835 c. M: 22.7000 c. 
 13:  0 1 12   N G T3   SD: 13.7070 c. M: 22.7000 c. 
 14:  0 1 13   N G T3   SD: 14.2523 c. M: 22.7000 c. 
 15:  0 1 14   N G T3   SD: 14.8461 c. M: 22.7000 c. 
 16:  1 0 15   N G T3   SD: 9.5475 c. M: 14.1625 c. 
 17:  1 1 15   N M DE S SD: 8.6497 c. M:-13.4000 c. 
 18:  1 1 16   N M DE S SD: 6.5410 c. M:-10.1333 c. 
 19:  1 1 17   N M DE S SD: 4.6544 c. M:-7.2105 c. 
 20:  1 1 18   N M DE S SD: 2.9564 c. M:-4.5800 c. 
 21:  1 1 19   N M DE S SD: 1.4201 c. M:-2.2000 c. 
 22:  1 1 20   N M DE S SD: 0.0235 c. M:-0.0364 c. 
 639: 29 29 581   N M DE S SD: 0.0224 c. M: 0.0347 c. 
 661: 30 30 601   N M DE S SD: 0.0209 c. M: 0.0324 c. 
 683: 31 31 621   N M DE S SD: 0.0195 c. M: 0.0302 c. 
 705: 32 32 641   N M DE S SD: 0.0181 c. M: 0.0281 c. 
 727: 33 33 661   N M DE S SD: 0.0169 c. M: 0.0261 c. 
 749: 34 34 681   N M DE S SD: 0.0157 c. M: 0.0243 c. 
 771: 35 35 701   N M DE S SD: 0.0146 c. M: 0.0226 c. 
 793: 36 36 721   N M DE S SD: 0.0135 c. M: 0.0209 c. 
 815: 37 37 741   N M DE S SD: 0.0125 c. M: 0.0194 c. 
 837: 38 38 761   N M DE S SD: 0.0116 c. M: 0.0179 c. 
 859: 39 39 781   N M DE S SD: 0.0107 c. M: 0.0165 c. 
 881: 40 40 801   N M DE S SD: 0.0098 c. M: 0.0152 c. 
 903: 41 41 821   N M DE S SD: 0.0090 c. M: 0.0140 c. 
 925: 42 42 841   N M DE S SD: 0.0082 c. M: 0.0128 c. 
 947: 43 43 861   N M DE S SD: 0.0075 c. M: 0.0116 c. 
 969: 44 44 881   N M DE S SD: 0.0068 c. M: 0.0105 c. 
 991: 45 45 901   N M DE S SD: 0.0061 c. M: 0.0095 c. 
 1013: 46 46 921   N M DE S SD: 0.0055 c. M: 0.0085 c. 
 1035: 47 47 941   N M DE S SD: 0.0049 c. M: 0.0075 c. 
 1057: 48 48 961   N M DE S SD: 0.0043 c. M: 0.0066 c. 
 1079: 49 49 981   N M DE S SD: 0.0037 c. M: 0.0057 c. 
 1101: 50 50 1001   N M DE S SD: 0.0032 c. M: 0.0049 c. 
 1123: 51 51 1021   N M DE S SD: 0.0026 c. M: 0.0041 c. 
 1145: 52 52 1041   N M DE S SD: 0.0021 c. M: 0.0033 c. 
 1167: 53 53 1061   N M DE S SD: 0.0017 c. M: 0.0026 c. 
 1189: 54 54 1081   N M DE S SD: 0.0012 c. M: 0.0019 c. 
 1211: 55 55 1101   N M DE S SD: 0.0007 c. M: 0.0012 c. 
 1233: 56 56 1121   N M DE S SD: 0.0003 c. M: 0.0005 c. 
 1255: 57 57 1141   N M DE S SD: 0.0001 c. M:-0.0002 c. 
FIT/HARMONIC
 1 x x 2  S SD: 700.2000 cents
 2 x x 3  S SD: 202.1550 cents
 3 x x 4  S SD: 1.7550 cents
 4 x x 5  S SD: 113.4863 cents
 5 x x 7    SD: 82.7122 cents
 6 x 7:8  S SD: 110.7389 cents
 7 x 8:9  S SD: 98.3618 cents
 8 x 9:11    SD: 83.3359 cents
 9 x 10:12  S SD: 68.5075 cents
 10 x 11:13    SD: 63.9986 cents
 11 x 12:15  S SD: 55.8010 cents
 12 x 13:16    SD: 46.5946 cents
 13 x 14:17    SD: 45.0647 cents
 14 x 15:19    SD: 39.7392 cents
 15 x 16:20  S SD: 33.1772 cents
 16 x 17:21    SD: 33.1246 cents
 17 x 18:23    SD: 29.2457 cents
 18 x 19:24    SD: 24.1175 cents
 19 x 20:25  S SD: 24.9650 cents
 20 x 21:27    SD: 21.8881 cents
 21 x 22:28    SD: 17.5904 cents
 22 x 23:29    SD: 19.1037 cents
 23 x 24:31    SD: 16.4885 cents
 24 x 25:32    SD: 12.6666 cents
 25 x 26:33    SD: 14.7746 cents
 26 x 27:35    SD: 12.4187 cents
 27 x 28:36    SD: 8.8242 cents
 28 x 29:37    SD: 11.5577 cents
 29 x 30:39    SD: 9.3330 cents
 30 x 31:40    SD: 5.7508 cents
 31 x 32:41    SD: 9.2232 cents
 32 x 33:43    SD: 7.0585 cents
 33 x 34:44    SD: 3.2615 cents
 34 x 35:45    SD: 7.6495 cents
 35 x 36:47    SD: 5.5457 cents
 36 x 37:48    SD: 1.3433 cents
 37 x 38:49    SD: 6.7571 cents
 38 x 39:51    SD: 4.8035 cents
 39 x 40:52    SD: 1.1770 cents
 40 x 41:53    SD: 6.4424 cents
 41 x 42:55    SD: 4.7553 cents
 42 x 43:56    SD: 2.4913 cents
 43 x 44:57    SD: 6.5531 cents
 44 x 45:59    SD: 5.1729 cents
 45 x 46:60    SD: 3.7780 cents
 46 x 47:61    SD: 6.9267 cents
 47 x 48:63    SD: 5.8165 cents
 48 x 49:64    SD: 4.9303 cents
 49 x 50:65    SD: 7.4372 cents
 50 x 51:67    SD: 6.5368 cents
 51:52 x 68    SD: 5.5287 cents
 52:53 x 69    SD: 7.2040 cents
 53:54 x 71    SD: 5.7918 cents
 54:55 x 72    SD: 4.6175 cents
 55:56 x 73    SD: 6.4250 cents
 56:57 x 75    SD: 4.9638 cents
 60:61:62:80    SD: 4.3113 cents
 62:63:64:83    SD: 3.9951 cents
 63:64:65:84    SD: 3.3283 cents
 65:66:67:87    SD: 3.1228 cents
 66:67:68:88    SD: 2.4419 cents
 68:69:70:91    SD: 2.3725 cents
 69:70:71:92    SD: 1.6502 cents
 72:73:74:96    SD: 0.9780 cents
 75:76:77:100    SD: 0.5925 cents
 149:151:153:199    SD: 0.4318 cents
 152:154:156:203    SD: 0.3913 cents
 224:227:230:299    SD: 0.1740 cents
 227:230:233:303    SD: 0.0935 cents
 451:457:463:602    SD: 0.0836 cents
 526:533:540:702    SD: 0.0767 cents
 529:536:543:706    SD: 0.0742 cents