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