Scala analysis: fractal-12-false-awakening
Sevish: False Awakening, One With the Fractal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/9 347.407941 undecimal neutral third 2: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 3: 13/7 1071.701755 16/3-tone 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/13 128.2982 2/3-tone 1: 11/9 347.4079 undecimal neutral third 2: 63/55 235.1043 3: 65/49 489.1896 4: 14/13 128.2982 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 14/13 128.298 cents 2/3-tone 1: 1 63/55 235.104 cents 1: 1 11/9 347.408 cents undecimal neutral third 1: 1 65/49 489.190 cents 2: 1 154/117 475.706 cents 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 2: 1 10/7 617.488 cents Euler's tritone 2: 1 117/77 724.294 cents 3: 1 98/65 710.810 cents 3: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 110/63 964.896 cents 3: 1 13/7 1071.702 cents 16/3-tone Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 0.0 : 347.4 582.5 1071.7 1200.0 347.4 : 235.1 724.3 852.6 1200.0 582.5 : 489.2 617.5 964.9 1200.0 1071.7: 128.3 475.7 710.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 489.1896 cents 845/686, 360.8913 cents 14/13, 128.2982 cents 2: 475.7062 .. 724.2938 cents 13689/11858, 248.5876 cents 7546/7605,-13.4834 cents 3: 710.8104 .. 1071.7018 cents 845/686, 360.8913 cents 7546/7605,-13.4834 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 65/49, 489.1896 cents Average / Smallest step : 2.338302 Largest / Average step : 1.630632 Largest / Smallest step : 3.812909 Median interval of one step : 291.25610 cents, amount: 0 Least squares average step : 317.58459 cents, oct.: 1270.33835 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : CBDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 13.48338 cents Scale diversity : 1.718903 Lumma stability : 0.213830 Lumma impropriety factor : 0.022472 Rothenberg efficiency : 0.500000 redundancy: 0.500000 Efficiency x scale size : 2.000000 Number of different interval sizes : 12 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 7605/7546, 13.4834 cents Number of recognisable fifths : 1, average 710.8104 cents Formal octave complements present : 1 = 25.0000% -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 117 U: 117) Highest odd numerator or denominator: 13 Scale harmonicity : 0.013579 Average absolute harmonicity : 0.283321 Specific harmonicity : 0.084871 Fundamental : 1/315, -8.2992 octaves, 0.8306 Hz. Guide tone : 2002, 10.9672 octaves, 523774.382 Hz. Exponens Consonantiae : 6.306300E+05, 19.26643 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 27.5, average 6.87500 Mersenne's string divisions : 60 Sum of van Prooijen's expressibility: 3.00043, average 0.75011 Sum of Tenney's harmonic distance : 5.79977, average 1.44994 Vogel's harmonic complexity : 21.50000 Wille's k value : 292 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 19.71908, average 1.97191 Lattice compactness (without 2's) : 17.86998, average 1.78700 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.25000 1 1 3: -2 .. 0 -0.50000 2 5: -1 .. 0 -0.25000 1 7: -1 .. 1 0.00000 2 1 11: 0 .. 1 0.25000 1 1 13: 0 .. 1 0.25000 1 1 Average exponent except 2's :-1 / 4 =-0.25000 Average absolute exponent except 2's: 7 / 4 = 1.75000 Scale is JI-epimorphic with val: <4 6 9 11 13 14| Scale is weakly epimorphic with val: <4 6 9 11 15 16| Scale is weakly epimorphic with val: <4 6 9 12 13 14|
FIT/MODE
4: 1 1 2 0 N T3 SD: 68.9452 c. M:-128.2982 c. 5: 1 1 2 1 P M ME SD: 92.9012 c. M: 111.7018 c. 6: 2 1 2 1 SP B ME SD: 45.3125 c. M: 71.7018 c. Messiaen truncated mode 6 inverse 7: 2 1 3 1 P G D3 SD: 40.4221 c. M: 68.2265 c. 8: 2 2 3 1 P T3 SD: 27.4968 c. M: 47.4079 c. 10: 3 2 4 1 P SD: 11.5460 c. M:-17.4878 c. 17: 5 3 7 2 P SD: 11.3306 c. M: 17.8063 c. 21: 6 4 9 2 N SD: 9.2183 c. M:-14.0125 c. 25: 7 5 10 3 P SD: 10.2359 c. M: 15.7018 c. 27: 8 5 11 3 P SD: 5.3421 c. M:-8.1476 c. 35: 10 7 14 4 P SD: 4.9763 c. M: 8.8446 c. 37: 11 7 15 4 P SD: 4.7714 c. M:-9.3488 c. 45: 13 9 18 5 P SD: 3.2849 c. M: 5.0351 c. 56: 16 11 23 6 N SD: 3.0131 c. M: 4.5508 c. 58: 17 11 24 6 N SD: 3.3981 c. M:-4.3162 c. 66: 19 13 27 7 N SD: 1.1564 c. M: 1.9534 c. 76: 22 15 31 8 N SD: 1.3054 c. M:-1.9825 c. 93: 27 18 38 10 N SD: 1.1162 c. M: 1.8670 c. 103: 30 20 42 11 N SD: 1.0557 c. M:-2.1066 c. 111: 32 22 45 12 N SD: 1.2045 c. M: 1.4620 c. 138: 40 27 56 15 N SD: 1.0896 c. M: 2.1365 c. 142: 41 28 58 15 N SD: 0.9449 c. M:-1.5377 c. 148: 43 29 60 16 N SD: 1.1408 c. M: 1.4315 c. 159: 46 31 65 17 N SD: 0.7003 c. M: 1.3801 c. 169: 49 33 69 18 N SD: 0.3804 c. M:-0.5211 c. 280: 81 55 114 30 N SD: 0.2569 c. M:-0.3450 c. 373: 108 73 152 40 N SD: 0.2210 c. M: 0.3881 c. 439: 127 86 179 47 N SD: 0.2088 c. M: 0.2798 c. 449: 130 88 183 48 N SD: 0.0603 c. M:-0.1159 c. 888: 257 174 362 95 N SD: 0.0791 c. M: 0.1106 c. 964: 279 189 393 103 N SD: 0.0733 c. M: 0.1050 c. 1057: 306 207 431 113 N SD: 0.0551 c. M: 0.1092 c. 1271: 368 249 518 136 N SD: 0.0562 c. M: 0.1046 c. 1337: 387 262 545 143 N SD: 0.0405 c. M: 0.0631 c. 1506: 436 295 614 161 N SD: 0.0218 c. M: 0.0421 c. 1786: 517 350 728 191 N SD: 0.0274 c. M: 0.0395 c. 1955: 566 383 797 209 N SD: 0.0079 c. M:-0.0118 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 59.7214 cents 3 x 4 x 6 S SD: 42.2336 cents 4:5:6:7:8 H SD: 40.5922 cents 5:6:7:9:10 SD: 15.6854 cents 8:10:11:15:16 SD: 13.1368 cents 10:12:14:19:20 SD: 12.6718 cents 12:15:17:22:24 SD: 12.3300 cents 13:16:18:24:26 SD: 6.2102 cents 22:27:31:41:44 SD: 3.6490 cents 27:33:38:50:54 SD: 2.5964 cents 35:43:49:65:70 SD: 2.2425 cents 40:49:56:74:80 SD: 1.9358 cents 50:61:70:93:100 SD: 1.0311 cents 63:77:88:117:126 SD: 0.9825 cents 77:94:108:143:154 SD: 0.9513 cents 85:104:119:158:170 SD: 0.6061 cents 90:110:126:167:180 SD: 0.3701 cents 140:171:196:260:280 SD: 0.2811 cents 175:214:245:325:350 SD: 0.2248 cents 225:275:315:418:450 SD: 0.1479 cents 315:385:441:585:630 SD: 0.0000 cents