Scala analysis: 008_H2
Hyperenharmonic tetrachord 64/63 * 81/80 * 35/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/63 27.264092 septimal comma, Archytas' comma 2: 36/35 48.770381 septimal diesis, 1/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 35/27 449.2746 septimal semi-diminished fourth, 9/4-tone 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 81/80 21.5063 syntonic comma, Didymus comma 3: 35/27 449.2746 septimal semi-diminished fourth, 9/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 36/35 48.770 cents septimal diesis, 1/4-tone 2: 1 21/16 470.781 cents narrow fourth 2: 1 320/243 476.539 cents grave fourth 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 : 27.3 48.8 498.0 27.3 : 21.5 470.8 498.0 48.8 : 449.3 476.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 449.2746 cents 2800/2187, 427.7683 cents 81/80, 21.5063 cents 2: 48.7704 .. 476.5387 cents 2800/2187, 427.7683 cents 972/1225,-400.5042 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 35/27, 449.2746 cents Average / Smallest step : 7.719370 Largest / Average step : 2.706229 Largest / Smallest step : 20.890383 Median interval of one step : 64/63, 27.2641 cents, amount: 1 Least squares average step : 115.63856 cents, oct.: 346.91568 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1297-tone equal temperament with octave 4/3 degrees: 71 127 1297 Least number of segments generator : 649 of 249.214 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1069 of 410.494 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 21.50629 cents Scale diversity : 0.050482 Lumma stability : 0.086363 Lumma impropriety factor : 0.804153 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 : 5120/5103, 5.7578 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 427.7683 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 63 Scale harmonicity : 0.029983 Average absolute harmonicity : 0.100724 Specific harmonicity : 0.141581 Fundamental : 1/315, -8.2992 octaves, 0.8306 Hz. Guide tone : 576, 9.1699 octaves, 150696.326 Hz. Exponens Consonantiae : 1.814400E+05, 17.46913 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 102.5, average 34.16667 Mersenne's string divisions : 63119 Sum of van Prooijen's expressibility: 3.82053, average 1.27351 Sum of Tenney's harmonic distance : 7.78507, average 2.59502 Vogel's harmonic complexity : 14.00000 Wille's k value : 52 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 25.10530, average 4.18422 Lattice compactness (without 2's) : 14.53950, average 2.42325 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 3.33333 10 3: -2 .. 2 -0.33333 5 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 19 19| Scale is JI-epimorphic with val: <7 11 15 19| Scale is weakly epimorphic with val: <7 11 15 22| Scale is weakly epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 18 19| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 12 15 20| Scale is weakly epimorphic with val: <8 11 16 19| Scale is weakly epimorphic with val: <8 12 15 22| Scale is weakly epimorphic with val: <8 12 17 21| Scale is weakly epimorphic with val: <8 12 18 19|
FIT/MODE
3: 0 0 3 N M DE S SD: 32.2587 c. M: 48.7704 c. 8: 0 1 7 N G T3 SD: 17.5612 c. M: 27.2641 c. 9: 0 1 8 N G T3 SD: 16.1912 c. M: 27.2641 c. 10: 1 0 9 N G T3 SD: 13.0274 c. M:-22.5404 c. 11: 1 0 10 N G T3 SD: 10.5934 c. M:-18.0127 c. 12: 1 0 11 N G T3 SD: 9.2299 c. M:-14.2397 c. 13: 1 0 12 N G T3 SD: 8.7832 c. M:-11.0471 c. 16: 1 1 14 N M DE S SD: 8.0990 c. M:-13.4852 c. 17: 1 1 15 N M DE S SD: 5.7915 c. M:-9.8231 c. 18: 1 1 16 N M DE S SD: 3.7992 c. M:-6.5680 c. 19: 1 1 17 N M DE S SD: 2.1960 c. M:-3.6554 c. 20: 1 1 18 N M DE S SD: 1.4886 c. M: 2.3618 c. 39: 2 2 35 N M DE S SD: 1.6645 c. M:-2.3112 c. 41: 2 2 37 N M DE S SD: 1.7174 c. M: 2.9692 c. 50: 3 2 45 N T3 SD: 1.6255 c. M:-2.6186 c. 51: 3 2 46 N T3 SD: 1.1740 c. M:-2.0327 c. 52: 3 2 47 N T3 SD: 0.9892 c. M:-1.4693 c. 70: 4 3 63 N T3 SD: 0.9127 c. M:-1.1956 c. 71: 4 3 64 N T3 SD: 0.4974 c. M:-0.7948 c. 72: 4 3 65 N T3 SD: 0.3088 c. M:-0.4051 c. 91: 5 4 82 N T3 SD: 0.2871 c. M:-0.4868 c. 92: 5 4 83 N T3 SD: 0.1168 c. M: 0.1964 c. 164: 9 7 148 N T3 SD: 0.1114 c. M: 0.1806 c. 255: 14 11 230 N T3 SD: 0.0567 c. M:-0.0796 c. 347: 19 15 313 N T3 SD: 0.0174 c. M:-0.0294 c. 786: 43 34 709 N T3 SD: 0.0154 c. M:-0.0203 c. 858: 47 37 774 N T3 SD: 0.0121 c. M:-0.0181 c. 950: 52 41 857 N T3 SD: 0.0085 c. M: 0.0144 c. 1297: 71 56 1170 N T3 SD: 0.0016 c. M: 0.0027 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x x 7 SD: 84.4672 cents 6 x 7:8 S SD: 109.0503 cents 7 x 8:9 S SD: 96.4821 cents 8 x 9:11 SD: 82.0157 cents 9 x 10:12 S SD: 66.8167 cents 10 x 11:13 SD: 62.1117 cents 11 x 12:15 S SD: 54.5217 cents 12 x 13:16 SD: 44.9011 cents 13 x 14:17 SD: 43.1706 cents 14 x 15:19 SD: 38.5147 cents 15 x 16:20 S SD: 31.4805 cents 16 x 17:21 SD: 31.2253 cents 17 x 18:23 SD: 28.0946 cents 18 x 19:24 SD: 22.4163 cents 19 x 20:25 S SD: 23.0664 cents 20 x 21:27 SD: 20.8374 cents 21 x 22:28 SD: 15.8833 cents 22 x 23:29 SD: 17.2187 cents 23 x 24:31 SD: 15.5790 cents 24 x 25:32 SD: 10.9510 cents 25 x 26:33 SD: 12.9296 cents 26 x 27:35 SD: 11.7146 cents 27 x 28:36 SD: 7.0953 cents 28 x 29:37 SD: 9.8059 cents 29 x 30:39 SD: 8.9340 cents 30 x 31:40 SD: 3.9982 cents 31 x 32:41 SD: 7.6628 cents 32 x 33:43 SD: 7.1026 cents 33 x 34:44 SD: 1.4560 cents 34 x 35:45 SD: 6.4273 cents 35 x 36:47 SD: 6.1610 cents 36 x 37:48 SD: 0.6682 cents 37 x 38:49 SD: 6.0110 cents 38 x 39:51 SD: 5.9859 cents 39 x 40:52 SD: 2.4697 cents 40 x 41:53 SD: 6.2063 cents 41 x 42:55 SD: 6.3342 cents 42 x 43:56 SD: 4.0168 cents 43 x 44:57 SD: 6.7522 cents 44 x 45:59 SD: 6.9556 cents 45 x 46:60 SD: 5.3599 cents 46:47 x 61 SD: 6.8625 cents 47:48 x 63 SD: 6.4943 cents 48:49 x 64 SD: 4.2164 cents 49:50 x 65 SD: 5.8713 cents 50:51 x 67 SD: 5.5637 cents 51:52 x 68 SD: 3.1766 cents 52:53 x 69 SD: 5.0559 cents 54:55:56:72 SD: 4.9626 cents 56:57:58:75 SD: 4.8810 cents 57:58:59:76 SD: 3.7658 cents 60:61:62:80 SD: 2.7033 cents 63:64:65:84 SD: 1.7784 cents 66:67:68:88 SD: 1.0537 cents 69:70:71:92 SD: 0.8183 cents 174:177:179:232 SD: 0.7822 cents 177:180:182:236 SD: 0.6373 cents 180:183:185:240 SD: 0.6337 cents 240:244:247:320 SD: 0.5609 cents 243:247:250:324 SD: 0.3590 cents 246:250:253:328 SD: 0.2293 cents 312:317:321:416 SD: 0.1768 cents 315:320:324:420 SD: 0.0000 cents