Scala analysis: 070_E6
Enharmonic tetrachord 78/77 * 28/27 * 33/26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78/77 22.338814 tridecimal minor third comma 2: 104/99 85.299718 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 33/26 412.7453 tridecimal major third 1: 78/77 22.3388 tridecimal minor third comma 2: 28/27 62.9609 Archytas' 1/3-tone 3: 33/26 412.7453 tridecimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 78/77 22.339 cents tridecimal minor third comma 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 33/26 412.745 cents tridecimal major third 2: 1 104/99 85.300 cents 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 154/117 475.706 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 : 22.3 85.3 498.0 22.3 : 63.0 475.7 498.0 85.3 : 412.7 435.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.3388 .. 412.7453 cents 847/676, 390.4065 cents 78/77, 22.3388 cents 2: 85.2997 .. 475.7062 cents 847/676, 390.4065 cents 2704/3267,-327.4456 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 78/77, 22.3388 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 33/26, 412.7453 cents Average / Smallest step : 7.431684 Largest / Average step : 2.486193 Largest / Smallest step : 18.476598 Median interval of one step : 28/27, 62.9609 cents, amount: 1 Least squares average step : 120.50523 cents, oct.: 361.51570 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2096-tone equal temperament with octave 4/3 degrees: 94 359 2096 Least number of segments generator : 1049 of 249.260 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1267 of 301.061 cents and inv. generated superset size: 62 = 59 more = 2066.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 22.33881 cents Scale diversity : 0.270009 Lumma stability : 0.089706 Lumma impropriety factor : 0.657462 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 : 78/77, 22.3388 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing 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 -- Rational properties -- Prime limit : 13 Odd number limit : 117 (O: 77 U: 117) Highest odd numerator or denominator: 99 Scale harmonicity : 0.016228 Average absolute harmonicity : 0.084417 Specific harmonicity : 0.069909 Fundamental : 1/693, -9.4367 octaves, 0.3775 Hz. Guide tone : 312, 8.2854 octaves, 81627.176 Hz. Exponens Consonantiae : 2.162160E+05, 17.72211 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 182.5, average 60.83333 Mersenne's string divisions : 31465 Sum of van Prooijen's expressibility: 4.35925, average 1.45308 Sum of Tenney's harmonic distance : 8.87044, average 2.95681 Vogel's harmonic complexity : 23.00000 Wille's k value : 175 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.91520, average 2.81920 Lattice compactness (without 2's) : 12.98957, average 2.16493 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -2 .. 1 -0.66667 4 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.66667 2 13: 0 .. 1 0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 19 23 29| Scale is weakly epimorphic with val: <6 10 19 24 30| Scale is weakly epimorphic with val: <6 10 20 23 28| Scale is weakly epimorphic with val: <6 10 20 24 29| Scale is weakly epimorphic with val: <6 10 20 25 30| Scale is weakly epimorphic with val: <6 11 19 23 30| Scale is weakly epimorphic with val: <6 11 20 23 29| Scale is weakly epimorphic with val: <6 11 20 24 30| Scale is weakly epimorphic with val: <6 11 22 23 30| Scale is weakly epimorphic with val: <7 10 18 23 27| Scale is weakly epimorphic with val: <7 10 18 24 28| Scale is weakly epimorphic with val: <7 10 18 25 29| Scale is weakly epimorphic with val: <7 10 18 26 30| Scale is weakly epimorphic with val: <7 10 20 23 25| Scale is weakly epimorphic with val: <7 10 20 24 26| Scale is weakly epimorphic with val: <7 10 20 25 27| Scale is weakly epimorphic with val: <7 10 20 26 28| Scale is weakly epimorphic with val: <7 10 20 27 29| Scale is weakly epimorphic with val: <7 10 21 23 30| Scale is weakly epimorphic with val: <7 11 18 23 25| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 24 26| Scale is weakly epimorphic with val: <7 11 18 24 29| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is JI-epimorphic with val: <7 11 20 23 26| Scale is weakly epimorphic with val: <7 11 20 23 29| Scale is JI-epimorphic with val: <7 11 20 24 27| Scale is weakly epimorphic with val: <7 11 20 24 30| Scale is weakly epimorphic with val: <7 11 20 25 25| Scale is JI-epimorphic with val: <7 11 20 25 28| Scale is weakly epimorphic with val: <7 11 20 26 26| Scale is JI-epimorphic with val: <7 11 20 26 29| Scale is weakly epimorphic with val: <7 11 20 27 27| Scale is JI-epimorphic with val: <7 11 20 27 30| Scale is weakly epimorphic with val: <7 11 21 23 25| Scale is weakly epimorphic with val: <7 11 21 23 28| Scale is weakly epimorphic with val: <7 11 21 24 26| Scale is weakly epimorphic with val: <7 11 21 24 29| Scale is weakly epimorphic with val: <7 11 21 25 27| Scale is weakly epimorphic with val: <7 11 21 25 30| Scale is weakly epimorphic with val: <7 11 21 26 28| Scale is weakly epimorphic with val: <7 11 21 27 29| Scale is weakly epimorphic with val: <7 12 18 23 29| Scale is weakly epimorphic with val: <7 12 18 24 30| Scale is weakly epimorphic with val: <7 12 20 23 27| Scale is weakly epimorphic with val: <7 12 20 24 28| Scale is weakly epimorphic with val: <7 12 20 25 29| Scale is weakly epimorphic with val: <7 12 20 26 30| Scale is weakly epimorphic with val: <7 12 21 23 29| Scale is weakly epimorphic with val: <7 12 21 24 30| Scale is weakly epimorphic with val: <8 11 18 23 25| Scale is weakly epimorphic with val: <8 11 18 24 26| Scale is weakly epimorphic with val: <8 11 18 25 27| Scale is weakly epimorphic with val: <8 11 18 26 28| Scale is weakly epimorphic with val: <8 11 18 27 29| Scale is weakly epimorphic with val: <8 11 19 24 25| Scale is weakly epimorphic with val: <8 11 19 25 26| Scale is weakly epimorphic with val: <8 11 19 26 27| Scale is weakly epimorphic with val: <8 11 19 27 28| Scale is weakly epimorphic with val: <8 11 21 23 28| Scale is weakly epimorphic with val: <8 11 21 24 29| Scale is weakly epimorphic with val: <8 11 21 25 30| Scale is weakly epimorphic with val: <8 11 22 24 25| Scale is weakly epimorphic with val: <8 11 22 25 26| Scale is weakly epimorphic with val: <8 11 22 26 27| Scale is weakly epimorphic with val: <8 11 22 27 28| Scale is weakly epimorphic with val: <8 12 18 23 26| Scale is weakly epimorphic with val: <8 12 18 24 27| Scale is weakly epimorphic with val: <8 12 18 25 28| Scale is weakly epimorphic with val: <8 12 18 26 29| Scale is weakly epimorphic with val: <8 12 18 27 30| Scale is weakly epimorphic with val: <8 12 19 23 25| Scale is weakly epimorphic with val: <8 12 19 24 26| Scale is weakly epimorphic with val: <8 12 19 25 27| Scale is weakly epimorphic with val: <8 12 19 26 28| Scale is weakly epimorphic with val: <8 12 19 27 29| Scale is weakly epimorphic with val: <8 12 21 23 26| Scale is weakly epimorphic with val: <8 12 21 24 27| Scale is weakly epimorphic with val: <8 12 21 25 28| Scale is weakly epimorphic with val: <8 12 21 26 29| Scale is weakly epimorphic with val: <8 12 21 27 30| Scale is weakly epimorphic with val: <8 12 22 23 28| Scale is weakly epimorphic with val: <8 12 22 24 29| Scale is weakly epimorphic with val: <8 12 22 25 30|
FIT/MODE
3: 0 0 3 N M DE S SD: 50.9086 c. M: 85.2997 c. 4: 0 1 3 N G T3 SD: 26.0549 c. M:-39.2115 c. 5: 0 1 4 N G T3 SD: 15.3164 c. M: 22.3388 c. 6: 0 1 5 N G T3 SD: 12.9650 c. M: 22.3388 c. 7: 0 1 6 N G T3 SD: 15.2671 c. M: 22.3388 c. 11: 0 2 9 N G T3 SD: 13.2492 c. M: 22.3388 c. 12: 0 2 10 N G T3 SD: 12.9650 c. M: 22.3388 c. 13: 0 2 11 N G T3 SD: 13.8362 c. M: 22.3388 c. 14: 1 1 12 N M DE S SD: 11.1866 c. M: 14.1504 c. 16: 1 2 13 N T3 SD: 6.8943 c. M:-8.7890 c. 17: 1 2 14 N T3 SD: 4.2866 c. M:-6.9580 c. 18: 1 2 15 N T3 SD: 3.3500 c. M:-5.3304 c. 22: 1 3 18 N T3 SD: 3.0383 c. M:-5.2539 c. 23: 1 3 19 N T3 SD: 0.8569 c. M:-1.3168 c. 47: 2 6 39 N T3 SD: 0.7277 c. M: 1.1454 c. 64: 3 8 53 N T3 SD: 0.6070 c. M:-1.0070 c. 70: 3 9 58 N T3 SD: 0.5757 c. M: 0.9940 c. 87: 4 11 72 N T3 SD: 0.4613 c. M:-0.5701 c. 88: 4 11 73 N T3 SD: 0.2912 c. M: 0.4057 c. 111: 5 14 92 N T3 SD: 0.0620 c. M:-0.0956 c. 245: 11 31 203 N T3 SD: 0.0476 c. M:-0.0794 c. 356: 16 45 295 N T3 SD: 0.0347 c. M:-0.0452 c. 625: 28 79 518 N T3 SD: 0.0250 c. M: 0.0344 c. 736: 33 93 610 N T3 SD: 0.0216 c. M: 0.0366 c. 759: 34 96 629 N T3 SD: 0.0167 c. M: 0.0285 c. 870: 39 110 721 N T3 SD: 0.0074 c. M: 0.0127 c. 981: 44 124 813 N T3 SD: 0.0044 c. M: 0.0076 c. 1851: 83 234 1534 N T3 SD: 0.0046 c. M: 0.0062 c. 2096: 94 265 1737 N T3 SD: 0.0032 c. M:-0.0047 c. 2207: 99 279 1829 N T3 SD: 0.0017 c. M:-0.0021 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: 90.7856 cents 7 x 8:9 S SD: 79.4409 cents 8 x 9:11 SD: 65.0123 cents 9 x 10:12 S SD: 48.5520 cents 10 x 11:13 SD: 45.4807 cents 11 x 12:15 S SD: 38.0218 cents 12 x 13:16 SD: 26.6365 cents 13 x 14:17 SD: 27.2901 cents 14 x 15:19 SD: 22.9384 cents 15 x 16:20 S SD: 13.2158 cents 16 x 17:21 SD: 16.8053 cents 17 x 18:23 SD: 14.3634 cents 18 x 19:24 SD: 4.1516 cents 19 x 20:25 S SD: 11.5982 cents 20 x 21:27 SD: 10.7612 cents 21 x 22:28 SD: 2.3813 cents 22 x 23:29 SD: 10.7365 cents 23 x 24:31 SD: 11.0148 cents 24 x 25:32 SD: 7.3136 cents 25 x 26:33 SD: 12.3033 cents 26 x 27:35 SD: 12.9707 cents 27 x 28:36 SD: 11.1694 cents 28 x 29:37 SD: 14.5233 cents 29 x 30:39 SD: 15.2384 cents 30 x 32:40 S SD: 13.2158 cents 31 x 33:41 SD: 13.4410 cents 32:33:34:43 SD: 13.0161 cents 33:34:35:44 SD: 11.2325 cents 34:35:36:45 S SD: 11.1807 cents 35:36:37:47 SD: 10.3782 cents 36:37:38:48 SD: 8.8111 cents 38:39:40:51 SD: 8.5198 cents 39:40:41:52 SD: 7.1768 cents 42:43:44:56 SD: 6.3348 cents 45:46:47:60 SD: 6.2111 cents 51:52:54:68 SD: 5.9035 cents 53:54:56:71 SD: 5.4492 cents 54:55:57:72 SD: 4.1877 cents 56:57:59:75 SD: 4.1349 cents 57:58:60:76 SD: 2.8409 cents 60:61:63:80 SD: 2.1107 cents 75:76:79:100 SD: 1.5641 cents 78:79:82:104 SD: 0.4371 cents 159:161:167:212 SD: 0.2552 cents 237:240:249:316 SD: 0.2001 cents 378:383:397:504 SD: 0.1903 cents 456:462:479:608 SD: 0.1040 cents 534:541:561:712 SD: 0.0760 cents