Scala analysis: 034_H8
Hyperenharmonic tetrachord 9/7 * 119/117 * 52/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/7 435.084095 septimal major third, BP third 2: 17/13 464.427748 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/51 33.6173 1: 9/7 435.0841 septimal major third, BP third 2: 119/117 29.3437 3: 52/51 33.6173
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 119/117 29.344 cents 1: 1 52/51 33.617 cents 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 28/27 62.961 cents Archytas' 1/3-tone 2: 1 17/13 464.428 cents 2: 1 156/119 468.701 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 : 435.1 464.4 498.0 435.1: 29.3 63.0 498.0 464.4: 33.6 468.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.3437 .. 435.0841 cents 1053/833, 405.7404 cents 119/117, 29.3437 cents 2: 62.9609 .. 468.7013 cents 1053/833, 405.7404 cents 196/243,-372.1232 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 119/117, 29.3437 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 5.657612 Largest / Average step : 2.620752 Largest / Smallest step : 14.827196 Median interval of one step : 52/51, 33.6173 cents, amount: 1 Least squares average step : 204.14818 cents, oct.: 612.44455 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 919 981 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 617 of 292.104 cents and inv. generated superset size: 40 = 37 more = 1333.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 29.34365 cents Scale diversity : 0.152715 Lumma stability : 0.117835 Lumma impropriety factor : 0.747168 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 : 2028/2023, 4.2736 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 405.7404 cents: 1 -- Rational properties -- Prime limit : 17 Odd number limit : 119 (O: 119 U: 119) Highest odd numerator or denominator: 17 Scale harmonicity : 0.013782 Average absolute harmonicity : 0.099147 Specific harmonicity : 0.073505 Fundamental : 1/273, -8.0928 octaves, 0.9583 Hz. Guide tone : 612, 9.2574 octaves, 160114.846 Hz. Exponens Consonantiae : 1.670760E+05, 17.35014 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 26.5, average 8.83333 Mersenne's string divisions : 1680 Sum of van Prooijen's expressibility: 2.66181, average 0.88727 Sum of Tenney's harmonic distance : 5.22291, average 1.74097 Vogel's harmonic complexity : 23.66667 Wille's k value : 178 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.91951, average 2.48658 Lattice compactness (without 2's) : 12.19036, average 2.03173 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 2 0.33333 3 1 7: -1 .. 0 -0.33333 1 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 19 25 28| Scale is weakly epimorphic with val: <6 10 19 26 29| Scale is weakly epimorphic with val: <6 10 19 27 30| Scale is weakly epimorphic with val: <6 10 19 28 31| Scale is weakly epimorphic with val: <6 10 19 29 32| Scale is weakly epimorphic with val: <6 10 19 30 33| Scale is weakly epimorphic with val: <6 10 22 25 28| Scale is weakly epimorphic with val: <6 10 22 26 29| Scale is weakly epimorphic with val: <6 10 22 27 30| Scale is weakly epimorphic with val: <6 10 22 28 31| Scale is weakly epimorphic with val: <6 10 22 29 32| Scale is weakly epimorphic with val: <6 10 22 30 33| Scale is weakly epimorphic with val: <6 11 19 25 27| Scale is weakly epimorphic with val: <6 11 19 25 30| Scale is weakly epimorphic with val: <6 11 19 25 33| Scale is weakly epimorphic with val: <6 11 19 26 28| Scale is weakly epimorphic with val: <6 11 19 26 31| Scale is weakly epimorphic with val: <6 11 19 27 29| Scale is weakly epimorphic with val: <6 11 19 27 32| Scale is weakly epimorphic with val: <6 11 19 28 30| Scale is weakly epimorphic with val: <6 11 19 28 33| Scale is weakly epimorphic with val: <6 11 19 29 31| Scale is weakly epimorphic with val: <6 11 19 30 32| Scale is weakly epimorphic with val: <6 11 20 25 28| Scale is weakly epimorphic with val: <6 11 20 26 29| Scale is weakly epimorphic with val: <6 11 20 27 30| Scale is weakly epimorphic with val: <6 11 20 28 31| Scale is weakly epimorphic with val: <6 11 20 29 32| Scale is weakly epimorphic with val: <6 11 20 30 33| Scale is weakly epimorphic with val: <7 10 18 25 28| Scale is weakly epimorphic with val: <7 10 18 26 29| Scale is weakly epimorphic with val: <7 10 18 27 30| Scale is weakly epimorphic with val: <7 10 18 28 31| Scale is weakly epimorphic with val: <7 10 18 29 32| Scale is weakly epimorphic with val: <7 10 18 30 33| Scale is weakly epimorphic with val: <7 10 21 25 28| Scale is weakly epimorphic with val: <7 10 21 26 29| Scale is weakly epimorphic with val: <7 10 21 27 30| Scale is weakly epimorphic with val: <7 10 21 28 31| Scale is weakly epimorphic with val: <7 10 21 29 32| Scale is weakly epimorphic with val: <7 10 21 30 33| 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 25 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is weakly epimorphic with val: <7 11 20 25 29| Scale is weakly epimorphic with val: <7 11 20 25 32| Scale is weakly epimorphic with val: <7 11 20 26 27| Scale is weakly epimorphic with val: <7 11 20 26 30| Scale is weakly epimorphic with val: <7 11 20 26 33| Scale is weakly epimorphic with val: <7 11 20 27 28| Scale is weakly epimorphic with val: <7 11 20 27 31| Scale is weakly epimorphic with val: <7 11 20 28 29| Scale is weakly epimorphic with val: <7 11 20 28 32| Scale is weakly epimorphic with val: <7 11 20 29 30| Scale is weakly epimorphic with val: <7 11 20 29 33| Scale is weakly epimorphic with val: <7 11 20 30 31| Scale is JI-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 25 33| Scale is JI-epimorphic with val: <7 11 21 26 28| Scale is weakly epimorphic with val: <7 11 21 26 31| Scale is JI-epimorphic with val: <7 11 21 27 29| Scale is weakly epimorphic with val: <7 11 21 27 32| Scale is JI-epimorphic with val: <7 11 21 28 30| Scale is weakly epimorphic with val: <7 11 21 28 33| Scale is JI-epimorphic with val: <7 11 21 29 31| Scale is JI-epimorphic with val: <7 11 21 30 32| Scale is weakly epimorphic with val: <7 12 20 25 28| Scale is weakly epimorphic with val: <7 12 20 26 29| Scale is weakly epimorphic with val: <7 12 20 27 30| Scale is weakly epimorphic with val: <7 12 20 28 31| Scale is weakly epimorphic with val: <7 12 20 29 32| Scale is weakly epimorphic with val: <7 12 20 30 33| Scale is weakly epimorphic with val: <7 12 21 25 29| Scale is weakly epimorphic with val: <7 12 21 25 32| Scale is weakly epimorphic with val: <7 12 21 26 27| Scale is weakly epimorphic with val: <7 12 21 26 30| Scale is weakly epimorphic with val: <7 12 21 26 33| Scale is weakly epimorphic with val: <7 12 21 27 28| Scale is weakly epimorphic with val: <7 12 21 27 31| Scale is weakly epimorphic with val: <7 12 21 28 29| Scale is weakly epimorphic with val: <7 12 21 28 32| Scale is weakly epimorphic with val: <7 12 21 29 30| Scale is weakly epimorphic with val: <7 12 21 29 33| Scale is weakly epimorphic with val: <7 12 21 30 31| Scale is weakly epimorphic with val: <8 11 18 25 28| Scale is weakly epimorphic with val: <8 11 18 26 29| Scale is weakly epimorphic with val: <8 11 18 27 30| Scale is weakly epimorphic with val: <8 11 18 28 31| Scale is weakly epimorphic with val: <8 11 18 29 32| Scale is weakly epimorphic with val: <8 11 18 30 33| Scale is weakly epimorphic with val: <8 11 19 25 29| Scale is weakly epimorphic with val: <8 11 19 25 32| Scale is weakly epimorphic with val: <8 11 19 26 27| Scale is weakly epimorphic with val: <8 11 19 26 30| Scale is weakly epimorphic with val: <8 11 19 26 33| Scale is weakly epimorphic with val: <8 11 19 27 28| Scale is weakly epimorphic with val: <8 11 19 27 31| Scale is weakly epimorphic with val: <8 11 19 28 29| Scale is weakly epimorphic with val: <8 11 19 28 32| Scale is weakly epimorphic with val: <8 11 19 29 30| Scale is weakly epimorphic with val: <8 11 19 29 33| Scale is weakly epimorphic with val: <8 11 19 30 31| Scale is weakly epimorphic with val: <8 11 21 25 28| Scale is weakly epimorphic with val: <8 11 21 26 29| Scale is weakly epimorphic with val: <8 11 21 27 30| Scale is weakly epimorphic with val: <8 11 21 28 31| Scale is weakly epimorphic with val: <8 11 21 29 32| Scale is weakly epimorphic with val: <8 11 21 30 33| Scale is weakly epimorphic with val: <8 12 19 25 28| Scale is weakly epimorphic with val: <8 12 19 26 29| Scale is weakly epimorphic with val: <8 12 19 27 30| Scale is weakly epimorphic with val: <8 12 19 28 31| Scale is weakly epimorphic with val: <8 12 19 29 32| Scale is weakly epimorphic with val: <8 12 19 30 33| Scale is weakly epimorphic with val: <8 12 21 25 27| Scale is weakly epimorphic with val: <8 12 21 25 30| Scale is weakly epimorphic with val: <8 12 21 25 33| Scale is weakly epimorphic with val: <8 12 21 26 28| Scale is weakly epimorphic with val: <8 12 21 26 31| Scale is weakly epimorphic with val: <8 12 21 27 29| Scale is weakly epimorphic with val: <8 12 21 27 32| Scale is weakly epimorphic with val: <8 12 21 28 30| Scale is weakly epimorphic with val: <8 12 21 28 33| Scale is weakly epimorphic with val: <8 12 21 29 31| Scale is weakly epimorphic with val: <8 12 21 30 32| Scale is weakly epimorphic with val: <8 12 22 25 28| Scale is weakly epimorphic with val: <8 12 22 26 29| Scale is weakly epimorphic with val: <8 12 22 27 30| Scale is weakly epimorphic with val: <8 12 22 28 31| Scale is weakly epimorphic with val: <8 12 22 29 32| Scale is weakly epimorphic with val: <8 12 22 30 33|
FIT/MODE
3: 3 0 0 N M DE S SD: 41.2076 c. M:-62.9609 c. 4: 4 0 0 N M DE S SD: 41.2076 c. M:-62.9609 c. 6: 5 0 1 N G T3 SD: 30.7748 c. M: 49.3902 c. 7: 6 0 1 N G T3 SD: 22.1788 c. M: 37.5320 c. 8: 7 0 1 N G T3 SD: 16.5394 c. M: 28.6384 c. 9: 8 0 1 N G T3 SD: 13.2905 c. M: 21.7211 c. 10: 9 0 1 N G T3 SD: 12.0432 c. M: 16.1872 c. 12: 10 1 1 N M DE S SD: 12.4373 c. M: 20.0466 c. 13: 11 1 1 N M DE S SD: 8.3400 c. M: 13.6614 c. 14: 12 1 1 N M DE S SD: 4.8608 c. M: 8.1884 c. 15: 13 1 1 N M DE S SD: 2.0034 c. M: 3.4451 c. 16: 14 1 1 N M DE S SD: 1.4938 c. M:-2.4894 c. 31: 27 2 2 N M DE S SD: 1.1407 c. M:-1.4853 c. 47: 41 3 3 N M DE S SD: 1.1139 c. M:-1.8271 c. 63: 55 4 4 N M DE S SD: 1.1635 c. M:-1.9953 c. 70: 61 4 5 N T3 SD: 1.2889 c. M: 1.9574 c. 71: 62 4 5 N T3 SD: 0.8466 c. M: 1.4563 c. 72: 63 4 5 N T3 SD: 0.6920 c. M: 0.9692 c. 86: 75 5 6 N T3 SD: 0.7807 c. M: 1.1301 c. 87: 76 5 6 N T3 SD: 0.4219 c. M: 0.7307 c. 88: 77 5 6 N T3 SD: 0.4521 c. M:-0.7053 c. 102: 89 6 7 N T3 SD: 0.4404 c. M: 0.5623 c. 103: 90 6 7 N T3 SD: 0.1452 c. M: 0.2305 c. 119: 104 7 8 N T3 SD: 0.1310 c. M:-0.1821 c. 222: 194 13 15 N T3 SD: 0.0857 c. M:-0.1444 c. 237: 207 14 16 N T3 SD: 0.0479 c. M: 0.0828 c. 340: 297 20 23 N T3 SD: 0.0455 c. M: 0.0740 c. 356: 311 21 24 N T3 SD: 0.0240 c. M:-0.0412 c. 459: 401 27 31 N T3 SD: 0.0194 c. M:-0.0271 c. 696: 608 41 47 N T3 SD: 0.0106 c. M: 0.0151 c. 1052: 919 62 71 N T3 SD: 0.0036 c. M: 0.0049 c. 1511: 1320 89 102 N T3 SD: 0.0034 c. M:-0.0049 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 4:5 x x S SD: 48.7704 cents 5:6 x 7 S SD: 73.1459 cents 6 x x 8 S SD: 0.0000 cents 7:9 x x SD: 0.0000 cents 8:10 x 11 S SD: 36.1129 cents 9 x x 12 S SD: 0.0000 cents 10 x 13 x SD: 10.2138 cents 11:14 x 15 SD: 21.3458 cents 12:15 x 16 S SD: 24.3852 cents 13 x 17 x SD: 0.0000 cents 14:18 x 19 SD: 15.3211 cents 15:19 x 20 SD: 12.9199 cents 16 x 21 x SD: 6.3532 cents 17:22 x 23 SD: 13.8381 cents 18:23 x 24 SD: 5.3599 cents 19:24:25 x SD: 16.2261 cents 20 x 26:27 SD: 11.9042 cents 21:27 x 28 SD: 0.0000 cents 22:28:29 x SD: 11.1829 cents 23 x 30:31 SD: 9.6171 cents 24:31 x 32 SD: 3.9982 cents 25:32:33 x SD: 8.9789 cents 27:35 x 36 SD: 7.0953 cents 28:36 x 37 SD: 7.7634 cents 29:37:38:39 SD: 6.7535 cents 30 x 39:40 SD: 5.1069 cents 31:40 x 41 SD: 7.6628 cents 32:41:42:43 SD: 5.3555 cents 34:44 x 45 SD: 8.5213 cents 35:45:46:47 SD: 5.0293 cents 36:46:47:48 SD: 3.6958 cents 37 x 48:49 SD: 9.0646 cents 38:49:50:51 SD: 5.4633 cents 39:50:51:52 SD: 1.6464 cents 42:54:55:56 SD: 0.8077 cents 123:158:161:164 SD: 0.7592 cents 147:189:192:196 SD: 0.6932 cents 150:193:196:200 SD: 0.6226 cents 189:243:247:252 SD: 0.3593 cents 231:297:302:308 SD: 0.1470 cents 273:351:357:364 SD: 0.0000 cents