Scala analysis: 087_E9
Enharmonic tetrachord 40/39 * 247/240 * 24/19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 19/18 93.603014 undevicesimal semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 24/19 404.4420 smaller undevicesimal major third 1: 40/39 43.8311 tridecimal minor diesis 2: 247/240 49.7720 3: 24/19 404.4420 smaller undevicesimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 247/240 49.772 cents 1: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 19/18 93.603 cents undevicesimal semitone 2: 1 320/247 448.273 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished 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 : 43.8 93.6 498.0 43.8 : 49.8 454.2 498.0 93.6 : 404.4 448.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 404.4420 cents 117/95, 360.6109 cents 40/39, 43.8311 cents 2: 93.6030 .. 454.2139 cents 117/95, 360.6109 cents 361/432,-310.8390 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 24/19, 404.4420 cents Average / Smallest step : 3.787612 Largest / Average step : 2.436177 Largest / Smallest step : 9.227294 Median interval of one step : 247/240, 49.7720 cents, amount: 1 Least squares average step : 123.22658 cents, oct.: 369.67973 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1591-tone equal temperament with octave 4/3 degrees: 140 299 1591 Least number of segments generator : 796 of 249.179 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1521 of 476.132 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 43.83105 cents Scale diversity : 0.378206 Lumma stability : 0.176012 Lumma impropriety factor : 0.624118 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 : 3211/3200, 5.9409 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% Limited inverse transpositions with margin 354.6700 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 247 (O: 247 U: 247) Highest odd numerator or denominator: 39 Scale harmonicity : 0.013890 Average absolute harmonicity : 0.089412 Specific harmonicity : 0.073402 Fundamental : 1/234, -7.8704 octaves, 1.1181 Hz. Guide tone : 760, 9.5699 octaves, 198835.430 Hz. Exponens Consonantiae : 1.778400E+05, 17.44022 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 61.5, average 20.50000 Mersenne's string divisions : 20461 Sum of van Prooijen's expressibility: 3.34694, average 1.11565 Sum of Tenney's harmonic distance : 6.80633, average 2.26878 Vogel's harmonic complexity : 21.00000 Wille's k value : 123 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 17.67047, average 2.94508 Lattice compactness (without 2's) : 9.79655, average 1.63276 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -2 ..-1 -1.33333 4 1 5: 0 .. 1 0.33333 1 13: -1 .. 0 -0.33333 1 1 19: 0 .. 1 0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 25 29| Scale is weakly epimorphic with val: <6 10 15 28 29| Scale is weakly epimorphic with val: <6 10 16 26 29| Scale is weakly epimorphic with val: <6 10 16 29 29| Scale is weakly epimorphic with val: <6 10 17 27 29| Scale is weakly epimorphic with val: <6 10 18 25 29| Scale is weakly epimorphic with val: <6 10 18 28 29| Scale is weakly epimorphic with val: <6 10 19 26 29| Scale is weakly epimorphic with val: <6 10 19 29 29| Scale is weakly epimorphic with val: <6 11 15 26 31| Scale is weakly epimorphic with val: <6 11 15 29 31| Scale is weakly epimorphic with val: <6 11 16 27 31| Scale is weakly epimorphic with val: <6 11 16 30 31| Scale is weakly epimorphic with val: <6 11 17 25 31| Scale is weakly epimorphic with val: <6 11 17 28 31| Scale is weakly epimorphic with val: <6 11 18 26 31| Scale is weakly epimorphic with val: <6 11 18 29 31| Scale is weakly epimorphic with val: <6 11 19 27 31| Scale is weakly epimorphic with val: <6 11 19 30 31| Scale is weakly epimorphic with val: <7 10 15 27 30| Scale is weakly epimorphic with val: <7 10 15 30 30| Scale is weakly epimorphic with val: <7 10 16 25 30| Scale is weakly epimorphic with val: <7 10 16 28 30| Scale is weakly epimorphic with val: <7 10 17 25 29| Scale is weakly epimorphic with val: <7 10 17 25 32| Scale is weakly epimorphic with val: <7 10 17 26 30| Scale is weakly epimorphic with val: <7 10 17 29 30| Scale is weakly epimorphic with val: <7 10 18 26 29| Scale is weakly epimorphic with val: <7 10 18 26 32| Scale is weakly epimorphic with val: <7 10 18 27 30| Scale is weakly epimorphic with val: <7 10 18 30 30| Scale is weakly epimorphic with val: <7 10 19 25 30| Scale is weakly epimorphic with val: <7 10 19 27 29| Scale is weakly epimorphic with val: <7 10 19 27 32| Scale is weakly epimorphic with val: <7 10 19 28 30| Scale is weakly epimorphic with val: <7 11 15 26 30| Scale is weakly epimorphic with val: <7 11 15 26 33| Scale is weakly epimorphic with val: <7 11 15 27 28| Scale is weakly epimorphic with val: <7 11 15 27 31| Scale is weakly epimorphic with val: <7 11 15 27 34| Scale is weakly epimorphic with val: <7 11 15 29 30| Scale is weakly epimorphic with val: <7 11 15 29 33| Scale is weakly epimorphic with val: <7 11 15 30 31| Scale is weakly epimorphic with val: <7 11 15 30 34| Scale is weakly epimorphic with val: <7 11 16 25 28| Scale is JI-epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 25 34| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 16 27 33| Scale is weakly epimorphic with val: <7 11 16 28 28| Scale is weakly epimorphic with val: <7 11 16 28 31| Scale is weakly epimorphic with val: <7 11 16 28 34| Scale is weakly epimorphic with val: <7 11 16 30 30| Scale is weakly epimorphic with val: <7 11 16 30 33| Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is weakly epimorphic with val: <7 11 17 26 28| Scale is JI-epimorphic with val: <7 11 17 26 31| Scale is weakly epimorphic with val: <7 11 17 26 34| Scale is weakly epimorphic with val: <7 11 17 28 30| Scale is weakly epimorphic with val: <7 11 17 28 33| Scale is weakly epimorphic with val: <7 11 17 29 31| Scale is weakly epimorphic with val: <7 11 17 29 34| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 26 33| Scale is weakly epimorphic with val: <7 11 18 27 28| Scale is JI-epimorphic with val: <7 11 18 27 31| Scale is weakly epimorphic with val: <7 11 18 27 34| Scale is weakly epimorphic with val: <7 11 18 29 30| Scale is weakly epimorphic with val: <7 11 18 29 33| Scale is weakly epimorphic with val: <7 11 18 30 31| Scale is weakly epimorphic with val: <7 11 18 30 34| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 11 19 28 28| Scale is JI-epimorphic with val: <7 11 19 28 31| Scale is weakly epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 30 30| Scale is weakly epimorphic with val: <7 11 19 30 33| Scale is weakly epimorphic with val: <7 12 15 26 34| Scale is weakly epimorphic with val: <7 12 15 29 34| Scale is weakly epimorphic with val: <7 12 16 27 34| Scale is weakly epimorphic with val: <7 12 16 30 34| Scale is weakly epimorphic with val: <7 12 17 25 34| Scale is weakly epimorphic with val: <7 12 17 28 34| Scale is weakly epimorphic with val: <7 12 18 26 34| Scale is weakly epimorphic with val: <7 12 18 29 34| Scale is weakly epimorphic with val: <7 12 19 25 29| Scale is weakly epimorphic with val: <7 12 19 25 32| Scale is weakly epimorphic with val: <7 12 19 27 34| Scale is weakly epimorphic with val: <7 12 19 30 34| Scale is weakly epimorphic with val: <8 11 15 25 28| Scale is weakly epimorphic with val: <8 11 15 25 31| Scale is weakly epimorphic with val: <8 11 15 25 34| Scale is weakly epimorphic with val: <8 11 15 27 33| Scale is weakly epimorphic with val: <8 11 15 30 33| Scale is weakly epimorphic with val: <8 11 16 25 33| Scale is weakly epimorphic with val: <8 11 16 26 28| Scale is weakly epimorphic with val: <8 11 16 26 31| Scale is weakly epimorphic with val: <8 11 16 26 34| Scale is weakly epimorphic with val: <8 11 16 28 33| Scale is weakly epimorphic with val: <8 11 17 26 33| Scale is weakly epimorphic with val: <8 11 17 27 28| Scale is weakly epimorphic with val: <8 11 17 27 31| Scale is weakly epimorphic with val: <8 11 17 27 34| Scale is weakly epimorphic with val: <8 11 17 29 33| Scale is weakly epimorphic with val: <8 11 18 27 33| Scale is weakly epimorphic with val: <8 11 18 28 28| Scale is weakly epimorphic with val: <8 11 18 28 31| Scale is weakly epimorphic with val: <8 11 18 28 34| Scale is weakly epimorphic with val: <8 11 18 30 33| Scale is weakly epimorphic with val: <8 11 19 25 33| Scale is weakly epimorphic with val: <8 11 19 28 33| Scale is weakly epimorphic with val: <8 11 19 29 31| Scale is weakly epimorphic with val: <8 11 19 29 34| Scale is weakly epimorphic with val: <8 12 16 25 28| Scale is weakly epimorphic with val: <8 12 16 25 31| Scale is weakly epimorphic with val: <8 12 16 25 34| Scale is weakly epimorphic with val: <8 12 17 26 28| Scale is weakly epimorphic with val: <8 12 17 26 31| Scale is weakly epimorphic with val: <8 12 17 26 34| Scale is weakly epimorphic with val: <8 12 18 27 28| Scale is weakly epimorphic with val: <8 12 18 27 31| Scale is weakly epimorphic with val: <8 12 18 27 34| Scale is weakly epimorphic with val: <8 12 19 28 28| Scale is weakly epimorphic with val: <8 12 19 28 31| Scale is weakly epimorphic with val: <8 12 19 28 34|
FIT/MODE
3: 0 0 3 N M DE S SD: 59.6732 c. M: 93.6030 c. 4: 0 1 3 N G T3 SD: 30.9649 c. M: 43.8311 c. 5: 0 1 4 N G T3 SD: 25.5423 c. M: 43.8311 c. 6: 0 1 5 N G T3 SD: 26.0348 c. M: 43.8311 c. 7: 0 1 6 N G T3 SD: 28.4331 c. M: 43.8311 c. 9: 1 1 7 N M DE S SD: 11.8873 c. M:-17.0737 c. 10: 1 1 8 N M DE S SD: 4.8906 c. M:-6.0060 c. 11: 1 1 9 N M DE S SD: 1.9484 c. M: 3.0494 c. 21: 2 2 17 N M DE S SD: 2.2036 c. M:-3.6018 c. 32: 3 3 26 N M DE S SD: 1.6565 c. M:-2.8607 c. 43: 4 4 35 N M DE S SD: 1.5420 c. M:-2.4987 c. 47: 4 5 38 N T3 SD: 1.3177 c. M:-1.7673 c. 48: 4 5 39 N T3 SD: 1.3496 c. M: 2.3273 c. 58: 5 6 47 N T3 SD: 0.7146 c. M: 0.8961 c. 69: 6 7 56 N T3 SD: 0.3301 c. M: 0.5228 c. 80: 7 8 65 N T3 SD: 0.1930 c. M: 0.2521 c. 170: 15 17 138 N T3 SD: 0.1073 c. M:-0.1466 c. 239: 21 24 194 N T3 SD: 0.1067 c. M:-0.1711 c. 250: 22 25 203 N T3 SD: 0.0171 c. M:-0.0294 c. 761: 67 76 618 N T3 SD: 0.0135 c. M:-0.0179 c. 1011: 89 101 821 N T3 SD: 0.0077 c. M:-0.0127 c. 1261: 111 126 1024 N T3 SD: 0.0057 c. M:-0.0095 c. 1511: 133 151 1227 N T3 SD: 0.0059 c. M:-0.0075 c. 1591: 140 159 1292 N T3 SD: 0.0041 c. M: 0.0056 c. 1841: 162 184 1495 N T3 SD: 0.0030 c. M: 0.0053 c. 2091: 184 209 1698 N T3 SD: 0.0036 c. M: 0.0050 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: 86.6339 cents 7 x 8:9 S SD: 75.6470 cents 8 x 9:11 SD: 61.2488 cents 9 x 10:12 S SD: 44.4003 cents 10 x 11:13 SD: 41.8906 cents 11 x 12:15 S SD: 34.5201 cents 12 x 13:16 SD: 22.4848 cents 13 x 14:17 SD: 24.1551 cents 14 x 15:19 SD: 20.0414 cents 15 x 16:20 S SD: 9.0641 cents 16 x 17:21 SD: 14.7666 cents 17 x 18:23 SD: 12.9172 cents 18 x 19:24 SD: 0.0000 cents 19 x 20:25 S SD: 11.7140 cents 20 x 21:27 SD: 11.6831 cents 21 x 22:28 SD: 6.5330 cents 22 x 23:29 SD: 12.9285 cents 23 x 24:31 SD: 13.6675 cents 24 x 25:32 SD: 11.4653 cents 25:26 x 33 SD: 14.8498 cents 26:27 x 35 SD: 13.5737 cents 27:28:29:36 SD: 11.8908 cents 28:29:30:37 SD: 11.5233 cents 29:30:31:39 SD: 10.1068 cents 30:31:32:40 S SD: 7.4235 cents 32:33:34:43 SD: 6.6628 cents 33:34:35:44 SD: 3.7996 cents 36:37:38:48 SD: 1.2010 cents 111:114:117:148 SD: 1.1323 cents 123:126:130:164 SD: 1.0217 cents 159:163:168:212 SD: 0.6342 cents 162:166:171:216 SD: 0.5346 cents 195:200:206:260 SD: 0.4671 cents 198:203:209:264 SD: 0.2186 cents 234:240:247:312 SD: 0.0000 cents