Scala analysis: 339_C27
Chromatic tetrachord 46/45 * 9/8 * 80/69
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 23/20 241.960633 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 80/69 256.0844 1: 46/45 38.0506 23rd-partial chroma 2: 9/8 203.9100 major whole tone 3: 80/69 256.0844
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 9/8 203.910 cents major whole tone 1: 1 80/69 256.084 cents 2: 1 23/20 241.961 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 30/23 459.994 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 : 38.1 242.0 498.0 38.1 : 203.9 460.0 498.0 242.0: 256.1 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 256.0844 cents 600/529, 218.0337 cents 46/45, 38.0506 cents 2: 241.9606 .. 459.9944 cents 600/529, 218.0337 cents 1587/1600,-14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 80/69, 256.0844 cents Average / Smallest step : 4.363002 Largest / Average step : 1.542538 Largest / Smallest step : 6.730095 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 144.00764 cents, oct.: 432.02291 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2081-tone equal temperament with octave 4/3 degrees: 159 1011 2081 Least number of segments generator : 1041 of 249.142 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1863 of 445.871 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 14.12373 cents Scale diversity : 0.633196 Lumma stability : 0.152800 Lumma impropriety factor : 0.028358 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 : 1600/1587, 14.1237 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 : 23 Odd number limit : 69 (O: 23 U: 69) Highest odd numerator or denominator: 45 Scale harmonicity : 0.017295 Average absolute harmonicity : 0.084111 Specific harmonicity : 0.070917 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 1.656000E+04, 14.01542 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 70.5, average 23.50000 Mersenne's string divisions : 3913 Sum of van Prooijen's expressibility: 3.49206, average 1.16402 Sum of Tenney's harmonic distance : 7.05791, average 2.35264 Vogel's harmonic complexity : 22.33333 Wille's k value : 103 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 17.29576, average 2.88263 Lattice compactness (without 2's) : 10.32780, average 1.72130 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -2 .. 0 -1.00000 3 1 5: -1 .. 0 -0.66667 2 23: 0 .. 1 0.66667 2 2 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 30| Scale is weakly epimorphic with val: <6 10 16 31| Scale is weakly epimorphic with val: <6 10 17 32| Scale is weakly epimorphic with val: <6 10 18 33| Scale is weakly epimorphic with val: <6 10 19 34| Scale is weakly epimorphic with val: <6 11 15 30| Scale is weakly epimorphic with val: <6 11 16 31| Scale is weakly epimorphic with val: <6 11 17 32| Scale is weakly epimorphic with val: <6 11 18 33| Scale is weakly epimorphic with val: <6 11 19 34| Scale is weakly epimorphic with val: <7 10 15 31| Scale is weakly epimorphic with val: <7 10 16 32| Scale is weakly epimorphic with val: <7 10 17 33| Scale is weakly epimorphic with val: <7 10 18 34| Scale is weakly epimorphic with val: <7 10 19 35| Scale is JI-epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 34| Scale is JI-epimorphic with val: <7 11 16 32| Scale is weakly epimorphic with val: <7 11 16 35| Scale is weakly epimorphic with val: <7 11 17 30| Scale is JI-epimorphic with val: <7 11 17 33| = patent Scale is weakly epimorphic with val: <7 11 17 36| Scale is weakly epimorphic with val: <7 11 18 31| Scale is JI-epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 19 32| Scale is JI-epimorphic with val: <7 11 19 35| Scale is weakly epimorphic with val: <8 11 15 32| Scale is weakly epimorphic with val: <8 11 16 33| Scale is weakly epimorphic with val: <8 11 17 34| Scale is weakly epimorphic with val: <8 11 18 35| Scale is weakly epimorphic with val: <8 11 19 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 49.0428 c. M: 75.9456 c. 4: 0 2 2 P M DE S SD: 22.3437 c. M: 38.0506 c. 8: 1 3 4 P T3 SD: 14.5574 c. M:-24.2050 c. 9: 1 3 5 N T3 SD: 15.5298 c. M: 20.6073 c. 10: 1 4 5 P T3 SD: 7.9167 c. M:-11.7539 c. 12: 1 5 6 P T3 SD: 4.5385 c. M:-7.0619 c. 14: 1 6 7 P T3 SD: 4.3205 c. M:-7.0619 c. 23: 2 9 12 N T3 SD: 3.7336 c. M:-5.2576 c. 25: 2 10 13 N T3 SD: 1.9680 c. M: 2.8990 c. 27: 2 11 14 N T3 SD: 1.4157 c. M: 2.1612 c. 37: 3 15 19 N T3 SD: 1.3596 c. M:-2.3314 c. 39: 3 16 20 N T3 SD: 0.4186 c. M:-0.6767 c. 66: 5 27 34 N T3 SD: 0.3351 c. M: 0.4843 c. 105: 8 43 54 N T3 SD: 0.0676 c. M: 0.1043 c. 249: 19 102 128 N T3 SD: 0.0446 c. M:-0.0612 c. 354: 27 145 182 N T3 SD: 0.0403 c. M: 0.0641 c. 459: 35 188 236 N T3 SD: 0.0427 c. M: 0.0733 c. 562: 43 230 289 N T3 SD: 0.0361 c. M:-0.0560 c. 601: 46 246 309 N T3 SD: 0.0413 c. M:-0.0693 c. 603: 46 247 310 N T3 SD: 0.0407 c. M: 0.0571 c. 667: 51 273 343 N T3 SD: 0.0255 c. M: 0.0317 c. 706: 54 289 363 N T3 SD: 0.0255 c. M:-0.0435 c. 772: 59 316 397 N T3 SD: 0.0212 c. M: 0.0346 c. 811: 62 332 417 N T3 SD: 0.0140 c. M:-0.0243 c. 916: 70 375 471 N T3 SD: 0.0067 c. M:-0.0096 c. 1021: 78 418 525 N T3 SD: 0.0066 c. M: 0.0113 c. 1165: 89 477 599 N T3 SD: 0.0049 c. M:-0.0080 c. 1976: 151 809 1016 N T3 SD: 0.0056 c. M:-0.0085 c. 2081: 159 852 1070 N T3 SD: 0.0019 c. M:-0.0028 c. 2186: 167 895 1124 N T3 SD: 0.0015 c. M: 0.0024 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 6:7 S SD: 56.0436 cents 6 x 7:8 S SD: 12.4551 cents 7 x 8:9 S SD: 31.9391 cents 8 x 9:11 SD: 32.7332 cents 9 x 10:12 S SD: 29.7785 cents 10 x 12:13 S SD: 42.8661 cents 11 x 13:15 SD: 30.6028 cents 14:15:16:19 SD: 29.2118 cents 15:16:17:20 SD: 25.9650 cents 17:18:20:23 SD: 25.6043 cents 18:19:21:24 SD: 20.2939 cents 19:20:22:25 SD: 18.9786 cents 20:21:23:27 SD: 17.0523 cents 21:22:24:28 S SD: 14.6114 cents 24:25:28:32 SD: 13.6817 cents 25:26:29:33 SD: 12.5539 cents 26:27:30:35 S SD: 10.8138 cents 27:28:31:36 SD: 8.3553 cents 32:33:37:43 SD: 7.4631 cents 33:34:38:44 SD: 4.6070 cents 39:40:45:52 SD: 2.7249 cents 48:49:55:64 SD: 2.2368 cents 81:83:93:108 SD: 1.6743 cents 87:89:100:116 SD: 0.5198 cents 93:95:107:124 SD: 0.4865 cents 180:184:207:240 SD: 0.0000 cents