Scala analysis: 084_E9
Enharmonic tetrachord 57/55 * 55/54 * 24/19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57/55 61.836361 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: 57/55 61.8364 2: 55/54 31.7667 telepathma 3: 24/19 404.4420 smaller undevicesimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 1 57/55 61.836 cents 1: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 19/18 93.603 cents undevicesimal semitone 2: 1 220/171 436.209 cents 2: 1 72/55 466.278 cents undecimal 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 : 61.8 93.6 498.0 61.8 : 31.8 436.2 498.0 93.6 : 404.4 466.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 404.4420 cents 1296/1045, 372.6753 cents 55/54, 31.7667 cents 2: 93.6030 .. 466.2783 cents 1296/1045, 372.6753 cents 361/432,-310.8390 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 24/19, 404.4420 cents Average / Smallest step : 5.226078 Largest / Average step : 2.436177 Largest / Smallest step : 12.731652 Median interval of one step : 57/55, 61.8364 cents, amount: 1 Least squares average step : 124.51267 cents, oct.: 373.53801 cents Scale is not proper Scale has trivalence property 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 31.76665 cents Scale diversity : 0.350179 Lumma stability : 0.127565 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 : 3078/3025, 30.0697 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 -- Rational properties -- Prime limit : 19 Odd number limit : 171 (O: 57 U: 171) Highest odd numerator or denominator: 57 Scale harmonicity : 0.014350 Average absolute harmonicity : 0.085104 Specific harmonicity : 0.065084 Fundamental : 1/990, -9.9513 octaves, 0.2643 Hz. Guide tone : 228, 7.8329 octaves, 59650.629 Hz. Exponens Consonantiae : 2.257200E+05, 17.78417 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 78.0, average 26.00000 Mersenne's string divisions : 4144 Sum of van Prooijen's expressibility: 3.51175, average 1.17058 Sum of Tenney's harmonic distance : 7.10944, average 2.36981 Vogel's harmonic complexity : 28.66667 Wille's k value : 522 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.78291, average 2.79715 Lattice compactness (without 2's) : 12.61266, average 2.10211 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -2 .. 1 -0.66667 4 1 5: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 19: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 23 29| Scale is weakly epimorphic with val: <6 10 15 25 33| Scale is weakly epimorphic with val: <6 10 15 26 29| Scale is weakly epimorphic with val: <6 10 16 24 33| Scale is weakly epimorphic with val: <6 10 16 25 29| Scale is weakly epimorphic with val: <6 10 17 23 33| Scale is weakly epimorphic with val: <6 10 17 24 29| Scale is weakly epimorphic with val: <6 10 17 27 29| Scale is weakly epimorphic with val: <6 10 18 23 29| Scale is weakly epimorphic with val: <6 10 18 26 29| Scale is weakly epimorphic with val: <6 10 19 25 29| Scale is weakly epimorphic with val: <6 11 15 23 30| Scale is weakly epimorphic with val: <6 11 15 25 31| Scale is weakly epimorphic with val: <6 11 15 26 33| Scale is weakly epimorphic with val: <6 11 16 24 31| Scale is weakly epimorphic with val: <6 11 16 25 33| Scale is weakly epimorphic with val: <6 11 16 27 31| Scale is weakly epimorphic with val: <6 11 17 23 31| Scale is weakly epimorphic with val: <6 11 17 24 33| Scale is weakly epimorphic with val: <6 11 17 26 31| Scale is weakly epimorphic with val: <6 11 18 23 33| Scale is weakly epimorphic with val: <6 11 18 25 31| Scale is weakly epimorphic with val: <6 11 19 24 31| Scale is weakly epimorphic with val: <6 11 19 27 31| Scale is weakly epimorphic with val: <7 10 15 23 30| Scale is weakly epimorphic with val: <7 10 15 24 32| Scale is weakly epimorphic with val: <7 10 15 26 30| Scale is weakly epimorphic with val: <7 10 16 23 32| Scale is weakly epimorphic with val: <7 10 16 25 30| Scale is weakly epimorphic with val: <7 10 17 24 30| Scale is weakly epimorphic with val: <7 10 17 27 30| Scale is weakly epimorphic with val: <7 10 18 23 30| Scale is weakly epimorphic with val: <7 10 18 26 30| Scale is weakly epimorphic with val: <7 10 19 25 30| Scale is weakly epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 23 31| Scale is weakly epimorphic with val: <7 11 15 23 34| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 24 33| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is JI-epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 26 34| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is weakly epimorphic with val: <7 11 16 23 30| Scale is weakly epimorphic with val: <7 11 16 23 33| 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 26 30| Scale is weakly epimorphic with val: <7 11 16 26 33| Scale is weakly epimorphic with val: <7 11 17 24 28| Scale is JI-epimorphic with val: <7 11 17 24 31| Scale is weakly epimorphic with val: <7 11 17 24 34| 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 27 28| Scale is weakly epimorphic with val: <7 11 17 27 31| Scale is weakly epimorphic with val: <7 11 17 27 34| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is JI-epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 23 34| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 24 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 26 34| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 19 23 30| Scale is weakly epimorphic with val: <7 11 19 23 33| 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 26 30| Scale is weakly epimorphic with val: <7 11 19 26 33| Scale is weakly epimorphic with val: <7 12 15 23 29| Scale is weakly epimorphic with val: <7 12 15 24 34| Scale is weakly epimorphic with val: <7 12 15 26 32| Scale is weakly epimorphic with val: <7 12 15 27 34| Scale is weakly epimorphic with val: <7 12 16 23 34| Scale is weakly epimorphic with val: <7 12 16 25 32| Scale is weakly epimorphic with val: <7 12 16 26 34| Scale is weakly epimorphic with val: <7 12 17 24 32| Scale is weakly epimorphic with val: <7 12 17 25 34| Scale is weakly epimorphic with val: <7 12 18 23 32| Scale is weakly epimorphic with val: <7 12 18 24 34| Scale is weakly epimorphic with val: <7 12 18 27 34| Scale is weakly epimorphic with val: <7 12 19 23 34| Scale is weakly epimorphic with val: <7 12 19 26 34| Scale is weakly epimorphic with val: <8 11 15 24 31| Scale is weakly epimorphic with val: <8 11 15 25 33| Scale is weakly epimorphic with val: <8 11 15 27 34| Scale is weakly epimorphic with val: <8 11 16 23 31| Scale is weakly epimorphic with val: <8 11 16 24 33| Scale is weakly epimorphic with val: <8 11 16 26 34| Scale is weakly epimorphic with val: <8 11 16 27 33| Scale is weakly epimorphic with val: <8 11 17 23 33| Scale is weakly epimorphic with val: <8 11 17 25 34| Scale is weakly epimorphic with val: <8 11 17 26 33| Scale is weakly epimorphic with val: <8 11 18 24 34| Scale is weakly epimorphic with val: <8 11 18 25 33| Scale is weakly epimorphic with val: <8 11 19 23 34| Scale is weakly epimorphic with val: <8 11 19 24 33| Scale is weakly epimorphic with val: <8 11 19 27 33| Scale is weakly epimorphic with val: <8 12 15 25 31| Scale is weakly epimorphic with val: <8 12 16 24 31| Scale is weakly epimorphic with val: <8 12 16 27 34| Scale is weakly epimorphic with val: <8 12 17 23 31| Scale is weakly epimorphic with val: <8 12 17 26 34| Scale is weakly epimorphic with val: <8 12 18 25 34| Scale is weakly epimorphic with val: <8 12 19 24 34|
FIT/MODE
3: 0 0 3 N M DE S SD: 64.7695 c. M: 93.6030 c. 4: 1 0 3 N G T3 SD: 40.3463 c. M:-62.6749 c. 5: 1 0 4 N G T3 SD: 22.0820 c. M:-37.7726 c. 6: 1 0 5 N G T3 SD: 13.6685 c. M:-21.1711 c. 9: 1 1 7 N M DE S SD: 10.5473 c. M:-17.0737 c. 10: 1 1 8 N M DE S SD: 7.7640 c. M: 12.0319 c. 14: 2 1 11 N T3 SD: 9.2896 c. M:-13.1209 c. 15: 2 1 12 N T3 SD: 4.3571 c. M:-6.0060 c. 16: 2 1 13 N T3 SD: 0.2732 c. M:-0.4193 c. 154: 19 10 125 N T3 SD: 0.2487 c. M: 0.3893 c. 170: 21 11 138 N T3 SD: 0.1996 c. M: 0.3132 c. 186: 23 12 151 N T3 SD: 0.1590 c. M: 0.2502 c. 202: 25 13 164 N T3 SD: 0.1248 c. M: 0.1971 c. 218: 27 14 177 N T3 SD: 0.0956 c. M: 0.1519 c. 234: 29 15 190 N T3 SD: 0.0705 c. M: 0.1128 c. 250: 31 16 203 N T3 SD: 0.0486 c. M: 0.0788 c. 266: 33 17 216 N T3 SD: 0.0294 c. M: 0.0488 c. 282: 35 18 229 N T3 SD: 0.0129 c. M: 0.0223 c. 298: 37 19 242 N T3 SD: 0.0062 c. M: 0.0107 c. 580: 72 37 471 N T3 SD: 0.0065 c. M: 0.0101 c. 878: 109 56 713 N T3 SD: 0.0053 c. M: 0.0069 c. 1176: 146 75 955 N T3 SD: 0.0051 c. M: 0.0078 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 22:23 x 29 SD: 12.4508 cents 23:24 x 31 SD: 11.0746 cents 24:25 x 32 SD: 4.4180 cents 25:26 x 33 SD: 9.2129 cents 26:27 x 35 SD: 8.4664 cents 30:31:32:40 S SD: 6.2746 cents 33:34:35:44 SD: 4.3639 cents 42 x 44:56 SD: 6.5330 cents 43 x 45:57 SD: 8.9975 cents 44:46 x 59 SD: 9.0115 cents 45:47:48:60 SD: 7.5236 cents 46:48:49:61 SD: 7.2887 cents 47:49:50:63 SD: 6.4408 cents 48:50:51:64 SD: 4.7953 cents 50:52:53:67 SD: 4.2719 cents 51:53:54:68 SD: 2.3869 cents 54:56:57:72 SD: 0.3748 cents 252:261:266:336 SD: 0.3617 cents 303:314:320:404 SD: 0.3025 cents 306:317:323:408 SD: 0.2316 cents 360:373:380:480 SD: 0.1406 cents 414:429:437:552 SD: 0.0734 cents 468:485:494:624 SD: 0.0216 cents 522:541:551:696 SD: 0.0194 cents