Scala analysis: 338_C27
Chromatic tetrachord 23/22 * 11/10 * 80/69
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/22 76.956405 2: 23/20 241.960633 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 80/69 256.0844 1: 23/22 76.9564 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 80/69 256.0844
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 23/22 76.956 cents 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 80/69 256.084 cents 2: 1 23/20 241.961 cents 2: 1 40/33 333.041 cents 2: 1 88/69 421.089 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 : 77.0 242.0 498.0 77.0 : 165.0 421.1 498.0 242.0: 256.1 333.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.9564 .. 256.0844 cents 1760/1587, 179.1280 cents 23/22, 76.9564 cents 2: 241.9606 .. 421.0886 cents 1760/1587, 179.1280 cents 1587/1600,-14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 23/22, 76.9564 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 80/69, 256.0844 cents Average / Smallest step : 2.157260 Largest / Average step : 1.542538 Largest / Smallest step : 3.327655 Median interval of one step : 11/10, 165.0042 cents, amount: 1 Least squares average step : 146.78662 cents, oct.: 440.35986 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1482-tone equal temperament with octave 4/3 degrees: 229 720 1482 Least number of segments generator : 743 of 249.695 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1295 of 435.201 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 14.12373 cents Scale diversity : 1.036529 Lumma stability : 0.309034 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 Best minor thirds form a closed circle 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: 23 Scale harmonicity : 0.013636 Average absolute harmonicity : 0.083471 Specific harmonicity : 0.060814 Fundamental : 1/660, -9.3663 octaves, 0.3964 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 6.072000E+04, 15.88988 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 47.5, average 15.83333 Mersenne's string divisions : 13545 Sum of van Prooijen's expressibility: 3.20058, average 1.06686 Sum of Tenney's harmonic distance : 6.44609, average 2.14870 Vogel's harmonic complexity : 29.66667 Wille's k value : 379 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 15.97266, average 2.66211 Lattice compactness (without 2's) : 8.70674, average 1.45112 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 15 23 30| Scale is weakly epimorphic with val: <6 10 15 25 34| Scale is weakly epimorphic with val: <6 10 15 26 30| Scale is weakly epimorphic with val: <6 10 16 23 32| Scale is weakly epimorphic with val: <6 10 16 24 31| Scale is weakly epimorphic with val: <6 10 16 26 35| Scale is weakly epimorphic with val: <6 10 16 27 31| Scale is weakly epimorphic with val: <6 10 17 24 33| Scale is weakly epimorphic with val: <6 10 17 25 32| Scale is weakly epimorphic with val: <6 10 17 27 36| Scale is weakly epimorphic with val: <6 10 18 23 33| Scale is weakly epimorphic with val: <6 10 18 25 34| Scale is weakly epimorphic with val: <6 10 18 26 33| Scale is weakly epimorphic with val: <6 10 19 23 32| Scale is weakly epimorphic with val: <6 10 19 24 34| Scale is weakly epimorphic with val: <6 10 19 26 35| Scale is weakly epimorphic with val: <6 10 19 27 34| Scale is weakly epimorphic with val: <6 11 15 23 32| Scale is weakly epimorphic with val: <6 11 15 25 30| Scale is weakly epimorphic with val: <6 11 15 26 35| Scale is weakly epimorphic with val: <6 11 16 23 31| Scale is weakly epimorphic with val: <6 11 16 24 33| Scale is weakly epimorphic with val: <6 11 16 26 31| Scale is weakly epimorphic with val: <6 11 16 27 36| Scale is weakly epimorphic with val: <6 11 17 24 32| Scale is weakly epimorphic with val: <6 11 17 25 34| Scale is weakly epimorphic with val: <6 11 17 27 32| Scale is weakly epimorphic with val: <6 11 18 23 32| Scale is weakly epimorphic with val: <6 11 18 25 33| Scale is weakly epimorphic with val: <6 11 18 26 35| Scale is weakly epimorphic with val: <6 11 19 23 34| Scale is weakly epimorphic with val: <6 11 19 24 33| Scale is weakly epimorphic with val: <6 11 19 26 34| Scale is weakly epimorphic with val: <6 11 19 27 36| Scale is weakly epimorphic with val: <7 10 15 23 32| Scale is weakly epimorphic with val: <7 10 15 24 34| Scale is weakly epimorphic with val: <7 10 15 26 32| Scale is weakly epimorphic with val: <7 10 16 24 33| Scale is weakly epimorphic with val: <7 10 16 25 35| Scale is weakly epimorphic with val: <7 10 16 27 33| Scale is weakly epimorphic with val: <7 10 17 23 33| Scale is weakly epimorphic with val: <7 10 17 25 34| Scale is weakly epimorphic with val: <7 10 17 26 36| Scale is weakly epimorphic with val: <7 10 18 23 35| Scale is weakly epimorphic with val: <7 10 18 24 34| Scale is weakly epimorphic with val: <7 10 18 26 35| Scale is weakly epimorphic with val: <7 10 19 24 36| Scale is weakly epimorphic with val: <7 10 19 25 35| Scale is weakly epimorphic with val: <7 10 19 27 36| Scale is JI-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 24 36| Scale is weakly 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 15 27 36| Scale is JI-epimorphic with val: <7 11 16 24 32| Scale is weakly epimorphic with val: <7 11 16 24 35| Scale is weakly 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 32| Scale is weakly epimorphic with val: <7 11 16 27 35| Scale is weakly epimorphic with val: <7 11 17 23 32| Scale is weakly epimorphic with val: <7 11 17 23 35| Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is JI-epimorphic with val: <7 11 17 25 33| = patent Scale is weakly epimorphic with val: <7 11 17 25 36| Scale is weakly epimorphic with val: <7 11 17 26 32| Scale is weakly epimorphic with val: <7 11 17 26 35| Scale is weakly 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 24 36| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is JI-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 18 27 36| Scale is weakly epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 24 35| 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 32| Scale is JI-epimorphic with val: <7 11 19 27 35| Scale is weakly epimorphic with val: <7 12 15 23 33| Scale is weakly epimorphic with val: <7 12 15 24 32| Scale is weakly epimorphic with val: <7 12 15 26 36| Scale is weakly epimorphic with val: <7 12 15 27 32| Scale is weakly epimorphic with val: <7 12 16 24 34| Scale is weakly epimorphic with val: <7 12 16 25 33| Scale is weakly epimorphic with val: <7 12 17 23 34| Scale is weakly epimorphic with val: <7 12 17 25 35| Scale is weakly epimorphic with val: <7 12 17 26 34| Scale is weakly epimorphic with val: <7 12 18 23 33| Scale is weakly epimorphic with val: <7 12 18 24 35| Scale is weakly epimorphic with val: <7 12 18 26 36| Scale is weakly epimorphic with val: <7 12 18 27 35| Scale is weakly epimorphic with val: <7 12 19 24 34| Scale is weakly epimorphic with val: <7 12 19 25 36| Scale is weakly epimorphic with val: <8 11 15 24 35| Scale is weakly epimorphic with val: <8 11 15 25 34| Scale is weakly epimorphic with val: <8 11 16 23 35| Scale is weakly epimorphic with val: <8 11 16 25 36| Scale is weakly epimorphic with val: <8 11 16 26 35| Scale is weakly epimorphic with val: <8 11 17 23 34| Scale is weakly epimorphic with val: <8 11 17 24 36| Scale is weakly epimorphic with val: <8 11 17 27 36| Scale is weakly epimorphic with val: <8 11 18 24 35| Scale is weakly epimorphic with val: <8 11 19 25 36| Scale is weakly epimorphic with val: <8 12 15 24 34| Scale is weakly epimorphic with val: <8 12 15 25 36| Scale is weakly epimorphic with val: <8 12 15 27 34| Scale is weakly epimorphic with val: <8 12 16 23 34| Scale is weakly epimorphic with val: <8 12 16 25 35| Scale is weakly epimorphic with val: <8 12 17 23 36| Scale is weakly epimorphic with val: <8 12 17 24 35| Scale is weakly epimorphic with val: <8 12 17 26 36| Scale is weakly epimorphic with val: <8 12 18 25 36| Scale is weakly epimorphic with val: <8 12 19 23 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 62.4234 c. M: 76.9564 c. 4: 1 1 2 P M ME S SD: 27.7569 c. M:-47.5548 c. 5: 1 1 3 N M DE S SD: 27.9289 c. M: 42.7426 c. 6: 1 2 3 P T3 SD: 5.3692 c. M:-7.0619 c. 14: 2 5 7 P T3 SD: 5.2787 c. M:-7.0619 c. 19: 3 6 10 N T3 SD: 3.6225 c. M: 6.0446 c. 21: 3 7 11 N T3 SD: 4.3485 c. M: 5.8071 c. 25: 4 8 13 N T3 SD: 2.2994 c. M: 2.8990 c. 27: 4 9 14 N T3 SD: 2.2160 c. M: 3.1720 c. 31: 5 10 16 N T3 SD: 2.0267 c. M:-3.3734 c. 33: 5 11 17 N T3 SD: 0.9073 c. M: 1.4950 c. 39: 6 13 20 N T3 SD: 0.4357 c. M:-0.6767 c. 97: 15 32 50 N T3 SD: 0.3711 c. M: 0.6399 c. 103: 16 34 53 N T3 SD: 0.2611 c. M:-0.4098 c. 136: 21 45 70 N T3 SD: 0.1544 c. M: 0.2623 c. 142: 22 47 73 N T3 SD: 0.1217 c. M:-0.2055 c. 175: 27 58 90 N T3 SD: 0.0732 c. M: 0.1152 c. 278: 43 92 143 N T3 SD: 0.0756 c. M: 0.1042 c. 317: 49 105 163 N T3 SD: 0.0171 c. M:-0.0285 c. 492: 76 163 253 N T3 SD: 0.0191 c. M: 0.0241 c. 673: 104 223 346 N T3 SD: 0.0187 c. M:-0.0315 c. 809: 125 268 416 N T3 SD: 0.0104 c. M: 0.0179 c. 848: 131 281 436 N T3 SD: 0.0131 c. M: 0.0178 c. 1126: 174 373 579 N T3 SD: 0.0094 c. M: 0.0151 c. 1165: 180 386 599 N T3 SD: 0.0055 c. M:-0.0080 c. 1482: 229 491 762 N T3 SD: 0.0029 c. M:-0.0045 c. 1974: 305 654 1015 N T3 SD: 0.0028 c. M: 0.0042 c. 2291: 354 759 1178 N T3 SD: 0.0020 c. M: 0.0034 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 11:12:13:15 SD: 31.9287 cents 12:13:14:16 S SD: 22.1537 cents 13:14:15:17 SD: 20.5467 cents 14:15:16:19 SD: 17.8275 cents 15:16:17:20 SD: 14.3297 cents 18:19:21:24 SD: 9.9868 cents 19:20:22:25 SD: 9.4656 cents 20:21:23:27 SD: 7.5934 cents 21:22:24:28 S SD: 3.7884 cents 39:41:45:52 SD: 3.7420 cents 45:47:52:60 SD: 2.8365 cents 60:63:69:80 SD: 2.5036 cents 66:69:76:88 SD: 0.7598 cents 87:91:100:116 SD: 0.4079 cents 153:160:176:204 SD: 0.2319 cents 240:251:276:320 SD: 0.2090 cents 354:370:407:472 SD: 0.2005 cents 420:439:483:560 SD: 0.1195 cents 507:530:583:676 SD: 0.0700 cents 573:599:659:764 SD: 0.0619 cents