Scala analysis: 289_C21
Chromatic tetrachord 40/39 * 221/200 * 20/17
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: 17/15 216.686695 septendecimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 40/39 43.8311 tridecimal minor diesis 2: 221/200 172.8556 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 221/200 172.856 cents 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 800/663 325.189 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 : 43.8 216.7 498.0 43.8 : 172.9 454.2 498.0 216.7: 281.4 325.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 281.3583 cents 39/34, 237.5273 cents 40/39, 43.8311 cents 2: 216.6867 .. 454.2139 cents 39/34, 237.5273 cents 289/300,-64.6716 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 : 20/17, 281.3583 cents Average / Smallest step : 3.787612 Largest / Average step : 1.694776 Largest / Smallest step : 6.419155 Median interval of one step : 221/200, 172.8556 cents, amount: 1 Least squares average step : 140.80996 cents, oct.: 422.42988 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1602-tone equal temperament with octave 4/3 degrees: 141 697 1602 Least number of segments generator : 803 of 249.644 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1393 of 433.069 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 : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 43.83105 cents Scale diversity : 0.786845 Lumma stability : 0.176012 Lumma impropriety factor : 0.129851 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 : 40/39, 43.8311 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% -- Rational properties -- Prime limit : 17 Odd number limit : 663 (O: 221 U: 663) Highest odd numerator or denominator: 39 Scale harmonicity : 0.014137 Average absolute harmonicity : 0.089676 Specific harmonicity : 0.074691 Fundamental : 1/195, -7.6073 octaves, 1.3417 Hz. Guide tone : 680, 9.4094 octaves, 177905.384 Hz. Exponens Consonantiae : 1.326000E+05, 17.01672 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 59.0, average 19.66667 Mersenne's string divisions : 17696 Sum of van Prooijen's expressibility: 3.29863, average 1.09954 Sum of Tenney's harmonic distance : 6.67885, average 2.22628 Vogel's harmonic complexity : 21.00000 Wille's k value : 110 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 15.48674, average 2.58112 Lattice compactness (without 2's) : 9.74202, average 1.62367 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.66667 5 3: -1 ..-1 -1.00000 3 1 5: -1 .. 1 0.00000 2 13: -1 .. 0 -0.33333 1 1 17: 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 28| Scale is weakly epimorphic with val: <6 10 15 28 28| 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 30| Scale is weakly epimorphic with val: <6 10 17 30 30| Scale is weakly epimorphic with val: <6 10 18 25 31| Scale is weakly epimorphic with val: <6 10 18 28 31| Scale is weakly epimorphic with val: <6 10 19 26 32| Scale is weakly epimorphic with val: <6 10 19 29 32| Scale is weakly epimorphic with val: <6 11 15 26 29| Scale is weakly epimorphic with val: <6 11 15 29 29| Scale is weakly epimorphic with val: <6 11 16 27 30| Scale is weakly epimorphic with val: <6 11 16 30 30| 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 32| Scale is weakly epimorphic with val: <6 11 18 29 32| Scale is weakly epimorphic with val: <6 11 19 27 33| Scale is weakly epimorphic with val: <6 11 19 30 33| Scale is weakly epimorphic with val: <7 10 15 27 28| Scale is weakly epimorphic with val: <7 10 16 25 29| Scale is weakly epimorphic with val: <7 10 16 28 29| 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 27| Scale is weakly epimorphic with val: <7 10 18 26 30| Scale is weakly epimorphic with val: <7 10 18 26 33| Scale is weakly epimorphic with val: <7 10 18 27 31| Scale is weakly epimorphic with val: <7 10 18 30 31| Scale is weakly epimorphic with val: <7 10 19 25 32| Scale is weakly epimorphic with val: <7 10 19 27 28| Scale is weakly epimorphic with val: <7 10 19 27 31| Scale is weakly epimorphic with val: <7 10 19 28 32| Scale is weakly epimorphic with val: <7 11 15 26 27| 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 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 JI-epimorphic with val: <7 11 16 25 29| Scale is weakly epimorphic with val: <7 11 16 25 32| Scale is weakly epimorphic with val: <7 11 16 27 28| Scale is weakly epimorphic with val: <7 11 16 27 31| Scale is weakly epimorphic with val: <7 11 16 28 29| Scale is weakly epimorphic with val: <7 11 16 28 32| Scale is weakly epimorphic with val: <7 11 16 30 31| Scale is weakly epimorphic with val: <7 11 17 25 29| Scale is weakly epimorphic with val: <7 11 17 25 32| Scale is weakly epimorphic with val: <7 11 17 26 27| Scale is JI-epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 26 33| Scale is weakly epimorphic with val: <7 11 17 28 29| Scale is weakly epimorphic with val: <7 11 17 28 32| Scale is weakly epimorphic with val: <7 11 17 29 30| Scale is weakly epimorphic with val: <7 11 17 29 33| Scale is weakly epimorphic with val: <7 11 18 26 27| 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 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 19 25 29| Scale is weakly epimorphic with val: <7 11 19 25 32| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 28 29| Scale is JI-epimorphic with val: <7 11 19 28 32| Scale is weakly epimorphic with val: <7 11 19 30 31| Scale is weakly epimorphic with val: <7 12 15 26 30| Scale is weakly epimorphic with val: <7 12 15 29 30| Scale is weakly epimorphic with val: <7 12 16 27 31| Scale is weakly epimorphic with val: <7 12 16 30 31| Scale is weakly epimorphic with val: <7 12 17 25 32| Scale is weakly epimorphic with val: <7 12 17 28 32| Scale is weakly epimorphic with val: <7 12 18 26 33| Scale is weakly epimorphic with val: <7 12 18 29 33| 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: <8 11 15 25 27| Scale is weakly epimorphic with val: <8 11 15 25 30| Scale is weakly epimorphic with val: <8 11 15 25 33| Scale is weakly epimorphic with val: <8 11 15 27 29| Scale is weakly epimorphic with val: <8 11 16 25 30| 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 28 30| Scale is weakly epimorphic with val: <8 11 17 26 31| Scale is weakly epimorphic with val: <8 11 17 27 29| Scale is weakly epimorphic with val: <8 11 17 27 32| Scale is weakly epimorphic with val: <8 11 17 29 31| Scale is weakly epimorphic with val: <8 11 18 27 32| Scale is weakly epimorphic with val: <8 11 18 28 30| Scale is weakly epimorphic with val: <8 11 18 28 33| Scale is weakly epimorphic with val: <8 11 18 30 32| 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 12 15 25 30| Scale is weakly epimorphic with val: <8 12 15 28 30| Scale is weakly epimorphic with val: <8 12 16 25 27| Scale is weakly epimorphic with val: <8 12 16 25 30| Scale is weakly epimorphic with val: <8 12 16 25 33| Scale is weakly epimorphic with val: <8 12 16 26 31| Scale is weakly epimorphic with val: <8 12 16 29 31| 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 27 32| Scale is weakly epimorphic with val: <8 12 17 30 32| Scale is weakly epimorphic with val: <8 12 18 25 33| Scale is weakly epimorphic with val: <8 12 18 27 29| Scale is weakly epimorphic with val: <8 12 18 27 32| Scale is weakly epimorphic with val: <8 12 18 28 33| Scale is weakly epimorphic with val: <8 12 19 28 30| Scale is weakly epimorphic with val: <8 12 19 28 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 38.6815 c. M: 50.6717 c. 4: 0 2 2 P M DE S SD: 31.4471 c. M: 43.8311 c. 5: 0 2 3 N G T3 SD: 27.2416 c. M: 43.8311 c. 7: 1 2 4 N T3 SD: 15.8827 c. M:-27.3182 c. 9: 1 3 5 N T3 SD: 7.1693 c. M:-11.5073 c. 11: 1 4 6 N T3 SD: 5.6607 c. M:-9.6974 c. 12: 1 4 7 N T3 SD: 5.4610 c. M: 9.1679 c. 14: 1 5 8 N T3 SD: 5.1205 c. M: 8.2564 c. 20: 2 7 11 N T3 SD: 5.5057 c. M:-7.4336 c. 21: 2 7 12 N T3 SD: 2.7966 c. M:-3.6018 c. 23: 2 8 13 N T3 SD: 0.3133 c. M: 0.5228 c. 124: 11 43 70 N T3 SD: 0.2340 c. M:-0.3504 c. 147: 13 51 83 N T3 SD: 0.1505 c. M:-0.2137 c. 170: 15 59 96 N T3 SD: 0.0912 c. M:-0.1141 c. 193: 17 67 109 N T3 SD: 0.0507 c. M:-0.0790 c. 216: 19 75 122 N T3 SD: 0.0342 c. M:-0.0551 c. 409: 36 142 231 N T3 SD: 0.0385 c. M:-0.0664 c. 455: 40 158 257 N T3 SD: 0.0375 c. M: 0.0469 c. 625: 55 217 353 N T3 SD: 0.0361 c. M:-0.0625 c. 671: 59 233 379 N T3 SD: 0.0357 c. M:-0.0482 c. 807: 71 280 456 N T3 SD: 0.0382 c. M: 0.0649 c. 830: 73 288 469 N T3 SD: 0.0418 c. M: 0.0671 c. 841: 74 292 475 N T3 SD: 0.0353 c. M:-0.0606 c. 887: 78 308 501 N T3 SD: 0.0350 c. M:-0.0499 c. 908: 80 315 513 N T3 SD: 0.0324 c. M:-0.0496 c. 931: 82 323 526 N T3 SD: 0.0265 c. M:-0.0354 c. 954: 84 331 539 N T3 SD: 0.0224 c. M: 0.0319 c. 977: 86 339 552 N T3 SD: 0.0206 c. M: 0.0346 c. 1000: 88 347 565 N T3 SD: 0.0215 c. M: 0.0371 c. 1023: 90 355 578 N T3 SD: 0.0244 c. M: 0.0396 c. 1124: 99 390 635 N T3 SD: 0.0216 c. M:-0.0359 c. 1147: 101 398 648 N T3 SD: 0.0162 c. M:-0.0247 c. 1170: 103 406 661 N T3 SD: 0.0122 c. M: 0.0158 c. 1193: 105 414 674 N T3 SD: 0.0108 c. M: 0.0183 c. 1216: 107 422 687 N T3 SD: 0.0125 c. M: 0.0207 c. 1363: 120 473 770 N T3 SD: 0.0101 c. M:-0.0174 c. 1386: 122 481 783 N T3 SD: 0.0056 c. M:-0.0084 c. 1409: 124 489 796 N T3 SD: 0.0041 c. M: 0.0071 c. 1602: 141 556 905 N T3 SD: 0.0032 c. M:-0.0044 c. 1625: 143 564 918 N T3 SD: 0.0019 c. M: 0.0031 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: 65.0514 cents 6 x 7:8 S SD: 25.0921 cents 7 x 8:9 S SD: 32.3031 cents 8 x 9:11 SD: 27.3918 cents 9 x 10:12 S SD: 17.1415 cents 10 x 11:13 SD: 33.8830 cents 11 x 12:15 S SD: 38.3282 cents 12 x 14:16 S SD: 25.0921 cents 15:16:17:20 SD: 22.6334 cents 17:18:19:23 SD: 21.7552 cents 18:19:20:24 S SD: 20.1455 cents 20:21:23:27 SD: 17.4884 cents 21:22:24:28 S SD: 13.1539 cents 22:23:25:29 SD: 12.9535 cents 23:24:26:31 SD: 11.8366 cents 24:25:27:32 SD: 9.9090 cents 27:28:31:36 SD: 9.8403 cents 28:29:32:37 SD: 9.0509 cents 29:30:33:39 SD: 7.3846 cents 30:31:34:40 SD: 4.3119 cents 36:37:41:48 SD: 3.0668 cents 39:40:44:52 SD: 2.6171 cents 45:46:51:60 SD: 1.9268 cents 75:77:85:100 SD: 0.5768 cents 120:123:136:160 SD: 0.3608 cents 195:200:221:260 SD: 0.0000 cents