Scala analysis: 144_C3
Chromatic tetrachord 40/39 * 221/210 * 21/17
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: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 40/39 43.8311 tridecimal minor diesis 2: 221/210 88.3885 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 221/210 88.388 cents 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 280/221 409.657 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 : 43.8 132.2 498.0 43.8 : 88.4 454.2 498.0 132.2: 365.8 409.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 365.8255 cents 819/680, 321.9944 cents 40/39, 43.8311 cents 2: 132.2195 .. 454.2139 cents 819/680, 321.9944 cents 1156/1323,-233.6060 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 : 21/17, 365.8255 cents Average / Smallest step : 3.787612 Largest / Average step : 2.203569 Largest / Smallest step : 8.346263 Median interval of one step : 221/210, 88.3885 cents, amount: 1 Least squares average step : 128.74322 cents, oct.: 386.22965 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2034-tone equal temperament with octave 4/3 degrees: 179 540 2034 Least number of segments generator : 1019 of 249.512 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1273 of 311.707 cents and inv. generated superset size: 62 = 59 more = 2066.667% 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 43.83105 cents Scale diversity : 0.619689 Lumma stability : 0.176012 Lumma impropriety factor : 0.469046 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 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 : 221 (O: 221 U: 221) Highest odd numerator or denominator: 63 Scale harmonicity : 0.012938 Average absolute harmonicity : 0.088152 Specific harmonicity : 0.069003 Fundamental : 1/819, -9.6777 octaves, 0.3194 Hz. Guide tone : 680, 9.4094 octaves, 177905.384 Hz. Exponens Consonantiae : 5.569200E+05, 19.08711 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 108.5, average 36.16667 Mersenne's string divisions : 72443 Sum of van Prooijen's expressibility: 3.86753, average 1.28918 Sum of Tenney's harmonic distance : 7.90416, average 2.63472 Vogel's harmonic complexity : 25.00000 Wille's k value : 136 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.77604, average 2.46267 Lattice compactness (without 2's) : 10.56387, average 1.76065 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 ..-1 -1.33333 4 1 5: 0 .. 1 0.33333 1 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 1 17: 0 .. 1 0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 16 19 27 31| Scale is weakly epimorphic with val: <7 11 16 19 28 29| Scale is weakly epimorphic with val: <7 11 16 20 27 29| Scale is weakly epimorphic with val: <7 11 16 20 28 30| Scale is weakly epimorphic with val: <7 11 16 21 27 30| Scale is weakly epimorphic with val: <7 11 16 21 28 31| Scale is JI-epimorphic with val: <7 11 17 19 26 29| Scale is weakly epimorphic with val: <7 11 17 19 28 31| Scale is JI-epimorphic with val: <7 11 17 20 26 30| Scale is weakly epimorphic with val: <7 11 17 20 28 29| Scale is JI-epimorphic with val: <7 11 17 21 26 31| Scale is weakly epimorphic with val: <7 11 17 21 28 30| Scale is weakly epimorphic with val: <7 11 18 19 26 31| Scale is JI-epimorphic with val: <7 11 18 19 27 29| Scale is weakly epimorphic with val: <7 11 18 20 26 29| Scale is JI-epimorphic with val: <7 11 18 20 27 30| Scale is weakly epimorphic with val: <7 11 18 21 26 30| Scale is JI-epimorphic with val: <7 11 18 21 27 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.9546 c. M: 43.8311 c. 4: 0 1 3 N G T3 SD: 25.6942 c. M: 43.8311 c. 7: 1 1 5 N M DE S SD: 16.8114 c. M:-27.3182 c. 8: 1 1 6 N M DE S SD: 11.5309 c. M:-18.4246 c. 10: 1 2 7 N T3 SD: 10.5090 c. M:-17.1940 c. 11: 1 2 8 N T3 SD: 2.2457 c. M:-3.6110 c. 23: 2 4 17 N T3 SD: 1.3588 c. M: 2.2947 c. 34: 3 6 25 N T3 SD: 0.2313 c. M: 0.3841 c. 79: 7 14 58 N T3 SD: 0.1995 c. M:-0.2995 c. 113: 10 20 83 N T3 SD: 0.1407 c. M:-0.2437 c. 147: 13 26 108 N T3 SD: 0.1328 c. M:-0.2137 c. 181: 16 32 133 N T3 SD: 0.1390 c. M:-0.1950 c. 192: 17 34 141 N T3 SD: 0.1597 c. M:-0.2667 c. 215: 19 38 158 N T3 SD: 0.1477 c. M:-0.1822 c. 260: 23 46 191 N T3 SD: 0.1336 c. M:-0.2268 c. 305: 27 54 224 N T3 SD: 0.1516 c. M:-0.2582 c. 328: 29 58 241 N T3 SD: 0.1352 c. M:-0.2034 c. 354: 31 63 260 N T3 SD: 0.1264 c. M: 0.2169 c. 365: 32 65 268 N T3 SD: 0.1249 c. M: 0.1668 c. 388: 34 69 285 N T3 SD: 0.1086 c. M: 0.1879 c. 399: 35 71 293 N T3 SD: 0.0985 c. M: 0.1429 c. 422: 37 75 310 N T3 SD: 0.0968 c. M: 0.1636 c. 433: 38 77 318 N T3 SD: 0.0778 c. M: 0.1227 c. 456: 40 81 335 N T3 SD: 0.0901 c. M: 0.1429 c. 467: 41 83 343 N T3 SD: 0.0624 c. M: 0.1055 c. 501: 44 89 368 N T3 SD: 0.0523 c. M: 0.0906 c. 512: 45 91 376 N T3 SD: 0.0540 c. M:-0.0737 c. 535: 47 95 393 N T3 SD: 0.0476 c. M: 0.0776 c. 546: 48 97 401 N T3 SD: 0.0376 c. M: 0.0469 c. 580: 51 103 426 N T3 SD: 0.0245 c. M: 0.0374 c. 614: 54 109 451 N T3 SD: 0.0168 c. M: 0.0290 c. 648: 57 115 476 N T3 SD: 0.0179 c. M: 0.0224 c. 693: 61 123 509 N T3 SD: 0.0112 c. M:-0.0176 c. 727: 64 129 534 N T3 SD: 0.0077 c. M:-0.0134 c. 1307: 115 232 960 N T3 SD: 0.0071 c. M: 0.0092 c. 1341: 118 238 985 N T3 SD: 0.0036 c. M: 0.0061 c. 2034: 179 361 1494 N T3 SD: 0.0029 c. M:-0.0048 c. 2068: 182 367 1519 N T3 SD: 0.0010 c. M: 0.0016 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: 67.3257 cents 7 x 8:9 S SD: 58.6432 cents 8 x 9:11 SD: 44.6585 cents 9 x 10:12 S SD: 25.0921 cents 10 x 11:13 SD: 27.3679 cents 11 x 12:15 S SD: 21.5225 cents 12 x 13:16 SD: 3.1766 cents 13 x 14:17 SD: 16.9226 cents 14 x 15:19 SD: 16.5996 cents 15 x 16:20 S SD: 10.2441 cents 16 x 17:21 SD: 19.2786 cents 17 x 18:23 SD: 20.8886 cents 18 x 19:24 SD: 19.3082 cents 19 x 21:25 SD: 23.5095 cents 20:21:22:27 SD: 18.8227 cents 21:22:23:28 SD: 14.8552 cents 22:23:24:29 SD: 14.2516 cents 23:24:25:31 SD: 12.4209 cents 24:25:26:32 SD: 9.1943 cents 26:27:28:35 S SD: 9.1431 cents 27:28:29:36 SD: 6.9787 cents 33:34:36:44 SD: 6.6738 cents 35:36:38:47 SD: 5.5711 cents 36:37:39:48 SD: 2.4346 cents 39:40:42:52 SD: 1.3071 cents 75:77:81:100 SD: 0.6692 cents 114:117:123:152 SD: 0.4404 cents 240:246:259:320 SD: 0.3761 cents 276:283:298:368 SD: 0.2421 cents 315:323:340:420 SD: 0.1374 cents 390:400:421:520 SD: 0.0653 cents 429:440:463:572 SD: 0.0593 cents