Scala analysis: 201_C11
Chromatic tetrachord 17/14 * 56/55 * 55/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/14 336.129503 supraminor third 2: 68/55 367.323753 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 55/51 130.7212 1: 17/14 336.1295 supraminor third 2: 56/55 31.1943 undecimal diesis, konbini comma 3: 55/51 130.7212
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 55/51 130.721 cents 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 68/55 367.324 cents 2: 1 55/42 466.851 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 : 336.1 367.3 498.0 336.1: 31.2 161.9 498.0 367.3: 130.7 466.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 336.1295 cents 935/784, 304.9353 cents 56/55, 31.1943 cents 2: 161.9155 .. 466.8507 cents 935/784, 304.9353 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 5.321974 Largest / Average step : 2.024694 Largest / Smallest step : 10.775367 Median interval of one step : 55/51, 130.7212 cents, amount: 1 Least squares average step : 183.20800 cents, oct.: 549.62400 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2027-tone equal temperament with octave 4/3 degrees: 1368 1495 2027 Least number of segments generator : 1014 of 249.145 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1951 of 479.371 cents and inv. generated superset size: 26 = 23 more = 866.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 31.19425 cents Scale diversity : 0.655242 Lumma stability : 0.125267 Lumma impropriety factor : 0.349796 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 : 56/55, 31.1943 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% -- Rational properties -- Prime limit : 17 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.014154 Average absolute harmonicity : 0.085358 Specific harmonicity : 0.065554 Fundamental : 1/2310, -11.1737 octaves, 0.1133 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.570800E+05, 17.26114 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 80.5, average 26.83333 Mersenne's string divisions : 26691 Sum of van Prooijen's expressibility: 3.44793, average 1.14931 Sum of Tenney's harmonic distance : 7.02863, average 2.34288 Vogel's harmonic complexity : 30.66667 Wille's k value : 1402 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 15.54207, average 2.59035 Lattice compactness (without 2's) : 9.61037, average 1.60173 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 16 19 25 31| Scale is weakly epimorphic with val: <7 11 16 19 26 30| Scale is weakly epimorphic with val: <7 11 16 20 24 31| Scale is weakly epimorphic with val: <7 11 16 20 26 29| Scale is weakly epimorphic with val: <7 11 16 21 24 30| Scale is JI-epimorphic with val: <7 11 16 21 25 29| Scale is weakly epimorphic with val: <7 11 17 19 24 31| Scale is weakly epimorphic with val: <7 11 17 19 25 30| Scale is weakly epimorphic with val: <7 11 17 20 25 29| Scale is weakly epimorphic with val: <7 11 17 20 26 31| Scale is JI-epimorphic with val: <7 11 17 21 24 29| Scale is weakly epimorphic with val: <7 11 17 21 26 30| Scale is weakly epimorphic with val: <7 11 18 19 24 30| Scale is weakly epimorphic with val: <7 11 18 19 26 31| Scale is weakly epimorphic with val: <7 11 18 20 24 29| Scale is weakly epimorphic with val: <7 11 18 20 25 31| Scale is weakly epimorphic with val: <7 11 18 21 25 30| Scale is weakly epimorphic with val: <7 11 18 21 26 29| Scale is weakly epimorphic with val: <7 12 16 19 25 30| Scale is weakly epimorphic with val: <7 12 16 19 26 29| Scale is weakly epimorphic with val: <7 12 16 20 24 30| Scale is weakly epimorphic with val: <7 12 16 20 26 31| Scale is weakly epimorphic with val: <7 12 16 21 24 29| Scale is weakly epimorphic with val: <7 12 16 21 25 31| Scale is weakly epimorphic with val: <7 12 17 19 24 30| Scale is weakly epimorphic with val: <7 12 17 19 25 29| Scale is weakly epimorphic with val: <7 12 17 20 25 31| Scale is weakly epimorphic with val: <7 12 17 20 26 30| Scale is weakly epimorphic with val: <7 12 17 21 24 31| Scale is weakly epimorphic with val: <7 12 18 19 24 29| Scale is weakly epimorphic with val: <7 12 18 20 24 31| Scale is weakly epimorphic with val: <7 12 18 20 25 30| Scale is weakly epimorphic with val: <7 12 18 21 26 31|
FIT/MODE
3: 2 0 1 N G T3 SD: 20.5139 c. M: 35.2938 c. 6: 4 0 2 N G T3 SD: 20.5139 c. M: 35.2938 c. 7: 5 0 2 N G T3 SD: 13.1511 c. M:-19.6169 c. 9: 6 1 2 N T3 SD: 11.8123 c. M:-20.0446 c. 10: 7 0 3 N G T3 SD: 12.9833 c. M: 18.6923 c. 11: 7 1 3 N T3 SD: 11.4663 c. M: 19.1918 c. 12: 8 1 3 N T3 SD: 4.2961 c. M:-6.2100 c. 15: 10 1 4 N T3 SD: 2.6569 c. M: 4.0995 c. 27: 18 2 7 N T3 SD: 2.5404 c. M: 4.0995 c. 31: 21 2 8 N T3 SD: 1.4593 c. M:-2.1935 c. 34: 23 2 9 N T3 SD: 0.7863 c. M: 1.1142 c. 46: 31 3 12 N T3 SD: 0.5400 c. M:-0.7965 c. 65: 44 4 17 N T3 SD: 0.6408 c. M:-1.0087 c. 80: 54 5 21 N T3 SD: 0.0307 c. M:-0.0509 c. 526: 355 33 138 N T3 SD: 0.0321 c. M:-0.0554 c. 606: 409 38 159 N T3 SD: 0.0272 c. M:-0.0461 c. 686: 463 43 180 N T3 SD: 0.0240 c. M:-0.0389 c. 766: 517 48 201 N T3 SD: 0.0219 c. M:-0.0332 c. 846: 571 53 222 N T3 SD: 0.0206 c. M:-0.0286 c. 926: 625 58 243 N T3 SD: 0.0199 c. M:-0.0248 c. 1006: 679 63 264 N T3 SD: 0.0196 c. M:-0.0261 c. 1086: 733 68 285 N T3 SD: 0.0195 c. M:-0.0279 c. 1101: 743 69 289 N T3 SD: 0.0173 c. M: 0.0283 c. 1181: 797 74 310 N T3 SD: 0.0145 c. M: 0.0229 c. 1261: 851 79 331 N T3 SD: 0.0122 c. M: 0.0182 c. 1341: 905 84 352 N T3 SD: 0.0103 c. M: 0.0141 c. 1421: 959 89 373 N T3 SD: 0.0088 c. M: 0.0112 c. 1501: 1013 94 394 N T3 SD: 0.0078 c. M: 0.0114 c. 1581: 1067 99 415 N T3 SD: 0.0071 c. M: 0.0116 c. 1661: 1121 104 436 N T3 SD: 0.0069 c. M: 0.0118 c. 1867: 1260 117 490 N T3 SD: 0.0069 c. M: 0.0092 c. 1947: 1314 122 511 N T3 SD: 0.0055 c. M:-0.0068 c. 2027: 1368 127 532 N T3 SD: 0.0043 c. M:-0.0059 c. 2107: 1422 132 553 N T3 SD: 0.0032 c. M:-0.0051 c. 2187: 1476 137 574 N T3 SD: 0.0025 c. M:-0.0044 c. 2267: 1530 142 595 N T3 SD: 0.0023 c. M:-0.0037 c. 2347: 1584 147 616 N T3 SD: 0.0025 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 5 x S SD: 18.9900 cents 5:6 x 7 S SD: 43.4582 cents 6:7 x 8 S SD: 34.6293 cents 7 x x 9 SD: 62.9609 cents 8 x 10:11 S SD: 28.2782 cents 9:11 x 12 SD: 5.6392 cents 10:12 x 13 S SD: 24.1916 cents 12 x 15:16 S SD: 9.4950 cents 13 x 16:17 SD: 17.2610 cents 14:17 x 19 SD: 15.3211 cents 17 x 21:23 SD: 12.6592 cents 18:22 x 24 SD: 5.6392 cents 19:23 x 25 SD: 11.7753 cents 20:24:25:27 SD: 11.7516 cents 21 x 26:28 SD: 1.2115 cents 22 x 27:29 SD: 11.7762 cents 23:28 x 31 SD: 9.6158 cents 24:29:30:32 SD: 6.9362 cents 26 x 32:35 SD: 9.1666 cents 27:33 x 36 SD: 5.6392 cents 31 x 38:41 SD: 10.2093 cents 32:39:40:43 SD: 8.0450 cents 33:40:41:44 SD: 3.0039 cents 35 x 43:47 SD: 8.2407 cents 36:44:45:48 SD: 7.3622 cents 37:45:46:49 SD: 5.1382 cents 38:46:47:51 SD: 4.1918 cents 40:49 x 53 SD: 9.3423 cents 41:50:51:55 SD: 5.5458 cents 42:51:52:56 SD: 0.8077 cents 93:113:115:124 SD: 0.3761 cents 228:277:282:304 SD: 0.3721 cents 309:375:382:412 SD: 0.3342 cents 318:386:393:424 SD: 0.3214 cents 351:426:434:468 SD: 0.2942 cents 360:437:445:480 SD: 0.2224 cents 402:488:497:536 SD: 0.1702 cents 444:539:549:592 SD: 0.1633 cents 453:550:560:604 SD: 0.1060 cents 495:601:612:660 SD: 0.0686 cents 546:663:675:728 SD: 0.0466 cents 588:714:727:784 SD: 0.0144 cents