Scala analysis: 311_C24
Chromatic tetrachord 10/9 * 36/35 * 7/6, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 10/9 182.4037 minor whole tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 6/5 315.641 cents minor third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 182.4 231.2 498.0 182.4: 48.8 315.6 498.0 231.2: 266.9 449.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 266.8709 cents 245/216, 218.1005 cents 36/35, 48.7704 cents 2: 231.1741 .. 449.2746 cents 245/216, 218.1005 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 3.404013 Largest / Average step : 1.607511 Largest / Smallest step : 5.471987 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 152.77764 cents, oct.: 458.33291 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1256-tone equal temperament with octave 4/3 degrees: 460 583 1256 Least number of segments generator : 629 of 249.419 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 919 of 364.413 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 0.800320 Lumma stability : 0.195847 Lumma impropriety factor : 0.071674 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 7 Odd number limit : 35 (O: 35 U: 35) Highest odd numerator or denominator: 9 Scale harmonicity : 0.039970 Average absolute harmonicity : 0.122696 Specific harmonicity : 0.203242 Fundamental : 1/63, -5.9773 octaves, 4.1528 Hz. Guide tone : 40, 5.3219 octaves, 10465.023 Hz. Exponens Consonantiae : 2.520000E+03, 11.29921 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 20.5, average 6.83333 Mersenne's string divisions : 1995 Sum of van Prooijen's expressibility: 2.27646, average 0.75882 Sum of Tenney's harmonic distance : 4.78161, average 1.59387 Vogel's harmonic complexity : 11.33333 Wille's k value : 17 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 14.47421, average 2.41237 Lattice compactness (without 2's) : 9.51398, average 1.58566 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -2 .. 0 -1.00000 3 1 5: 0 .. 1 0.33333 1 1 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 17 20| Scale is weakly epimorphic with val: <6 11 19 19| Scale is weakly epimorphic with val: <6 11 19 22| Scale is weakly epimorphic with val: <7 10 15 18| Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 18 18| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <7 12 15 18| Scale is weakly epimorphic with val: <7 12 18 18| Scale is weakly epimorphic with val: <8 11 15 21| Scale is weakly epimorphic with val: <8 11 17 20| Scale is weakly epimorphic with val: <8 11 18 21| Scale is weakly epimorphic with val: <8 12 15 21| Scale is weakly epimorphic with val: <8 12 18 21| Scale is weakly epimorphic with val: <8 12 19 19| Scale is weakly epimorphic with val: <8 12 19 22|
FIT/MODE
3: 1 0 2 N G T3 SD: 38.7913 c. M: 65.1591 c. 4: 1 1 2 P M ME S SD: 34.9767 c. M: 57.8925 c. 5: 2 0 3 N G T3 SD: 20.8480 c. M: 31.9561 c. 6: 2 1 3 P T3 SD: 13.9899 c. M:-17.8484 c. 8: 3 1 4 P T3 SD: 10.6082 c. M:-17.8484 c. 9: 3 1 5 N T3 SD: 11.0308 c. M: 16.3887 c. 11: 4 1 6 N T3 SD: 2.8650 c. M: 4.7900 c. 19: 7 2 10 N T3 SD: 2.8087 c. M:-4.7420 c. 24: 9 2 13 N T3 SD: 3.0259 c. M:-4.3632 c. 28: 10 3 15 N T3 SD: 2.6159 c. M: 4.5305 c. 30: 11 3 16 N T3 SD: 0.7303 c. M:-1.2469 c. 41: 15 4 22 N T3 SD: 0.2421 c. M: 0.3728 c. 71: 26 7 38 N T3 SD: 0.1803 c. M:-0.3116 c. 112: 41 11 60 N T3 SD: 0.0598 c. M: 0.0837 c. 265: 97 26 142 N T3 SD: 0.0581 c. M: 0.1004 c. 377: 138 37 202 N T3 SD: 0.0557 c. M: 0.0955 c. 418: 153 41 224 N T3 SD: 0.0622 c. M: 0.1049 c. 489: 179 48 262 N T3 SD: 0.0554 c. M: 0.0928 c. 571: 209 56 306 N T3 SD: 0.0646 c. M: 0.1070 c. 601: 220 59 322 N T3 SD: 0.0556 c. M: 0.0911 c. 625: 229 61 335 N T3 SD: 0.0658 c. M: 0.0812 c. 642: 235 63 344 N T3 SD: 0.0564 c. M: 0.0975 c. 655: 240 64 351 N T3 SD: 0.0511 c. M:-0.0861 c. 685: 251 67 367 N T3 SD: 0.0566 c. M:-0.0916 c. 696: 255 68 373 N T3 SD: 0.0467 c. M:-0.0697 c. 726: 266 71 389 N T3 SD: 0.0442 c. M:-0.0756 c. 737: 270 72 395 N T3 SD: 0.0469 c. M: 0.0596 c. 767: 281 75 411 N T3 SD: 0.0357 c. M:-0.0613 c. 808: 296 79 433 N T3 SD: 0.0320 c. M:-0.0484 c. 838: 307 82 449 N T3 SD: 0.0331 c. M:-0.0543 c. 849: 311 83 455 N T3 SD: 0.0330 c. M: 0.0437 c. 879: 322 86 471 N T3 SD: 0.0247 c. M:-0.0428 c. 920: 337 90 493 N T3 SD: 0.0209 c. M:-0.0323 c. 961: 352 94 515 N T3 SD: 0.0224 c. M: 0.0315 c. 991: 363 97 531 N T3 SD: 0.0170 c. M:-0.0285 c. 1032: 378 101 553 N T3 SD: 0.0123 c. M:-0.0197 c. 1103: 404 108 591 N T3 SD: 0.0123 c. M:-0.0171 c. 1144: 419 112 613 N T3 SD: 0.0056 c. M:-0.0096 c. 1256: 460 123 673 N T3 SD: 0.0027 c. M:-0.0044 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8:9 x 11 SD: 28.7251 cents 9:10 x 12 S SD: 0.0000 cents 10:11 x 13 SD: 23.5791 cents 12:13:14:16 S SD: 18.8427 cents 14 x 16:19 SD: 15.3211 cents 15 x 17:20 SD: 7.2437 cents 16:18 x 21 S SD: 17.3627 cents 17:19 x 23 SD: 13.6187 cents 18:20:21:24 S SD: 11.8989 cents 19:21:22:25 SD: 11.1626 cents 20:22:23:27 SD: 9.8973 cents 21:23:24:28 SD: 8.3034 cents 23 x 26:31 SD: 13.3069 cents 24:27 x 32 SD: 10.7531 cents 26:29:30:35 SD: 8.1178 cents 27:30:31:36 SD: 2.6655 cents 36:40:41:48 SD: 2.0072 cents 63:70:72:84 S SD: 0.0000 cents