Scala analysis: 205_C12
Chromatic tetrachord 33/32 * 16/15 * 40/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 2: 11/10 165.004228 Ptolemy's second, 4/5-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/33 333.0408 1: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 16/15 111.7313 minor diatonic semitone 3: 40/33 333.0408
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 40/33 333.041 cents 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 5/4 386.314 cents major third 2: 1 128/99 444.772 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 : 53.3 165.0 498.0 53.3 : 111.7 444.8 498.0 165.0: 333.0 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 333.0408 cents 1280/1089, 279.7678 cents 33/32, 53.2729 cents 2: 165.0042 .. 444.7721 cents 1280/1089, 279.7678 cents 363/400,-168.0365 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 40/33, 333.0408 cents Average / Smallest step : 3.116310 Largest / Average step : 2.006088 Largest / Smallest step : 6.251593 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 134.10117 cents, oct.: 402.30351 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1150-tone equal temperament with octave 4/3 degrees: 123 381 1150 Least number of segments generator : 577 of 249.889 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 663 of 287.134 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 53.27294 cents Scale diversity : 0.824549 Lumma stability : 0.213928 Lumma impropriety factor : 0.337392 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 : 33/32, 53.2729 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% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.027089 Average absolute harmonicity : 0.097354 Specific harmonicity : 0.123145 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 6.336000E+04, 15.95128 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 46.5, average 15.50000 Mersenne's string divisions : 1365 Sum of van Prooijen's expressibility: 3.03703, average 1.01234 Sum of Tenney's harmonic distance : 6.14424, average 2.04808 Vogel's harmonic complexity : 17.33333 Wille's k value : 247 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 24.21948, average 4.03658 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.33333 8 3: -1 .. 1 0.00000 2 1 5: -1 .. 0 -0.33333 1 11: 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 24| Scale is weakly epimorphic with val: <6 10 16 23| Scale is weakly epimorphic with val: <6 10 18 27| Scale is weakly epimorphic with val: <6 10 19 23| Scale is weakly epimorphic with val: <6 11 15 24| Scale is weakly epimorphic with val: <6 11 18 27| Scale is weakly epimorphic with val: <7 10 17 27| Scale is weakly epimorphic with val: <7 11 15 23| Scale is weakly epimorphic with val: <7 11 15 26| Scale is JI-epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 12 15 26| Scale is weakly epimorphic with val: <7 12 17 27| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <8 11 16 27| Scale is weakly epimorphic with val: <8 12 16 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 30.7627 c. M: 53.2729 c. 6: 1 1 4 N M DE S SD: 17.1772 c. M:-29.7346 c. 7: 1 1 5 N M DE S SD: 16.6844 c. M: 22.7057 c. 8: 1 2 5 N T3 SD: 13.5929 c. M:-21.7626 c. 9: 1 2 6 N T3 SD: 1.3276 c. M:-2.0654 c. 48: 5 11 32 N T3 SD: 0.9938 c. M: 1.3933 c. 57: 6 13 38 N T3 SD: 0.7614 c. M:-1.0108 c. 66: 7 15 44 N T3 SD: 0.6388 c. M:-1.0108 c. 75: 8 17 50 N T3 SD: 0.5898 c. M:-1.0108 c. 84: 9 19 56 N T3 SD: 0.5858 c. M:-1.0108 c. 85: 9 19 57 N T3 SD: 0.6267 c. M: 0.9423 c. 93: 10 21 62 N T3 SD: 0.6056 c. M:-1.0108 c. 94: 10 21 63 N T3 SD: 0.4670 c. M: 0.7553 c. 103: 11 23 69 N T3 SD: 0.3503 c. M: 0.6010 c. 112: 12 25 75 N T3 SD: 0.2770 c. M: 0.4715 c. 121: 13 27 81 N T3 SD: 0.2491 c. M: 0.3613 c. 151: 16 34 101 N T3 SD: 0.2932 c. M: 0.5000 c. 160: 17 36 107 N T3 SD: 0.2059 c. M: 0.3557 c. 169: 18 38 113 N T3 SD: 0.1319 c. M: 0.2267 c. 178: 19 40 119 N T3 SD: 0.0783 c. M: 0.1108 c. 187: 20 42 125 N T3 SD: 0.0711 c. M:-0.1230 c. 290: 31 65 194 N T3 SD: 0.0799 c. M: 0.1342 c. 299: 32 67 200 N T3 SD: 0.0600 c. M: 0.0997 c. 308: 33 69 206 N T3 SD: 0.0644 c. M:-0.0890 c. 459: 49 103 307 N T3 SD: 0.0741 c. M: 0.1047 c. 468: 50 105 313 N T3 SD: 0.0477 c. M: 0.0630 c. 477: 51 107 319 N T3 SD: 0.0233 c. M: 0.0333 c. 486: 52 109 325 N T3 SD: 0.0122 c. M:-0.0158 c. 664: 71 149 444 N T3 SD: 0.0121 c. M: 0.0181 c. 1141: 122 256 763 N T3 SD: 0.0124 c. M: 0.0201 c. 1150: 123 258 769 N T3 SD: 0.0022 c. M: 0.0038 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: 86.3514 cents 6 x 7:8 S SD: 50.9333 cents 7 x 8:9 S SD: 45.6687 cents 8 x 9:11 SD: 32.9836 cents 9 x 10:12 S SD: 8.6997 cents 10 x 11:13 SD: 21.9155 cents 11 x 12:15 S SD: 20.7369 cents 12 x 13:16 SD: 13.2158 cents 13 x 14:17 SD: 24.8870 cents 14 x 15:19 SD: 27.4535 cents 15 x 17:20 SD: 25.8412 cents 16:17:18:21 S SD: 23.4001 cents 17:18:19:23 SD: 19.6773 cents 18:19:20:24 S SD: 14.6411 cents 19:20:21:25 SD: 14.3617 cents 20:21:22:27 SD: 12.6298 cents 21:22:23:28 SD: 9.4266 cents 27:28:30:36 S SD: 6.6383 cents 29:30:32:39 SD: 5.5733 cents 30:31:33:40 SD: 1.1646 cents 99:102:109:132 SD: 0.7494 cents 129:133:142:172 SD: 0.4285 cents 159:164:175:212 SD: 0.3477 cents 291:300:320:388 SD: 0.2550 cents 321:331:353:428 SD: 0.1723 cents 351:362:386:468 SD: 0.1576 cents 450:464:495:600 SD: 0.0777 cents 480:495:528:640 SD: 0.0000 cents