Scala analysis: 207_C12
Chromatic tetrachord 66/65 * 13/12 * 40/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66/65 26.431568 Winmeanma 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: 66/65 26.4316 Winmeanma 2: 13/12 138.5727 tridecimal 2/3-tone 3: 40/33 333.0408
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66/65 26.432 cents Winmeanma 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 40/33 333.041 cents 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 130/99 471.613 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 : 26.4 165.0 498.0 26.4 : 138.6 471.6 498.0 165.0: 333.0 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.4316 .. 333.0408 cents 1300/1089, 306.6092 cents 66/65, 26.4316 cents 2: 165.0042 .. 471.6134 cents 1300/1089, 306.6092 cents 363/400,-168.0365 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66/65, 26.4316 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 40/33, 333.0408 cents Average / Smallest step : 6.280937 Largest / Average step : 2.006088 Largest / Smallest step : 12.600114 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 132.18393 cents, oct.: 396.55179 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1319-tone equal temperament with octave 4/3 degrees: 70 437 1319 Least number of segments generator : 660 of 249.211 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1022 of 385.900 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 26.43157 cents Scale diversity : 0.619014 Lumma stability : 0.106141 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 : 66/65, 26.4316 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 -- Rational properties -- Prime limit : 13 Odd number limit : 99 (O: 65 U: 99) Highest odd numerator or denominator: 65 Scale harmonicity : 0.018159 Average absolute harmonicity : 0.091072 Specific harmonicity : 0.083862 Fundamental : 1/390, -8.6073 octaves, 0.6708 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 5.148000E+04, 15.65172 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 79.5, average 26.50000 Mersenne's string divisions : 2751 Sum of van Prooijen's expressibility: 3.33143, average 1.11048 Sum of Tenney's harmonic distance : 6.75303, average 2.25101 Vogel's harmonic complexity : 22.33333 Wille's k value : 214 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.94621, average 2.49103 Lattice compactness (without 2's) : 10.20623, average 1.70104 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 1 0.00000 2 1 5: -1 .. 0 -0.66667 2 11: 0 .. 1 0.66667 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 24 27| Scale is weakly epimorphic with val: <6 10 15 24 30| Scale is weakly epimorphic with val: <6 10 16 25 27| Scale is weakly epimorphic with val: <6 10 16 25 30| Scale is weakly epimorphic with val: <6 10 17 26 27| Scale is weakly epimorphic with val: <6 10 17 26 30| Scale is weakly epimorphic with val: <6 10 18 27 27| Scale is weakly epimorphic with val: <6 10 18 27 30| Scale is weakly epimorphic with val: <6 11 15 24 27| Scale is weakly epimorphic with val: <6 11 15 24 30| Scale is weakly epimorphic with val: <6 11 16 25 27| Scale is weakly epimorphic with val: <6 11 16 25 30| Scale is weakly epimorphic with val: <6 11 17 26 27| Scale is weakly epimorphic with val: <6 11 17 26 30| Scale is weakly epimorphic with val: <6 11 18 27 27| Scale is weakly epimorphic with val: <6 11 18 27 30| Scale is weakly epimorphic with val: <7 10 15 25 25| Scale is weakly epimorphic with val: <7 10 15 25 28| Scale is weakly epimorphic with val: <7 10 16 26 28| Scale is weakly epimorphic with val: <7 10 17 27 28| Scale is weakly epimorphic with val: <7 11 15 23 27| Scale is weakly epimorphic with val: <7 11 15 23 30| Scale is JI-epimorphic with val: <7 11 15 24 26| Scale is weakly epimorphic with val: <7 11 15 24 29| 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 27 29| Scale is weakly epimorphic with val: <7 11 16 24 27| Scale is weakly epimorphic with val: <7 11 16 24 30| Scale is JI-epimorphic with val: <7 11 16 25 26| Scale is weakly epimorphic with val: <7 11 16 25 29| Scale is weakly epimorphic with val: <7 11 16 27 27| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 17 23 26| Scale is weakly epimorphic with val: <7 11 17 23 29| Scale is weakly epimorphic with val: <7 11 17 25 27| = patent Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is JI-epimorphic with val: <7 11 17 26 26| Scale is weakly epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 18 23 27| Scale is weakly epimorphic with val: <7 11 18 23 30| Scale is weakly epimorphic with val: <7 11 18 24 26| Scale is weakly epimorphic with val: <7 11 18 24 29| 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 27 29| Scale is weakly epimorphic with val: <7 11 19 24 27| Scale is weakly epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 25 26| Scale is weakly epimorphic with val: <7 11 19 25 29| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 12 15 25 25| Scale is weakly epimorphic with val: <7 12 15 25 28| Scale is weakly epimorphic with val: <7 12 15 26 27| Scale is weakly epimorphic with val: <7 12 16 26 28| Scale is weakly epimorphic with val: <7 12 16 27 27| Scale is weakly epimorphic with val: <7 12 17 27 28| Scale is weakly epimorphic with val: <8 11 15 24 25| Scale is weakly epimorphic with val: <8 11 15 26 26| Scale is weakly epimorphic with val: <8 11 15 26 29| Scale is weakly epimorphic with val: <8 11 15 27 28| Scale is weakly epimorphic with val: <8 11 16 25 25| Scale is weakly epimorphic with val: <8 11 16 27 29| Scale is weakly epimorphic with val: <8 12 15 25 27| Scale is weakly epimorphic with val: <8 12 15 26 26| Scale is weakly epimorphic with val: <8 12 15 26 29| Scale is weakly epimorphic with val: <8 12 16 26 27| Scale is weakly epimorphic with val: <8 12 16 27 29| Scale is weakly epimorphic with val: <8 12 17 27 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 15.2714 c. M: 26.4316 c. 10: 0 3 7 N G T3 SD: 17.7172 c. M: 26.4316 c. 12: 1 3 8 N T3 SD: 8.7215 c. M:-15.0722 c. 13: 1 3 9 N T3 SD: 9.6508 c. M:-11.8796 c. 14: 1 4 9 N T3 SD: 9.1142 c. M:-12.8690 c. 15: 1 4 10 N T3 SD: 3.9528 c. M:-6.7714 c. 18: 1 5 12 N T3 SD: 0.9226 c. M:-1.2376 c. 39: 2 11 26 N T3 SD: 0.7779 c. M:-1.0108 c. 57: 3 16 38 N T3 SD: 0.5971 c. M:-1.0108 c. 75: 4 21 50 N T3 SD: 0.5884 c. M:-1.0108 c. 91: 5 25 61 N T3 SD: 0.7149 c. M:-0.9335 c. 93: 5 26 62 N T3 SD: 0.6166 c. M:-1.0108 c. 94: 5 26 63 N T3 SD: 0.4375 c. M: 0.7553 c. 112: 6 31 75 N T3 SD: 0.3080 c. M: 0.4715 c. 115: 6 32 77 N T3 SD: 0.3591 c. M: 0.4466 c. 130: 7 36 87 N T3 SD: 0.2709 c. M:-0.3862 c. 133: 7 37 89 N T3 SD: 0.1864 c. M: 0.2375 c. 151: 8 42 101 N T3 SD: 0.0574 c. M: 0.0887 c. 169: 9 47 113 N T3 SD: 0.0553 c. M:-0.0915 c. 320: 17 89 214 N T3 SD: 0.0220 c. M:-0.0271 c. 830: 44 231 555 N T3 SD: 0.0179 c. M: 0.0292 c. 848: 45 236 567 N T3 SD: 0.0185 c. M:-0.0319 c. 981: 52 273 656 N T3 SD: 0.0185 c. M: 0.0316 c. 999: 53 278 668 N T3 SD: 0.0094 c. M:-0.0137 c. 1150: 61 320 769 N T3 SD: 0.0078 c. M: 0.0135 c. 1319: 70 367 882 N T3 SD: 0.0022 c. M:-0.0039 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 x 18:21 S SD: 23.7539 cents 17 x 19:23 SD: 18.6947 cents 21:22:23:28 SD: 18.2081 cents 24:25:26:32 SD: 17.1784 cents 26:27:29:35 SD: 16.2149 cents 27:28:30:36 S SD: 13.4872 cents 28:29:31:37 SD: 13.1000 cents 29:30:32:39 SD: 11.9764 cents 30:31:33:40 SD: 10.1118 cents 33:34:36:44 SD: 9.6840 cents 36:37:40:48 SD: 9.0912 cents 37:38:41:49 SD: 8.7495 cents 38:39:42:51 SD: 7.7519 cents 39:40:43:52 SD: 5.9534 cents 42:43:46:56 SD: 5.3857 cents 48:49:53:64 SD: 3.7813 cents 51:52:56:68 SD: 2.6071 cents 60:61:66:80 SD: 0.7282 cents 129:131:142:172 SD: 0.4121 cents 189:192:208:252 SD: 0.3925 cents 201:204:221:268 SD: 0.3692 cents 261:265:287:348 SD: 0.2038 cents 321:326:353:428 SD: 0.1964 cents 330:335:363:440 SD: 0.1325 cents 390:396:429:520 SD: 0.0000 cents