Scala analysis: 163_C6
Chromatic tetrachord 39/38 * 19/18 * 16/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39/38 44.969647 2: 13/12 138.572661 tridecimal 2/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 16/13 359.4723 tridecimal neutral third 1: 39/38 44.9696 2: 19/18 93.6030 undevicesimal semitone 3: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 39/38 44.970 cents 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 152/117 453.075 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 : 45.0 138.6 498.0 45.0 : 93.6 453.1 498.0 138.6: 359.5 404.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.9696 .. 359.4723 cents 608/507, 314.5027 cents 39/38, 44.9696 cents 2: 138.5727 .. 453.0754 cents 608/507, 314.5027 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 39/38, 44.9696 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 3.691712 Largest / Average step : 2.165300 Largest / Smallest step : 7.993666 Median interval of one step : 19/18, 93.6030 cents, amount: 1 Least squares average step : 129.73214 cents, oct.: 389.19642 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2027-tone equal temperament with octave 4/3 degrees: 183 564 2027 Least number of segments generator : 1014 of 249.145 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1204 of 295.829 cents and inv. generated superset size: 16 = 13 more = 533.333% 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 44.96965 cents Scale diversity : 0.658750 Lumma stability : 0.180585 Lumma impropriety factor : 0.443534 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 : 39/38, 44.9696 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 : 19 Odd number limit : 117 (O: 39 U: 117) Highest odd numerator or denominator: 39 Scale harmonicity : 0.015246 Average absolute harmonicity : 0.089419 Specific harmonicity : 0.071878 Fundamental : 1/228, -7.8329 octaves, 1.1475 Hz. Guide tone : 156, 7.2854 octaves, 40813.588 Hz. Exponens Consonantiae : 3.556800E+04, 15.11829 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 54.5, average 18.16667 Mersenne's string divisions : 1925 Sum of van Prooijen's expressibility: 3.18213, average 1.06071 Sum of Tenney's harmonic distance : 6.44315, average 2.14772 Vogel's harmonic complexity : 25.00000 Wille's k value : 123 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 17.13114, average 2.85519 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 1 -0.33333 3 1 13: 0 .. 1 0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 25 28| Scale is weakly epimorphic with val: <6 10 25 31| Scale is weakly epimorphic with val: <6 10 25 34| Scale is weakly epimorphic with val: <6 10 29 30| Scale is weakly epimorphic with val: <6 11 26 29| Scale is weakly epimorphic with val: <6 11 26 32| Scale is weakly epimorphic with val: <6 11 28 30| Scale is weakly epimorphic with val: <7 10 27 28| Scale is weakly epimorphic with val: <7 10 27 31| Scale is weakly epimorphic with val: <7 10 27 34| Scale is weakly epimorphic with val: <7 10 29 29| Scale is weakly epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 26 34| Scale is JI-epimorphic with val: <7 11 27 30| Scale is weakly epimorphic with val: <7 11 27 33| Scale is weakly epimorphic with val: <7 11 29 31| Scale is weakly epimorphic with val: <7 11 29 34| Scale is weakly epimorphic with val: <7 11 30 30| Scale is weakly epimorphic with val: <7 11 30 33| Scale is weakly epimorphic with val: <7 12 27 29| Scale is weakly epimorphic with val: <7 12 29 30| Scale is weakly epimorphic with val: <7 12 29 33| Scale is weakly epimorphic with val: <7 12 30 32| Scale is weakly epimorphic with val: <8 11 28 28| Scale is weakly epimorphic with val: <8 11 30 32| Scale is weakly epimorphic with val: <8 12 27 28| Scale is weakly epimorphic with val: <8 12 30 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 30.4157 c. M: 44.9696 c. 4: 0 1 3 N G T3 SD: 27.2029 c. M: 44.9696 c. 7: 1 1 5 N M DE S SD: 15.2671 c. M:-26.1796 c. 8: 1 1 6 N M DE S SD: 12.8650 c. M:-17.2860 c. 10: 1 2 7 N T3 SD: 6.8532 c. M:-10.8408 c. 11: 1 2 8 N T3 SD: 1.5931 c. M: 2.7422 c. 32: 3 6 23 N T3 SD: 1.3195 c. M:-1.7221 c. 43: 4 8 31 N T3 SD: 0.8213 c. M:-1.3601 c. 54: 5 10 39 N T3 SD: 0.6743 c. M:-1.1456 c. 65: 6 12 47 N T3 SD: 0.6912 c. M:-1.0037 c. 68: 6 13 49 N T3 SD: 0.6817 c. M: 1.0245 c. 76: 7 14 55 N T3 SD: 0.7588 c. M: 0.9550 c. 79: 7 15 57 N T3 SD: 0.4897 c. M: 0.8391 c. 90: 8 17 65 N T3 SD: 0.4243 c. M: 0.6990 c. 101: 9 19 73 N T3 SD: 0.4465 c. M: 0.5894 c. 111: 10 21 80 N T3 SD: 0.3064 c. M:-0.5210 c. 122: 11 23 88 N T3 SD: 0.1360 c. M:-0.2268 c. 133: 12 25 96 N T3 SD: 0.0221 c. M: 0.0333 c. 841: 76 158 607 N T3 SD: 0.0220 c. M:-0.0380 c. 963: 87 181 695 N T3 SD: 0.0234 c. M:-0.0318 c. 974: 88 183 703 N T3 SD: 0.0163 c. M:-0.0283 c. 1096: 99 206 791 N T3 SD: 0.0181 c. M:-0.0256 c. 1107: 100 208 799 N T3 SD: 0.0121 c. M:-0.0209 c. 1229: 111 231 887 N T3 SD: 0.0140 c. M:-0.0208 c. 1240: 112 233 895 N T3 SD: 0.0090 c. M:-0.0151 c. 1373: 124 258 991 N T3 SD: 0.0067 c. M:-0.0104 c. 1506: 136 283 1087 N T3 SD: 0.0053 c. M:-0.0065 c. 1639: 148 308 1183 N T3 SD: 0.0047 c. M: 0.0074 c. 1772: 160 333 1279 N T3 SD: 0.0048 c. M: 0.0082 c. 1894: 171 356 1367 N T3 SD: 0.0045 c. M:-0.0069 c. 1905: 172 358 1375 N T3 SD: 0.0053 c. M: 0.0090 c. 2027: 183 381 1463 N T3 SD: 0.0044 c. M: 0.0055 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: 98.0918 cents 6 x 7:8 S SD: 64.1491 cents 7 x 8:9 S SD: 55.9891 cents 8 x 9:11 SD: 42.1514 cents 9 x 10:12 S SD: 21.9155 cents 10 x 11:13 SD: 25.5919 cents 11 x 12:15 S SD: 20.3667 cents 12 x 13:16 SD: 0.0000 cents 13 x 14:17 SD: 17.5761 cents 14 x 15:19 SD: 18.0616 cents 15 x 16:20 S SD: 13.4207 cents 16 x 17:21 SD: 21.6417 cents 17 x 18:23 SD: 23.4966 cents 18 x 20:24 S SD: 21.9155 cents 19:20:21:25 SD: 20.1404 cents 20:21:22:27 SD: 17.3884 cents 21:22:23:28 SD: 13.4290 cents 22:23:24:29 SD: 13.1664 cents 23:24:25:31 SD: 11.5856 cents 24:25:26:32 SD: 8.5676 cents 27:28:29:36 SD: 7.7783 cents 32:33:35:43 SD: 7.6371 cents 33:34:36:44 SD: 4.6021 cents 35:36:38:47 SD: 4.4811 cents 36:37:39:48 SD: 0.8215 cents 120:123:130:160 SD: 0.7403 cents 156:160:169:208 SD: 0.3795 cents 192:197:208:256 SD: 0.1542 cents 228:234:247:304 SD: 0.0000 cents