Scala analysis: 168_C6
Chromatic tetrachord 169/168 * 14/13 * 16/13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 169/168 10.274416 Schulter's comma 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: 169/168 10.2744 Schulter's comma 2: 14/13 128.2982 2/3-tone 3: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 169/168 10.274 cents Schulter's comma 1: 1 14/13 128.298 cents 2/3-tone 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 26/21 369.747 cents 2: 1 224/169 487.771 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 : 10.3 138.6 498.0 10.3 : 128.3 487.8 498.0 138.6: 359.5 369.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 10.2744 .. 359.4723 cents 2688/2197, 349.1979 cents 169/168, 10.2744 cents 2: 138.5727 .. 487.7706 cents 2688/2197, 349.1979 cents 169/192,-220.8997 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 169/168, 10.2744 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 16.158096 Largest / Average step : 2.165300 Largest / Smallest step : 34.987130 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 127.25391 cents, oct.: 381.76173 cents Scale is not proper Scale has trivalence property 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 10.27442 cents Scale diversity : 0.422321 Lumma stability : 0.041259 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 : 169/168, 10.2744 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 487.7706 cents 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 : 169 (O: 169 U: 169) Highest odd numerator or denominator: 169 Scale harmonicity : 0.016062 Average absolute harmonicity : 0.089388 Specific harmonicity : 0.075853 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 676, 9.4009 octaves, 176858.882 Hz. Exponens Consonantiae : 1.135680E+05, 16.79320 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 184.5, average 61.50000 Mersenne's string divisions : 58975 Sum of van Prooijen's expressibility: 3.81895, average 1.27298 Sum of Tenney's harmonic distance : 7.72550, average 2.57517 Vogel's harmonic complexity : 19.66667 Wille's k value : 84 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 19.89092, average 3.31515 Lattice compactness (without 2's) : 9.51398, average 1.58566 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -1.00000 7 3: -1 ..-1 -1.00000 3 1 7: -1 .. 0 -0.33333 1 13: 0 .. 2 1.00000 3 2 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 18 25| Scale is weakly epimorphic with val: <6 10 21 25| Scale is weakly epimorphic with val: <6 10 21 26| Scale is weakly epimorphic with val: <6 11 18 25| Scale is weakly epimorphic with val: <6 11 18 26| Scale is weakly epimorphic with val: <6 11 21 26| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 10 18 27| Scale is weakly epimorphic with val: <7 10 21 27| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 21 26| Scale is JI-epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 21 29| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <7 12 21 29| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 11 18 30| Scale is weakly epimorphic with val: <8 11 21 30| Scale is weakly epimorphic with val: <8 12 21 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 16.9179 c. M:-27.4423 c. 4: 0 1 3 N G T3 SD: 10.0546 c. M: 14.0614 c. 7: 0 2 5 N G T3 SD: 6.3099 c. M: 10.2744 c. 11: 0 3 8 N G T3 SD: 6.1396 c. M: 10.2744 c. 15: 0 4 11 N G T3 SD: 6.8007 c. M: 10.2744 c. 18: 0 5 13 N G T3 SD: 5.9334 c. M: 10.2744 c. 25: 1 6 18 N T3 SD: 5.5930 c. M:-9.6474 c. 28: 1 7 20 N T3 SD: 4.8417 c. M:-7.5129 c. 29: 1 7 21 N T3 SD: 4.0414 c. M:-6.8995 c. 32: 1 8 23 N T3 SD: 3.1747 c. M:-5.2895 c. 33: 1 8 24 N T3 SD: 3.2006 c. M:-4.8179 c. 35: 1 9 25 N T3 SD: 3.1373 c. M:-3.9554 c. 36: 1 9 26 N T3 SD: 2.0596 c. M:-3.5602 c. 39: 1 10 28 N T3 SD: 1.8116 c. M:-2.4960 c. 40: 1 10 29 N T3 SD: 1.5632 c. M:-2.1767 c. 43: 1 11 31 N T3 SD: 0.7926 c. M:-1.3080 c. 47: 1 12 34 N T3 SD: 0.5063 c. M: 0.8155 c. 90: 2 23 65 N T3 SD: 0.4763 c. M:-0.7933 c. 93: 2 24 67 N T3 SD: 0.4595 c. M:-0.6657 c. 97: 2 25 70 N T3 SD: 0.0339 c. M:-0.0584 c. 435: 9 112 314 N T3 SD: 0.0270 c. M: 0.0360 c. 532: 11 137 384 N T3 SD: 0.0174 c. M:-0.0235 c. 629: 13 162 454 N T3 SD: 0.0117 c. M:-0.0190 c. 726: 15 187 524 N T3 SD: 0.0092 c. M:-0.0158 c. 823: 17 212 594 N T3 SD: 0.0091 c. M:-0.0133 c. 1549: 32 399 1118 N T3 SD: 0.0089 c. M:-0.0144 c. 1743: 36 449 1258 N T3 SD: 0.0096 c. M:-0.0122 c. 2038: 42 525 1471 N T3 SD: 0.0082 c. M: 0.0105 c. 2135: 44 550 1541 N T3 SD: 0.0070 c. M: 0.0103 c. 2232: 46 575 1611 N T3 SD: 0.0062 c. M: 0.0100 c. 2329: 48 600 1681 N T3 SD: 0.0057 c. M: 0.0099 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 x 21:25 SD: 20.7941 cents 20 x 22:27 SD: 17.0378 cents 21 x 23:28 SD: 9.4604 cents 22 x 24:29 SD: 11.5869 cents 44:45:48:59 SD: 10.8603 cents 45:46:49:60 SD: 9.7179 cents 46:47:50:61 SD: 9.7134 cents 47:48:51:63 SD: 9.2942 cents 48:49:52:64 SD: 8.4741 cents 51:52:55:68 SD: 8.2093 cents 56:57:61:75 SD: 7.9183 cents 57:58:62:76 SD: 7.0107 cents 59:60:64:79 SD: 6.7739 cents 60:61:65:80 SD: 6.1139 cents 63:64:68:84 SD: 6.0462 cents 68:69:74:91 SD: 6.0225 cents 69:70:75:92 SD: 5.2453 cents 71:72:77:95 SD: 5.1082 cents 72:73:78:96 SD: 4.5350 cents 81:82:88:108 SD: 4.0077 cents 83:84:90:111 SD: 3.9310 cents 84:85:91:112 SD: 3.4046 cents 93:94:101:124 SD: 3.0972 cents 95:96:103:127 SD: 3.0614 cents 96:97:104:128 SD: 2.5553 cents 105:106:114:140 SD: 2.4058 cents 107:108:116:143 SD: 2.4005 cents 108:109:117:144 SD: 1.8939 cents 117:118:127:156 SD: 1.8716 cents 120:121:130:160 SD: 1.3643 cents 132:133:143:176 SD: 0.9305 cents 144:145:156:192 SD: 0.5688 cents 156:157:169:208 SD: 0.2626 cents 168:169:182:224 SD: 0.0000 cents