Scala analysis: 174_C7
Chromatic tetrachord 55/54 * 16/15 * 27/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55/54 31.766654 telepathma 2: 88/81 143.497939 2nd undecimal neutral second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi 1: 55/54 31.7667 telepathma 2: 16/15 111.7313 minor diatonic semitone 3: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/54 31.767 cents telepathma 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 88/81 143.498 cents 2nd undecimal neutral second 2: 1 5/4 386.314 cents major third 2: 1 72/55 466.278 cents undecimal semi-diminished fourth 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 : 31.8 143.5 498.0 31.8 : 111.7 466.3 498.0 143.5: 354.5 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.7667 .. 354.5471 cents 729/605, 322.7804 cents 55/54, 31.7667 cents 2: 143.4979 .. 466.2783 cents 729/605, 322.7804 cents 1936/2187,-211.0491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55/54, 31.7667 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/22, 354.5471 cents Average / Smallest step : 5.226078 Largest / Average step : 2.135633 Largest / Smallest step : 11.160982 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 129.49268 cents, oct.: 388.47804 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1364-tone equal temperament with octave 4/3 degrees: 87 393 1364 Least number of segments generator : 683 of 249.388 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 699 of 255.230 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 31.76665 cents Scale diversity : 0.604097 Lumma stability : 0.127565 Lumma impropriety factor : 0.423755 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 : 55/54, 31.7667 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 : 11 Odd number limit : 81 (O: 55 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.025479 Average absolute harmonicity : 0.091820 Specific harmonicity : 0.111684 Fundamental : 1/162, -7.3399 octaves, 1.6150 Hz. Guide tone : 440, 8.7814 octaves, 115115.249 Hz. Exponens Consonantiae : 7.128000E+04, 16.12121 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 142.5, average 47.50000 Mersenne's string divisions : 128947 Sum of van Prooijen's expressibility: 4.12597, average 1.37532 Sum of Tenney's harmonic distance : 8.40491, average 2.80164 Vogel's harmonic complexity : 15.33333 Wille's k value : 82 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 22.23144, average 3.70524 Lattice compactness (without 2's) : 15.46571, average 2.57762 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -4 ..-1 -2.66667 8 1 5: 0 .. 1 0.33333 1 11: 0 .. 1 0.66667 2 2 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 10 15 25| Scale is weakly epimorphic with val: <6 10 16 23| Scale is weakly epimorphic with val: <6 10 18 25| Scale is weakly epimorphic with val: <6 11 17 25| Scale is weakly epimorphic with val: <7 10 16 24| Scale is weakly epimorphic with val: <7 11 15 24| Scale is weakly epimorphic with val: <7 11 15 27| Scale is JI-epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <8 11 16 23| Scale is weakly epimorphic with val: <8 11 17 27| Scale is weakly epimorphic with val: <8 11 19 23| Scale is weakly epimorphic with val: <8 12 16 27| Scale is weakly epimorphic with val: <8 12 19 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 22.4806 c. M: 31.7667 c. 4: 0 1 3 N G T3 SD: 21.3668 c. M: 31.7667 c. 7: 0 2 5 N G T3 SD: 18.3536 c. M: 31.7667 c. 8: 0 2 6 N G T3 SD: 21.3668 c. M: 31.7667 c. 10: 1 2 7 N T3 SD: 10.9599 c. M:-18.0378 c. 11: 1 2 8 N T3 SD: 8.9687 c. M:-13.5102 c. 13: 1 3 9 N T3 SD: 6.7781 c. M:-9.7467 c. 14: 1 3 10 N T3 SD: 2.3050 c. M:-3.8080 c. 17: 1 4 12 N T3 SD: 2.2372 c. M:-2.9859 c. 31: 2 7 22 N T3 SD: 0.6669 c. M:-1.0958 c. 76: 5 17 54 N T3 SD: 0.6957 c. M:-0.9995 c. 80: 5 18 57 N T3 SD: 0.4100 c. M: 0.6388 c. 94: 6 21 67 N T3 SD: 0.2558 c. M: 0.4425 c. 111: 7 25 79 N T3 SD: 0.2124 c. M: 0.3584 c. 125: 8 28 89 N T3 SD: 0.0717 c. M:-0.1082 c. 236: 15 53 168 N T3 SD: 0.0643 c. M: 0.1113 c. 361: 23 81 257 N T3 SD: 0.0226 c. M: 0.0353 c. 486: 31 109 346 N T3 SD: 0.0163 c. M: 0.0282 c. 847: 54 190 603 N T3 SD: 0.0157 c. M: 0.0233 c. 878: 56 197 625 N T3 SD: 0.0093 c. M:-0.0162 c. 1003: 64 225 714 N T3 SD: 0.0083 c. M:-0.0129 c. 1239: 79 278 882 N T3 SD: 0.0073 c. M: 0.0108 c. 1364: 87 306 971 N T3 SD: 0.0002 c. M:-0.0004 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: 95.8750 cents 6 x 7:8 S SD: 61.6865 cents 7 x 8:9 S SD: 53.9703 cents 8 x 9:11 SD: 40.2729 cents 9 x 10:12 S SD: 19.4529 cents 10 x 11:13 SD: 24.4115 cents 11 x 12:15 S SD: 19.7777 cents 12 x 13:16 SD: 2.4626 cents 13 x 14:17 SD: 18.4469 cents 14 x 15:19 SD: 19.4781 cents 15 x 16:20 S SD: 15.8833 cents 16 x 17:21 SD: 23.6054 cents 17 x 18:23 SD: 25.6070 cents 18 x 20:24 S SD: 19.4529 cents 19 x 21:25 SD: 18.7887 cents 21:22:23:28 SD: 16.9129 cents 22:23:24:29 SD: 16.6151 cents 23:24:25:31 SD: 15.3036 cents 24:25:26:32 SD: 13.0721 cents 27:28:29:36 SD: 12.3133 cents 30:31:33:40 SD: 10.9926 cents 31:32:34:41 SD: 10.5637 cents 32:33:35:43 SD: 9.3069 cents 33:34:36:44 SD: 7.0522 cents 35:36:38:47 SD: 7.0097 cents 36:37:39:48 SD: 5.4744 cents 44:45:48:59 SD: 4.6921 cents 45:46:49:60 SD: 2.4706 cents 48:49:52:64 SD: 2.1004 cents 57:58:62:76 SD: 0.8838 cents 105:107:114:140 SD: 0.4799 cents 162:165:176:216 SD: 0.0000 cents