Scala analysis: 307_C24
Chromatic tetrachord 16/15 * 15/14 * 7/6, Al-Farabi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 16/15 111.7313 minor diatonic semitone 2: 15/14 119.4428 major diatonic semitone 3: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 7/6 266.871 cents septimal minor third 2: 1 8/7 231.174 cents septimal whole tone 2: 1 56/45 378.602 cents septimal narrow major third 2: 1 5/4 386.314 cents major third 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 : 111.7 231.2 498.0 111.7: 119.4 386.3 498.0 231.2: 266.9 378.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 266.8709 cents 35/32, 155.1396 cents 16/15, 111.7313 cents 2: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.485842 Largest / Average step : 1.607511 Largest / Smallest step : 2.388507 Median interval of one step : 15/14, 119.4428 cents, amount: 1 Least squares average step : 147.72960 cents, oct.: 443.18881 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1618-tone equal temperament with octave 4/3 degrees: 363 751 1618 Least number of segments generator : 811 of 249.638 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1245 of 383.230 cents and inv. generated superset size: 39 = 36 more = 1300.000% 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 35.69681 cents Scale diversity : 1.137337 Lumma stability : 0.448679 Lumma impropriety factor : 0.071674 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 : 225/224, 7.7115 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions with margin 147.4281 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 45 (O: 15 U: 45) Highest odd numerator or denominator: 15 Scale harmonicity : 0.042822 Average absolute harmonicity : 0.122028 Specific harmonicity : 0.217026 Fundamental : 1/105, -6.7142 octaves, 2.4917 Hz. Guide tone : 16, 4.0000 octaves, 4186.009 Hz. Exponens Consonantiae : 1.680000E+03, 10.71425 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 26.5, average 8.83333 Mersenne's string divisions : 3255 Sum of van Prooijen's expressibility: 2.49831, average 0.83277 Sum of Tenney's harmonic distance : 5.20758, average 1.73586 Vogel's harmonic complexity : 12.00000 Wille's k value : 17 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 15.60911, average 2.60152 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 1 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 10 15 19| Scale is weakly epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 10 16 18| Scale is weakly epimorphic with val: <7 11 15 20| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <7 12 15 18| Scale is weakly epimorphic with val: <7 12 18 18| Scale is weakly epimorphic with val: <8 11 17 21| Scale is weakly epimorphic with val: <8 11 18 20| Scale is weakly epimorphic with val: <8 12 15 21| Scale is weakly epimorphic with val: <8 12 17 19| Scale is weakly epimorphic with val: <8 12 17 22| Scale is weakly epimorphic with val: <8 12 18 21|
FIT/MODE
3: 1 0 2 N G T3 SD: 48.9640 c. M: 65.1591 c. 4: 1 1 2 P M ME S SD: 12.6740 c. M:-17.8484 c. 9: 2 2 5 N M DE S SD: 5.7026 c. M: 9.8208 c. 13: 3 3 7 N M DE S SD: 1.9969 c. M:-3.2022 c. 32: 7 8 17 N T3 SD: 2.0792 c. M: 2.7839 c. 41: 9 10 22 N T3 SD: 1.4047 c. M: 2.4043 c. 45: 10 11 24 N T3 SD: 0.9429 c. M:-1.2469 c. 54: 12 13 29 N T3 SD: 0.6999 c. M: 1.0546 c. 58: 13 14 31 N T3 SD: 0.3937 c. M:-0.6744 c. 67: 15 16 36 N T3 SD: 0.4446 c. M: 0.7354 c. 71: 16 17 38 N T3 SD: 0.3422 c. M:-0.5042 c. 112: 25 27 60 N T3 SD: 0.3255 c. M: 0.5605 c. 125: 28 30 67 N T3 SD: 0.1084 c. M: 0.1692 c. 183: 41 44 98 N T3 SD: 0.1249 c. M:-0.1583 c. 196: 44 47 105 N T3 SD: 0.0557 c. M:-0.0747 c. 321: 72 77 172 N T3 SD: 0.0121 c. M: 0.0203 c. 838: 188 201 449 N T3 SD: 0.0108 c. M:-0.0186 c. 1159: 260 278 621 N T3 SD: 0.0090 c. M:-0.0150 c. 1297: 291 311 695 N T3 SD: 0.0082 c. M:-0.0120 c. 1422: 319 341 762 N T3 SD: 0.0084 c. M: 0.0140 c. 1618: 363 388 867 N T3 SD: 0.0043 c. M:-0.0056 c. 1939: 435 465 1039 N T3 SD: 0.0020 c. M: 0.0031 c. 2260: 507 542 1211 N T3 SD: 0.0015 c. M: 0.0019 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: 59.7273 cents 6 x 7:8 S SD: 17.8484 cents 7 x 8:9 S SD: 31.4805 cents 8 x 9:11 SD: 29.9221 cents 9 x 10:12 S SD: 24.3852 cents 10:11 x 13 SD: 34.4934 cents 11:12:13:15 SD: 26.6572 cents 12:13:14:16 S SD: 14.8874 cents 13:14:15:17 SD: 13.6587 cents 14:15:16:19 SD: 10.5325 cents 15:16:17:20 SD: 4.8291 cents 27:29:31:36 SD: 4.8015 cents 42:45:48:56 S SD: 2.5705 cents 57:61:65:76 SD: 2.2796 cents 63:67:72:84 SD: 1.7201 cents 78:83:89:104 SD: 1.6690 cents 90:96:103:120 SD: 0.8009 cents 105:112:120:140 S SD: 0.0000 cents