Scala analysis: 481_R5
Reduplicated tetrachord 15/14 * 15/14 * 784/675, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 225/196 238.885617 two (major diatonic semitone) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 784/675 259.1594 1: 15/14 119.4428 major diatonic semitone 2: 15/14 119.4428 major diatonic semitone 3: 784/675 259.1594
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 784/675 259.159 cents 2: 1 225/196 238.886 cents two (major diatonic semitone) 2: 2 56/45 378.602 cents septimal narrow major third Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 119.4 238.9 498.0 119.4: 119.4 378.6 498.0 238.9: 259.2 378.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 259.1594 cents 10976/10125, 139.7166 cents 15/14, 119.4428 cents 2: 238.8856 .. 378.6022 cents 10976/10125, 139.7166 cents 151875/153664,-20.2738 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 784/675, 259.1594 cents Average / Smallest step : 1.389912 Largest / Average step : 1.561060 Largest / Smallest step : 2.169736 Median interval of one step : 15/14, 119.4428 cents, amount: 2 Most common interval of one step : 15/14, 119.4428 cents, amount: 2 Least squares average step : 149.38207 cents, oct.: 448.14622 cents Scale is not proper Scale has Myhill's property chromas: 10976/10125, 139.7166 cents and 153664/151875, 20.2738 cents, ratio: 6.891496 generators: 1 of 119.44281 cents and 378.60219 cents ET pair of linear temperament : 42&50 Scale is distributional even Scale is a mode of a 221-tone equal temperament with octave 4/3 degrees: 53 106 221 generators: 53 and 168 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAB Step pattern size order : SSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 20.27377 cents Scale diversity : 1.116389 Lumma stability : 0.479647 Lumma impropriety factor : 0.040707 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 153664/151875, 20.2738 cents Most common intervals : 15/14, 119.4428 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are 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 Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 7 Odd number limit : 675 (O: 225 U: 675) Highest odd numerator or denominator: 225 Scale harmonicity : 0.022040 Average absolute harmonicity : 0.095995 Specific harmonicity : 0.102258 Fundamental : 1/588, -9.1997 octaves, 0.4449 Hz. Guide tone : 900, 9.8138 octaves, 235463.009 Hz. Exponens Consonantiae : 5.292000E+05, 19.01345 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 228.5, average 76.16667 Mersenne's string divisions : 85463 Sum of van Prooijen's expressibility: 4.00540, average 1.33513 Sum of Tenney's harmonic distance : 8.04584, average 2.68195 Vogel's harmonic complexity : 18.66667 Wille's k value : 337 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.85361, average 3.30894 Lattice compactness (without 2's) : 14.50080, average 2.41680 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 2 0.66667 4 1 5: 0 .. 2 1.00000 3 7: -2 .. 0 -1.00000 3 2 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is JI-epimorphic with val: <7 11 15 18| Scale is weakly epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 15 21| Scale is weakly epimorphic with val: <7 11 16 18| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 17 19| Scale is JI-epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 11 18 20| Scale is JI-epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 21| Scale is JI-epimorphic with val: <7 11 19 22|
FIT/MODE
3: 1 0 2 N G T3 SD: 49.9303 c. M: 72.8706 c. 4: 1 1 2 P M ME S SD: 6.5433 c. M:-10.1369 c. 13: 3 3 7 N M DE S SD: 5.8215 c. M: 9.0187 c. 17: 4 4 9 N M DE S SD: 2.9122 c. M: 4.5115 c. 21: 5 5 11 N M DE S SD: 1.1111 c. M: 1.7213 c. 25: 6 6 13 N M DE S SD: 0.1136 c. M:-0.1760 c. 121: 29 29 63 N M DE S SD: 0.0990 c. M: 0.1533 c. 146: 35 35 76 N M DE S SD: 0.0626 c. M: 0.0969 c. 171: 41 41 89 N M DE S SD: 0.0368 c. M: 0.0570 c. 196: 47 47 102 N M DE S SD: 0.0176 c. M: 0.0273 c. 221: 53 53 115 N M DE S SD: 0.0028 c. M: 0.0043 c. 688: 165 165 358 N M DE S SD: 0.0015 c. M:-0.0022 c. 909: 218 218 473 N M DE S SD: 0.0004 c. M:-0.0007 c. 1130: 271 271 588 N M DE S SD: 0.0002 c. M: 0.0003 c. 2039: 489 489 1061 N M DE S SD: 0.0001 c. M:-0.0001 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: 57.0661 cents 6 x 7:8 S SD: 13.9926 cents 7 x 8:9 S SD: 31.7157 cents 8 x 9:11 SD: 31.8642 cents 9 x 10:12 S SD: 28.2410 cents 10:11 x 13 SD: 31.6109 cents 11:12:13:15 SD: 23.6156 cents 12:13:14:16 S SD: 11.2996 cents 14:15:16:19 SD: 10.5325 cents 15:16:17:20 SD: 7.8334 cents 26:28:30:35 S SD: 6.9226 cents 27:29:31:36 SD: 1.4263 cents 96:103:110:128 SD: 1.3363 cents 114:122:131:152 SD: 0.8933 cents 141:151:162:188 SD: 0.5617 cents 156:167:179:208 SD: 0.5592 cents 168:180:193:224 SD: 0.4273 cents 183:196:210:244 SD: 0.2974 cents 210:225:241:280 SD: 0.1710 cents 351:376:403:468 SD: 0.1450 cents 378:405:434:504 SD: 0.0950 cents 561:601:644:748 SD: 0.0687 cents 588:630:675:784 SD: 0.0000 cents