Scala analysis: 488_R12
Reduplicated tetrachord 28/27 * 28/27 * 243/196
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 784/729 125.921808 two (Archytas' 1/3-tone) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 243/196 372.1232 1: 28/27 62.9609 Archytas' 1/3-tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 243/196 372.1232
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 243/196 372.123 cents 2: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 2 9/7 435.084 cents septimal major third, BP 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 : 63.0 125.9 498.0 63.0 : 63.0 435.1 498.0 125.9: 372.1 435.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 372.1232 cents 6561/5488, 309.1623 cents 28/27, 62.9609 cents 2: 125.9218 .. 435.0841 cents 6561/5488, 309.1623 cents 153664/177147,-246.2014 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 243/196, 372.1232 cents Average / Smallest step : 2.636795 Largest / Average step : 2.241503 Largest / Smallest step : 5.910385 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Most common interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 129.20997 cents, oct.: 387.62990 cents Scale is not proper Scale has Myhill's property chromas: 6561/5488, 309.1623 cents and 177147/153664, 246.2014 cents, ratio: 1.255729 generators: 1 of 62.96090 cents and 435.08410 cents ET pair of linear temperament : 174&1060 Scale is distributional even Scale is a mode of a 443-tone equal temperament with octave 4/3 degrees: 56 112 443 generators: 56 and 387 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 62.96090 cents Scale diversity : 0.626253 Lumma stability : 0.252832 Lumma impropriety factor : 0.494336 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 : 28/27, 62.9609 cents Most common intervals : 28/27, 62.9609 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 : 729 (O: 243 U: 729) Highest odd numerator or denominator: 729 Scale harmonicity : 0.024648 Average absolute harmonicity : 0.096076 Specific harmonicity : 0.116504 Fundamental : 1/729, -9.5098 octaves, 0.3589 Hz. Guide tone : 784, 9.6147 octaves, 205114.443 Hz. Exponens Consonantiae : 5.715360E+05, 19.12448 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 787.5, average 262.50000 Mersenne's string divisions : 582505 Sum of van Prooijen's expressibility: 4.77121, average 1.59040 Sum of Tenney's harmonic distance : 9.71475, average 3.23825 Vogel's harmonic complexity : 17.66667 Wille's k value : 121 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 25.18333, average 4.19722 Lattice compactness (without 2's) : 21.27034, average 3.54506 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 2.66667 8 3: -6 ..-1 -3.33333 10 1 7: 0 .. 2 1.00000 3 2 Average exponent except 2's :-7 / 3 =-2.33333 Average absolute exponent except 2's: 13 / 3 = 4.33333 Scale is weakly epimorphic with val: <7 11 18| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 11 21|
FIT/MODE
3: 0 1 2 N G T3 SD: 43.0950 c. M: 62.9609 c. 4: 0 1 3 N G T3 SD: 36.3596 c. M: 62.9609 c. 5: 0 1 4 N G T3 SD: 39.3973 c. M: 62.9609 c. 6: 1 1 4 N M DE S SD: 25.8800 c. M:-40.0932 c. 7: 1 1 5 N M DE S SD: 10.5712 c. M:-16.3768 c. 8: 1 1 6 N M DE S SD: 0.9105 c. M: 1.4106 c. 47: 6 6 35 N M DE S SD: 0.7995 c. M:-1.2386 c. 55: 7 7 41 N M DE S SD: 0.5508 c. M:-0.8533 c. 63: 8 8 47 N M DE S SD: 0.3652 c. M:-0.5658 c. 71: 9 9 53 N M DE S SD: 0.2215 c. M:-0.3431 c. 79: 10 10 59 N M DE S SD: 0.1069 c. M:-0.1655 c. 87: 11 11 65 N M DE S SD: 0.0133 c. M:-0.0206 c. 356: 45 45 266 N M DE S SD: 0.0075 c. M: 0.0116 c. 443: 56 56 331 N M DE S SD: 0.0034 c. M: 0.0052 c. 530: 67 67 396 N M DE S SD: 0.0006 c. M: 0.0010 c. 1147: 145 145 857 N M DE S SD: 0.0004 c. M:-0.0006 c. 1677: 212 212 1253 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 70.4745 cents 7 x 8:9 S SD: 61.3232 cents 8 x 9:11 SD: 47.2233 cents 9 x 10:12 S SD: 28.2410 cents 10 x 11:13 SD: 29.3624 cents 11 x 12:15 S SD: 23.0462 cents 12 x 13:16 SD: 6.3254 cents 13 x 14:17 SD: 16.8506 cents 14 x 15:19 SD: 15.6598 cents 15 x 16:20 S SD: 7.0953 cents 16 x 17:21 SD: 17.1968 cents 17 x 18:23 SD: 18.4797 cents 18:19 x 24 SD: 15.3211 cents 19:20 x 25 S SD: 17.2736 cents 20:21:22:27 SD: 16.5075 cents 21:22:23:28 SD: 12.0448 cents 22:23:24:29 SD: 11.5383 cents 23:24:25:31 SD: 9.4570 cents 24:25:26:32 SD: 4.9386 cents 27:28:29:36 SD: 0.7365 cents 105:109:113:140 SD: 0.7113 cents 132:137:142:176 SD: 0.4972 cents 159:165:171:212 SD: 0.3890 cents 186:193:200:248 SD: 0.3456 cents 213:221:229:284 SD: 0.3395 cents 384:398:413:512 SD: 0.3246 cents 408:423:439:544 SD: 0.3244 cents 411:426:442:548 SD: 0.3011 cents 435:451:468:580 SD: 0.2647 cents 462:479:497:616 SD: 0.2142 cents 489:507:526:652 SD: 0.1725 cents 516:535:555:688 SD: 0.1402 cents 543:563:584:724 SD: 0.1184 cents 570:591:613:760 SD: 0.1086 cents