Scala analysis: 480_R4
Reduplicated tetrachord 14/13 * 14/13 * 169/147, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 196/169 256.596489 two (2/3-tone) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 169/147 241.4485 1: 14/13 128.2982 2/3-tone 2: 14/13 128.2982 2/3-tone 3: 169/147 241.4485
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 14/13 128.298 cents 2/3-tone 1: 1 169/147 241.449 cents 2: 1 196/169 256.596 cents two (2/3-tone) 2: 2 26/21 369.747 cents 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 : 128.3 256.6 498.0 128.3: 128.3 369.7 498.0 256.6: 241.4 369.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 241.4485 cents 2197/2058, 113.1503 cents 14/13, 128.2982 cents 2: 256.5965 .. 369.7468 cents 2197/2058, 113.1503 cents 28812/28561, 15.1480 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 169/147, 241.4485 cents Average / Smallest step : 1.293977 Largest / Average step : 1.454378 Largest / Smallest step : 1.881932 Median interval of one step : 14/13, 128.2982 cents, amount: 2 Most common interval of one step : 14/13, 128.2982 cents, amount: 2 Least squares average step : 152.54473 cents, oct.: 457.63419 cents Scale is strictly proper Scale has Myhill's property chromas: 2197/2058, 113.1503 cents and 28812/28561, 15.1480 cents, ratio: 7.469660 generators: 1 of 128.29824 cents and 369.74675 cents ET pair of linear temperament : 62&132 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 493-tone equal temperament with octave 4/3 degrees: 127 254 493 generators: 127 and 366 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 15.14798 cents Scale diversity : 1.166283 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.545622 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 : 28812/28561, 15.1480 cents Most common intervals : 14/13, 128.2982 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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 : 13 Odd number limit : 169 (O: 169 U: 169) Highest odd numerator or denominator: 169 Scale harmonicity : 0.014379 Average absolute harmonicity : 0.086380 Specific harmonicity : 0.066094 Fundamental : 1/507, -8.9858 octaves, 0.5160 Hz. Guide tone : 196, 7.6147 octaves, 51278.611 Hz. Exponens Consonantiae : 9.937200E+04, 16.60055 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 199.5, average 66.50000 Mersenne's string divisions : 68985 Sum of van Prooijen's expressibility: 3.81895, average 1.27298 Sum of Tenney's harmonic distance : 7.85940, average 2.61980 Vogel's harmonic complexity : 23.66667 Wille's k value : 136 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.16427, average 2.36071 Lattice compactness (without 2's) : 11.38891, average 1.89815 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.33333 1 1 7: 0 .. 2 1.00000 3 13: -2 .. 0 -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: <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 JI-epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 20 25| Scale is JI-epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 20 29| 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 11 22 25| Scale is weakly epimorphic with val: <7 11 22 27| Scale is JI-epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 11 22 30|
FIT/MODE
3: 1 1 1 SP B ME I SD: 48.6921 c. M:-75.4335 c. 4: 1 1 2 P M ME S SD: 4.8890 c. M: 7.5740 c. 19: 5 5 9 SP M DE S SD: 3.5712 c. M:-5.5325 c. 23: 6 6 11 SP M DE S SD: 2.0999 c. M:-3.2531 c. 27: 7 7 13 SP M DE S SD: 1.0645 c. M:-1.6491 c. 31: 8 8 15 SP M DE S SD: 0.2963 c. M:-0.4590 c. 66: 17 17 32 SP M DE S SD: 0.0180 c. M: 0.0279 c. 295: 76 76 143 SP M DE S SD: 0.0150 c. M:-0.0233 c. 361: 93 93 175 SP M DE S SD: 0.0090 c. M:-0.0140 c. 427: 110 110 207 SP M DE S SD: 0.0048 c. M:-0.0075 c. 493: 127 127 239 SP M DE S SD: 0.0018 c. M:-0.0028 c. 559: 144 144 271 SP M DE S SD: 0.0006 c. M: 0.0009 c. 1052: 271 271 510 SP M DE S SD: 0.0005 c. M:-0.0008 c. 1611: 415 415 781 SP M DE S SD: 0.0002 c. M:-0.0003 c. 2170: 559 559 1052 SP M DE S SD: 0.0000 c. M: 0.0000 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: 51.5291 cents 6 x 7:8 S SD: 5.1372 cents 7 x 8:9 S SD: 33.9499 cents 8 x 9:11 SD: 37.4629 cents 9:10 x 12 S SD: 27.0527 cents 11:12:13:15 SD: 18.4881 cents 12:13:14:16 S SD: 4.8434 cents 37:40:43:49 SD: 4.6555 cents 38:41:44:51 SD: 4.0447 cents 39:42:45:52 SD: 2.9518 cents 51:55:59:68 SD: 1.6555 cents 63:68:73:84 SD: 1.4046 cents 93:100:108:124 SD: 1.1677 cents 105:113:122:140 SD: 1.1347 cents 132:142:153:176 SD: 0.7089 cents 144:155:167:192 SD: 0.2870 cents 156:168:181:208 SD: 0.2453 cents 300:323:348:400 SD: 0.1810 cents 351:378:407:468 SD: 0.1091 cents 507:546:588:676 SD: 0.0000 cents