Scala analysis: 479_R3
Reduplicated tetrachord 13/12 * 13/12 * 192/169, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 169/144 277.145322 two (tridecimal 2/3-tone) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 192/169 220.8997 1: 13/12 138.5727 tridecimal 2/3-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 192/169 220.8997
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 192/169 220.900 cents 2: 1 169/144 277.145 cents two (tridecimal 2/3-tone) 2: 2 16/13 359.472 cents tridecimal neutral 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 : 138.6 277.1 498.0 138.6: 138.6 359.5 498.0 277.1: 220.9 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 220.8997 cents 2304/2197, 82.3270 cents 13/12, 138.5727 cents 2: 277.1453 .. 359.4723 cents 2304/2197, 82.3270 cents 28561/27648, 56.2456 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 192/169, 220.8997 cents Average / Smallest step : 1.198036 Largest / Average step : 1.330601 Largest / Smallest step : 1.594107 Median interval of one step : 13/12, 138.5727 cents, amount: 2 Most common interval of one step : 13/12, 138.5727 cents, amount: 2 Least squares average step : 156.21416 cents, oct.: 468.64249 cents Scale is strictly proper Scale has Myhill's property chromas: 2304/2197, 82.3270 cents and 28561/27648, 56.2456 cents, ratio: 1.463705 generators: 1 of 138.57266 cents and 359.47234 cents ET pair of linear temperament : 36&230 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 363-tone equal temperament with octave 4/3 degrees: 101 202 363 generators: 101 and 262 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 56.24564 cents Scale diversity : 1.303203 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.669399 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 : 28561/27648, 56.2456 cents Most common intervals : 13/12, 138.5727 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle 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 : 0.017972 Average absolute harmonicity : 0.090071 Specific harmonicity : 0.083735 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 676, 9.4009 octaves, 176858.882 Hz. Exponens Consonantiae : 9.734400E+04, 16.57080 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 172.5, average 57.50000 Mersenne's string divisions : 54775 Sum of van Prooijen's expressibility: 3.81895, average 1.27298 Sum of Tenney's harmonic distance : 7.65856, average 2.55285 Vogel's harmonic complexity : 17.66667 Wille's k value : 84 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 22.56026, average 3.76004 Lattice compactness (without 2's) : 9.89292, average 1.64882 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.33333 8 3: -2 ..-1 -1.33333 4 1 13: 0 .. 2 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 JI-epimorphic with val: <7 11 26| Scale is weakly epimorphic with val: <7 11 27| = patent Scale is weakly epimorphic with val: <7 11 29| Scale is weakly epimorphic with val: <7 11 30|
FIT/MODE
3: 1 1 1 SP B ME I SD: 35.4279 c. M:-54.8847 c. 4: 1 1 2 P M ME S SD: 18.1532 c. M: 28.1228 c. 6: 2 1 3 P T3 SD: 22.6861 c. M: 28.1228 c. 7: 2 2 3 SP M ME S SD: 4.8101 c. M:-7.4518 c. 11: 3 3 5 SP M DE S SD: 3.5402 c. M: 5.4844 c. 18: 5 5 8 SP M DE S SD: 0.2928 c. M: 0.4537 c. 61: 17 17 27 SP M DE S SD: 0.2928 c. M:-0.4535 c. 79: 22 22 35 SP M DE S SD: 0.1593 c. M:-0.2468 c. 97: 27 27 43 SP M DE S SD: 0.0754 c. M:-0.1168 c. 115: 32 32 51 SP M DE S SD: 0.0178 c. M:-0.0275 c. 248: 69 69 110 SP M DE S SD: 0.0048 c. M: 0.0074 c. 363: 101 101 161 SP M DE S SD: 0.0024 c. M:-0.0037 c. 611: 170 170 271 SP M DE S SD: 0.0005 c. M: 0.0008 c. 1585: 441 441 703 SP M DE S SD: 0.0001 c. M:-0.0002 c. 2196: 611 611 974 SP M DE S SD: 0.0000 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 5 x S SD: 109.1684 cents 5 x 6:7 S SD: 46.4129 cents 6 x 7:8 S SD: 5.1372 cents 7 x 8:9 S SD: 38.9789 cents 8:9 x 11 SD: 42.1514 cents 9:10:11:12 H SD: 27.6043 cents 10:11:12:13 H SD: 21.3482 cents 11:12:13:15 SD: 14.1608 cents 12:13:14:16 S SD: 3.4248 cents 51:55:60:68 SD: 2.9701 cents 57:62:67:76 SD: 2.4985 cents 63:68:74:84 SD: 2.1731 cents 69:75:81:92 SD: 1.9325 cents 75:81:88:100 SD: 1.7836 cents 81:88:95:108 SD: 1.6851 cents 87:94:102:116 SD: 1.6420 cents 93:101:109:124 SD: 1.6250 cents 108:117:127:144 SD: 1.1371 cents 120:130:141:160 SD: 0.6825 cents 132:143:155:176 SD: 0.3103 cents 144:156:169:192 SD: 0.0000 cents