Scala analysis: 483_R7
Reduplicated tetrachord 17/16 * 17/16 * 1024/867
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 289/256 209.910819 two (17th harmonic) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 1024/867 288.1342 1: 17/16 104.9554 17th harmonic 2: 17/16 104.9554 17th harmonic 3: 1024/867 288.1342
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 17/16 104.955 cents 17th harmonic 1: 1 1024/867 288.134 cents 2: 1 289/256 209.911 cents two (17th harmonic) 2: 2 64/51 393.090 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 : 105.0 209.9 498.0 105.0: 105.0 393.1 498.0 209.9: 288.1 393.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.9554 .. 288.1342 cents 16384/14739, 183.1788 cents 17/16, 104.9554 cents 2: 209.9108 .. 393.0896 cents 16384/14739, 183.1788 cents 250563/262144,-78.2234 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 17/16, 104.9554 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 1024/867, 288.1342 cents Average / Smallest step : 1.581767 Largest / Average step : 1.735591 Largest / Smallest step : 2.745301 Median interval of one step : 17/16, 104.9554 cents, amount: 2 Most common interval of one step : 17/16, 104.9554 cents, amount: 2 Least squares average step : 144.20800 cents, oct.: 432.62401 cents Scale is not proper Scale has Myhill's property chromas: 16384/14739, 183.1788 cents and 262144/250563, 78.2234 cents, ratio: 2.341740 generators: 1 of 104.95541 cents and 393.08959 cents ET pair of linear temperament : 28&38 Scale is distributional even Scale is a mode of a 503-tone equal temperament with octave 4/3 degrees: 106 212 503 generators: 106 and 397 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 78.22336 cents Scale diversity : 1.102169 Lumma stability : 0.421470 Lumma impropriety factor : 0.157061 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 : 262144/250563, 78.2234 cents Most common intervals : 17/16, 104.9554 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 : 17 Odd number limit : 867 (O: 289 U: 867) Highest odd numerator or denominator: 289 Scale harmonicity : 0.013717 Average absolute harmonicity : 0.086083 Specific harmonicity : 0.063285 Fundamental : 1/768, -9.5850 octaves, 0.3407 Hz. Guide tone : 1156, 10.1749 octaves, 302439.153 Hz. Exponens Consonantiae : 8.878080E+05, 19.75989 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 292.5, average 97.50000 Mersenne's string divisions : 125895 Sum of van Prooijen's expressibility: 4.16847, average 1.38949 Sum of Tenney's harmonic distance : 8.38289, average 2.79430 Vogel's harmonic complexity : 23.66667 Wille's k value : 433 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 3 Triangular lattice diameter : 3 Lattice compactness : 35.13986, average 5.85664 Lattice compactness (without 2's) : 8.65028, average 1.44171 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -8 .. 2 -3.33333 14 3: -1 .. 0 -0.33333 1 1 17: 0 .. 2 1.00000 3 2 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 11 27| Scale is JI-epimorphic with val: <7 11 29| Scale is weakly epimorphic with val: <7 11 30| = patent Scale is weakly epimorphic with val: <7 11 32| Scale is weakly epimorphic with val: <7 11 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 65.6823 c. M: 104.9554 c. 4: 1 1 2 P M ME S SD: 25.2465 c. M:-39.1117 c. 5: 1 1 3 N M DE S SD: 6.9022 c. M: 10.6928 c. 14: 3 3 8 N M DE S SD: 2.2831 c. M:-3.5370 c. 19: 4 4 11 N M DE S SD: 0.1340 c. M: 0.2077 c. 128: 27 27 74 N M DE S SD: 0.1303 c. M:-0.2019 c. 147: 31 31 85 N M DE S SD: 0.0962 c. M:-0.1490 c. 166: 35 35 96 N M DE S SD: 0.0698 c. M:-0.1082 c. 185: 39 39 107 N M DE S SD: 0.0489 c. M:-0.0757 c. 204: 43 43 118 N M DE S SD: 0.0318 c. M:-0.0493 c. 223: 47 47 129 N M DE S SD: 0.0177 c. M:-0.0274 c. 242: 51 51 140 N M DE S SD: 0.0058 c. M:-0.0090 c. 261: 55 55 151 N M DE S SD: 0.0044 c. M: 0.0068 c. 503: 106 106 291 N M DE S SD: 0.0005 c. M:-0.0008 c. 1267: 267 267 733 N M DE S SD: 0.0005 c. M: 0.0008 c. 1770: 373 373 1024 N M DE S SD: 0.0002 c. M: 0.0003 c. 2273: 479 479 1315 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: 67.6639 cents 6 x 7:8 S SD: 28.4800 cents 7 x 8:9 S SD: 33.2273 cents 8 x 9:11 SD: 26.8049 cents 9 x 10:12 S SD: 13.7536 cents 10 x 11:13 SD: 31.3758 cents 11:12 x 15 S SD: 30.0020 cents 12:13:14:16 S SD: 22.0468 cents 13:14:15:17 SD: 18.5776 cents 14:15:16:19 SD: 13.3373 cents 15:16:17:20 SD: 3.1942 cents 48:51:54:64 SD: 2.0003 cents 63:67:71:84 SD: 1.1212 cents 78:83:88:104 SD: 0.9407 cents 147:156:166:196 SD: 0.7153 cents 162:172:183:216 SD: 0.5589 cents 210:223:237:280 SD: 0.3659 cents 225:239:254:300 SD: 0.1512 cents 240:255:271:320 SD: 0.1331 cents 465:494:525:620 SD: 0.0974 cents 528:561:596:704 SD: 0.0605 cents