Scala analysis: 029_H8
Hyperenharmonic tetrachord 64/63 * 49/48 * 9/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/63 27.264092 septimal comma, Archytas' comma 2: 28/27 62.960904 Archytas' 1/3-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 9/7 435.0841 septimal major third, BP third 1: 64/63 27.2641 septimal comma, Archytas' comma 2: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 9/7 435.0841 septimal major third, BP third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 28/27 62.961 cents Archytas' 1/3-tone 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 2: 1 21/16 470.781 cents narrow fourth Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 27.3 63.0 498.0 27.3 : 35.7 470.8 498.0 63.0 : 435.1 462.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 435.0841 cents 81/64, 407.8200 cents 64/63, 27.2641 cents 2: 62.9609 .. 470.7809 cents 81/64, 407.8200 cents 196/243,-372.1232 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/7, 435.0841 cents Average / Smallest step : 6.089145 Largest / Average step : 2.620752 Largest / Smallest step : 15.958136 Median interval of one step : 49/48, 35.6968 cents, amount: 1 Least squares average step : 117.66578 cents, oct.: 352.99734 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1242-tone equal temperament with octave 4/3 degrees: 68 157 1242 Least number of segments generator : 623 of 249.825 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 763 of 305.965 cents and inv. generated superset size: 53 = 50 more = 1766.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 0.149049 Lumma stability : 0.109484 Lumma impropriety factor : 0.747168 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1029/1024, 8.4327 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly 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 with margin 399.3873 cents: 2 -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 49 U: 63) Highest odd numerator or denominator: 63 Scale harmonicity : 0.028926 Average absolute harmonicity : 0.103279 Specific harmonicity : 0.150402 Fundamental : 1/189, -7.5622 octaves, 1.3843 Hz. Guide tone : 448, 8.8074 octaves, 117208.253 Hz. Exponens Consonantiae : 8.467200E+04, 16.36960 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 94.5, average 31.50000 Mersenne's string divisions : 48895 Sum of van Prooijen's expressibility: 3.70783, average 1.23594 Sum of Tenney's harmonic distance : 7.56322, average 2.52107 Vogel's harmonic complexity : 13.33333 Wille's k value : 31 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 23.44213, average 3.90702 Lattice compactness (without 2's) : 12.28470, average 2.04745 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 3.33333 10 3: -3 ..-1 -2.00000 6 1 7: -1 .. 1 0.00000 2 2 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 21|
FIT/MODE
3: 0 0 3 N M DE S SD: 39.6123 c. M: 62.9609 c. 6: 0 1 5 N G T3 SD: 19.5380 c. M: 27.2641 c. 7: 0 1 6 N G T3 SD: 16.4355 c. M: 27.2641 c. 8: 0 1 7 N G T3 SD: 15.7462 c. M: 27.2641 c. 9: 0 1 8 N G T3 SD: 16.3446 c. M: 27.2641 c. 10: 0 1 9 N G T3 SD: 17.4778 c. M: 27.2641 c. 13: 1 1 11 N M DE S SD: 10.1435 c. M:-13.6614 c. 14: 1 1 12 N M DE S SD: 6.7358 c. M:-8.3106 c. 15: 1 1 13 N M DE S SD: 3.9640 c. M:-5.9389 c. 16: 1 1 14 N M DE S SD: 2.2676 c. M:-3.8637 c. 33: 2 2 29 N M DE S SD: 2.2544 c. M:-2.9205 c. 38: 2 3 33 N T3 SD: 1.6038 c. M:-2.5713 c. 39: 2 3 34 N T3 SD: 1.1201 c. M: 1.7233 c. 54: 3 4 47 N T3 SD: 0.9532 c. M:-1.6005 c. 55: 3 4 48 N T3 SD: 0.2527 c. M:-0.4266 c. 111: 6 8 97 N T3 SD: 0.2147 c. M: 0.3427 c. 127: 7 9 111 N T3 SD: 0.1646 c. M: 0.2151 c. 166: 9 12 145 N T3 SD: 0.1533 c. M: 0.2617 c. 182: 10 13 159 N T3 SD: 0.0596 c. M:-0.1010 c. 237: 13 17 207 N T3 SD: 0.0573 c. M:-0.0828 c. 293: 16 21 256 N T3 SD: 0.0551 c. M: 0.0678 c. 348: 19 25 304 N T3 SD: 0.0420 c. M: 0.0720 c. 419: 23 30 366 N T3 SD: 0.0484 c. M:-0.0749 c. 475: 26 34 415 N T3 SD: 0.0289 c. M: 0.0500 c. 530: 29 38 463 N T3 SD: 0.0073 c. M: 0.0126 c. 1242: 68 89 1085 N T3 SD: 0.0031 c. M:-0.0041 c. 1772: 97 127 1548 N T3 SD: 0.0016 c. M: 0.0026 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: 101.9550 cents 7 x 8:9 S SD: 89.8050 cents 8 x 9:11 SD: 75.3403 cents 9 x 10:12 S SD: 59.7214 cents 10 x 11:13 SD: 55.5293 cents 11 x 12:15 S SD: 47.9603 cents 12 x 13:16 SD: 37.8059 cents 13 x 14:17 SD: 36.7392 cents 14 x 15:19 SD: 32.1292 cents 15 x 16:20 S SD: 24.3852 cents 16 x 17:21 SD: 25.0343 cents 17 x 18:23 SD: 21.9904 cents 18 x 19:24 SD: 15.3211 cents 19 x 20:25 S SD: 17.2736 cents 20 x 21:27 SD: 15.2072 cents 21 x 22:28 SD: 8.7881 cents 22 x 23:29 SD: 12.1177 cents 23 x 24:31 SD: 10.7844 cents 24 x 25:32 SD: 3.8558 cents 25 x 26:33 SD: 9.0435 cents 26 x 27:35 SD: 8.3683 cents 27 x 28:36 SD: 0.0000 cents 28 x 29:37 SD: 7.8417 cents 29 x 30:39 SD: 7.7308 cents 30 x 31:40 SD: 3.0970 cents 31 x 32:41 SD: 8.0693 cents 32 x 33:43 SD: 8.2971 cents 33 x 34:44 SD: 5.6392 cents 34 x 35:45 SD: 9.0345 cents 35 x 36:47 SD: 9.3968 cents 36 x 37:48 SD: 7.7634 cents 37 x 38:49 SD: 10.2437 cents 38:39 x 51 SD: 10.5162 cents 39:40 x 52 SD: 8.2835 cents 40:41 x 53 SD: 9.4550 cents 41:42:43:55 SD: 8.8174 cents 42:43:44:56 SD: 7.3819 cents 44:45:46:59 SD: 6.8929 cents 45:46:47:60 SD: 5.4587 cents 47:48:49:63 SD: 5.3026 cents 48:49:50:64 SD: 3.8090 cents 51:52:53:68 SD: 2.4396 cents 54:55:56:72 SD: 1.5009 cents 57:58:59:76 SD: 1.4416 cents 111:113:115:148 SD: 1.3387 cents 129:131:134:172 SD: 0.9805 cents 132:134:137:176 SD: 0.6224 cents 135:137:140:180 SD: 0.6014 cents 186:189:193:248 SD: 0.3627 cents 189:192:196:252 SD: 0.0000 cents