Scala analysis: 056_E4
Enharmonic tetrachord 33/32 * 64/63 * 14/11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 2: 22/21 80.537035 undecimal minor semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 14/11 417.5080 undecimal diminished fourth or major third 1: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 64/63 27.2641 septimal comma, Archytas' comma 3: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 22/21 80.537 cents undecimal minor semitone 2: 1 128/99 444.772 cents 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 : 53.3 80.5 498.0 53.3 : 27.3 444.8 498.0 80.5 : 417.5 470.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 417.5080 cents 441/352, 390.2439 cents 64/63, 27.2641 cents 2: 80.5370 .. 470.7809 cents 441/352, 390.2439 cents 121/147,-336.9709 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 : 14/11, 417.5080 cents Average / Smallest step : 6.089145 Largest / Average step : 2.514881 Largest / Smallest step : 15.313474 Median interval of one step : 33/32, 53.2729 cents, amount: 1 Least squares average step : 122.03443 cents, oct.: 366.10329 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2356-tone equal temperament with octave 4/3 degrees: 252 381 2356 Least number of segments generator : 1179 of 249.234 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1585 of 335.060 cents and inv. generated superset size: 93 = 90 more = 3100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.26409 cents Scale diversity : 0.257805 Lumma stability : 0.109484 Lumma impropriety factor : 0.676587 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 : 2079/2048, 26.0089 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 390.2439 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.024509 Average absolute harmonicity : 0.094697 Specific harmonicity : 0.110917 Fundamental : 1/672, -9.3923 octaves, 0.3893 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 8.870400E+04, 16.43671 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 57.5, average 19.16667 Mersenne's string divisions : 19565 Sum of van Prooijen's expressibility: 3.31785, average 1.10595 Sum of Tenney's harmonic distance : 6.76749, average 2.25583 Vogel's harmonic complexity : 18.33333 Wille's k value : 346 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 24.91586, average 4.15264 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -0.66667 8 3: -1 .. 1 -0.33333 3 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 2 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 23| Scale is weakly epimorphic with val: <6 10 20 27| Scale is weakly epimorphic with val: <6 10 21 23| Scale is weakly epimorphic with val: <6 11 19 27| Scale is weakly epimorphic with val: <7 10 18 24| Scale is weakly epimorphic with val: <7 10 21 27| Scale is weakly epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 18 26| Scale is JI-epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 21 23| Scale is weakly epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 11 22 25| Scale is weakly epimorphic with val: <7 12 19 27| Scale is weakly epimorphic with val: <7 12 20 26| Scale is weakly epimorphic with val: <8 11 18 24| Scale is weakly epimorphic with val: <8 11 21 27| Scale is weakly epimorphic with val: <8 12 20 27|
FIT/MODE
3: 0 0 3 N M DE S SD: 55.7501 c. M: 80.5370 c. 4: 0 1 3 N G T3 SD: 39.8821 c. M: 53.2729 c. 5: 1 0 4 N G T3 SD: 28.9296 c. M:-46.3361 c. 6: 1 0 5 N G T3 SD: 17.2264 c. M:-29.7346 c. 7: 1 0 6 N G T3 SD: 11.6575 c. M:-17.8763 c. 10: 1 1 8 N M DE S SD: 11.1918 c. M:-19.0720 c. 11: 1 1 9 N M DE S SD: 7.3998 c. M:-10.0166 c. 12: 1 1 10 N M DE S SD: 6.9430 c. M: 11.7692 c. 17: 2 1 14 N T3 SD: 5.2402 c. M:-7.3533 c. 18: 2 1 15 N T3 SD: 1.8591 c. M:-2.4705 c. 19: 2 1 16 N T3 SD: 1.2002 c. M: 1.8984 c. 37: 4 2 31 N T3 SD: 0.3541 c. M:-0.5698 c. 56: 6 3 47 N T3 SD: 0.2899 c. M: 0.4941 c. 93: 10 5 78 N T3 SD: 0.2012 c. M:-0.2803 c. 130: 14 7 109 N T3 SD: 0.2149 c. M:-0.3627 c. 216: 23 12 181 N T3 SD: 0.1682 c. M: 0.2404 c. 235: 25 13 197 N T3 SD: 0.1671 c. M: 0.2894 c. 253: 27 14 212 N T3 SD: 0.1226 c. M:-0.1738 c. 272: 29 15 228 N T3 SD: 0.1010 c. M: 0.1726 c. 309: 33 17 259 N T3 SD: 0.0571 c. M: 0.0837 c. 346: 37 19 290 N T3 SD: 0.0420 c. M:-0.0714 c. 365: 39 20 306 N T3 SD: 0.0376 c. M: 0.0572 c. 402: 43 22 337 N T3 SD: 0.0043 c. M: 0.0074 c. 1954: 209 107 1638 N T3 SD: 0.0040 c. M:-0.0066 c. 2356: 252 129 1975 N T3 SD: 0.0026 c. M:-0.0042 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: 93.1669 cents 7 x 8:9 S SD: 81.6327 cents 8 x 9:11 SD: 67.1917 cents 9 x 10:12 S SD: 50.9333 cents 10 x 11:13 SD: 47.5812 cents 11 x 12:15 S SD: 40.0864 cents 12 x 13:16 SD: 29.0178 cents 13 x 14:17 SD: 29.2030 cents 14 x 15:19 SD: 24.7619 cents 15 x 16:20 S SD: 15.5971 cents 16 x 17:21 SD: 18.3002 cents 17 x 18:23 SD: 15.6363 cents 18 x 19:24 SD: 6.5330 cents 19 x 20:25 S SD: 12.1871 cents 20 x 21:27 SD: 10.9312 cents 21 x 22:28 SD: 0.0000 cents 22 x 23:29 SD: 10.0536 cents 23 x 24:31 SD: 9.9663 cents 24 x 25:32 SD: 4.9323 cents 25 x 26:33 SD: 10.7521 cents 26:27 x 35 SD: 10.2471 cents 27:28 x 36 SD: 4.8440 cents 28:29 x 37 SD: 8.6170 cents 29:30 x 39 SD: 7.9088 cents 30:31 x 40 SD: 1.7470 cents 31:32 x 41 SD: 7.0599 cents 35:36:37:47 SD: 6.8115 cents 36:37:38:48 SD: 4.7704 cents 39:40:41:52 SD: 3.7367 cents 48 x 50:64 SD: 4.9323 cents 49 x 51:65 SD: 7.1698 cents 50 x 52:67 SD: 7.6525 cents 51:53 x 68 SD: 6.6606 cents 52:54 x 69 SD: 7.3342 cents 53:55:56:71 SD: 6.6897 cents 54:56:57:72 SD: 5.4219 cents 56:58:59:75 SD: 4.8489 cents 57:59:60:76 SD: 3.4903 cents 59:61:62:79 SD: 3.3612 cents 60:62:63:80 SD: 1.7529 cents 63:65:66:84 SD: 0.2775 cents 318:328:333:424 SD: 0.2708 cents 354:365:371:472 SD: 0.2432 cents 417:430:437:556 SD: 0.1933 cents 420:433:440:560 SD: 0.1666 cents 480:495:503:640 SD: 0.1639 cents 483:498:506:644 SD: 0.1086 cents 546:563:572:728 SD: 0.0641 cents