Scala analysis: ForJustin-pentatonic001
Pentatonic mode for Justin, possibly applicable to Japanese styles
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 11/7 782.492036 undecimal augmented fifth 5: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/11 417.5080 undecimal diminished fourth or major third 1: 22/21 80.5370 undecimal minor semitone 2: 14/11 417.5080 undecimal diminished fourth or major third 3: 9/8 203.9100 major whole tone 4: 22/21 80.5370 undecimal minor semitone 5: 14/11 417.5080 undecimal diminished fourth or major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 33/28 284.447 cents undecimal minor third 2: 3 4/3 498.045 cents perfect fourth 2: 1 63/44 621.418 cents 3: 1 88/63 578.582 cents 3: 3 3/2 701.955 cents perfect fifth 3: 1 56/33 915.553 cents 4: 2 11/7 782.492 cents undecimal augmented fifth 4: 1 16/9 996.090 cents Pythagorean minor seventh 4: 2 21/11 1119.463 cents undecimal major seventh 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 4 5 0.0 : 80.5 498.0 702.0 782.5 1200.0 80.5 : 417.5 621.4 702.0 1119.5 1200.0 498.0 : 203.9 284.4 702.0 782.5 1200.0 702.0 : 80.5 498.0 578.6 996.1 1200.0 782.5 : 417.5 498.0 915.6 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 417.5080 cents 147/121, 336.9709 cents 22/21, 80.5370 cents 2: 284.4470 .. 621.4180 cents 147/121, 336.9709 cents 363/392,-133.0609 cents 3: 578.5820 .. 915.5530 cents 147/121, 336.9709 cents 3872/3969,-42.8359 cents 4: 782.4920 .. 1119.4630 cents 147/121, 336.9709 cents 363/392,-133.0609 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 14/11, 417.5080 cents Average / Smallest step : 2.979995 Largest / Average step : 1.739617 Largest / Smallest step : 5.184049 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 223.86291 cents, oct.: 1119.31456 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCAB Step pattern size order : SLMSL Scale is a Constant Structure, by a margin of 42.83593 cents Scale diversity : 1.546154 Lumma stability : 0.134228 Lumma impropriety factor : 0.257465 Rothenberg efficiency : 0.580000 redundancy: 0.420000 Efficiency x scale size : 2.900000 Number of different interval sizes : 12 = 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 : 3969/3872, 42.8359 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 80.537 498.045 cents Number of recognisable fifths : 3, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 60.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.027173 Average absolute harmonicity : 0.310652 Specific harmonicity : 0.127928 Fundamental : 1/42, -5.3923 octaves, 6.2292 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 5.544000E+03, 12.43671 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 38.0, average 7.60000 Mersenne's string divisions : 27090 Sum of van Prooijen's expressibility: 3.31785, average 0.66357 Sum of Tenney's harmonic distance : 6.70950, average 1.34190 Vogel's harmonic complexity : 12.60000 Wille's k value : 31 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 29.73872, average 1.98258 Lattice compactness (without 2's) : 20.62033, average 1.37469 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.60000 5 1 3: -1 .. 1 -0.20000 3 2 7: -1 .. 0 -0.40000 2 11: 0 .. 1 0.40000 2 2 Average exponent except 2's :-1 / 5 =-0.20000 Average absolute exponent except 2's: 7 / 5 = 1.40000 Scale is weakly epimorphic with val: <5 7 13 19| Scale is weakly epimorphic with val: <5 7 14 15| Scale is weakly epimorphic with val: <5 7 15 16| Scale is JI-epimorphic with val: <5 8 13 17| Scale is JI-epimorphic with val: <5 8 14 18| Scale is JI-epimorphic with val: <5 8 15 19| Scale is weakly epimorphic with val: <5 9 13 15| Scale is weakly epimorphic with val: <5 9 14 16| Scale is weakly epimorphic with val: <5 9 15 17|
FIT/MODE
5: 0 2 1 0 2 N T3 SD: 46.9951 c. M: 80.5370 c. 9: 1 3 1 1 3 N M DE S SD: 33.4201 c. M:-52.7963 c. 10: 1 3 2 1 3 P T3 SD: 33.2137 c. M:-57.5080 c. 12: 1 4 2 1 4 N T3 SD: 11.7727 c. M:-19.4630 c. Hon-kumoi-joshi, Sakura, Akebono II: Japan, Olympos Enharmonic, Raga Gunakri (Gunakali), Latantapriya, Salanganata, Saveri, Ambassel: Ethiopia 14: 1 5 2 1 5 N T3 SD: 11.6338 c. M:-16.2407 c. 17: 1 6 3 1 6 N T3 SD: 5.7634 c. M: 9.9488 c. 29: 2 10 5 2 10 N T3 SD: 2.1539 c. M:-3.7149 c. 46: 3 16 8 3 16 N T3 SD: 1.8246 c. M: 2.3928 c. 60: 4 21 10 4 21 N T3 SD: 1.6818 c. M: 2.4920 c. 75: 5 26 13 5 26 N T3 SD: 1.4783 c. M:-2.0450 c. 89: 6 31 15 6 31 N T3 SD: 0.5889 c. M:-0.8314 c. 118: 8 41 20 8 41 N T3 SD: 0.4729 c. M:-0.8189 c. 135: 9 47 23 9 47 N T3 SD: 0.3175 c. M: 0.5370 c. 164: 11 57 28 11 57 N T3 SD: 0.3633 c. M:-0.4840 c. 224: 15 78 38 15 78 N T3 SD: 0.2057 c. M: 0.3492 c. 253: 17 88 43 17 88 N T3 SD: 0.0687 c. M:-0.1167 c. 477: 32 166 81 32 166 N T3 SD: 0.0646 c. M: 0.1021 c. 641: 43 223 109 43 223 N T3 SD: 0.0517 c. M:-0.0731 c. 730: 49 254 124 49 254 N T3 SD: 0.0267 c. M:-0.0372 c. 983: 66 342 167 66 342 N T3 SD: 0.0208 c. M:-0.0326 c. 1118: 75 389 190 75 389 N T3 SD: 0.0209 c. M: 0.0361 c. 1371: 92 477 233 92 477 N T3 SD: 0.0106 c. M:-0.0144 c. 2101: 141 731 357 141 731 N T3 SD: 0.0044 c. M: 0.0075 c. 2354: 158 819 400 158 819 N T3 SD: 0.0040 c. M:-0.0067 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 0.0000 cents 3 x 4 x 5:6 S SD: 33.9556 cents 4 x 5:6 x 8 S SD: 37.2438 cents 5 x 7 x 8:10 SD: 30.0144 cents 6:7:8:9 x 12 S SD: 46.5835 cents 7:8:9 x 11:14 SD: 40.8164 cents 8:9:11:12:13:16 SD: 29.2759 cents 9:10:12 x 14:18 SD: 25.8430 cents 10:11:13:15:16:20 SD: 20.0289 cents 11:12:15 x 17:22 SD: 21.3018 cents 12:13:16:18:19:24 SD: 11.8977 cents 13:14:17 x 20:26 SD: 17.2456 cents 14:15:19:21:22:28 SD: 9.9047 cents 16:17:21:24:25:32 SD: 7.5813 cents 18:19:24:27:28:36 SD: 4.3801 cents 24:25:32:36:38:48 SD: 3.2743 cents 38:40:51:57:60:76 SD: 3.2585 cents 40:42:53:60:63:80 SD: 2.4389 cents 42:44:56:63:66:84 SD: 0.0000 cents