Scala analysis: ForJustin001
Scale for Justin, possibly applicable to Japanese modes
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: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 11/7 782.492036 undecimal augmented fifth 6: 39/22 991.164720 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 44/39 208.8353 1: 22/21 80.5370 undecimal minor semitone 2: 9/8 203.9100 major whole tone 3: 112/99 213.5980 4: 9/8 203.9100 major whole tone 5: 22/21 80.5370 undecimal minor semitone 6: 273/242 208.6727 7: 44/39 208.8353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 9/8 203.910 cents major whole tone 1: 1 273/242 208.673 cents 1: 1 44/39 208.835 cents 1: 1 112/99 213.598 cents 2: 2 33/28 284.447 cents undecimal minor third 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 968/819 289.372 cents 2: 3 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 117/88 493.120 cents tridecimal gentle fourth 3: 1 121/91 493.282 cents 3: 4 4/3 498.045 cents perfect fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 182/121 706.718 cents 4: 1 176/117 706.880 cents 5: 3 11/7 782.492 cents undecimal augmented fifth 5: 1 819/484 910.628 cents 5: 1 22/13 910.790 cents tridecimal major sixth 5: 2 56/33 915.553 cents 6: 1 99/56 986.402 cents 6: 1 39/22 991.165 cents 6: 1 484/273 991.327 cents 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 80.5 284.4 498.0 702.0 782.5 991.2 1200.0 80.5 : 203.9 417.5 621.4 702.0 910.6 1119.5 1200.0 284.4 : 213.6 417.5 498.0 706.7 915.6 996.1 1200.0 498.0 : 203.9 284.4 493.1 702.0 782.5 986.4 1200.0 702.0 : 80.5 289.2 498.0 578.6 782.5 996.1 1200.0 782.5 : 208.7 417.5 498.0 702.0 915.6 1119.5 1200.0 991.2 : 208.8 289.4 493.3 706.9 910.8 991.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 213.5980 cents 392/363, 133.0609 cents 22/21, 80.5370 cents 2: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents 3: 493.1197 .. 621.4180 cents 14/13, 128.2982 cents 117/112, 75.6118 cents 4: 578.5820 .. 706.8803 cents 14/13, 128.2982 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 915.5530 cents 392/363, 133.0609 cents 117/112, 75.6118 cents 6: 986.4020 .. 1119.4630 cents 392/363, 133.0609 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 2.128568 Largest / Average step : 1.245988 Largest / Smallest step : 2.652171 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 165.79168 cents, oct.: 1160.54173 cents Scale is not proper Step pattern alph. order: ABCBADE Step pattern size order : ABEBACD Scale is a Constant Structure, by a margin of 42.83593 cents Scale diversity : 1.309178 Lumma stability : 0.378330 Lumma impropriety factor : 0.035697 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 10648/10647, 0.1626 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 6, average 703.5697 cents Best major thirds form a closed circle Best minor thirds form a closed circle 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 = 42.8571% Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions : 5 Inversional symmetry on degrees : 6 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 13 Odd number limit : 819 (O: 819 U: 819) Highest odd numerator or denominator: 39 Scale harmonicity : 0.012798 Average absolute harmonicity : 0.229452 Specific harmonicity : 0.077541 Fundamental : 1/924, -9.8517 octaves, 0.2831 Hz. Guide tone : 1716, 10.7448 octaves, 448949.470 Hz. Exponens Consonantiae : 1.585584E+06, 20.59658 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 99.0, average 14.14286 Mersenne's string divisions : 1652490 Sum of van Prooijen's expressibility: 6.42743, average 0.91820 Sum of Tenney's harmonic distance : 12.60865, average 1.80124 Vogel's harmonic complexity : 25.42857 Wille's k value : 544 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 67.26145, average 2.40219 Lattice compactness (without 2's) : 46.53346, average 1.66191 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 8 1 3: -1 .. 1 0.14286 5 2 7: -1 .. 0 -0.42857 3 11: -1 .. 1 0.28571 4 3 13: 0 .. 1 0.14286 1 1 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 18 23 26| Scale is weakly epimorphic with val: <7 10 19 24 27| Scale is weakly epimorphic with val: <7 10 20 22 27| Scale is weakly epimorphic with val: <7 10 20 25 28| Scale is weakly epimorphic with val: <7 10 21 23 28| Scale is weakly epimorphic with val: <7 10 21 26 29| Scale is weakly epimorphic with val: <7 10 22 24 29| Scale is JI-epimorphic with val: <7 11 18 23 25| Scale is JI-epimorphic with val: <7 11 19 24 26| Scale is weakly epimorphic with val: <7 11 20 22 26| Scale is JI-epimorphic with val: <7 11 20 25 27| Scale is weakly epimorphic with val: <7 11 21 23 27| Scale is JI-epimorphic with val: <7 11 21 26 28| Scale is weakly epimorphic with val: <7 11 22 24 28| Scale is weakly epimorphic with val: <7 12 18 24 29| Scale is weakly epimorphic with val: <7 12 21 22 28| Scale is weakly epimorphic with val: <7 12 22 23 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 52.3348 c. M:-90.8915 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 36.3419 c. M: 57.8314 c. Pseudo Pelog, Pelogic-7, Antiionian 12: 1 2 2 2 1 2 2 P M ME S SD: 12.0293 c. M:-19.4630 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 17: 1 3 3 3 1 3 3 N M DE S SD: 5.0575 c. M: 9.9488 c. 29: 2 5 5 5 2 5 5 N M DE S SD: 2.7795 c. M:-5.2081 c. 46: 3 8 8 8 3 8 8 N M DE S SD: 1.8112 c. M:-2.5095 c. 75: 5 13 13 13 5 13 13 N M DE S SD: 1.8612 c. M:-3.5530 c. 118: 8 20 21 20 8 20 21 N T3 SD: 1.8332 c. M: 4.7240 c. 121: 8 21 21 21 8 21 21 N M DE S SD: 1.7794 c. M:-3.1563 c. 132: 9 22 24 22 9 23 23 N S SD: 1.5453 c. M: 2.6289 c. 147: 10 25 26 25 10 25 26 N T3 SD: 1.5044 c. M: 3.4096 c. 149: 10 25 27 25 10 26 26 N S SD: 1.3013 c. M: 2.5678 c. 159: 11 27 28 27 11 27 28 N T3 SD: 1.8390 c. M: 2.4855 c. 161: 11 27 29 27 11 28 28 N S SD: 1.0126 c. M:-1.4505 c. 178: 12 30 32 30 12 31 31 N S SD: 0.7020 c. M: 1.3010 c. 195: 13 33 35 33 13 34 34 N S SD: 0.7150 c. M: 1.3701 c. 207: 14 35 37 35 14 36 36 N S SD: 0.3934 c. M:-0.6224 c. 224: 15 38 40 38 15 39 39 N S SD: 0.2643 c. M: 0.5185 c. 253: 17 43 45 43 17 44 44 N S SD: 0.0942 c. M:-0.1396 c. 477: 32 81 85 81 32 83 83 N S SD: 0.0852 c. M: 0.1703 c. 730: 49 124 130 124 49 127 127 N S SD: 0.0418 c. M:-0.0682 c. 983: 66 167 175 167 66 171 171 N S SD: 0.0374 c. M:-0.0866 c. 1713: 115 291 305 291 115 298 298 N S SD: 0.0369 c. M:-0.0787 c. 1983: 133 337 353 337 133 345 345 N S SD: 0.0365 c. M:-0.0607 c. 2219: 149 377 395 377 149 386 386 N S SD: 0.0402 c. M:-0.0926 c. 2236: 150 380 398 380 150 389 389 N S SD: 0.0319 c. M:-0.0696 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 33.9556 cents 4 x 5 x 6 x 7:8 S SD: 26.0718 cents 5 x 6:7 x 8:9:10 S SD: 19.7783 cents 6 x 7:8:9 x 11:12 SD: 12.1589 cents 7 x 8:9 x 11:12:14 SD: 20.1695 cents 8 x 9:11:12:13:14:16 SD: 19.1423 cents 9:10:11:12 x 14:16:18 S SD: 20.1894 cents 10:11:12:13:15:16:18:20 SD: 15.4528 cents 11:12:13:15 x 17:20:22 SD: 15.9897 cents 12:13:14:16:18:19:21:24 SD: 9.4186 cents 13:14:15:17 x 20:23:26 SD: 13.0358 cents 14:15:17:19:21:22:25:28 SD: 10.3838 cents 15:16:18:20:23:24:27:30 SD: 10.1677 cents 16:17:19:21:24:25:28:32 SD: 6.5569 cents 18:19:21:24:27:28:32:36 SD: 4.0729 cents 28:29:33:37:42:44:50:56 SD: 4.0210 cents 34:36:40:45:51:53:60:68 SD: 3.9591 cents 36:38:42:48:54:57:64:72 SD: 3.7105 cents 38:40:45:51:57:60:67:76 SD: 2.9331 cents 39:41:46:52:59:61:69:78 SD: 2.6051 cents 40:42:47:53:60:63:71:80 SD: 1.9232 cents 44:46:52:59:66:69:78:88 SD: 1.7175 cents 60:63:71:80:90:94:106:120 SD: 1.6095 cents 62:65:73:83:93:97:110:124 SD: 1.5207 cents 66:69:78:88:99:104:117:132 SD: 1.0897 cents 84:88:99:112:126:132:149:168 SD: 0.1509 cents 504:528:594:672:756:792:893:1008 SD: 0.1259 cents 588:616:693:784:882:924:1042:1176 SD: 0.0863 cents