Scala analysis: synpor6
Sixth 81/80&250/243 scale = inverse synpor7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 40/27 680.448711 grave fifth 5: 8/5 813.686286 minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 10/9 182.4037 minor whole tone 3: 10/9 182.4037 minor whole tone 4: 10/9 182.4037 minor whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 9/8 203.9100 major whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 4 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 3 6/5 315.641 cents minor third 2: 1 243/200 337.148 cents acute minor third 2: 2 100/81 364.807 cents grave major third 2: 1 5/4 386.314 cents major third 3: 3 4/3 498.045 cents perfect fourth 3: 3 27/20 519.551 cents acute fourth 3: 1 1000/729 547.211 cents 4: 1 729/500 652.789 cents 4: 3 40/27 680.449 cents grave fifth 4: 3 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 81/50 835.193 cents acute minor sixth 5: 1 400/243 862.852 cents grave major sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 50/27 1066.762 cents grave major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 133.2 315.6 498.0 680.4 813.7 1017.6 1200.0 133.2 : 182.4 364.8 547.2 680.4 884.4 1066.8 1200.0 315.6 : 182.4 364.8 498.0 702.0 884.4 1017.6 1200.0 498.0 : 182.4 315.6 519.6 702.0 835.2 1017.6 1200.0 680.4 : 133.2 337.1 519.6 652.8 835.2 1017.6 1200.0 813.7 : 203.9 386.3 519.6 702.0 884.4 1066.8 1200.0 1017.6: 182.4 315.6 498.0 680.4 862.9 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 203.9100 cents 25/24, 70.6724 cents 27/25, 133.2376 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 498.0450 .. 547.2111 cents 250/243, 49.1661 cents 16/15, 111.7313 cents 4: 652.7889 .. 701.9550 cents 250/243, 49.1661 cents 531441/500000, 105.5777 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1066.7624 cents 25/24, 70.6724 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.286638 Largest / Average step : 1.189475 Largest / Smallest step : 1.530424 Median interval of one step : 10/9, 182.4037 cents, amount: 4 Most common interval of one step : 10/9, 182.4037 cents, amount: 4 Least squares average step : 168.24614 cents, oct.: 1177.72296 cents Scale is strictly proper Step pattern alph. order: ABBBACB Step pattern size order : SMMMSLM Scale is a Constant Structure, by a margin of 105.57773 cents Scale diversity : 1.330270 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.682482 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 4 Most common triad is 0.0 182.404 1017.596 cents, amount: 2 Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 5 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited transpositions with margin 70.6724 cents: 4 Limited inverse transpositions with margin 70.6724 cents: 1 5 -- Rational properties -- Prime limit : 5 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.026178 Average absolute harmonicity : 0.230111 Specific harmonicity : 0.162436 Fundamental : 1/675, -9.3987 octaves, 0.3876 Hz. Guide tone : 1080, 10.0768 octaves, 282555.611 Hz. Exponens Consonantiae : 7.290000E+05, 19.47556 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 83.5, average 11.92857 Mersenne's string divisions : 804804 Sum of van Prooijen's expressibility: 5.69203, average 0.81315 Sum of Tenney's harmonic distance : 11.97533, average 1.71076 Vogel's harmonic complexity : 18.42857 Wille's k value : 607 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 86.09573, average 3.07485 Lattice compactness (without 2's) : 69.34060, average 2.47645 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.42857 10 1 3: -3 .. 3 0.28571 10 1 5: -2 .. 1 -0.57143 6 5 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 25.3537 c. M:-43.4566 c. Lebeng 12: 1 2 2 2 1 2 2 P M ME S SD: 17.8582 c. M: 33.2376 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 16: 2 2 3 2 2 3 2 SP M ME S SD: 18.7460 c. M:-32.4037 c. Antimixolydian 18: 2 3 2 3 2 3 3 SP M ME S SD: 16.8375 c. M: 31.3783 c. 19: 2 3 3 3 2 3 3 SP M ME S SD: 7.6386 c. M:-14.2881 c. Nineteen-tone Phrygian 27: 3 4 4 4 3 5 4 SP D3 SD: 8.4771 c. M: 13.7820 c. 34: 4 5 5 5 4 6 5 SP D3 SD: 5.5882 c. M: 9.8605 c. 46: 5 7 7 7 5 8 7 SP SD: 2.6743 c. M: 4.9906 c. 53: 6 8 8 8 6 9 8 SP SD: 1.3973 c. M:-2.6115 c. 99: 11 15 15 15 11 17 15 SP SD: 0.9969 c. M: 1.6608 c. 118: 13 18 18 18 13 20 18 SP SD: 0.6030 c. M: 1.0342 c. 171: 19 26 26 26 19 29 26 SP SD: 0.1927 c. M:-0.3488 c. 388: 43 59 59 59 43 66 59 SP SD: 0.1654 c. M: 0.2842 c. 441: 49 67 67 67 49 75 67 SP SD: 0.0945 c. M: 0.1766 c. 559: 62 85 85 85 62 95 85 SP SD: 0.0772 c. M: 0.1428 c. 612: 68 93 93 93 68 104 93 SP SD: 0.0515 c. M:-0.0958 c. 1000: 111 152 152 152 111 170 152 SP SD: 0.0462 c. M: 0.0863 c. 1171: 130 178 178 178 130 199 178 SP SD: 0.0129 c. M: 0.0228 c. 1783: 198 271 271 271 198 303 271 SP SD: 0.0134 c. M: 0.0225 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: 10.7531 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 22.1298 cents 5 x 6:7 x 8:9:10 S SD: 16.8934 cents 6 x 7:8:9:10:11:12 S SD: 15.6745 cents 7 x 8:9:10:11:13:14 SD: 22.9512 cents 8:9:10:11:12:13:14:16 S SD: 18.2883 cents 9:10:11:12:13:14:16:18 S SD: 12.9273 cents 10:11:12:13:15:16:18:20 SD: 8.3211 cents 14:15:17:19:21:22:25:28 SD: 8.0495 cents 15:16:18:20:22:24:27:30 S SD: 3.9519 cents 25:27:30:33:37:40:45:50 SD: 2.4979 cents 35:38:42:47:52:56:63:70 SD: 2.3021 cents 40:43:48:53:59:64:72:80 SD: 2.2130 cents 50:54:60:67:74:80:90:100 SD: 1.2581 cents 60:65:72:80:89:96:108:120 SD: 0.8224 cents 75:81:90:100:111:120:135:150 SD: 0.2474 cents 210:227:252:280:311:336:378:420 SD: 0.2352 cents 285:308:342:380:422:456:513:570 SD: 0.2068 cents 360:389:432:480:533:576:648:720 SD: 0.2002 cents 375:405:450:500:556:600:675:750 SD: 0.1978 cents 390:421:468:520:578:624:702:780 SD: 0.1511 cents 450:486:540:600:667:720:810:900 SD: 0.1236 cents 465:502:558:620:689:744:837:930 SD: 0.1063 cents 525:567:630:700:778:840:945:1050 SD: 0.0707 cents 600:648:720:800:889:960:1080:1200 SD: 0.0309 cents