Scala analysis: synpor2
Second 81/80&250/243 scale = inverse synpor3
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: 81/50 835.192576 acute 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: 2187/2000 154.7439 Gorgo limma 6: 10/9 182.4037 minor whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 1 2187/2000 154.744 cents Gorgo limma 1: 5 10/9 182.404 cents minor whole tone 2: 2 6/5 315.641 cents minor third 2: 2 243/200 337.148 cents acute minor third 2: 3 100/81 364.807 cents grave 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: 3 81/50 835.193 cents acute minor sixth 5: 2 400/243 862.852 cents grave major sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 6: 5 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 4000/2187 1045.256 cents 6: 1 50/27 1066.762 cents grave 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 6 7 0.0 : 133.2 315.6 498.0 680.4 835.2 1017.6 1200.0 133.2 : 182.4 364.8 547.2 702.0 884.4 1066.8 1200.0 315.6 : 182.4 364.8 519.6 702.0 884.4 1017.6 1200.0 498.0 : 182.4 337.1 519.6 702.0 835.2 1017.6 1200.0 680.4 : 154.7 337.1 519.6 652.8 835.2 1017.6 1200.0 835.2 : 182.4 364.8 498.0 680.4 862.9 1045.3 1200.0 1017.6: 182.4 315.6 498.0 680.4 862.9 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 182.4037 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 2: 315.6413 .. 364.8074 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 3: 498.0450 .. 547.2111 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 4: 652.7889 .. 701.9550 cents 250/243, 49.1661 cents 531441/500000, 105.5777 cents 5: 835.1926 .. 884.3587 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 6: 1017.5963 .. 1066.7624 cents 250/243, 49.1661 cents 27/25, 133.2376 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 : 10/9, 182.4037 cents Average / Smallest step : 1.286638 Largest / Average step : 1.064022 Largest / Smallest step : 1.369011 Median interval of one step : 10/9, 182.4037 cents, amount: 5 Most common interval of one step : 10/9, 182.4037 cents, amount: 5 Least squares average step : 169.01422 cents, oct.: 1183.09953 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABBBCBB Step pattern size order : SLLLMLL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 105.57773 cents Scale diversity : 1.255905 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.754169 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 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 : 81/80, 21.5063 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 519.551 1017.596 cents Most common triad is 0.0 182.404 1017.596 cents, amount: 3 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 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited transpositions with margin 49.1661 cents: 4 Limited inverse transpositions with margin 49.1661 cents: 1 5 -- Rational properties -- Prime limit : 5 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.023885 Average absolute harmonicity : 0.220753 Specific harmonicity : 0.136557 Fundamental : 1/1350, -10.3987 octaves, 0.1938 Hz. Guide tone : 3240, 11.6618 octaves, 847666.832 Hz. Exponens Consonantiae : 4.374000E+06, 22.06052 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 142.5, average 20.35714 Mersenne's string divisions : 105429324 Sum of van Prooijen's expressibility: 6.90155, average 0.98594 Sum of Tenney's harmonic distance : 13.98073, average 1.99725 Vogel's harmonic complexity : 19.85714 Wille's k value : 1093 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 10 Triangular lattice diameter : 7 Lattice compactness : 97.01292, average 3.46475 Lattice compactness (without 2's) : 84.50211, average 3.01793 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.85714 8 1 3: -3 .. 4 0.85714 14 1 5: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 21 / 7 = 3.00000 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: 21.0204 c. M:-38.1910 c. Lebeng 12: 1 2 2 2 1 2 2 P M ME S SD: 21.6584 c. M: 35.1926 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: 18.6539 c. M:-32.4037 c. Antimixolydian 19: 2 3 3 3 2 3 3 SP M ME S SD: 8.8971 c. M:-14.2881 c. Nineteen-tone Phrygian 26: 3 4 4 4 3 4 4 SP M ME S SD: 6.9769 c. M:-11.8590 c. 39: 4 6 6 6 5 6 6 SP T3 SD: 5.8092 c. M: 10.1607 c. 46: 5 7 7 7 6 7 7 SP T3 SD: 1.9021 c. M: 2.8028 c. 53: 6 8 8 8 7 8 8 SP T3 SD: 1.6104 c. M:-2.6115 c. 72: 8 11 11 11 9 11 11 SP T3 SD: 1.5823 c. M:-2.8846 c. 99: 11 15 15 15 13 15 15 SP T3 SD: 0.9164 c. M: 1.6608 c. 118: 13 18 18 18 15 18 18 SP T3 SD: 0.7750 c. M: 1.2943 c. 125: 14 19 19 19 16 19 19 SP T3 SD: 0.8745 c. M:-1.1624 c. 164: 18 25 25 25 21 25 25 SP T3 SD: 0.8418 c. M: 1.5303 c. 171: 19 26 26 26 22 26 26 SP T3 SD: 0.1460 c. M:-0.2530 c. 388: 43 59 59 59 50 59 59 SP T3 SD: 0.1365 c. M: 0.2479 c. 441: 49 67 67 67 57 67 67 SP T3 SD: 0.1127 c. M:-0.1816 c. 559: 62 85 85 85 72 85 85 SP T3 SD: 0.0849 c. M: 0.1428 c. 612: 68 93 93 93 79 93 93 SP T3 SD: 0.0625 c. M:-0.1015 c. 783: 87 119 119 119 101 119 119 SP T3 SD: 0.0526 c. M:-0.0958 c. 1000: 111 152 152 152 129 152 152 SP T3 SD: 0.0329 c. M: 0.0487 c. 1171: 130 178 178 178 151 178 178 SP T3 SD: 0.0101 c. M: 0.0181 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: 16.3887 cents 4 x 5 x 6 x 7:8 S SD: 22.1298 cents 5 x 6:7 x 8:9:10 S SD: 17.4324 cents 6 x 7:8:9:10:11:12 S SD: 13.1946 cents 7 x 8:9:10:11:13:14 SD: 24.0183 cents 8:9:10:11:12:13:14:16 S SD: 17.8981 cents 9:10:11:12:13:15:16:18 SD: 12.9579 cents 10:11:12:13:15:16:18:20 SD: 8.8702 cents 14:15:17:19:21:23:25:28 SD: 7.5460 cents 15:16:18:20:22:24:27:30 S SD: 5.0057 cents 21:23:25:28:31:34:38:42 SD: 4.2893 cents 24:26:29:32:36:39:43:48 SD: 3.8532 cents 29:31:35:39:43:47:52:58 SD: 3.7315 cents 34:37:41:45:50:55:61:68 SD: 3.5270 cents 35:38:42:47:52:57:63:70 SD: 2.6463 cents 36:39:43:48:53:58:65:72 SD: 2.5952 cents 39:42:47:52:58:63:70:78 SD: 1.8728 cents 50:54:60:67:74:81:90:100 SD: 1.2581 cents 60:65:72:80:89:97:108:120 SD: 0.9674 cents 90:97:108:120:133:146:162:180 SD: 0.8705 cents 100:108:120:133:148:162:180:200 SD: 0.6667 cents 126:136:151:168:187:204:227:252 SD: 0.6259 cents 135:146:162:180:200:219:243:270 SD: 0.4795 cents 150:162:180:200:222:243:270:300 SD: 0.2474 cents 276:298:331:368:409:447:497:552 SD: 0.2134 cents 324:350:389:432:480:525:583:648 SD: 0.1725 cents 390:421:468:520:578:632:702:780 SD: 0.1702 cents 411:444:493:548:609:666:740:822 SD: 0.1597 cents 426:460:511:568:631:690:767:852 SD: 0.1383 cents 450:486:540:600:667:729:810:900 SD: 0.1236 cents 540:583:648:720:800:875:972:1080 SD: 0.1019 cents 600:648:720:800:889:972:1080:1200 SD: 0.0309 cents