Scala analysis: semipor3
Third 16/15&250/243 = 648/625&250/243 scale = inverse semipor4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 25/18 568.717426 classic augmented fourth 5: 3/2 701.955001 perfect fifth 6: 5/3 884.358713 major sixth, BP sixth 7: 9/5 1017.596288 just minor seventh, BP seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 10/9 182.4037 minor whole tone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 10/9 182.4037 minor whole tone 7: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 8: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 4 10/9 182.404 cents minor whole tone 2: 1 9/8 203.910 cents major whole tone 2: 1 125/108 253.076 cents semi-augmented whole tone 2: 5 6/5 315.641 cents minor third 2: 1 100/81 364.807 cents grave major third 3: 3 5/4 386.314 cents major third 3: 1 162/125 448.879 cents 3: 4 4/3 498.045 cents perfect fourth 4: 2 27/20 519.551 cents acute fourth 4: 2 25/18 568.717 cents classic augmented fourth 4: 2 36/25 631.283 cents classic diminished fifth 4: 2 40/27 680.449 cents grave fifth 5: 4 3/2 701.955 cents perfect fifth 5: 1 125/81 751.121 cents 5: 3 8/5 813.686 cents minor sixth 6: 1 81/50 835.193 cents acute minor sixth 6: 5 5/3 884.359 cents major sixth, BP sixth 6: 1 216/125 946.924 cents semi-augmented sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 7: 4 9/5 1017.596 cents just minor seventh, BP seventh 7: 3 50/27 1066.762 cents grave major seventh 7: 1 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.42857 = 24/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 182.4 315.6 498.0 568.7 702.0 884.4 1017.6 1200.0 182.4 : 133.2 315.6 386.3 519.6 702.0 835.2 1017.6 1200.0 315.6 : 182.4 253.1 386.3 568.7 702.0 884.4 1066.8 1200.0 498.0 : 70.7 203.9 386.3 519.6 702.0 884.4 1017.6 1200.0 568.7 : 133.2 315.6 448.9 631.3 813.7 946.9 1129.3 1200.0 702.0 : 182.4 315.6 498.0 680.4 813.7 996.1 1066.8 1200.0 884.4 : 133.2 315.6 498.0 631.3 813.7 884.4 1017.6 1200.0 1017.6: 182.4 364.8 498.0 680.4 751.1 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 182.4037 cents 16/15, 111.7313 cents 25/24, 70.6724 cents 2: 203.9100 .. 364.8074 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 3: 386.3137 .. 498.0450 cents 16/15, 111.7313 cents 81/80, 21.5063 cents 4: 519.5513 .. 680.4487 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 5: 701.9550 .. 813.6863 cents 16/15, 111.7313 cents 81/80, 21.5063 cents 6: 835.1926 .. 996.0900 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 7: 1017.5963 .. 1129.3276 cents 16/15, 111.7313 cents 81/80, 21.5063 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 2.122469 Largest / Average step : 1.216025 Largest / Smallest step : 2.580974 Median interval of one step : 157.82064 cents, amount: 0 Most common interval of one step : 10/9, 182.4037 cents, amount: 4 Least squares average step : 147.65584 cents, oct.: 1181.24676 cents Scale is strictly proper Step pattern alph. order: ABACBABA Step pattern size order : LMLSMLML Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.494750 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.225319 Rothenberg efficiency : 0.444643 redundancy: 0.555357 Efficiency x scale size : 3.557143 Number of different interval sizes : 24 = 3.42857 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.42857 = 24/7 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 5 Most common triad is 0.0 315.641 884.359 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale contains two identical disjunct tetrachords Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 3 5 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 87.5000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 -- Rational properties -- Prime limit : 5 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.030426 Average absolute harmonicity : 0.239083 Specific harmonicity : 0.176855 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 900, 9.8138 octaves, 235463.009 Hz. Exponens Consonantiae : 8.100000E+04, 16.30563 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 55.0, average 6.87500 Mersenne's string divisions : 7549080 Sum of van Prooijen's expressibility: 5.65861, average 0.70733 Sum of Tenney's harmonic distance : 11.07224, average 1.38403 Vogel's harmonic complexity : 12.87500 Wille's k value : 67 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 93.07926, average 2.58554 Lattice compactness (without 2's) : 75.89324, average 2.10815 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.37500 7 1 3: -2 .. 2 -0.25000 10 2 5: -1 .. 2 0.25000 6 5 Average exponent except 2's : 0 / 8 = 0.00000 Average absolute exponent except 2's: 16 / 8 = 2.00000 Scale is JI-epimorphic with val: <8 13 19| = patent
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 31.9854 c. M:-48.0450 c. 12: 2 1 2 1 1 2 1 2 P D3 I SD: 16.1818 c. M:-31.2826 c. Blues scale II 15: 2 2 2 1 2 2 2 2 SP M ME SD: 14.8706 c. M: 22.4037 c. 19: 3 2 3 1 2 3 2 3 P SD: 5.0535 c. M:-7.2182 c. 34: 5 4 5 2 4 5 4 5 SP SD: 3.9590 c. M: 5.9331 c. 46: 7 5 7 3 5 7 5 7 SP SD: 2.5502 c. M:-5.1956 c. 53: 8 6 8 3 6 8 6 8 SP SD: 1.3236 c. M: 2.6797 c. 72: 11 8 11 4 8 11 8 11 SP SD: 1.4000 c. M: 2.0508 c. 99: 15 11 15 6 11 15 11 15 SP SD: 0.7448 c. M:-1.0753 c. 118: 18 13 18 7 13 18 13 18 SP SD: 0.4837 c. M:-0.7741 c. 171: 26 19 26 10 19 26 19 26 SP SD: 0.1650 c. M: 0.2964 c. 270: 41 30 41 16 30 41 30 41 SP SD: 0.1778 c. M:-0.2672 c. 388: 59 43 59 23 43 59 43 59 SP SD: 0.1664 c. M:-0.3547 c. 441: 67 49 67 26 49 67 49 67 SP SD: 0.0626 c. M: 0.0908 c. 612: 93 68 93 36 68 93 68 93 SP SD: 0.0466 c. M: 0.0900 c. 730: 111 81 111 43 81 111 81 111 SP SD: 0.0421 c. M: 0.0620 c. 1000: 152 111 152 59 111 152 111 152 SP SD: 0.0423 c. M:-0.0826 c. 1171: 178 130 178 69 130 178 130 178 SP SD: 0.0128 c. M:-0.0272 c. 1342: 204 149 204 79 149 204 149 204 SP SD: 0.0119 c. M:-0.0176 c. 1783: 271 198 271 105 198 271 198 271 SP SD: 0.0100 c. M: 0.0145 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x x 5 x 6 S SD: 0.0000 cents 4 x 5 x x 6 x 7:8 S SD: 21.4668 cents 5 x 6 x 7 x 8:9:10 S SD: 14.4012 cents 6 x 7:8 x 9:10:11:12 S SD: 9.7006 cents 7:8 x 9:10:11:12:13:14 S SD: 20.4607 cents 8:9:10 x 11:12:13:14:16 S SD: 14.3282 cents 9:10:11:12 x 14:15:16:18 S SD: 10.5325 cents 10:11:12:13:14:15:17:18:20 SD: 7.4891 cents 11:12:13 x 15:17:18:20:22 SD: 11.6932 cents 12:13:14:16:17:18:20:22:24 S SD: 10.0655 cents 14:16:17:19 x 21:23:25:28 SD: 9.6342 cents 15:17:18:20:21:23:25:27:30 SD: 6.6303 cents 16:18:19:21:22:24:27:29:32 SD: 6.1787 cents 18:20:22:24:25:27:30:32:36 SD: 4.7952 cents 20:22:24:27:28:30:33:36:40 S SD: 4.4341 cents 24:27:29:32:33:36:40:43:48 SD: 3.8998 cents 26:29:31:35:36:39:43:47:52 SD: 3.3173 cents 30:33:36:40:42:45:50:54:60 SD: 2.7756 cents 36:40:43:48:50:54:60:65:72 SD: 1.2055 cents 54:60:65:72:75:81:90:97:108 SD: 0.8021 cents 90:100:108:120:125:135:150:162:180 SD: 0.0000 cents