Scala analysis: semipor5
Fifth 16/15&250/243 = 648/625&250/243 scale = inverse semipor6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 9/8 203.910002 major whole tone 3: 5/4 386.313714 major third 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: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 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: 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: 1 27/20 519.551 cents acute fourth 4: 3 25/18 568.717 cents classic augmented fourth 4: 3 36/25 631.283 cents classic diminished fifth 4: 1 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 : 70.7 203.9 386.3 568.7 702.0 884.4 1017.6 1200.0 70.7 : 133.2 315.6 498.0 631.3 813.7 946.9 1129.3 1200.0 203.9 : 182.4 364.8 498.0 680.4 813.7 996.1 1066.8 1200.0 386.3 : 182.4 315.6 498.0 631.3 813.7 884.4 1017.6 1200.0 568.7 : 133.2 315.6 448.9 631.3 702.0 835.2 1017.6 1200.0 702.0 : 182.4 315.6 498.0 568.7 702.0 884.4 1066.8 1200.0 884.4 : 133.2 315.6 386.3 519.6 702.0 884.4 1017.6 1200.0 1017.6: 182.4 253.1 386.3 568.7 751.1 884.4 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 : 144.36963 cents, oct.: 1154.95704 cents Scale is strictly proper Step pattern alph. order: ABCCBCBC Step pattern size order : SMLLMLML Scale is sum-free (all different intervals) 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 : 0.437946 redundancy: 0.562054 Efficiency x scale size : 3.503571 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: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 12.5000% 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 -- Rational properties -- Prime limit : 5 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.029528 Average absolute harmonicity : 0.226714 Specific harmonicity : 0.167540 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 450, 8.8138 octaves, 117731.504 Hz. Exponens Consonantiae : 1.620000E+05, 17.30563 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 74.0, average 9.25000 Mersenne's string divisions : 12894840 Sum of van Prooijen's expressibility: 6.57943, average 0.82243 Sum of Tenney's harmonic distance : 12.49821, average 1.56228 Vogel's harmonic complexity : 16.37500 Wille's k value : 202 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 105.35381, average 2.92649 Lattice compactness (without 2's) : 76.14517, average 2.11514 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.12500 11 1 3: -2 .. 2 0.12500 9 2 5: -1 .. 2 0.62500 7 5 Average exponent except 2's : 6 / 8 = 0.75000 Average absolute exponent except 2's: 16 / 8 = 2.00000 Scale is JI-epimorphic with val: <8 13 19| = patent
FIT/MODE
8: 0 1 1 1 1 1 1 2 N T3 SD: 94.6842 c. M: 134.3587 c. 9: 0 1 1 2 1 1 1 2 N D3 SD: 71.5935 c. M: 119.6470 c. 10: 0 1 2 1 1 2 1 2 N T3 SD: 67.3410 c. M: 101.9550 c. 11: 0 2 1 2 1 2 1 2 P D3 SD: 40.1377 c. M: 70.6724 c. 12: 1 1 2 2 1 2 1 2 P D3 SD: 18.0257 c. M:-31.2826 c. 15: 1 2 2 2 2 2 2 2 SP M ME SD: 17.6754 c. M:-36.0900 c. 19: 1 2 3 3 2 3 2 3 P SD: 7.2572 c. M: 14.4363 c. 31: 2 3 5 5 3 5 3 5 P SD: 7.7651 c. M:-11.9277 c. 34: 2 4 5 5 4 5 4 5 SP SD: 4.1252 c. M:-7.8547 c. 46: 3 5 7 7 5 7 5 7 SP SD: 4.2559 c. M:-7.5884 c. 53: 3 6 8 8 6 8 6 8 SP SD: 1.5870 c. M: 2.7479 c. 99: 6 11 15 15 11 15 11 15 SP SD: 1.3227 c. M:-2.1506 c. 118: 7 13 18 18 13 18 13 18 SP SD: 0.4725 c. M:-0.7741 c. 171: 10 19 26 26 19 26 19 26 SP SD: 0.2921 c. M: 0.4970 c. 289: 17 32 44 44 32 44 32 44 SP SD: 0.2224 c. M: 0.4498 c. 323: 19 36 49 49 36 49 36 49 SP SD: 0.2439 c. M:-0.4244 c. 441: 26 49 67 67 49 67 49 67 SP SD: 0.0848 c. M:-0.1716 c. 559: 33 62 85 85 62 85 62 85 SP SD: 0.0948 c. M:-0.1684 c. 612: 36 68 93 93 68 93 68 93 SP SD: 0.0518 c. M: 0.0900 c. 730: 43 81 111 111 81 111 81 111 SP SD: 0.0421 c. M: 0.0744 c. 1171: 69 130 178 178 130 178 130 178 SP SD: 0.0200 c. M:-0.0364 c. 1342: 79 149 204 204 149 204 149 204 SP SD: 0.0209 c. M: 0.0352 c. 1783: 105 198 271 271 198 271 198 271 SP SD: 0.0098 c. M:-0.0160 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 x 4 x 5 x 6 S SD: 23.5575 cents 4 x x 5 x 6 x 7:8 S SD: 12.1926 cents 5 x x 6:7 x 8:9:10 S SD: 20.1787 cents 6 x 7 x 8:9:10:11:12 S SD: 16.6398 cents 7 x 8:9:10:11:12:13:14 S SD: 18.7859 cents 8 x 9:10:11:12:13:14:16 S SD: 9.6916 cents 9 x 10:11 x 14:15:16:18 SD: 13.3362 cents 10 x 11:13:14:15:17:18:20 SD: 12.3633 cents 11 x 12:14:15:17:18:20:22 SD: 13.4036 cents 12 x 14:15:17:18:20:22:24 SD: 11.2018 cents 14:15:16:18:19:21:23:25:28 SD: 11.1199 cents 15:16:17:19:21:23:25:27:30 SD: 7.9186 cents 16:17:18:20:22:24:27:29:32 SD: 5.7065 cents 21:22:24:26:29:32:35:38:42 SD: 5.6462 cents 23:24:26:29:32:35:38:41:46 SD: 4.7501 cents 24:25:27:30:33:36:40:43:48 SD: 2.3956 cents 48:50:54:60:67:72:80:86:96 SD: 1.4742 cents 64:67:72:80:89:96:107:115:128 SD: 1.3547 cents 72:75:81:90:100:108:120:130:144 SD: 0.6669 cents 96:100:108:120:133:144:160:173:192 SD: 0.5967 cents 120:125:135:150:167:180:200:216:240 SD: 0.4324 cents 144:150:162:180:200:216:240:259:288 SD: 0.1670 cents 216:225:243:270:300:324:360:389:432 SD: 0.1113 cents 360:375:405:450:500:540:600:648:720 SD: 0.0000 cents