Scala analysis: semipor6
Sixth 16/15&250/243 = 648/625&250/243 scale = inverse semipor5
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: 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: 10/9 182.4037 minor whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 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 : 182.4 315.6 386.3 568.7 702.0 884.4 1017.6 1200.0 182.4 : 133.2 203.9 386.3 519.6 702.0 835.2 1017.6 1200.0 315.6 : 70.7 253.1 386.3 568.7 702.0 884.4 1066.8 1200.0 386.3 : 182.4 315.6 498.0 631.3 813.7 996.1 1129.3 1200.0 568.7 : 133.2 315.6 448.9 631.3 813.7 946.9 1017.6 1200.0 702.0 : 182.4 315.6 498.0 680.4 813.7 884.4 1066.8 1200.0 884.4 : 133.2 315.6 498.0 631.3 702.0 884.4 1017.6 1200.0 1017.6: 182.4 364.8 498.0 568.7 751.1 884.4 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 : 146.01274 cents, oct.: 1168.10190 cents Scale is strictly proper Step pattern alph. order: ABCABABA Step pattern size order : LMSLMLML 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 Scale contains a complete diamond : 3 5 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 62.5000% 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 : 0.227179 Specific harmonicity : 0.173274 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 450, 8.8138 octaves, 117731.504 Hz. Exponens Consonantiae : 8.100000E+04, 16.30563 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 56.0, average 7.00000 Mersenne's string divisions : 22647240 Sum of van Prooijen's expressibility: 5.88046, average 0.73506 Sum of Tenney's harmonic distance : 11.29409, average 1.41176 Vogel's harmonic complexity : 14.37500 Wille's k value : 112 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 94.54977, average 2.62638 Lattice compactness (without 2's) : 75.55939, average 2.09887 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.12500 7 1 3: -2 .. 2 -0.12500 9 1 5: -1 .. 2 0.37500 7 6 Average exponent except 2's : 2 / 8 = 0.25000 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: 35.2352 c. M:-63.6863 c. 11: 1 2 0 2 1 2 1 2 P D3 SD: 40.6203 c. M: 73.3128 c. 12: 2 1 1 2 1 2 1 2 P D3 SD: 16.8756 c. M:-31.2826 c. 15: 2 2 1 2 2 2 2 2 SP M ME SD: 14.2775 c. M: 22.4037 c. Pentadecaphonic "Major", Jones's Porcupine-8 19: 3 2 1 3 2 3 2 3 P SD: 5.0802 c. M: 7.3663 c. 34: 5 4 2 5 4 5 4 5 SP SD: 3.7693 c. M: 5.9331 c. 46: 7 5 3 7 5 7 5 7 SP SD: 2.9834 c. M:-5.1956 c. 53: 8 6 3 8 6 8 6 8 SP SD: 1.4139 c. M: 2.6797 c. 99: 15 11 6 15 11 15 11 15 SP SD: 0.8464 c. M:-1.5651 c. 118: 18 13 7 18 13 18 13 18 SP SD: 0.4770 c. M:-0.7741 c. 171: 26 19 10 26 19 26 19 26 SP SD: 0.1934 c. M: 0.3488 c. 289: 44 32 17 44 32 44 32 44 SP SD: 0.1866 c. M: 0.2952 c. 441: 67 49 26 67 49 67 49 67 SP SD: 0.0618 c. M: 0.0908 c. 612: 93 68 36 93 68 93 68 93 SP SD: 0.0486 c. M: 0.0900 c. 730: 111 81 43 111 81 111 81 111 SP SD: 0.0402 c. M: 0.0620 c. 1171: 178 130 69 178 130 178 130 178 SP SD: 0.0148 c. M:-0.0272 c. 1342: 204 149 79 204 149 204 149 204 SP SD: 0.0134 c. M: 0.0246 c. 1783: 271 198 105 271 198 271 198 271 SP SD: 0.0096 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 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 6 x 7 x 8:9:10 S SD: 14.4012 cents 6 x 7 x 8:9:10:11:12 S SD: 15.2591 cents 7:8 x 9:10:11:12:13:14 S SD: 19.6541 cents 8:9 x 10:11:12:13:14:16 S SD: 10.1669 cents 9:10:11 x x 14:15:16:18 SD: 12.2879 cents 10:11:12:13:14:15:17:18:20 SD: 9.9049 cents 13:14 x 16:18:20:22:23:26 SD: 12.1110 cents 14:16:17:18:19:21:23:25:28 SD: 10.8902 cents 15:17:18:19:21:23:25:27:30 SD: 7.2233 cents 16:18:19:20:22:24:27:29:32 SD: 5.1538 cents 20:22:24:25:28:30:33:36:40 SD: 3.5262 cents 34:38:41:43:47:51:57:61:68 SD: 3.5060 cents 35:39:42:44:49:53:58:63:70 SD: 3.2589 cents 36:40:43:45:50:54:60:65:72 SD: 1.2055 cents 64:71:77:80:89:96:107:115:128 SD: 1.0496 cents 80:89:96:100:111:120:133:144:160 SD: 0.6430 cents 100:111:120:125:139:150:167:180:200 SD: 0.5136 cents 136:151:163:170:189:204:227:245:272 SD: 0.4943 cents 144:160:173:180:200:216:240:259:288 SD: 0.3009 cents 180:200:216:225:250:270:300:324:360 SD: 0.0000 cents