Scala analysis: semipor8
Eigth 16/15&250/243 scale = 648/625&250/243 inverse semipor7
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: 9/8 203.910002 major whole tone 3: 5/4 386.313714 major third 4: 27/20 519.551289 acute 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: 81/80 21.5063 syntonic comma, Didymus comma 3: 10/9 182.4037 minor whole tone 4: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.4037 minor whole tone 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 81/80 21.506 cents syntonic comma, Didymus comma 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 5 10/9 182.404 cents minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 4 6/5 315.641 cents minor third 2: 2 100/81 364.807 cents grave major third 3: 1 243/200 337.148 cents acute minor third 3: 2 5/4 386.314 cents major third 3: 5 4/3 498.045 cents perfect fourth 4: 3 27/20 519.551 cents acute fourth 4: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 3 40/27 680.449 cents grave fifth 5: 5 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 400/243 862.852 cents grave major sixth 6: 2 81/50 835.193 cents acute minor sixth 6: 4 5/3 884.359 cents major sixth, BP sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 7: 5 9/5 1017.596 cents just minor seventh, BP seventh 7: 2 50/27 1066.762 cents grave major seventh 7: 1 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.14286 = 22/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 182.4 203.9 386.3 519.6 702.0 884.4 1017.6 1200.0 182.4 : 21.5 203.9 337.1 519.6 702.0 835.2 1017.6 1200.0 203.9 : 182.4 315.6 498.0 680.4 813.7 996.1 1178.5 1200.0 386.3 : 133.2 315.6 498.0 631.3 813.7 996.1 1017.6 1200.0 519.6 : 182.4 364.8 498.0 680.4 862.9 884.4 1066.8 1200.0 702.0 : 182.4 315.6 498.0 680.4 702.0 884.4 1017.6 1200.0 884.4 : 133.2 315.6 498.0 519.6 702.0 835.2 1017.6 1200.0 1017.6: 182.4 364.8 386.3 568.7 702.0 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 182.4037 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 2: 203.9100 .. 364.8074 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 3: 337.1476 .. 498.0450 cents 800/729, 160.8974 cents 19683/20000,-27.6598 cents 4: 519.5513 .. 680.4487 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 5: 701.9550 .. 862.8524 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 6: 835.1926 .. 996.0900 cents 800/729, 160.8974 cents 19683/20000,-27.6598 cents 7: 1017.5963 .. 1178.4937 cents 800/729, 160.8974 cents 81/80, 21.5063 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 6.974704 Largest / Average step : 1.216025 Largest / Smallest step : 8.481412 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 : 143.95329 cents, oct.: 1151.62633 cents Scale is not proper Step pattern alph. order: ABACAACA Step pattern size order : LSLMLLML Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.309147 Lumma stability : 0.107531 Lumma impropriety factor : 0.046100 Rothenberg efficiency : 0.478125 redundancy: 0.521875 Efficiency x scale size : 3.825000 Number of different interval sizes : 22 = 3.14286 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.14286 = 22/7 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Most common triad is 0.0 701.955 1017.596 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 5 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 37.5000% 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 : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.033186 Average absolute harmonicity : 0.230850 Specific harmonicity : 0.181560 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 270, 8.0768 octaves, 70638.903 Hz. Exponens Consonantiae : 9.720000E+04, 16.56867 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 61.0, average 7.62500 Mersenne's string divisions : 38256120 Sum of van Prooijen's expressibility: 6.16915, average 0.77114 Sum of Tenney's harmonic distance : 11.75348, average 1.46919 Vogel's harmonic complexity : 15.75000 Wille's k value : 202 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 106.34541, average 2.95404 Lattice compactness (without 2's) : 78.86473, average 2.19069 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.75000 10 1 3: -2 .. 3 0.62500 11 2 5: -1 .. 1 0.12500 5 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: 1 0 1 1 1 1 1 2 N T3 SD: 85.5276 c. M: 134.3587 c. 9: 1 0 1 1 2 1 1 2 N SD: 80.2019 c. M: 119.6470 c. 10: 1 1 1 1 2 1 1 2 P D3 S SD: 40.4105 c. M: 62.4037 c. 12: 2 0 2 1 2 2 1 2 N T3 SD: 13.4749 c. M: 19.5513 c. 19: 3 0 3 2 3 3 2 3 N SD: 8.7957 c. M: 14.4363 c. 33: 5 1 5 3 5 5 4 5 N SD: 9.7366 c. M:-14.2718 c. 34: 5 1 5 4 5 5 4 5 P SD: 5.6177 c. M:-9.8605 c. 41: 6 1 6 5 6 6 5 6 P SD: 5.2466 c. M:-7.2780 c. 46: 7 1 7 5 7 7 5 7 N SD: 2.8538 c. M:-4.9906 c. 53: 8 1 8 6 8 8 6 8 N SD: 1.0298 c. M: 1.4081 c. 99: 15 2 15 11 15 15 11 15 N SD: 1.2204 c. M:-2.1506 c. 118: 18 2 18 13 18 18 13 18 N SD: 0.5202 c. M: 0.9072 c. 171: 26 3 26 19 26 26 19 26 N SD: 0.2276 c. M: 0.4012 c. 388: 59 7 59 43 59 59 43 59 N SD: 0.1502 c. M:-0.2842 c. 441: 67 8 67 49 67 67 49 67 N SD: 0.1067 c. M:-0.1766 c. 559: 85 10 85 62 85 85 62 85 N SD: 0.0573 c. M:-0.0906 c. 612: 93 11 93 68 93 93 68 93 N SD: 0.0389 c. M:-0.0566 c. 1171: 178 21 178 130 178 178 130 178 N SD: 0.0122 c. M:-0.0228 c. 1783: 271 32 271 198 271 271 198 271 N SD: 0.0127 c. M:-0.0225 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: 7.1688 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: 23.6248 cents 6 x 7 x 8:9:10:11:12 S SD: 12.2879 cents 7 x 8:9 x 11:12:13:14 SD: 20.3538 cents 8 x 9:10:11:12:13:14:16 S SD: 10.4088 cents 9:10 x 11:12:14:15:16:18 S SD: 11.4310 cents 10:11 x x 14:15:17:18:20 SD: 12.2951 cents 11:12 x 14:15:17:18:20:22 SD: 11.3100 cents 12:13:14:15:16:18:20:22:24 S SD: 10.7215 cents 14 x 16:18:19:21:23:25:28 SD: 9.0533 cents 15 x 17:19:20:23:25:27:30 SD: 7.2835 cents 16 x 18:20:22:24:27:29:32 SD: 5.7413 cents 17:19 x 21:23:26:28:31:34 SD: 7.2738 cents 18:20 x 23:24:27:30:32:36 SD: 6.9589 cents 19:21 x 24:26:29:32:34:38 SD: 6.8526 cents 20:22:23:25:27:30:33:36:40 SD: 5.6642 cents 23 x 26:29:31:35:38:41:46 SD: 5.4092 cents 24 x 27:30:32:36:40:43:48 SD: 3.2797 cents 25 x 28:31:34:38:42:45:50 SD: 4.8068 cents 26:29 x 33:35:39:43:47:52 SD: 4.5185 cents 27:30 x 34:36:41:45:49:54 SD: 5.1078 cents 28:31:32:35:38:42:47:50:56 SD: 4.3433 cents 32 x 36:40:43:48:53:58:64 SD: 2.5789 cents 33 x 37:41:45:50:55:59:66 SD: 4.2551 cents 34:38 x 43:46:51:57:61:68 SD: 3.6771 cents 35:39 x 44:47:53:58:63:70 SD: 3.4219 cents 36:40:41:45:49:54:60:65:72 SD: 3.2622 cents 39:43:44:49:53:59:65:70:78 SD: 3.1978 cents 40:44:45:50:54:60:67:72:80 SD: 2.4280 cents 41 x 46:51:55:62:68:74:82 SD: 3.2086 cents 42 x 47:53:57:63:70:76:84 SD: 3.2594 cents 43:48 x 54:58:65:72:77:86 SD: 3.0473 cents 44:49:50:55:59:66:73:79:88 SD: 2.8950 cents 45:50:51:56:61:68:75:81:90 SD: 2.6116 cents 46:51:52:58:62:69:77:83:92 SD: 2.4689 cents 48:53:54:60:65:72:80:86:96 SD: 1.8149 cents 50 x 56:63:68:75:83:90:100 SD: 3.0678 cents 51:57 x 64:69:77:85:92:102 SD: 2.4933 cents 52:58:59:65:70:78:87:94:104 SD: 2.4505 cents 54:60:61:68:73:81:90:97:108 SD: 1.9045 cents 56:62:63:70:76:84:93:101:112 SD: 1.6392 cents 59 x 66:74:80:89:98:106:118 SD: 2.5892 cents 60:67:68:75:81:90:100:108:120 SD: 1.9276 cents 63:70:71:79:85:95:105:113:126 SD: 1.5877 cents 64:71:72:80:86:96:107:115:128 SD: 1.3116 cents 72:80:81:90:97:108:120:130:144 SD: 0.8021 cents 80:89:90:100:108:120:133:144:160 SD: 0.6054 cents 120:133:135:150:162:180:200:216:240 SD: 0.5417 cents 144:160:162:180:194:216:240:259:288 SD: 0.4760 cents 160:178:180:200:216:240:267:288:320 SD: 0.3823 cents 200:222:225:250:270:300:333:360:400 SD: 0.3062 cents 240:267:270:300:324:360:400:432:480 SD: 0.2703 cents 280:311:315:350:378:420:467:504:560 SD: 0.1728 cents 360:400:405:450:486:540:600:648:720 SD: 0.0000 cents