Scala analysis: semipor2
Second 16/15&250/243 = 648/625&250/243 scale
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: 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: 81/80 21.5063 syntonic comma, Didymus comma 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 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: 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: 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 : 182.4 203.9 386.3 568.7 702.0 884.4 1017.6 1200.0 182.4 : 21.5 203.9 386.3 519.6 702.0 835.2 1017.6 1200.0 203.9 : 182.4 364.8 498.0 680.4 813.7 996.1 1178.5 1200.0 386.3 : 182.4 315.6 498.0 631.3 813.7 996.1 1017.6 1200.0 568.7 : 133.2 315.6 448.9 631.3 813.7 835.2 1017.6 1200.0 702.0 : 182.4 315.6 498.0 680.4 702.0 884.4 1066.8 1200.0 884.4 : 133.2 315.6 498.0 519.6 702.0 884.4 1017.6 1200.0 1017.6: 182.4 364.8 386.3 568.7 751.1 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 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: 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 .. 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 : 144.91733 cents, oct.: 1159.33866 cents Scale is strictly proper Step pattern alph. order: ABAACACA Step pattern size order : LSLLMLML Scale is a Constant Structure, by a margin of 21.50629 cents Scale diversity : 1.362423 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.143375 Rothenberg efficiency : 0.466964 redundancy: 0.533036 Efficiency x scale size : 3.735714 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 intervals : 10/9, 182.4037 cents & inv., amount: 5 Most common triad is 0.0 182.404 1017.596 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic 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 Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 5-6 -- 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 : 0.229761 Specific harmonicity : 0.177217 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 : 59.0, average 7.37500 Mersenne's string divisions : 35000280 Sum of van Prooijen's expressibility: 6.13573, average 0.76697 Sum of Tenney's harmonic distance : 11.67430, average 1.45929 Vogel's harmonic complexity : 15.87500 Wille's k value : 202 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 103.64356, average 2.87899 Lattice compactness (without 2's) : 77.81186, average 2.16144 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.62500 9 1 3: -2 .. 2 0.00000 10 2 5: -1 .. 2 0.50000 6 5 Average exponent except 2's : 4 / 8 = 0.50000 Average absolute exponent except 2's: 16 / 8 = 2.00000 Scale is JI-epimorphic with val: <8 13 19| = patent Scale is weakly epimorphic with val: <8 14 19|
FIT/MODE
8: 1 0 2 1 1 1 1 1 N T3 SD: 39.6765 c. M:-63.6863 c. 11: 1 1 1 2 1 2 1 2 P D3 SD: 40.7254 c. M: 73.3128 c. 12: 2 0 2 2 1 2 1 2 P D3 SD: 16.0036 c. M:-31.2826 c. 19: 3 0 3 3 2 3 2 3 P SD: 7.2011 c. M: 14.4363 c. 31: 5 0 5 5 3 5 3 5 P SD: 8.3745 c. M:-11.9277 c. 34: 5 1 5 5 4 5 4 5 SP SD: 4.6278 c. M:-7.8547 c. 46: 7 1 7 7 5 7 5 7 SP SD: 3.3046 c. M:-5.1956 c. 53: 8 1 8 8 6 8 6 8 SP SD: 1.3330 c. M: 2.6797 c. 99: 15 2 15 15 11 15 11 15 SP SD: 1.1245 c. M:-2.1506 c. 118: 18 2 18 18 13 18 13 18 SP SD: 0.4926 c. M:-0.7741 c. 171: 26 3 26 26 19 26 19 26 SP SD: 0.2340 c. M: 0.4012 c. 388: 59 7 59 59 43 59 43 59 SP SD: 0.1953 c. M:-0.3547 c. 441: 67 8 67 67 49 67 49 67 SP SD: 0.0866 c. M:-0.1716 c. 559: 85 10 85 85 62 85 62 85 SP SD: 0.0772 c. M:-0.1556 c. 612: 93 11 93 93 68 93 68 93 SP SD: 0.0461 c. M: 0.0900 c. 730: 111 13 111 111 81 111 81 111 SP SD: 0.0472 c. M: 0.0744 c. 1171: 178 21 178 178 130 178 130 178 SP SD: 0.0154 c. M:-0.0272 c. 1783: 271 32 271 271 198 271 198 271 SP SD: 0.0109 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 9:10 x 11 x 14:15:16:18 SD: 12.8455 cents 10:11 x 13:14:15:17:18:20 SD: 11.3198 cents 11:12 x 14:15:17:18:20:22 SD: 11.9303 cents 12:13:14:15:17:18:20:22:24 SD: 11.2289 cents 14 x 16:18:19:21:23:25:28 SD: 10.6283 cents 15 x 17:19:21:23:25:27:30 SD: 6.8916 cents 16 x 18:20:22:24:27:29:32 SD: 4.3066 cents 17:19 x 21:24:26:28:31:34 SD: 8.3031 cents 18:20 x 23:25:27:30:32:36 SD: 6.2440 cents 19:21 x 24:26:29:32:34:38 SD: 7.0146 cents 20:22:23:25:28:30:33:36:40 SD: 5.9209 cents 23 x 26:29:32:35:38:41:46 SD: 5.4116 cents 24 x 27:30:33:36:40:43:48 SD: 2.7378 cents 25 x 28:31:35:38:42:45:50 SD: 4.8639 cents 26:29 x 33:36:39:43:47:52 SD: 4.5277 cents 27:30 x 34:38:41:45:49:54 SD: 5.2327 cents 28:31:32:35:39:42:47:50:56 SD: 4.2357 cents 32 x 36:40:44:48:53:58:64 SD: 3.3930 cents 33 x 37:41:46:50:55:59:66 SD: 3.5683 cents 34:38 x 43:47:51:57:61:68 SD: 3.8200 cents 35:39 x 44:49:53:58:63:70 SD: 3.7245 cents 36:40:41:45:50:54:60:65:72 SD: 2.7378 cents 41 x 46:51:57:62:68:74:82 SD: 2.8093 cents 42 x 47:53:58:63:70:76:84 SD: 3.3059 cents 43:48 x 54:60:65:72:77:86 SD: 3.2493 cents 44:49:50:55:61:66:73:79:88 SD: 2.5295 cents 46:51:52:58:64:69:77:83:92 SD: 2.4729 cents 48:53:54:60:67:72:80:86:96 SD: 2.0035 cents 50 x 56:63:69:75:83:90:100 SD: 2.9328 cents 51:57 x 64:71:77:85:92:102 SD: 2.5029 cents 52:58:59:65:72:78:87:94:104 SD: 2.4635 cents 54:60:61:68:75:81:90:97:108 SD: 1.8813 cents 56:62:63:70:78:84:93:101:112 SD: 1.3282 cents 59 x 66:74:82:89:98:106:118 SD: 2.3571 cents 60:67:68:75:83:90:100:108:120 SD: 2.1137 cents 62:69:70:78:86:93:103:112:124 SD: 1.9556 cents 64:71:72:80:89:96:107:115:128 SD: 0.8859 cents 72:80:81:90:100:108:120:130:144 SD: 0.6669 cents 80:89:90:100:111:120:133:144:160 SD: 0.6430 cents 136:151:153:170:189:204:227:245:272 SD: 0.4170 cents 144:160:162:180:200:216:240:259:288 SD: 0.1670 cents 216:240:243:270:300:324:360:389:432 SD: 0.1113 cents 360:400:405:450:500:540:600:648:720 SD: 0.0000 cents