Scala analysis: semipor4
Fourth 16/15&250/243 = 648/625&250/243 scale = inverse semipor3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 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: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 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 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 : 133.2 203.9 386.3 519.6 702.0 884.4 1017.6 1200.0 133.2 : 70.7 253.1 386.3 568.7 751.1 884.4 1066.8 1200.0 203.9 : 182.4 315.6 498.0 680.4 813.7 996.1 1129.3 1200.0 386.3 : 133.2 315.6 498.0 631.3 813.7 946.9 1017.6 1200.0 519.6 : 182.4 364.8 498.0 680.4 813.7 884.4 1066.8 1200.0 702.0 : 182.4 315.6 498.0 631.3 702.0 884.4 1017.6 1200.0 884.4 : 133.2 315.6 448.9 519.6 702.0 835.2 1017.6 1200.0 1017.6: 182.4 315.6 386.3 568.7 702.0 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 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 : 143.71228 cents, oct.: 1149.69824 cents Scale is strictly proper Step pattern alph. order: ABCACCAC Step pattern size order : MSLMLLML 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 : 0.444643 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 Number of recognisable fifths : 4, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic 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 Scale is n-1 differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 5 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 27 Scale harmonicity : 0.029528 Average absolute harmonicity : 0.227043 Specific harmonicity : 0.170406 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 270, 8.0768 octaves, 70638.903 Hz. Exponens Consonantiae : 1.620000E+05, 17.30563 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 77.5, average 9.68750 Mersenne's string divisions : 26175240 Sum of van Prooijen's expressibility: 6.64627, average 0.83078 Sum of Tenney's harmonic distance : 12.62855, average 1.57857 Vogel's harmonic complexity : 17.62500 Wille's k value : 337 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 103.83644, average 2.88435 Lattice compactness (without 2's) : 78.18236, average 2.17173 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.87500 9 1 3: -1 .. 3 1.25000 12 2 5: -2 .. 1 -0.25000 6 5 Average exponent except 2's : 8 / 8 = 1.00000 Average absolute exponent except 2's: 18 / 8 = 2.25000 Scale is JI-epimorphic with val: <8 13 19| = patent
FIT/MODE
8: 0 1 1 1 1 1 1 2 N T3 SD: 96.9677 c. M: 134.3587 c. 9: 1 1 1 1 1 2 1 1 P M ME SD: 35.9989 c. M:-62.7567 c. 11: 1 1 1 2 1 2 1 2 P D3 SD: 32.7998 c. M: 59.0410 c. 12: 1 1 2 1 2 2 1 2 P D3 S SD: 16.7619 c. M: 33.2376 c. 16: 2 1 2 2 2 3 2 2 P G D3 SD: 19.0548 c. M:-32.4037 c. 18: 2 1 3 2 3 2 2 3 P T3 SD: 15.8106 c. M:-31.3783 c. 19: 2 1 3 2 3 3 2 3 P SD: 8.7809 c. M: 14.4363 c. 34: 4 2 5 4 5 5 4 5 SP SD: 5.9192 c. M:-9.8605 c. 46: 5 3 7 5 7 7 5 7 SP SD: 3.0201 c. M:-4.9906 c. 53: 6 3 8 6 8 8 6 8 SP SD: 1.3080 c. M:-2.6115 c. 99: 11 6 15 11 15 15 11 15 SP SD: 1.2032 c. M:-2.1506 c. 118: 13 7 18 13 18 18 13 18 SP SD: 0.5932 c. M: 1.0342 c. 171: 19 10 26 19 26 26 19 26 SP SD: 0.2293 c. M: 0.4012 c. 388: 43 23 59 43 59 59 43 59 SP SD: 0.1721 c. M:-0.2842 c. 441: 49 26 67 49 67 67 49 67 SP SD: 0.1072 c. M:-0.1766 c. 559: 62 33 85 62 85 85 62 85 SP SD: 0.0728 c. M: 0.1428 c. 612: 68 36 93 68 93 93 68 93 SP SD: 0.0483 c. M:-0.0958 c. 1000: 111 59 152 111 152 152 111 152 SP SD: 0.0537 c. M:-0.0900 c. 1171: 130 69 178 130 178 178 130 178 SP SD: 0.0136 c. M:-0.0228 c. 1783: 198 105 271 198 271 271 198 271 SP SD: 0.0138 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 x 10:11:12:14:15:16:18 S SD: 11.8367 cents 10:11 x x 14:15:17:18:20 SD: 13.0687 cents 11:12 x 14:15:17:18:20:22 SD: 10.6536 cents 12:13:14:15:16:18:20:22:24 S SD: 9.2400 cents 14:15:16:18:19:21:23:25:28 SD: 8.1072 cents 15:16:17:19:20:23:25:27:30 SD: 6.9169 cents 16:17:18:20:22:24:27:29:32 SD: 6.1429 cents 19 x 21:24:26:29:32:34:38 SD: 8.0260 cents 20:22:23:25:27:30:33:36:40 SD: 6.5666 cents 22:24:25:28:30:33:37:40:44 SD: 6.1613 cents 23:25:26:29:31:35:38:41:46 SD: 4.9328 cents 24:26:27:30:32:36:40:43:48 SD: 2.9462 cents 39:42:44:49:53:59:65:70:78 SD: 2.7955 cents 40:43:45:50:54:60:67:72:80 SD: 1.4742 cents 48:52:54:60:65:72:80:86:96 SD: 1.3776 cents 64:69:72:80:86:96:107:115:128 SD: 1.3218 cents 72:78:81:90:97:108:120:130:144 SD: 1.0431 cents 88:95:99:110:119:132:147:158:176 SD: 0.8256 cents 112:121:126:140:151:168:187:202:224 SD: 0.6483 cents 136:147:153:170:184:204:227:245:272 SD: 0.6208 cents 152:164:171:190:205:228:253:274:304 SD: 0.5198 cents 160:173:180:200:216:240:267:288:320 SD: 0.3684 cents 200:216:225:250:270:300:333:360:400 SD: 0.2165 cents 240:259:270:300:324:360:400:432:480 SD: 0.1670 cents 360:389:405:450:486:540:600:648:720 SD: 0.1113 cents 400:432:450:500:540:600:667:720:800 SD: 0.1082 cents 560:605:630:700:756:840:933:1008:1120 SD: 0.1053 cents 600:648:675:750:810:900:1000:1080:1200 SD: 0.0000 cents