Scala analysis: octone
octone around 49/40-7/4 interval
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 49/40 351.338099 larger approximation to neutral third 3: 5/4 386.313714 major third 4: 10/7 617.487807 Euler's tritone 5: 3/2 701.955001 perfect fifth 6: 12/7 933.129094 septimal major sixth 7: 7/4 968.825906 harmonic seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 15/14 119.4428 major diatonic semitone 2: 343/300 231.8953 3: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 4: 8/7 231.1741 septimal whole tone 5: 21/20 84.4672 minor semitone 6: 8/7 231.1741 septimal whole tone 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 21/20 84.467 cents minor semitone 1: 1 15/14 119.443 cents major diatonic semitone 1: 3 8/7 231.174 cents septimal whole tone 1: 1 343/300 231.895 cents 2: 1 400/343 266.150 cents 2: 3 7/6 266.871 cents septimal minor third 2: 2 6/5 315.641 cents minor third 2: 1 60/49 350.617 cents smaller approximation to neutral third 2: 1 49/40 351.338 cents larger approximation to neutral third 3: 1 60/49 350.617 cents smaller approximation to neutral third 3: 1 49/40 351.338 cents larger approximation to neutral third 3: 2 5/4 386.314 cents major third 3: 2 4/3 498.045 cents perfect fourth 3: 1 48/35 546.815 cents septimal semi-augmented fourth 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 480/343 581.791 cents 4: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 3 10/7 617.488 cents Euler's tritone 4: 1 343/240 618.209 cents 5: 1 10/7 617.488 cents Euler's tritone 5: 1 35/24 653.185 cents septimal semi-diminished fifth 5: 2 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 80/49 848.662 cents smaller approximation to neutral sixth 5: 1 49/30 849.383 cents larger approximation to neutral sixth 6: 1 80/49 848.662 cents smaller approximation to neutral sixth 6: 1 49/30 849.383 cents larger approximation to neutral sixth 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 3 12/7 933.129 cents septimal major sixth 6: 1 343/200 933.850 cents 7: 1 600/343 968.105 cents 7: 3 7/4 968.826 cents harmonic seventh 7: 1 28/15 1080.557 cents grave major seventh 7: 1 40/21 1115.533 cents acute major seventh 7: 1 96/49 1164.303 cents 7: 1 49/25 1165.024 cents BP eighth Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.42857 = 38/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 119.4 351.3 386.3 617.5 702.0 933.1 968.8 1200.0 119.4 : 231.9 266.9 498.0 582.5 813.7 849.4 1080.6 1200.0 351.3 : 35.0 266.1 350.6 581.8 617.5 848.7 968.1 1200.0 386.3 : 231.2 315.6 546.8 582.5 813.7 933.1 1165.0 1200.0 617.5 : 84.5 315.6 351.3 582.5 702.0 933.9 968.8 1200.0 702.0 : 231.2 266.9 498.0 617.5 849.4 884.4 1115.5 1200.0 933.1 : 35.7 266.9 386.3 618.2 653.2 884.4 968.8 1200.0 968.8 : 231.2 350.6 582.5 617.5 848.7 933.1 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 231.8953 cents 16807/15000, 196.9197 cents 50/49, 34.9756 cents 2: 266.1497 .. 351.3381 cents 16807/16000, 85.1884 cents 120000/117649, 34.2544 cents 3: 350.6169 .. 582.5122 cents 343/300, 231.8953 cents 2400/2401,-0.7212 cents 4: 581.7910 .. 618.2090 cents 117649/115200, 36.4180 cents 2400/2401,-0.7212 cents 5: 617.4878 .. 849.3831 cents 343/300, 231.8953 cents 2400/2401,-0.7212 cents 6: 848.6619 .. 933.8503 cents 16807/16000, 85.1884 cents 2400/2401,-0.7212 cents 7: 968.1047 .. 1165.0244 cents 16807/15000, 196.9197 cents 120000/117649, 34.2544 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 343/300, 231.8953 cents Average / Smallest step : 4.288702 Largest / Average step : 1.545969 Largest / Smallest step : 6.630199 Median interval of one step : 175.30845 cents, amount: 0 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 146.77129 cents, oct.: 1174.17029 cents Scale is not proper Step pattern alph. order: ABCDEDFD Step pattern size order : DFAECEBE Scale is not a Constant Structure Scale diversity : 1.389885 Lumma stability : 0.115383 Lumma impropriety factor : 0.002404 Rothenberg efficiency : 0.369643 redundancy: 0.630357 Efficiency x scale size : 2.957143 Number of different interval sizes : 32 = 4.57143 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.42857 = 38/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 4 Number of recognisable fifths : 2, average 701.9550 cents 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 n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 196.1985 cents: 1 -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.019484 Average absolute harmonicity : 0.209886 Specific harmonicity : 0.116074 Fundamental : 1/280, -8.1293 octaves, 0.9344 Hz. Guide tone : 2940, 11.5216 octaves, 769179.162 Hz. Exponens Consonantiae : 8.232000E+05, 19.65088 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 91.0, average 11.37500 Mersenne's string divisions : 412663185 Sum of van Prooijen's expressibility: 6.57767, average 0.82221 Sum of Tenney's harmonic distance : 13.21122, average 1.65140 Vogel's harmonic complexity : 16.75000 Wille's k value : 171 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 98.72106, average 2.74225 Lattice compactness (without 2's) : 59.82006, average 1.66167 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.62500 13 1 3: 0 .. 1 0.37500 3 1 5: -1 .. 1 0.25000 4 1 7: -1 .. 2 0.00000 6 5 Average exponent except 2's : 5 / 8 = 0.62500 Average absolute exponent except 2's: 13 / 8 = 1.62500 Scale is weakly epimorphic with val: <8 14 17 20|
FIT/MODE
8: 1 1 1 1 1 1 0 2 N T3 SD: 44.8246 c. M: 68.8259 c. 9: 1 2 0 2 0 2 0 2 N SD: 30.9674 c. M:-49.1789 c. 10: 1 2 0 2 1 2 0 2 P B D3 SD: 16.5799 c. M:-26.8709 c. 17: 2 3 1 3 1 3 1 3 P SD: 18.7378 c. M:-37.2157 c. 19: 2 4 0 4 1 4 0 4 N SD: 14.9064 c. M:-27.6093 c. 21: 2 4 1 4 1 4 1 4 P SD: 11.3704 c. M: 18.8434 c. 27: 3 5 1 5 2 5 1 5 P SD: 8.5475 c. M:-13.8905 c. 31: 3 6 1 6 2 6 1 6 P SD: 2.9281 c. M: 5.1808 c. 68: 7 13 2 13 5 13 2 13 P SD: 2.4033 c. M:-4.0866 c. 72: 7 14 2 14 5 14 2 14 P SD: 1.8568 c. M: 2.9804 c. 99: 10 19 3 19 7 19 3 19 P SD: 1.0031 c. M:-1.7693 c. 130: 13 25 4 25 9 25 4 25 P SD: 0.7496 c. M:-1.3786 c. 140: 14 27 4 27 10 27 4 27 P SD: 0.6137 c. M:-1.1566 c. 171: 17 33 5 33 12 33 5 33 P SD: 0.2748 c. M: 0.4609 c. 441: 44 85 13 85 31 85 13 85 P SD: 0.1909 c. M: 0.3177 c. 612: 61 118 18 118 43 118 18 118 P SD: 0.1814 c. M: 0.3577 c. 935: 93 181 27 180 66 180 28 180 N SD: 0.1470 c. M:-0.3197 c. 966: 96 187 28 186 68 186 29 186 N SD: 0.1404 c. M:-0.2147 c. 1034: 103 200 30 199 73 199 31 199 N SD: 0.1636 c. M:-0.3060 c. 1065: 106 206 31 205 75 205 32 205 N SD: 0.1311 c. M:-0.2112 c. 1106: 110 214 32 213 78 213 33 213 N SD: 0.0972 c. M:-0.1990 c. 1137: 113 220 33 219 80 219 34 219 N SD: 0.1045 c. M: 0.1816 c. 1205: 120 233 35 232 85 232 36 232 N SD: 0.1032 c. M:-0.1972 c. 1236: 123 239 36 238 87 238 37 238 N SD: 0.0785 c. M: 0.1194 c. 1277: 127 247 37 246 90 246 38 246 N SD: 0.0727 c. M:-0.1106 c. 1376: 137 266 40 265 97 265 41 265 N SD: 0.0596 c. M:-0.1154 c. 1407: 140 272 41 271 99 271 42 271 N SD: 0.0435 c. M: 0.0801 c. 1547: 154 299 45 298 109 298 46 298 N SD: 0.0318 c. M:-0.0517 c. 1578: 157 305 46 304 111 304 47 304 N SD: 0.0317 c. M: 0.0539 c. 1718: 171 332 50 331 121 331 51 331 N SD: 0.0292 c. M: 0.0506 c. 1848: 184 357 54 356 130 356 55 356 N SD: 0.0310 c. M:-0.0499 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 4 x x 5 x 6 S SD: 40.6372 cents 4 x x 5 x 6 x 7:8 S SD: 0.0000 cents 5 x 6 x 7:8 x 9:10 S SD: 26.3515 cents 6 x 7:8 x 9:10:11:12 S SD: 28.1284 cents 7:8 x 9:10:11:12 x 14 S SD: 24.3520 cents 8:9 x 10:11:12 x 14:16 S SD: 17.8832 cents 9:10:11 x 13:14:15:16:18 SD: 15.2740 cents 10:11:12:13:14:15:17:18:20 SD: 13.5625 cents 11:12:13:14:16:17:19 x 22 SD: 14.0124 cents 12:13 x 15:17:18 x 21:24 SD: 3.9994 cents 13:14:16 x 19:20:22:23:26 SD: 9.5648 cents 14:15:17:18:20:21:24:25:28 SD: 7.7390 cents 15:16:18:19:21:23 x 26:30 SD: 9.9027 cents 16:17 x 20:23:24:27:28:32 SD: 4.6720 cents 17:18:21 x 24:26:29:30:34 SD: 7.0881 cents 19:20:23:24:27:29 x 33:38 SD: 7.6288 cents 20:21 x 25:29:30:34:35:40 SD: 6.5427 cents 21:23 x 26:30:32:36:37:42 SD: 7.2891 cents 22:24:27:28:31:33:38:39:44 SD: 7.0614 cents 23:25:28:29:33:35:39:40:46 SD: 5.7457 cents 24:26:29:30:34:36:41:42:48 SD: 4.2839 cents 25:27 x 31:36:38:43:44:50 SD: 5.0107 cents 26:28:32:33:37:39:45:46:52 SD: 4.8737 cents 27:29:33:34:39:41:46:47:54 SD: 4.3542 cents 28:30:34:35:40:42:48:49:56 SD: 1.9011 cents 29:31 x 36:41:44:50:51:58 SD: 4.6198 cents 30:32:37:38:43:45:51:53:60 SD: 4.3935 cents 31:33:38:39:44:47:53:54:62 SD: 3.5463 cents 32:34:39:40:46:48:55:56:64 SD: 2.5767 cents 40:43:49:50:57:60:69:70:80 SD: 1.6217 cents 44:47:54:55:63:66:75:77:88 SD: 1.5343 cents 56:60:69:70:80:84:96:98:112 SD: 1.2582 cents 68:73:83:85:97:102:117:119:136 SD: 1.2334 cents 72:77:88:90:103:108:123:126:144 SD: 1.0291 cents 80:86:98:100:114:120:137:140:160 SD: 0.9289 cents 84:90:103:105:120:126:144:147:168 SD: 0.2102 cents 196:210:240:245:280:294:336:343:392 S SD: 0.0901 cents 280:300:343:350:400:420:480:490:560 SD: 0.0000 cents