Scala analysis: octone_tuning-math_12214_12214
octone around 60/49-7/4 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: 60/49 350.616902 smaller 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: 8/7 231.1741 septimal whole tone 3: 49/48 35.6968 slendro diesis, septimal 1/6-tone 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: 2 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: 4 8/7 231.174 cents septimal whole tone 2: 4 7/6 266.871 cents septimal minor third 2: 2 6/5 315.641 cents minor third 2: 2 60/49 350.617 cents smaller approximation to neutral third 3: 2 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: 1 480/343 581.791 cents 4: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 4 10/7 617.488 cents Euler's tritone 5: 1 343/240 618.209 cents 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: 2 80/49 848.662 cents smaller approximation to neutral sixth 6: 2 49/30 849.383 cents larger approximation to neutral sixth 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 4 12/7 933.129 cents septimal major sixth 7: 4 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: 2 96/49 1164.303 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.71429 = 26/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 119.4 350.6 386.3 617.5 702.0 933.1 968.8 1200.0 119.4 : 231.2 266.9 498.0 582.5 813.7 849.4 1080.6 1200.0 350.6 : 35.7 266.9 351.3 582.5 618.2 849.4 968.8 1200.0 386.3 : 231.2 315.6 546.8 582.5 813.7 933.1 1164.3 1200.0 617.5 : 84.5 315.6 351.3 582.5 702.0 933.1 968.8 1200.0 702.0 : 231.2 266.9 498.0 617.5 848.7 884.4 1115.5 1200.0 933.1 : 35.7 266.9 386.3 617.5 653.2 884.4 968.8 1200.0 968.8 : 231.2 350.6 581.8 617.5 848.7 933.1 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 231.1741 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 2: 266.8709 .. 350.6169 cents 360/343, 83.7460 cents 49/48, 35.6968 cents 3: 351.3381 .. 581.7910 cents 19200/16807, 230.4529 cents 2401/2400, 0.7212 cents 4: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 2401/2400, 0.7212 cents 5: 618.2090 .. 848.6619 cents 19200/16807, 230.4529 cents 2401/2400, 0.7212 cents 6: 849.3831 .. 933.1291 cents 360/343, 83.7460 cents 2401/2400, 0.7212 cents 7: 968.8259 .. 1164.3032 cents 384/343, 195.4773 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 4.202056 Largest / Average step : 1.541161 Largest / Smallest step : 6.476043 Median interval of one step : 175.30845 cents, amount: 0 Most common interval of one step : 8/7, 231.1741 cents, amount: 4 Least squares average step : 146.76422 cents, oct.: 1174.11372 cents Scale is strictly proper Step pattern alph. order: ABCBDBCB Step pattern size order : CDADBDAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.72120 cents Scale diversity : 1.388082 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.121393 Rothenberg efficiency : 0.421429 redundancy: 0.578571 Efficiency x scale size : 3.371429 Number of different interval sizes : 26 = 3.71429 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 3.71429 = 26/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 2401/2400, 0.7212 cents Number of recognisable fifths : 2, average 701.9550 cents All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 4-5 -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.022767 Average absolute harmonicity : 0.209666 Specific harmonicity : 0.130725 Fundamental : 1/196, -7.6147 octaves, 1.3348 Hz. Guide tone : 420, 8.7142 octaves, 109882.737 Hz. Exponens Consonantiae : 8.232000E+04, 16.32896 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 101.0, average 12.62500 Mersenne's string divisions : 505396485 Sum of van Prooijen's expressibility: 6.57767, average 0.82221 Sum of Tenney's harmonic distance : 13.38731, average 1.67341 Vogel's harmonic complexity : 16.50000 Wille's k value : 171 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 92.51165, average 2.56977 Lattice compactness (without 2's) : 54.50813, average 1.51411 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 12 1 3: 0 .. 1 0.50000 4 1 5: 0 .. 1 0.50000 4 1 7: -2 .. 1 -0.50000 6 5 Average exponent except 2's : 4 / 8 = 0.50000 Average absolute exponent except 2's: 14 / 8 = 1.75000 Scale is weakly epimorphic with val: <8 13 18 20| Scale is weakly epimorphic with val: <8 13 18 22| Scale is JI-epimorphic with val: <8 13 19 23| Scale is weakly epimorphic with val: <8 14 17 20| Scale is weakly epimorphic with val: <8 14 19 20|
FIT/MODE
8: 1 1 0 2 0 2 0 2 N T3 SD: 58.6100 c. M: 101.9550 c. 9: 1 2 0 2 0 2 0 2 N SD: 31.1098 c. M:-49.3831 c. 10: 1 2 0 2 1 2 0 2 P B D3 SD: 16.6289 c. M:-26.8709 c. 17: 2 3 1 3 1 3 1 3 P SD: 18.7472 c. M:-37.2157 c. 19: 2 4 0 4 1 4 0 4 N SD: 15.0746 c. M:-28.3305 c. 21: 2 4 1 4 1 4 1 4 P SD: 11.3059 c. M: 18.8434 c. 27: 3 5 1 5 2 5 1 5 P SD: 8.5956 c. M:-13.8905 c. 31: 3 6 1 6 2 6 1 6 P SD: 2.8472 c. M: 5.1808 c. 68: 7 13 2 13 5 13 2 13 P SD: 2.4758 c. M:-4.0866 c. 72: 7 14 2 14 5 14 2 14 P SD: 1.8087 c. M: 2.9804 c. 99: 10 19 3 19 7 19 3 19 P SD: 1.0503 c. M:-1.7693 c. 130: 13 25 4 25 9 25 4 25 P SD: 0.7241 c. M:-1.3786 c. 140: 14 27 4 27 10 27 4 27 P SD: 0.6768 c. M:-1.1566 c. 171: 17 33 5 33 12 33 5 33 P SD: 0.2396 c. M: 0.4049 c. 441: 44 85 13 85 31 85 13 85 P SD: 0.2102 c. M:-0.4035 c. 472: 47 91 14 91 33 91 14 91 P SD: 0.1850 c. M:-0.3088 c. 612: 61 118 18 118 43 118 18 118 P SD: 0.1828 c. M:-0.3635 c. 643: 64 124 19 124 45 124 19 124 P SD: 0.1707 c. M: 0.2443 c. 904: 90 174 27 174 64 174 27 174 SP SD: 0.1562 c. M:-0.2574 c. 935: 93 180 28 180 66 180 28 180 SP SD: 0.1273 c. M: 0.2426 c. 1034: 103 199 31 199 73 199 31 199 SP SD: 0.1314 c. M:-0.2263 c. 1065: 106 205 32 205 75 205 32 205 SP SD: 0.1278 c. M: 0.1944 c. 1075: 107 207 32 207 76 207 32 207 SP SD: 0.1137 c. M: 0.1855 c. 1106: 110 213 33 213 78 213 33 213 SP SD: 0.0888 c. M: 0.1648 c. 1205: 120 232 36 232 85 232 36 232 SP SD: 0.0809 c. M:-0.1367 c. 1236: 123 238 37 238 87 238 37 238 SP SD: 0.0811 c. M: 0.1315 c. 1277: 127 246 38 246 90 246 38 246 SP SD: 0.0722 c. M: 0.1079 c. 1376: 137 265 41 265 97 265 41 265 SP SD: 0.0453 c. M:-0.0799 c. 1547: 154 298 46 298 109 298 46 298 SP SD: 0.0260 c. M:-0.0489 c. 1848: 184 356 55 356 130 356 55 356 SP SD: 0.0300 c. M:-0.0499 c. 2019: 201 389 60 389 142 389 60 389 SP SD: 0.0295 c. M:-0.0517 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: 26.3127 cents 6 x 7:8 x 9:10:11:12 S SD: 28.0684 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: 15.2705 cents 10:11:12:13:14:15:17:18:20 SD: 13.5331 cents 11:12:13:14:16:17:19 x 22 SD: 13.9473 cents 12:13 x 15:17:18 x 21:24 SD: 3.9994 cents 13:14:16 x 19:20:22:23:26 SD: 9.5779 cents 14:15:17:18:20:21:24:25:28 SD: 7.7174 cents 15:16:18:19:21:23 x 26:30 SD: 9.8501 cents 16:17 x 20:23:24:27:28:32 SD: 4.6720 cents 17:18:21 x 24:26:29:30:34 SD: 7.1188 cents 19:20:23:24:27:29 x 33:38 SD: 7.5897 cents 20:21:24:25:29:30:34:35:40 SD: 7.2034 cents 21:23 x 26:30:32:36:37:42 SD: 7.2891 cents 22:24:27:28:31:33:38:39:44 SD: 7.0671 cents 23:25:28:29:33:35:39:40:46 SD: 5.7252 cents 24:26:29:30:34:36:41:42:48 SD: 4.2221 cents 25:27 x 31:36:38:43:44:50 SD: 5.0107 cents 26:28:32:33:37:39:45:46:52 SD: 4.8933 cents 27:29:33:34:39:41:46:47:54 SD: 4.3449 cents 28:30:34:35:40:42:48:49:56 SD: 1.8109 cents 29:31 x 36:41:44:50:51:58 SD: 4.6198 cents 30:32:37:38:43:45:51:53:60 SD: 4.4245 cents 31:33:38:39:44:47:53:54:62 SD: 3.5511 cents 32:34:39:40:46:48:55:56:64 SD: 2.5393 cents 40:43:49:50:57:60:69:70:80 SD: 1.6242 cents 44:47:54:55:63:66:75:77:88 SD: 1.5603 cents 56:60:69:70:80:84:96:98:112 SD: 1.3483 cents 68:73:83:85:97:102:117:119:136 SD: 1.1785 cents 72:77:88:90:103:108:123:126:144 SD: 0.9892 cents 80:86:98:100:114:120:137:140:160 SD: 0.9333 cents 84:90:103:105:120:126:144:147:168 SD: 0.3004 cents 112:120:137:140:160:168:192:196:224 SD: 0.2255 cents 196:210:240:245:280:294:336:343:392 S SD: 0.0000 cents