Scala analysis: cx3
Third 10/4 scale <10 16 23 28| epimorphic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 9/8 203.910002 major whole tone 3: 5/4 386.313714 major third 4: 21/16 470.780907 narrow fourth 5: 10/7 617.487807 Euler's tritone 6: 3/2 701.955001 perfect fifth 7: 5/3 884.358713 major sixth, BP sixth 8: 7/4 968.825906 harmonic seventh 9: 15/8 1088.268715 classic major seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 21/20 84.4672 minor semitone 2: 15/14 119.4428 major diatonic semitone 3: 10/9 182.4037 minor whole tone 4: 21/20 84.4672 minor semitone 5: 160/147 146.7069 6: 21/20 84.4672 minor semitone 7: 10/9 182.4037 minor whole tone 8: 21/20 84.4672 minor semitone 9: 15/14 119.4428 major diatonic semitone 10: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 160/147 146.707 cents 1: 2 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 2: 2 9/8 203.910 cents major whole tone 2: 3 8/7 231.174 cents septimal whole tone 2: 3 7/6 266.871 cents septimal minor third 2: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 1 49/40 351.338 cents larger approximation to neutral third 3: 3 5/4 386.314 cents major third 3: 2 80/63 413.578 cents wide major third 4: 1 63/50 400.108 cents quasi-equal major third 4: 1 9/7 435.084 cents septimal major third, BP third 4: 2 21/16 470.781 cents narrow fourth 4: 5 4/3 498.045 cents perfect fourth 4: 1 200/147 533.021 cents 5: 1 27/20 519.551 cents acute fourth 5: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 4 10/7 617.488 cents Euler's tritone 5: 1 40/27 680.449 cents grave fifth 6: 1 147/100 666.979 cents 6: 5 3/2 701.955 cents perfect fifth 6: 2 32/21 729.219 cents wide fifth 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 100/63 799.892 cents quasi-equal minor sixth 7: 2 63/40 786.422 cents narrow minor sixth 7: 3 8/5 813.686 cents minor sixth 7: 1 80/49 848.662 cents smaller approximation to neutral sixth 7: 4 5/3 884.359 cents major sixth, BP sixth 8: 1 42/25 898.153 cents quasi-equal major sixth 8: 3 12/7 933.129 cents septimal major sixth 8: 3 7/4 968.826 cents harmonic seventh 8: 2 16/9 996.090 cents Pythagorean minor seventh 8: 1 25/14 1003.802 cents middle minor seventh 9: 2 9/5 1017.596 cents just minor seventh, BP seventh 9: 1 147/80 1053.293 cents 9: 2 28/15 1080.557 cents grave major seventh 9: 1 15/8 1088.269 cents classic major seventh 9: 4 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 84.5 203.9 386.3 470.8 617.5 702.0 884.4 968.8 1088.3 1200.0 84.5 : 119.4 301.8 386.3 533.0 617.5 799.9 884.4 1003.8 1115.5 1200.0 203.9 : 182.4 266.9 413.6 498.0 680.4 764.9 884.4 996.1 1080.6 1200.0 386.3 : 84.5 231.2 315.6 498.0 582.5 702.0 813.7 898.2 1017.6 1200.0 470.8 : 146.7 231.2 413.6 498.0 617.5 729.2 813.7 933.1 1115.5 1200.0 617.5 : 84.5 266.9 351.3 470.8 582.5 667.0 786.4 968.8 1053.3 1200.0 702.0 : 182.4 266.9 386.3 498.0 582.5 702.0 884.4 968.8 1115.5 1200.0 884.4 : 84.5 203.9 315.6 400.1 519.6 702.0 786.4 933.1 1017.6 1200.0 968.8 : 119.4 231.2 315.6 435.1 617.5 702.0 848.7 933.1 1115.5 1200.0 1088.3: 111.7 196.2 315.6 498.0 582.5 729.2 813.7 996.1 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 182.4037 cents 200/189, 97.9365 cents 21/20, 84.4672 cents 2: 196.1985 .. 301.8465 cents 625/588, 105.6480 cents 126/125, 13.7948 cents 3: 315.6413 .. 413.5778 cents 200/189, 97.9365 cents 126/125, 13.7948 cents 4: 400.1085 .. 533.0206 cents 10000/9261, 132.9121 cents 3969/4000,-13.4693 cents 5: 519.5513 .. 680.4487 cents 800/729, 160.8974 cents 3969/4000,-13.4693 cents 6: 666.9794 .. 799.8915 cents 10000/9261, 132.9121 cents 3969/4000,-13.4693 cents 7: 786.4222 .. 884.3587 cents 200/189, 97.9365 cents 3969/4000,-13.4693 cents 8: 898.1535 .. 1003.8015 cents 625/588, 105.6480 cents 126/125, 13.7948 cents 9: 1017.5963 .. 1115.5328 cents 200/189, 97.9365 cents 126/125, 13.7948 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.420670 Largest / Average step : 1.520031 Largest / Smallest step : 2.159462 Median interval of one step : 115.58705 cents, amount: 0 Most common interval of one step : 21/20, 84.4672 cents, amount: 4 Least squares average step : 120.95859 cents, oct.: 1209.58591 cents Scale is not proper Step pattern alph. order: ABCADACABE Step pattern size order : ACEADAEACB Scale is a Constant Structure, by a margin of 13.46933 cents Scale diversity : 1.501490 Lumma stability : 0.186761 Lumma impropriety factor : 0.044898 Rothenberg efficiency : 0.325079 redundancy: 0.674921 Efficiency x scale size : 3.250794 Number of different interval sizes : 42 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 5, average 701.9550 cents Length of longest harmonic part : 2 at degree 8 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 10.0000% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 21 Scale harmonicity : 0.021565 Average absolute harmonicity : 0.194870 Specific harmonicity : 0.144694 Fundamental : 1/1680, -10.7142 octaves, 0.1557 Hz. Guide tone : 630, 9.2992 octaves, 164824.106 Hz. Exponens Consonantiae : 1.058400E+06, 20.01345 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 85.5, average 8.55000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.34003, average 0.83400 Sum of Tenney's harmonic distance : 15.93466, average 1.59347 Vogel's harmonic complexity : 21.90000 Wille's k value : 1102 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 149.40939, average 2.71653 Lattice compactness (without 2's) : 87.72078, average 1.59492 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.50000 19 1 3: -1 .. 2 0.50000 7 2 5: -1 .. 1 0.30000 5 3 7: -1 .. 1 0.20000 4 4 Average exponent except 2's : 10 / 10 = 1.00000 Average absolute exponent except 2's: 16 / 10 = 1.60000 Scale is JI-epimorphic with val: <10 16 23 28| = patent
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 24.6736 c. M: 44.3587 c. 12: 1 1 2 1 1 1 2 1 1 1 P D3 SD: 17.2086 c. M:-31.1741 c. 19: 1 2 3 1 3 1 3 1 2 2 N SD: 15.6935 c. M: 28.6756 c. 22: 2 2 3 2 2 2 3 2 2 2 SP D3 SD: 13.7955 c. M:-24.6237 c. Standard Pentachordal Major 23: 2 2 3 2 3 1 4 2 2 2 P SD: 14.3756 c. M: 23.6941 c. 24: 2 2 4 1 3 2 4 1 3 2 N SD: 13.8638 c. M: 20.7809 c. 25: 2 2 4 2 3 2 3 2 3 2 P SD: 12.1370 c. M: 20.3587 c. 26: 2 2 4 2 3 2 4 2 2 3 P T3 SD: 14.0707 c. M: 26.7303 c. 27: 2 3 4 2 3 2 4 2 3 2 P SD: 12.6443 c. M:-22.8424 c. 28: 2 3 4 2 3 2 5 2 2 3 N SD: 12.2190 c. M: 17.4878 c. 29: 2 3 4 2 4 2 4 2 3 3 P SD: 10.6981 c. M: 17.1018 c. 31: 2 3 5 2 4 2 5 2 3 3 N SD: 5.3226 c. M: 10.3616 c. 41: 3 4 6 3 5 3 6 3 4 4 P SD: 3.7118 c. M: 6.3099 c. 53: 4 5 8 4 6 4 8 4 5 5 P SD: 3.5477 c. M: 6.1671 c. 72: 5 7 11 5 9 5 11 5 7 7 N SD: 2.7740 c. M: 4.9354 c. 84: 6 8 13 6 10 6 13 6 8 8 N SD: 2.1641 c. M: 3.9100 c. 87: 6 9 13 6 11 6 13 6 9 8 N SD: 2.0750 c. M: 3.3087 c. 99: 7 10 15 7 12 7 15 7 10 9 N SD: 1.4358 c. M:-2.6404 c. 130: 9 13 20 9 16 9 20 9 13 12 N SD: 0.9981 c. M:-1.7951 c. 140: 10 14 21 10 17 10 21 10 14 13 N SD: 0.9452 c. M:-1.8043 c. 171: 12 17 26 12 21 12 26 12 17 16 N SD: 0.3530 c. M: 0.6055 c. 270: 19 27 41 19 33 19 41 19 27 25 N SD: 0.3273 c. M:-0.6202 c. 441: 31 44 67 31 54 31 67 31 44 41 N SD: 0.1178 c. M:-0.1993 c. 612: 43 61 93 43 75 43 93 43 61 57 N SD: 0.1141 c. M: 0.1985 c. 966: 68 96 147 68 118 68 147 68 96 90 N SD: 0.0918 c. M: 0.1833 c. 1053: 74 105 160 74 129 74 160 74 105 98 N SD: 0.1019 c. M:-0.1760 c. 1106: 78 110 168 78 135 78 168 78 110 103 N SD: 0.0875 c. M:-0.1621 c. 1137: 80 113 173 80 139 80 173 80 113 106 N SD: 0.0990 c. M: 0.2161 c. 1236: 87 123 188 87 151 87 188 87 123 115 N SD: 0.0691 c. M:-0.1073 c. 1277: 90 127 194 90 156 90 194 90 127 119 N SD: 0.0706 c. M:-0.1060 c. 1407: 99 140 214 99 172 99 214 99 140 131 N SD: 0.0412 c. M:-0.0763 c. 1718: 121 171 261 121 210 121 261 121 171 160 N SD: 0.0393 c. M: 0.0747 c. 1848: 130 184 281 130 226 130 281 130 184 172 N SD: 0.0354 c. M:-0.0569 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.0000 cents 3 x x x 4 x x 5 x x 6 S SD: 9.0880 cents 4 x x 5 x x 6 x 7 x 8 S SD: 0.0000 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 23.3161 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 13.1456 cents 7 x 8 x 9:10:11 x 12:13:14 S SD: 14.3232 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 9.9213 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 9.9108 cents 10 x 11 x 13:14:15:17:18:19:20 SD: 10.5261 cents 11 x 12:14 x 16:17:18:19:21:22 SD: 12.4685 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 9.6398 cents 14:15:16 x 18:20:21:23:25:26:28 SD: 8.1340 cents 15:16:17:19:20:21:23:25:26:28:30 SD: 7.1978 cents 16:17:18:20:21:23:24:27:28:30:32 SD: 3.1601 cents 32:34:36:40:42:46:48:53:56:60:64 SD: 2.5572 cents 39:41:44:49:51:56:59:65:68:73:78 SD: 2.2184 cents 40:42:45:50:53:57:60:67:70:75:80 SD: 1.9043 cents 48:50:54:60:63:69:72:80:84:90:96 SD: 1.7511 cents 56:59:63:70:74:80:84:93:98:105:112 SD: 1.4515 cents 63:66:71:79:83:90:95:105:110:118:126 SD: 1.4134 cents 64:67:72:80:84:91:96:107:112:120:128 SD: 1.1044 cents 80:84:90:100:105:114:120:133:140:150:160 SD: 0.6129 cents 96:101:108:120:126:137:144:160:168:180:192 SD: 0.3877 cents 144:151:162:180:189:206:216:240:252:270:288 SD: 0.3320 cents 224:235:252:280:294:320:336:373:392:420:448 SD: 0.2136 cents 240:252:270:300:315:343:360:400:420:450:480 SD: 0.0721 cents 560:588:630:700:735:800:840:933:980:1050:1120 SD: 0.0618 cents