Scala analysis: cx2
Second 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: 15/14 119.442808 major diatonic semitone 2: 7/6 266.870906 septimal minor third 3: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 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: 15/14 119.4428 major diatonic semitone 2: 49/45 147.4281 BP minor semitone 3: 15/14 119.4428 major diatonic semitone 4: 16/15 111.7313 minor diatonic semitone 5: 21/20 84.4672 minor semitone 6: 15/14 119.4428 major diatonic 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: 2 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 4 15/14 119.443 cents major diatonic semitone 1: 1 49/45 147.428 cents BP minor semitone 1: 1 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: 3 6/5 315.641 cents minor third 3: 1 60/49 350.617 cents smaller approximation to neutral third 3: 2 56/45 378.602 cents septimal narrow major third 3: 4 5/4 386.314 cents major third 4: 2 9/7 435.084 cents septimal major third, BP third 4: 1 98/75 463.069 cents 4: 1 21/16 470.781 cents narrow fourth 4: 5 4/3 498.045 cents perfect fourth 4: 1 75/56 505.757 cents marvelous fourth 5: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 1 45/32 590.224 cents diatonic tritone 5: 1 64/45 609.776 cents 2nd tritone 5: 4 10/7 617.488 cents Euler's tritone 6: 1 112/75 694.243 cents marvelous fifth 6: 5 3/2 701.955 cents perfect fifth 6: 1 32/21 729.219 cents wide fifth 6: 1 75/49 736.931 cents BP fifth 6: 2 14/9 764.916 cents septimal minor sixth 7: 4 8/5 813.686 cents minor sixth 7: 2 45/28 821.398 cents septimale wide minor sixth 7: 1 49/30 849.383 cents larger approximation to neutral sixth 7: 3 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: 1 9/5 1017.596 cents just minor seventh, BP seventh 9: 1 90/49 1052.572 cents 9: 4 28/15 1080.557 cents grave major seventh 9: 2 15/8 1088.269 cents classic major seventh 9: 2 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 : 119.4 266.9 386.3 498.0 582.5 702.0 884.4 968.8 1088.3 1200.0 119.4 : 147.4 266.9 378.6 463.1 582.5 764.9 849.4 968.8 1080.6 1200.0 266.9 : 119.4 231.2 315.6 435.1 617.5 702.0 821.4 933.1 1052.6 1200.0 386.3 : 111.7 196.2 315.6 498.0 582.5 702.0 813.7 933.1 1080.6 1200.0 498.0 : 84.5 203.9 386.3 470.8 590.2 702.0 821.4 968.8 1088.3 1200.0 582.5 : 119.4 301.8 386.3 505.8 617.5 736.9 884.4 1003.8 1115.5 1200.0 702.0 : 182.4 266.9 386.3 498.0 617.5 764.9 884.4 996.1 1080.6 1200.0 884.4 : 84.5 203.9 315.6 435.1 582.5 702.0 813.7 898.2 1017.6 1200.0 968.8 : 119.4 231.2 350.6 498.0 617.5 729.2 813.7 933.1 1115.5 1200.0 1088.3: 111.7 231.2 378.6 498.0 609.8 694.2 813.7 996.1 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 .. 386.3137 cents 25/24, 70.6724 cents 126/125, 13.7948 cents 4: 435.0841 .. 505.7565 cents 25/24, 70.6724 cents 36/35, 48.7704 cents 5: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 392/375, 76.7557 cents 6: 694.2435 .. 764.9159 cents 25/24, 70.6724 cents 392/375, 76.7557 cents 7: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 36/35, 48.7704 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 : 15/14, 119.4428 cents, amount: 4 Most common interval of one step : 15/14, 119.4428 cents, amount: 4 Least squares average step : 121.20554 cents, oct.: 1212.05541 cents Scale is strictly proper Step pattern alph. order: ABACDAEDAC Step pattern size order : CDCBACEACB Scale is a Constant Structure, by a margin of 13.79477 cents Scale diversity : 1.444756 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.395971 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 Number of recognisable fifths : 6, average 700.6697 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 9 Formal octave complements present : 3 = 30.0000% 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 : 75 (O: 75 U: 75) Highest odd numerator or denominator: 15 Scale harmonicity : 0.022881 Average absolute harmonicity : 0.206136 Specific harmonicity : 0.148847 Fundamental : 1/840, -9.7142 octaves, 0.3115 Hz. Guide tone : 420, 8.7142 octaves, 109882.737 Hz. Exponens Consonantiae : 3.528000E+05, 18.42849 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 60.0, average 6.00000 Mersenne's string divisions : 240360120 Sum of van Prooijen's expressibility: 7.23966, average 0.72397 Sum of Tenney's harmonic distance : 13.65136, average 1.36514 Vogel's harmonic complexity : 20.20000 Wille's k value : 787 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 135.20199, average 2.45822 Lattice compactness (without 2's) : 85.59377, average 1.55625 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.70000 13 1 3: -1 .. 1 0.00000 6 2 5: -1 .. 1 0.30000 5 3 7: -1 .. 1 0.20000 4 4 Average exponent except 2's : 5 / 10 = 0.50000 Average absolute exponent except 2's: 15 / 10 = 1.50000 Scale is JI-epimorphic with val: <10 16 23 28| = patent Scale is weakly epimorphic with val: <10 17 21 26|
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 21.1797 c. M: 44.3587 c. 12: 1 2 1 1 1 1 2 1 1 1 P B ME S SD: 18.2495 c. M:-33.1291 c. 19: 2 2 2 2 1 2 3 1 2 2 P D3 SD: 11.3145 c. M: 21.4575 c. 22: 2 3 2 2 2 2 3 2 2 2 SP B ME S SD: 9.3829 c. M:-17.4878 c. Dynamic Symmetrical Major 27: 3 3 3 2 2 3 4 2 3 2 P SD: 10.9216 c. M:-22.8424 c. 29: 3 3 3 3 2 3 4 2 3 3 SP D3 SD: 11.2209 c. M: 18.5950 c. 31: 3 4 3 3 2 3 5 2 3 3 P SD: 3.7634 c. M:-5.9639 c. 41: 4 5 4 4 3 4 6 3 4 4 SP SD: 3.7054 c. M: 6.3099 c. 53: 5 7 5 5 4 5 8 4 5 5 SP SD: 3.5893 c. M: 6.2353 c. 68: 7 8 7 6 5 7 10 5 7 6 SP SD: 3.1192 c. M:-5.8489 c. 72: 7 9 7 7 5 7 11 5 7 7 SP SD: 2.3457 c. M: 4.9354 c. 87: 9 10 9 8 6 9 13 6 9 8 SP SD: 2.7433 c. M: 4.8019 c. 94: 9 12 9 9 7 9 14 7 9 9 SP SD: 2.8262 c. M:-4.7218 c. 99: 10 12 10 9 7 10 15 7 10 9 SP SD: 1.2801 c. M:-2.6404 c. 130: 13 16 13 12 9 13 20 9 13 12 SP SD: 0.9216 c. M:-1.7951 c. 140: 14 17 14 13 10 14 21 10 14 13 SP SD: 0.7852 c. M: 1.5016 c. 171: 17 21 17 16 12 17 26 12 17 16 SP SD: 0.2749 c. M: 0.5494 c. 441: 44 54 44 41 31 44 67 31 44 41 SP SD: 0.1503 c. M:-0.2851 c. 612: 61 75 61 57 43 61 93 43 61 57 SP SD: 0.1177 c. M: 0.2042 c. 783: 78 96 78 73 55 78 119 55 78 73 SP SD: 0.1302 c. M: 0.2435 c. 935: 93 115 93 87 66 93 142 66 93 87 SP SD: 0.0941 c. M:-0.1616 c. 1106: 110 136 110 103 78 110 168 78 110 103 SP SD: 0.0678 c. M:-0.1280 c. 1236: 123 152 123 115 87 123 188 87 123 115 SP SD: 0.0732 c. M:-0.1194 c. 1277: 127 157 127 119 90 127 194 90 127 119 SP SD: 0.0697 c. M:-0.1033 c. 1376: 137 169 137 128 97 137 209 97 137 128 SP SD: 0.0595 c. M:-0.1034 c. 1407: 140 173 140 131 99 140 214 99 140 131 SP SD: 0.0447 c. M:-0.0801 c. 1547: 154 190 154 144 109 154 235 109 154 144 SP SD: 0.0363 c. M: 0.0665 c. 1578: 157 194 157 147 111 157 240 111 157 147 SP SD: 0.0409 c. M: 0.0558 c. 1718: 171 211 171 160 121 171 261 121 171 160 SP SD: 0.0370 c. M: 0.0747 c. 1848: 184 227 184 172 130 184 281 130 184 172 SP SD: 0.0336 c. M:-0.0569 c. 2019: 201 248 201 188 142 201 307 142 201 188 SP SD: 0.0254 c. M: 0.0456 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: 0.0000 cents 4 x x 5 x x 6 x 7 x 8 S SD: 0.0000 cents 5 x 6 x x 7 x 8:9 x 10 S SD: 19.7501 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 6.4843 cents 7 x 8:9 x 10:11 x 12:13:14 S SD: 16.2324 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 10.3519 cents 9:10 x 11:12:13:14:15:16:17:18 S SD: 12.8023 cents 10:11:12 x 13:14:15:17:18:19:20 SD: 11.3612 cents 11:12:13:14:15 x 17:18:19:21:22 SD: 10.6135 cents 12:13:14:15:16:17:18:20:21:23:24 SD: 4.7261 cents 24:26:28:30:32:34:36:40:42:45:48 S SD: 2.8031 cents 36:39:42:45:48:50:54:60:63:68:72 SD: 2.6823 cents 40:43:47:50:53:56:60:67:70:75:80 SD: 1.9427 cents 48:51:56:60:64:67:72:80:84:90:96 SD: 1.5379 cents 60:64:70:75:80:84:90:100:105:113:120 SD: 1.0882 cents 72:77:84:90:96:101:108:120:126:135:144 SD: 0.4698 cents 156:167:182:195:208:218:234:260:273:293:312 SD: 0.4583 cents 168:180:196:210:224:235:252:280:294:315:336 SD: 0.1473 cents 240:257:280:300:320:336:360:400:420:450:480 SD: 0.0962 cents 408:437:476:510:544:571:612:680:714:765:816 SD: 0.0829 cents 432:463:504:540:576:605:648:720:756:810:864 SD: 0.0783 cents 600:643:700:750:800:840:900:1000:1050:1125:1200 SD: 0.0385 cents