Scala analysis: centr
Marvel projection to the 5-limit of centaur
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 9/8 203.910002 major whole tone 3: 75/64 274.582429 classic augmented second 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 45/32 590.223716 diatonic tritone 7: 3/2 701.955001 perfect fifth 8: 25/16 772.627428 classic augmented fifth 9: 5/3 884.358713 major sixth, BP sixth 10: 225/128 976.537429 augmented sixth 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 135/128 92.1787 major chroma, major limma 2: 16/15 111.7313 minor diatonic semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 16/15 111.7313 minor diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 16/15 111.7313 minor diatonic semitone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 16/15 111.7313 minor diatonic semitone 10: 135/128 92.1787 major chroma, major limma 11: 16/15 111.7313 minor diatonic semitone 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 135/128 92.179 cents major chroma, major limma 1: 7 16/15 111.731 cents minor diatonic semitone 2: 4 10/9 182.404 cents minor whole tone 2: 6 9/8 203.910 cents major whole tone 2: 2 256/225 223.463 cents Neapolitan diminished third 3: 3 75/64 274.582 cents classic augmented second 3: 3 32/27 294.135 cents Pythagorean minor third 3: 6 6/5 315.641 cents minor third 4: 7 5/4 386.314 cents major third 4: 1 512/405 405.866 cents narrow diminished fourth 4: 1 81/64 407.820 cents Pythagorean major third 4: 3 32/25 427.373 cents classic diminished fourth 5: 1 675/512 478.492 cents wide augmented third 5: 9 4/3 498.045 cents perfect fourth 5: 2 27/20 519.551 cents acute fourth 6: 1 25/18 568.717 cents classic augmented fourth 6: 5 45/32 590.224 cents diatonic tritone 6: 5 64/45 609.776 cents 2nd tritone 6: 1 36/25 631.283 cents classic diminished fifth 7: 2 40/27 680.449 cents grave fifth 7: 9 3/2 701.955 cents perfect fifth 7: 1 1024/675 721.508 cents narrow diminished sixth 8: 3 25/16 772.627 cents classic augmented fifth 8: 1 128/81 792.180 cents Pythagorean minor sixth 8: 1 405/256 794.134 cents wide augmented fifth 8: 7 8/5 813.686 cents minor sixth 9: 6 5/3 884.359 cents major sixth, BP sixth 9: 3 27/16 905.865 cents Pythagorean major sixth 9: 3 128/75 925.418 cents diminished seventh 10: 2 225/128 976.537 cents augmented sixth 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 4 9/5 1017.596 cents just minor seventh, BP seventh 11: 7 15/8 1088.269 cents classic major seventh 11: 3 256/135 1107.821 cents octave - major chroma 11: 2 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: 3.27273 = 36/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 203.9 274.6 386.3 498.0 590.2 702.0 772.6 884.4 976.5 1088.3 1200.0 92.2 : 111.7 182.4 294.1 405.9 498.0 609.8 680.4 792.2 884.4 996.1 1107.8 1200.0 203.9 : 70.7 182.4 294.1 386.3 498.0 568.7 680.4 772.6 884.4 996.1 1088.3 1200.0 274.6 : 111.7 223.5 315.6 427.4 498.0 609.8 702.0 813.7 925.4 1017.6 1129.3 1200.0 386.3 : 111.7 203.9 315.6 386.3 498.0 590.2 702.0 813.7 905.9 1017.6 1088.3 1200.0 498.0 : 92.2 203.9 274.6 386.3 478.5 590.2 702.0 794.1 905.9 976.5 1088.3 1200.0 590.2 : 111.7 182.4 294.1 386.3 498.0 609.8 702.0 813.7 884.4 996.1 1107.8 1200.0 702.0 : 70.7 182.4 274.6 386.3 498.0 590.2 702.0 772.6 884.4 996.1 1088.3 1200.0 772.6 : 111.7 203.9 315.6 427.4 519.6 631.3 702.0 813.7 925.4 1017.6 1129.3 1200.0 884.4 : 92.2 203.9 315.6 407.8 519.6 590.2 702.0 813.7 905.9 1017.6 1088.3 1200.0 976.5 : 111.7 223.5 315.6 427.4 498.0 609.8 721.5 813.7 925.4 996.1 1107.8 1200.0 1088.3: 111.7 203.9 315.6 386.3 498.0 609.8 702.0 813.7 884.4 996.1 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 111.7313 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 2: 182.4037 .. 223.4626 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 3: 274.5824 .. 315.6413 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 5: 478.4924 .. 519.5513 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 6: 568.7174 .. 631.2826 cents 648/625, 62.5651 cents 250/243, 49.1661 cents 7: 680.4487 .. 721.5076 cents 128/125, 41.0589 cents 250/243, 49.1661 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 9: 884.3587 .. 925.4176 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 10: 976.5374 .. 1017.5963 cents 128/125, 41.0589 cents 16875/16384, 51.1199 cents 11: 1088.2687 .. 1129.3276 cents 128/125, 41.0589 cents 25/24, 70.6724 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.414979 Largest / Average step : 1.117313 Largest / Smallest step : 1.580974 Median interval of one step : 16/15, 111.7313 cents, amount: 7 Most common interval of one step : 16/15, 111.7313 cents, amount: 7 Least squares average step : 98.60128 cents, oct.: 1183.21534 cents Scale is strictly proper Step pattern alph. order: ABCBBABCBABB Step pattern size order : MLSLLMLSLMLL Scale is a Constant Structure, by a margin of 49.16614 cents Scale diversity : 1.315000 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.605705 Rothenberg efficiency : 0.416997 redundancy: 0.583003 Efficiency x scale size : 5.003968 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 9, average 701.9550 cents Best fifths form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 8 and 9 combined -- Rational properties -- Prime limit : 5 Odd number limit : 675 (O: 675 U: 675) Highest odd numerator or denominator: 225 Scale harmonicity : 0.030801 Average absolute harmonicity : 0.180967 Specific harmonicity : 0.164610 Fundamental : 1/384, -8.5850 octaves, 0.6813 Hz. Guide tone : 2700, 11.3987 octaves, 706389.026 Hz. Exponens Consonantiae : 1.036800E+06, 19.98371 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 472.5, average 39.37500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 13.89125, average 1.15760 Sum of Tenney's harmonic distance : 26.71060, average 2.22588 Vogel's harmonic complexity : 14.16667 Wille's k value : 337 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 325.43697, average 4.17227 Lattice compactness (without 2's) : 149.00632, average 1.91034 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 2 -2.91667 41 1 3: -1 .. 3 0.83333 14 3 5: 0 .. 2 0.91667 11 8 Average exponent except 2's : 21 / 12 = 1.75000 Average absolute exponent except 2's: 25 / 12 = 2.08333 Scale is JI-epimorphic with val: <12 19 28| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.9863 c. M:-27.3726 c. Twelve-tone Chromatic (1/11-comma) 22: 2 2 1 2 2 2 2 1 2 2 2 2 P D3 S SD: 8.9525 c. M:-16.9122 c. 29: 2 3 2 2 3 2 3 2 2 3 2 3 SP M ME SD: 11.1480 c. M:-16.5660 c. Schismic-12 31: 2 3 2 3 3 2 3 2 3 2 3 3 SP M ME SD: 7.1823 c. M: 14.7594 c. 34: 3 3 2 3 3 3 3 2 3 3 3 3 SP D3 S SD: 7.2447 c. M:-13.7036 c. 39: 3 4 2 4 3 3 4 2 4 3 3 4 SP SD: 7.5854 c. M:-13.6863 c. 41: 3 4 2 4 4 3 4 2 4 3 4 4 SP SD: 6.5895 c. M: 11.6518 c. 43: 3 4 3 4 4 3 4 3 4 3 4 4 SP M ME SD: 5.7029 c. M:-8.7679 c. 53: 4 5 3 5 5 4 5 3 5 4 5 5 SP SD: 1.7306 c. M: 2.9525 c. 65: 5 6 4 6 6 5 6 4 6 5 6 6 SP SD: 1.4197 c. M:-2.7572 c. 118: 9 11 7 11 11 9 11 7 11 9 11 11 SP SD: 0.3299 c. M: 0.6533 c. 323: 25 30 19 30 30 25 30 19 30 25 30 30 SP SD: 0.3581 c. M:-0.7005 c. 376: 29 35 22 35 35 29 35 22 35 29 35 35 SP SD: 0.2199 c. M:-0.3745 c. 441: 34 41 26 41 41 34 41 26 41 34 41 41 SP SD: 0.1948 c. M:-0.3383 c. 494: 38 46 29 46 46 38 46 29 46 38 46 46 SP SD: 0.0959 c. M: 0.1578 c. 612: 47 57 36 57 57 47 57 36 57 47 57 57 SP SD: 0.0428 c. M: 0.0784 c. 1171: 90 109 69 109 109 90 109 69 109 90 109 109 SP SD: 0.0360 c. M:-0.0638 c. 1289: 99 120 76 120 120 99 120 76 120 99 120 120 SP SD: 0.0329 c. M:-0.0646 c. 1783: 137 166 105 166 166 137 166 105 166 137 166 166 SP SD: 0.0128 c. M:-0.0254 c. 1901: 146 177 112 177 177 146 177 112 177 146 177 177 SP SD: 0.0117 c. M:-0.0185 c. 2395: 184 223 141 223 223 184 223 141 223 184 223 223 SP SD: 0.0105 c. M: 0.0178 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 1.9279 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 14.3066 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.6104 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 11.1769 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 7.3891 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.6446 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 10.1257 cents 11 x 12:13:14:15 x x 17:18:19:21:22 SD: 10.4244 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.0359 cents 13:14 x 15:16:17:18 x 20:22:23:24:26 S SD: 8.2833 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 7.7583 cents 15:16:17:18:19:20:21 x 23:25:26:28:30 SD: 6.1185 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.8607 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.5942 cents 20:21 x 23:25:27:28:30:31:33:35:38:40 SD: 4.7474 cents 22:23:25:26:28:29:31:33:34:37:39:41:44 SD: 4.6067 cents 23:24:26:27:29:31:32:35:36:38:40:43:46 SD: 4.2193 cents 24:25:27:28:30:32:34:36:38:40:42:45:48 SD: 2.9704 cents 32:34:36:38:40:43:45:48:50:53:56:60:64 SD: 2.6975 cents 36:38:41:42:45:48:51:54:56:60:63:68:72 SD: 2.5795 cents 39:41:44:46:49:52:55:59:61:65:69:73:78 SD: 2.1059 cents 40:42:45:47:50:53:56:60:63:67:70:75:80 SD: 2.0109 cents 48:51:54:56:60:64:68:72:75:80:84:90:96 S SD: 1.7588 cents 54:57:61:63:68:72:76:81:84:90:95:101:108 SD: 1.5748 cents 57:60:64:67:71:76:80:86:89:95:100:107:114 SD: 1.2298 cents 71:75:80:83:89:95:100:107:111:118:125:133:142 SD: 1.1819 cents 72:76:81:84:90:96:101:108:113:120:127:135:144 SD: 1.1007 cents 87:92:98:102:109:116:122:131:136:145:153:163:174 SD: 0.8848 cents 96:101:108:113:120:128:135:144:150:160:169:180:192 SD: 0.7630 cents 111:117:125:130:139:148:156:167:173:185:195:208:222 SD: 0.6677 cents 128:135:144:150:160:171:180:192:200:213:225:240:256 SD: 0.3607 cents 216:228:243:253:270:288:304:324:338:360:380:405:432 SD: 0.3049 cents 240:253:270:281:300:320:338:360:375:400:422:450:480 SD: 0.2626 cents 256:270:288:300:320:341:360:384:400:427:450:480:512 SD: 0.1805 cents 384:405:432:450:480:512:540:576:600:640:675:720:768 SD: 0.0000 cents