Scala analysis: dualhex
Aaron Johnson's dual-hexany CPS January 2 2004
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 35/32 155.139620 septimal neutral second 3: 75/64 274.582429 classic augmented second 4: 5/4 386.313714 major third 5: 21/16 470.780907 narrow fourth 6: 175/128 541.453334 7: 3/2 701.955001 perfect fifth 8: 25/16 772.627428 classic augmented fifth 9: 105/64 857.094621 septimal neutral sixth 10: 7/4 968.825906 harmonic seventh 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: 16/15 111.7313 minor diatonic semitone 2: 525/512 43.4083 Avicenna enharmonic diesis 3: 15/14 119.4428 major diatonic semitone 4: 16/15 111.7313 minor diatonic semitone 5: 21/20 84.4672 minor semitone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 192/175 160.5017 septimal 4/5-tone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 21/20 84.4672 minor semitone 10: 16/15 111.7313 minor diatonic semitone 11: 15/14 119.4428 major diatonic semitone 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 525/512 43.408 cents Avicenna enharmonic diesis 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 192/175 160.502 cents septimal 4/5-tone 2: 3 35/32 155.140 cents septimal neutral second 2: 1 1125/1024 162.851 cents double augmented prime 2: 2 28/25 196.198 cents middle second 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 5 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 2 75/64 274.582 cents classic augmented second 3: 1 25/21 301.847 cents BP second, quasi-equal minor third 3: 4 6/5 315.641 cents minor third 3: 2 128/105 342.905 cents septimal neutral third 4: 1 315/256 359.050 cents 4: 7 5/4 386.314 cents major third 4: 3 32/25 427.373 cents classic diminished fourth 4: 1 2048/1575 454.637 cents 5: 1 2625/2048 429.722 cents 5: 2 21/16 470.781 cents narrow fourth 5: 5 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 5: 1 512/375 539.104 cents double diminished fifth 5: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 1 175/128 541.453 cents 6: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 1 45/32 590.224 cents diatonic tritone 6: 1 64/45 609.776 cents 2nd tritone 6: 4 10/7 617.488 cents Euler's tritone 6: 1 256/175 658.547 cents 7: 2 35/24 653.185 cents septimal semi-diminished fifth 7: 1 375/256 660.896 cents double augmented fourth 7: 1 112/75 694.243 cents marvelous fifth 7: 5 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 7: 1 4096/2625 770.278 cents 8: 1 1575/1024 745.363 cents 8: 3 25/16 772.627 cents classic augmented fifth 8: 7 8/5 813.686 cents minor sixth 8: 1 512/315 840.950 cents 9: 2 105/64 857.095 cents septimal neutral sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 42/25 898.153 cents quasi-equal major sixth 9: 2 128/75 925.418 cents diminished seventh 9: 3 12/7 933.129 cents septimal major sixth 10: 5 7/4 968.826 cents harmonic seventh 10: 1 225/128 976.537 cents augmented sixth 10: 2 25/14 1003.802 cents middle minor seventh 10: 1 2048/1125 1037.149 cents double diminished octave 10: 3 64/35 1044.860 cents septimal neutral seventh 11: 1 175/96 1039.498 cents 11: 2 28/15 1080.557 cents grave major seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 2 48/25 1129.328 cents classic diminished octave 11: 1 1024/525 1156.592 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.27273 = 58/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 155.1 274.6 386.3 470.8 541.5 702.0 772.6 857.1 968.8 1088.3 1200.0 111.7 : 43.4 162.9 274.6 359.0 429.7 590.2 660.9 745.4 857.1 976.5 1088.3 1200.0 155.1 : 119.4 231.2 315.6 386.3 546.8 617.5 702.0 813.7 933.1 1044.9 1156.6 1200.0 274.6 : 111.7 196.2 266.9 427.4 498.0 582.5 694.2 813.7 925.4 1037.1 1080.6 1200.0 386.3 : 84.5 155.1 315.6 386.3 470.8 582.5 702.0 813.7 925.4 968.8 1088.3 1200.0 470.8 : 70.7 231.2 301.8 386.3 498.0 617.5 729.2 841.0 884.4 1003.8 1115.5 1200.0 541.5 : 160.5 231.2 315.6 427.4 546.8 658.5 770.3 813.7 933.1 1044.9 1129.3 1200.0 702.0 : 70.7 155.1 266.9 386.3 498.0 609.8 653.2 772.6 884.4 968.8 1039.5 1200.0 772.6 : 84.5 196.2 315.6 427.4 539.1 582.5 702.0 813.7 898.2 968.8 1129.3 1200.0 857.1 : 111.7 231.2 342.9 454.6 498.0 617.5 729.2 813.7 884.4 1044.9 1115.5 1200.0 968.8 : 119.4 231.2 342.9 386.3 505.8 617.5 702.0 772.6 933.1 1003.8 1088.3 1200.0 1088.3: 111.7 223.5 266.9 386.3 498.0 582.5 653.2 813.7 884.4 968.8 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.4083 .. 160.5017 cents 32768/30625, 117.0933 cents 525/512, 43.4083 cents 2: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 6125/6144,-5.3620 cents 3: 266.8709 .. 342.9054 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 4: 359.0496 .. 454.6367 cents 524288/496125, 95.5870 cents 33075/32768, 16.1442 cents 5: 429.7220 .. 546.8154 cents 32768/30625, 117.0933 cents 4134375/4194304,-24.9146 cents 6: 541.4533 .. 658.5467 cents 32768/30625, 117.0933 cents 6125/6144,-5.3620 cents 7: 653.1846 .. 770.2780 cents 32768/30625, 117.0933 cents 6125/6144,-5.3620 cents 8: 745.3633 .. 840.9504 cents 524288/496125, 95.5870 cents 4134375/4194304,-24.9146 cents 9: 857.0946 .. 933.1291 cents 256/245, 76.0345 cents 33075/32768, 16.1442 cents 10: 968.8259 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1039.4983 .. 1156.5917 cents 32768/30625, 117.0933 cents 6125/6144,-5.3620 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 525/512, 43.4083 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 192/175, 160.5017 cents Average / Smallest step : 2.303705 Largest / Average step : 1.605017 Largest / Smallest step : 3.697485 Median interval of one step : 16/15, 111.7313 cents, amount: 4 Most common interval of one step : 16/15, 111.7313 cents, amount: 4 Least squares average step : 97.32524 cents, oct.: 1167.90292 cents Scale is not proper Step pattern alph. order: ABCADEFEDACA Step pattern size order : DAEDCBFBCDED Scale is a Constant Structure, by a margin of 2.34948 cents Scale diversity : 1.509761 Lumma stability : 0.158749 Lumma impropriety factor : 0.059398 Rothenberg efficiency : 0.294192 redundancy: 0.705808 Efficiency x scale size : 3.530303 Number of different interval sizes : 58 = 5.27273 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.27273 = 58/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 65625/65536, 2.3495 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 7 Most common triad is 0.0 386.314 813.686 cents, amount: 3 Number of recognisable fifths : 6, average 700.6697 cents Scale contains a complete diamond : 1 15 Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 9 Formal octave complements present : 3 = 25.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 2625 (O: 2625 U: 2625) Highest odd numerator or denominator: 175 Scale harmonicity : 0.021825 Average absolute harmonicity : 0.159705 Specific harmonicity : 0.123025 Fundamental : 1/1920, -10.9069 octaves, 0.1363 Hz. Guide tone : 8400, 13.0362 octaves, 2197654.749 Hz. Exponens Consonantiae : 1.612800E+07, 23.94306 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 419.0, average 34.91667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.77689, average 1.23141 Sum of Tenney's harmonic distance : 28.32324, average 2.36027 Vogel's harmonic complexity : 19.75000 Wille's k value : 1312 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 321.97266, average 4.12785 Lattice compactness (without 2's) : 128.05059, average 1.64167 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -7 .. 4 -2.91667 45 1 3: -1 .. 1 0.33333 6 1 5: -1 .. 2 0.75000 11 5 7: 0 .. 1 0.41667 5 5 Average exponent except 2's : 18 / 12 = 1.50000 Average absolute exponent except 2's: 22 / 12 = 1.83333 Scale is weakly epimorphic with val: <12 18 25 33| Scale is weakly epimorphic with val: <12 18 29 33| Scale is JI-epimorphic with val: <12 19 28 34| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 30.2329 c. M:-58.5467 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 1 1 1 2 0 1 1 2 1 N D3 SD: 24.9094 c. M: 45.7490 c. 15: 2 0 2 1 1 1 2 1 1 1 2 1 N D3 SD: 25.3588 c. M:-48.2687 c. 16: 1 1 1 2 1 1 2 1 1 2 1 2 P D3 SD: 26.5139 c. M: 49.5824 c. 17: 2 0 2 2 1 1 2 1 1 2 2 1 N D3 SD: 21.9717 c. M:-41.1430 c. 19: 1 1 2 2 1 1 3 1 1 2 2 2 N SD: 25.9802 c. M: 48.5734 c. 20: 2 1 2 1 2 1 3 1 1 2 2 2 N T3 SD: 15.6270 c. M: 26.3137 c. 21: 2 1 2 2 1 1 3 2 1 2 2 2 N SD: 14.5301 c. M:-27.3726 c. 22: 2 1 2 2 2 1 3 1 2 2 2 2 P D3 SD: 9.4687 c. M:-20.1282 c. 25: 2 1 3 2 2 1 4 1 2 2 3 2 N SD: 11.3395 c. M:-18.0450 c. 28: 3 1 2 3 2 2 3 2 2 3 2 3 N SD: 12.6952 c. M: 17.4396 c. 31: 3 1 3 3 2 2 4 2 2 3 3 3 N SD: 3.5643 c. M: 6.2648 c. 53: 5 2 5 5 4 3 7 3 4 5 5 5 N SD: 2.7843 c. M:-4.7590 c. 84: 8 3 8 8 6 5 11 5 6 8 8 8 N SD: 1.8663 c. M: 3.1539 c. 87: 8 3 9 8 6 5 12 5 6 8 9 8 N SD: 2.0367 c. M: 3.5223 c. 109: 10 4 11 10 8 6 15 6 8 10 11 10 N SD: 1.6367 c. M:-2.6322 c. 118: 11 4 12 11 8 7 16 7 8 11 12 11 N SD: 1.7683 c. M: 2.9843 c. 130: 12 5 13 12 9 8 17 8 9 12 13 12 N SD: 1.6385 c. M:-3.1621 c. 140: 13 5 14 13 10 8 19 8 10 13 14 13 N SD: 0.7194 c. M: 1.4533 c. 171: 16 6 17 16 12 10 23 10 12 16 17 16 N SD: 0.6636 c. M: 1.1025 c. 270: 25 10 27 25 19 16 36 16 19 25 27 25 N SD: 0.5593 c. M:-0.9731 c. 301: 28 11 30 28 21 18 40 18 21 28 30 28 N SD: 0.4019 c. M:-0.7945 c. 388: 36 14 39 36 27 23 52 23 27 36 39 36 N SD: 0.4747 c. M: 0.7847 c. 410: 38 15 41 38 29 24 55 24 29 38 41 38 N SD: 0.3494 c. M:-0.5395 c. 441: 41 16 44 41 31 26 59 26 31 41 44 41 N SD: 0.1216 c. M:-0.2475 c. 913: 85 33 91 85 64 54 122 54 64 85 91 85 N SD: 0.1241 c. M: 0.2442 c. 935: 87 34 93 87 66 55 125 55 66 87 93 87 N SD: 0.1298 c. M:-0.2351 c. 966: 90 35 96 90 68 57 129 57 68 90 96 90 N SD: 0.0844 c. M:-0.1616 c. 1106: 103 40 110 103 78 65 148 65 78 103 110 103 N SD: 0.0614 c. M: 0.1139 c. 1407: 131 51 140 131 99 83 188 83 99 131 140 131 N SD: 0.0565 c. M:-0.1245 c. 1547: 144 56 154 144 109 91 207 91 109 144 154 144 N SD: 0.0334 c. M:-0.0659 c. 1578: 147 57 157 147 111 93 211 93 111 147 157 147 N SD: 0.0405 c. M: 0.0604 c. 1988: 185 72 198 185 140 117 266 117 140 185 198 185 N SD: 0.0405 c. M:-0.0655 c. 2019: 188 73 201 188 142 119 270 119 142 188 201 188 N SD: 0.0245 c. M: 0.0528 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: 12.8524 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 17.2465 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2192 cents 7 x x 8 x 9:10 x 11 x 12:13:14 S SD: 14.6982 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 6.5554 cents 9 x 10 x 11:12 x x 14:15:16:17:18 S SD: 8.5784 cents 10 x 11:12 x 13:14:15:16 x 18:19:20 S SD: 10.1432 cents 11 x 12:13:14 x 15 x 17:18:19:21:22 SD: 6.1801 cents 12 x 13:14:15:16 x 18:19:20:21:23:24 SD: 6.1598 cents 13:14 x 15:16:17:18 x 20:21:23:24:26 SD: 6.8964 cents 14:15 x 16 x 18:19:21:22:23:25:26:28 SD: 7.0580 cents 15:16 x 18:19:20:21 x 23:25:26:28:30 SD: 8.2354 cents 16:17:18:19:20:21:22:24:25:26:28:30:32 S SD: 4.8031 cents 23 x 25:27:29:30:31:35:36:38:40:43:46 SD: 4.0603 cents 24 x 26:28:30:32:33:36:38:39:42:45:48 S SD: 4.0399 cents 25:27 x 29:31:33:34:38:39:41:44:47:50 SD: 3.8568 cents 26:28 x 30:33:34:36:39:41:43:46:49:52 SD: 5.0594 cents 27:29:30:32:34:35:37:41:42:44:47:51:54 SD: 4.4135 cents 28:30:31:33:35:37:38:42:44:46:49:53:56 SD: 2.9740 cents 32:34:35:38:40:42:44:48:50:53:56:60:64 SD: 2.5527 cents 41:44:45:48:51:54:56:62:64:67:72:77:82 SD: 1.9563 cents 44:47:48:52:55:58:60:66:69:72:77:83:88 SD: 1.8365 cents 52:55:57:61:65:68:71:78:81:85:91:98:104 SD: 1.7167 cents 57:61:62:67:71:75:78:86:89:94:100:107:114 SD: 1.6998 cents 60:64:66:70:75:79:82:90:94:98:105:113:120 SD: 1.5069 cents 63:67:69:74:79:83:86:95:98:103:110:118:126 SD: 1.5055 cents 64:68:70:75:80:84:88:96:100:105:112:120:128 S SD: 0.9973 cents 76:81:83:89:95:100:104:114:119:125:133:143:152 SD: 0.8346 cents 105:112:115:123:131:138:144:158:164:172:184:197:210 SD: 0.8148 cents 116:124:127:136:145:152:159:174:181:190:203:218:232 SD: 0.7205 cents 128:137:140:150:160:168:175:192:200:210:224:240:256 SD: 0.4923 cents 164:175:179:192:205:215:224:246:256:269:287:308:328 SD: 0.4877 cents 169:180:185:198:211:222:231:254:264:277:296:317:338 SD: 0.4754 cents 180:192:197:211:225:236:246:270:281:295:315:338:360 SD: 0.3492 cents 192:205:210:225:240:252:263:288:300:315:336:360:384 SD: 0.3085 cents 256:273:280:300:320:336:350:384:400:420:448:480:512 SD: 0.0352 cents