Scala analysis: akj
64/63 6561/6272 Fokker block 5,5,4,4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 9/7 435.084095 septimal major third, BP third 5: 4/3 498.044999 perfect fourth 6: 81/56 638.994097 7: 3/2 701.955001 perfect fifth 8: 14/9 764.915905 septimal minor sixth 9: 27/16 905.865003 Pythagorean major sixth 10: 16/9 996.089998 Pythagorean minor seventh 11: 27/14 1137.039096 septimal major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 243/224 140.9491 Archytas' 2/3-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 54/49 168.2132 Zalzal's mujannab 5: 28/27 62.9609 Archytas' 1/3-tone 6: 243/224 140.9491 Archytas' 2/3-tone 7: 28/27 62.9609 Archytas' 1/3-tone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 243/224 140.9491 Archytas' 2/3-tone 10: 256/243 90.2250 limma, Pythagorean minor second 11: 243/224 140.9491 Archytas' 2/3-tone 12: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 28/27 62.961 cents Archytas' 1/3-tone 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 4 243/224 140.949 cents Archytas' 2/3-tone 1: 1 54/49 168.213 cents Zalzal's mujannab 2: 2 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 6 9/8 203.910 cents major whole tone 2: 4 8/7 231.174 cents septimal whole tone 3: 6 7/6 266.871 cents septimal minor third 3: 3 32/27 294.135 cents Pythagorean minor third 3: 3 243/196 372.123 cents 4: 2 98/81 329.832 cents 4: 2 896/729 357.096 cents 4: 2 81/64 407.820 cents Pythagorean major third 4: 6 9/7 435.084 cents septimal major third, BP third 5: 2 21/16 470.781 cents narrow fourth 5: 9 4/3 498.045 cents perfect fourth 5: 1 2187/1568 576.033 cents 6: 6 112/81 561.006 cents 6: 6 81/56 638.994 cents 7: 1 3136/2187 623.967 cents 7: 9 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 8: 6 14/9 764.916 cents septimal minor sixth 8: 2 128/81 792.180 cents Pythagorean minor sixth 8: 2 729/448 842.904 cents 8: 2 81/49 870.168 cents two (septimal major third, BP third) 9: 3 392/243 827.877 cents 9: 3 27/16 905.865 cents Pythagorean major sixth 9: 6 12/7 933.129 cents septimal major sixth 10: 4 7/4 968.826 cents harmonic seventh 10: 6 16/9 996.090 cents Pythagorean minor seventh 10: 2 729/392 1074.078 cents 11: 1 49/27 1031.787 cents 11: 4 448/243 1059.051 cents 11: 1 243/128 1109.775 cents Pythagorean major seventh 11: 6 27/14 1137.039 cents septimal major seventh 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 : 63.0 203.9 266.9 435.1 498.0 639.0 702.0 764.9 905.9 996.1 1137.0 1200.0 63.0 : 140.9 203.9 372.1 435.1 576.0 639.0 702.0 842.9 933.1 1074.1 1137.0 1200.0 203.9 : 63.0 231.2 294.1 435.1 498.0 561.0 702.0 792.2 933.1 996.1 1059.1 1200.0 266.9 : 168.2 231.2 372.1 435.1 498.0 639.0 729.2 870.2 933.1 996.1 1137.0 1200.0 435.1 : 63.0 203.9 266.9 329.8 470.8 561.0 702.0 764.9 827.9 968.8 1031.8 1200.0 498.0 : 140.9 203.9 266.9 407.8 498.0 639.0 702.0 764.9 905.9 968.8 1137.0 1200.0 639.0 : 63.0 125.9 266.9 357.1 498.0 561.0 624.0 764.9 827.9 996.1 1059.1 1200.0 702.0 : 63.0 203.9 294.1 435.1 498.0 561.0 702.0 764.9 933.1 996.1 1137.0 1200.0 764.9 : 140.9 231.2 372.1 435.1 498.0 639.0 702.0 870.2 933.1 1074.1 1137.0 1200.0 905.9 : 90.2 231.2 294.1 357.1 498.0 561.0 729.2 792.2 933.1 996.1 1059.1 1200.0 996.1 : 140.9 203.9 266.9 407.8 470.8 639.0 702.0 842.9 905.9 968.8 1109.8 1200.0 1137.0: 63.0 125.9 266.9 329.8 498.0 561.0 702.0 764.9 827.9 968.8 1059.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 168.2132 cents 729/686, 105.2523 cents 28/27, 62.9609 cents 2: 125.9218 .. 231.1741 cents 729/686, 105.2523 cents 19208/19683,-42.2914 cents 3: 266.8709 .. 372.1232 cents 729/686, 105.2523 cents 49/48, 35.6968 cents 4: 329.8318 .. 435.0841 cents 729/686, 105.2523 cents 19208/19683,-42.2914 cents 5: 470.7809 .. 576.0332 cents 729/686, 105.2523 cents 49/48, 35.6968 cents 6: 561.0059 .. 638.9941 cents 6561/6272, 77.9882 cents 175616/177147,-15.0273 cents 7: 623.9668 .. 729.2191 cents 729/686, 105.2523 cents 175616/177147,-15.0273 cents 8: 764.9159 .. 870.1682 cents 729/686, 105.2523 cents 49/48, 35.6968 cents 9: 827.8768 .. 933.1291 cents 729/686, 105.2523 cents 19208/19683,-42.2914 cents 10: 968.8259 .. 1074.0782 cents 729/686, 105.2523 cents 49/48, 35.6968 cents 11: 1031.7868 .. 1137.0391 cents 729/686, 105.2523 cents 19208/19683,-42.2914 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 54/49, 168.2132 cents Average / Smallest step : 1.588287 Largest / Average step : 1.682132 Largest / Smallest step : 2.671709 Median interval of one step : 76.59295 cents, amount: 0 Most common interval of one step : 28/27, 62.9609 cents, amount: 6 Least squares average step : 100.60007 cents, oct.: 1207.20087 cents Scale is not proper Step pattern alph. order: ABACABAABDBA Step pattern size order : ACADACAACBCA Scale is a Constant Structure, by a margin of 15.02729 cents Scale diversity : 1.392871 Lumma stability : 0.223924 Lumma impropriety factor : 0.166017 Rothenberg efficiency : 0.415278 redundancy: 0.584722 Efficiency x scale size : 4.983333 Number of different interval sizes : 36 = 3.27273 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.27273 = 36/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 177147/175616, 15.0273 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 Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 75.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties -- Prime limit : 7 Odd number limit : 2187 (O: 2187 U: 2187) Highest odd numerator or denominator: 81 Scale harmonicity : 0.021169 Average absolute harmonicity : 0.178021 Specific harmonicity : 0.122955 Fundamental : 1/3024, -11.5622 octaves, 0.0865 Hz. Guide tone : 9072, 13.1472 octaves, 2373467.128 Hz. Exponens Consonantiae : 2.743373E+07, 24.70945 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 192.5, average 16.04167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.81889, average 0.98491 Sum of Tenney's harmonic distance : 23.44519, average 1.95377 Vogel's harmonic complexity : 21.25000 Wille's k value : 2551 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 320.38664, average 4.10752 Lattice compactness (without 2's) : 221.97257, average 2.84580 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 -0.25000 23 1 3: -3 .. 4 0.50000 24 5 7: -1 .. 1 0.00000 6 6 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 30 / 12 = 2.50000 Scale is weakly epimorphic with val: <12 17 35| Scale is JI-epimorphic with val: <12 19 34| = patent Scale is weakly epimorphic with val: <12 19 37|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 25.6520 c. M: 38.9941 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 2 0 2 1 0 2 1 1 1 N D3 SD: 24.1190 c. M:-36.5065 c. 14: 1 1 1 2 1 1 1 1 2 1 1 1 P D3 I SD: 23.7021 c. M: 38.9941 c. 15: 1 1 1 2 1 2 1 0 2 1 2 1 N D3 SD: 27.5422 c. M: 44.9159 c. 17: 1 2 1 2 1 2 1 1 2 1 2 1 P M ME SD: 8.8025 c. M:-15.4820 c. 36: 2 4 2 5 2 4 2 2 4 3 4 2 N SD: 3.3949 c. M: 5.8650 c. 41: 2 5 2 6 2 5 2 2 5 3 5 2 N SD: 3.0371 c. M:-4.9083 c. 58: 3 7 3 8 3 7 3 3 7 4 7 3 N SD: 2.1362 c. M:-4.4798 c. 77: 4 9 4 11 4 9 4 4 9 6 9 4 N SD: 1.1541 c. M: 1.9689 c. 94: 5 11 5 13 5 11 5 5 11 7 11 5 N SD: 0.7191 c. M:-1.2142 c. 135: 7 16 7 19 7 16 7 7 16 10 16 7 N SD: 0.5735 c. M:-1.0059 c. 171: 9 20 9 24 9 20 9 9 20 13 20 9 N SD: 0.2947 c. M: 0.6018 c. 265: 14 31 14 37 14 31 14 14 31 20 31 14 N SD: 0.3000 c. M: 0.5035 c. 306: 16 36 16 43 16 36 16 16 36 23 36 16 N SD: 0.1508 c. M:-0.2216 c. 400: 21 47 21 56 21 47 21 21 47 30 47 21 N SD: 0.0777 c. M:-0.1350 c. 571: 30 67 30 80 30 67 30 30 67 43 67 30 N SD: 0.0653 c. M: 0.1149 c. 706: 37 83 37 99 37 83 37 37 83 53 83 37 N SD: 0.0570 c. M:-0.0994 c. 877: 46 103 46 123 46 103 46 46 103 66 103 46 N SD: 0.0306 c. M: 0.0522 c. 1277: 67 150 67 179 67 150 67 67 150 96 150 67 N SD: 0.0039 c. M:-0.0081 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: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 13.9684 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 18.3410 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.5750 cents 7 x 8 x 9 x 10 x 11:12 x x 14 S SD: 7.9199 cents 8 x 9 x 10:11 x 12 x x 14:15:16 S SD: 13.0450 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 10.3712 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 10.5453 cents 11 x 12:13:14:15:16 x 17:19:20:21:22 SD: 9.3967 cents 12 x x 14:15:16:17:18:19:20:21:23:24 SD: 7.7031 cents 13:14 x 15:17 x 19 x 20:22:23:25:26 SD: 8.8219 cents 14:15:16 x 18:19:20:21:22:24:25:27:28 SD: 7.2992 cents 15:16:17:18:19:20:22 x 23:25:27:29:30 SD: 7.9930 cents 16:17:18:19 x 21:23:24:25:27:28:31:32 SD: 6.0490 cents 17:18:19:20:22:23:25 x 26:29:30:33:34 SD: 6.2496 cents 18:19:20:21:23:24:26:27:28:30:32:35:36 SD: 3.8961 cents 20:21 x 23:26:27:29:30:31:34:36:39:40 SD: 4.9458 cents 22:23:25:26:28:29:32:33:34:37:39:42:44 SD: 3.9847 cents 24:25:27:28:31:32:35:36:37:41:43:46:48 SD: 3.0202 cents 30:31:34:35:39:40:43:45:47:51:53:58:60 SD: 2.9658 cents 31:32:35:36:40:41:45:47:48:52:55:60:62 SD: 2.6411 cents 32:33:36:37:41:43:46:48:50:54:57:62:64 SD: 2.3606 cents 42:44:47:49:54:56:61:63:65:71:75:81:84 SD: 2.0259 cents 48:50:54:56:62:64:69:72:75:81:85:93:96 SD: 1.6825 cents 54:56:61:63:69:72:78:81:84:91:96:104:108 SD: 1.1255 cents 78:81:88:91:100:104:113:117:121:132:139:150:156 SD: 1.0220 cents 80:83:90:93:103:107:116:120:124:135:142:154:160 SD: 1.0143 cents 90:93:101:105:116:120:130:135:140:152:160:174:180 SD: 0.8367 cents 102:106:115:119:131:136:148:153:159:172:181:197:204 SD: 0.7984 cents 108:112:122:126:139:144:156:162:168:182:192:208:216 SD: 0.7005 cents 112:116:126:131:144:149:162:168:174:189:199:216:224 SD: 0.5598 cents 126:131:142:147:162:168:182:189:196:213:224:243:252 SD: 0.5510 cents 144:149:162:168:185:192:208:216:224:243:256:278:288 SD: 0.4214 cents 168:174:189:196:216:224:243:252:261:284:299:324:336 SD: 0.3979 cents 186:193:209:217:239:248:269:279:289:314:331:359:372 SD: 0.3313 cents 192:199:216:224:247:256:278:288:299:324:341:370:384 SD: 0.3060 cents 240:249:270:280:309:320:347:360:373:405:427:463:480 SD: 0.2812 cents 270:280:304:315:347:360:391:405:420:456:480:521:540 SD: 0.2595 cents 294:305:331:343:378:392:425:441:457:496:523:567:588 SD: 0.2066 cents 354:367:398:413:455:472:512:531:551:597:629:683:708 SD: 0.1939 cents 378:392:425:441:486:504:547:567:588:638:672:729:756 SD: 0.1111 cents 486:504:547:567:625:648:703:729:756:820:864:937:972 SD: 0.0889 cents