Scala analysis: aaron_tuning_53040_53059
akj 64/63 729/686 Fokker block
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: 49/36 533.741811 Arabic lute acute fourth 7: 3/2 701.955001 perfect fifth 8: 14/9 764.915905 septimal minor sixth 9: 12/7 933.129094 septimal major sixth 10: 7/4 968.825906 harmonic seventh 11: 49/27 1031.786810 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 54/49 168.2132 Zalzal's mujannab 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: 49/48 35.6968 slendro diesis, septimal 1/6-tone 7: 54/49 168.2132 Zalzal's mujannab 8: 28/27 62.9609 Archytas' 1/3-tone 9: 54/49 168.2132 Zalzal's mujannab 10: 49/48 35.6968 slendro diesis, septimal 1/6-tone 11: 28/27 62.9609 Archytas' 1/3-tone 12: 54/49 168.2132 Zalzal's mujannab
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 5 28/27 62.961 cents Archytas' 1/3-tone 1: 1 243/224 140.949 cents Archytas' 2/3-tone 1: 4 54/49 168.213 cents Zalzal's mujannab 2: 2 343/324 98.658 cents 2: 4 9/8 203.910 cents major whole tone 2: 6 8/7 231.174 cents septimal whole tone 3: 7 7/6 266.871 cents septimal minor third 3: 2 32/27 294.135 cents Pythagorean minor third 3: 2 243/196 372.123 cents 3: 1 432/343 399.387 cents 4: 4 98/81 329.832 cents 4: 8 9/7 435.084 cents septimal major third, BP third 5: 3 21/16 470.781 cents narrow fourth 5: 8 4/3 498.045 cents perfect fourth 5: 1 486/343 603.297 cents 6: 4 49/36 533.742 cents Arabic lute acute fourth 6: 2 112/81 561.006 cents 6: 2 81/56 638.994 cents 6: 4 72/49 666.258 cents Arabic lute grave fifth 7: 1 343/243 596.703 cents 7: 8 3/2 701.955 cents perfect fifth 7: 3 32/21 729.219 cents wide fifth 8: 8 14/9 764.916 cents septimal minor sixth 8: 4 81/49 870.168 cents two (septimal major third, BP third) 9: 1 343/216 800.613 cents 9: 2 392/243 827.877 cents 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 7 12/7 933.129 cents septimal major sixth 10: 6 7/4 968.826 cents harmonic seventh 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 648/343 1101.342 cents 11: 4 49/27 1031.787 cents 11: 1 448/243 1059.051 cents 11: 5 27/14 1137.039 cents septimal major seventh 11: 2 96/49 1164.303 cents 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 : 63.0 203.9 266.9 435.1 498.0 533.7 702.0 764.9 933.1 968.8 1031.8 1200.0 63.0 : 140.9 203.9 372.1 435.1 470.8 639.0 702.0 870.2 905.9 968.8 1137.0 1200.0 203.9 : 63.0 231.2 294.1 329.8 498.0 561.0 729.2 764.9 827.9 996.1 1059.1 1200.0 266.9 : 168.2 231.2 266.9 435.1 498.0 666.3 702.0 764.9 933.1 996.1 1137.0 1200.0 435.1 : 63.0 98.7 266.9 329.8 498.0 533.7 596.7 764.9 827.9 968.8 1031.8 1200.0 498.0 : 35.7 203.9 266.9 435.1 470.8 533.7 702.0 764.9 905.9 968.8 1137.0 1200.0 533.7 : 168.2 231.2 399.4 435.1 498.0 666.3 729.2 870.2 933.1 1101.3 1164.3 1200.0 702.0 : 63.0 231.2 266.9 329.8 498.0 561.0 702.0 764.9 933.1 996.1 1031.8 1200.0 764.9 : 168.2 203.9 266.9 435.1 498.0 639.0 702.0 870.2 933.1 968.8 1137.0 1200.0 933.1 : 35.7 98.7 266.9 329.8 470.8 533.7 702.0 764.9 800.6 968.8 1031.8 1200.0 968.8 : 63.0 231.2 294.1 435.1 498.0 666.3 729.2 764.9 933.1 996.1 1164.3 1200.0 1031.8: 168.2 231.2 372.1 435.1 603.3 666.3 702.0 870.2 933.1 1101.3 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 168.2132 cents 2592/2401, 132.5164 cents 49/48, 35.6968 cents 2: 98.6577 .. 231.1741 cents 2592/2401, 132.5164 cents 16807/17496,-69.5555 cents 3: 266.8709 .. 399.3873 cents 2592/2401, 132.5164 cents 49/48, 35.6968 cents 4: 329.8318 .. 435.0841 cents 729/686, 105.2523 cents 16807/17496,-69.5555 cents 5: 470.7809 .. 603.2973 cents 2592/2401, 132.5164 cents 49/48, 35.6968 cents 6: 533.7418 .. 666.2582 cents 2592/2401, 132.5164 cents 16807/17496,-69.5555 cents 7: 596.7027 .. 729.2191 cents 2592/2401, 132.5164 cents 16807/17496,-69.5555 cents 8: 764.9159 .. 870.1682 cents 729/686, 105.2523 cents 49/48, 35.6968 cents 9: 800.6127 .. 933.1291 cents 2592/2401, 132.5164 cents 16807/17496,-69.5555 cents 10: 968.8259 .. 1101.3423 cents 2592/2401, 132.5164 cents 49/48, 35.6968 cents 11: 1031.7868 .. 1164.3032 cents 2592/2401, 132.5164 cents 16807/17496,-69.5555 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 54/49, 168.2132 cents Average / Smallest step : 2.801371 Largest / Average step : 1.682132 Largest / Smallest step : 4.712275 Median interval of one step : 28/27, 62.9609 cents, amount: 5 Most common interval of one step : 28/27, 62.9609 cents, amount: 5 Least squares average step : 97.80538 cents, oct.: 1173.66450 cents Scale is not proper Step pattern alph. order: ABACADCACDAC Step pattern size order : BCBDBADBDABD Scale is a Constant Structure, by a margin of 6.59457 cents Scale diversity : 1.436707 Lumma stability : 0.178484 Lumma impropriety factor : 0.342282 Rothenberg efficiency : 0.395893 redundancy: 0.604107 Efficiency x scale size : 4.750722 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 : 118098/117649, 6.5946 cents Number of recognisable fifths : 8, average 701.9550 cents Scale contains a complete diamond : 3 7 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 58.3333% 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 : 3 Inversional symmetry on intervals : 1-2 7-8 -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.020329 Average absolute harmonicity : 0.172607 Specific harmonicity : 0.115919 Fundamental : 1/1512, -10.5622 octaves, 0.1730 Hz. Guide tone : 1764, 10.7846 octaves, 461507.497 Hz. Exponens Consonantiae : 2.667168E+06, 21.34688 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 165.0, average 13.75000 Mersenne's string divisions : 1784742960 Sum of van Prooijen's expressibility: 11.16402, average 0.93034 Sum of Tenney's harmonic distance : 22.15667, average 1.84639 Vogel's harmonic complexity : 20.91667 Wille's k value : 850 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 262.94806, average 3.37113 Lattice compactness (without 2's) : 190.02463, average 2.43621 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.08333 17 1 3: -3 .. 2 -0.50000 18 3 7: -1 .. 2 0.50000 10 8 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 28 / 12 = 2.33333 Scale is JI-epimorphic with val: <12 19 34| = patent Scale is weakly epimorphic with val: <12 21 34|
FIT/MODE
12: 1 1 1 1 1 0 2 1 1 1 0 2 N T3 SD: 27.6472 c. M:-37.0391 c. 13: 1 1 1 2 0 1 2 0 2 0 1 2 N SD: 26.2471 c. M: 45.7490 c. 14: 1 1 1 2 1 0 2 1 2 0 1 2 N D3 SD: 16.9254 c. M: 32.4814 c. 17: 1 2 1 2 1 1 2 1 2 1 1 2 P M ME SD: 15.7152 c. M:-30.9641 c. 19: 1 2 1 3 1 0 3 1 3 0 1 3 N SD: 14.5494 c. M: 28.4787 c. 21: 1 3 1 3 1 0 3 1 3 1 1 3 N SD: 16.4533 c. M:-24.6614 c. 22: 1 3 1 3 1 1 3 1 3 1 1 3 N M DE SD: 8.0372 c. M:-14.2718 c. 36: 2 4 2 5 2 1 5 2 5 1 2 5 N SD: 2.0433 c. M: 3.9100 c. 58: 3 7 3 8 3 2 8 3 8 2 3 8 N SD: 2.2613 c. M:-4.1892 c. 77: 4 9 4 11 4 2 11 4 11 2 4 11 N SD: 1.9534 c. M: 3.8717 c. 94: 5 11 5 13 5 3 13 5 13 3 5 13 N SD: 1.2570 c. M:-2.4284 c. 99: 5 12 5 14 5 3 14 5 14 3 5 14 N SD: 1.2572 c. M: 2.3548 c. 130: 7 15 7 18 7 4 18 7 18 4 7 18 N SD: 1.1290 c. M:-2.0593 c. 135: 7 16 7 19 7 4 19 7 19 4 7 19 N SD: 0.4213 c. M: 0.7387 c. 171: 9 20 9 24 9 5 24 9 24 5 9 24 N SD: 0.2479 c. M: 0.4085 c. 306: 16 36 16 43 16 9 43 16 43 9 16 43 N SD: 0.2229 c. M: 0.4143 c. 400: 21 47 21 56 21 12 56 21 56 12 21 56 N SD: 0.1302 c. M:-0.2582 c. 535: 28 63 28 75 28 16 75 28 75 16 28 75 N SD: 0.1024 c. M:-0.2021 c. 571: 30 67 30 80 30 17 80 30 80 17 30 80 N SD: 0.0515 c. M:-0.0871 c. 706: 37 83 37 99 37 21 99 37 99 21 37 99 N SD: 0.0394 c. M: 0.0714 c. 1277: 67 150 67 179 67 38 179 67 179 38 67 179 N SD: 0.0048 c. M:-0.0092 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: 16.2568 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 12.1926 cents 5 x x 6 x x 7 x 8 x x 9:10 S SD: 17.1313 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.6401 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 14.0399 cents 8 x 9 x 10 x 11:12 x x 14:15:16 S SD: 10.9523 cents 9 x 10:11 x 12 x x 14:15:16 x 18 S SD: 14.3361 cents 10 x 11:12:13 x 14:15:16:17 x 18:20 S SD: 10.7878 cents 11 x 12:13:14 x 15 x 17:19 x 20:22 SD: 7.8705 cents 12 x x 14:15:16 x 18:19 x 21:22:24 SD: 7.5275 cents 13:14 x 15:17 x 18 x 20:22:23:24:26 SD: 10.2295 cents 14:15:16 x 18 x 19:21:22:24 x 25:28 SD: 7.8969 cents 15:16:17:18:19:20 x x 23 x 26:27:30 SD: 9.0842 cents 16:17:18:19 x 21:22:24:25:27:28:29:32 SD: 6.1405 cents 17:18:19:20:22 x 23 x 26:29:30:31:34 SD: 5.5518 cents 18:19:20:21:23:24:25:27:28:31:32:33:36 SD: 5.1746 cents 19:20:21:22:24:25:26:29:30 x 33:34:38 SD: 6.8428 cents 20:21 x 23:26 x 27:30:31:34:35:36:40 SD: 4.5826 cents 22:23:25:26:28:29:30:33:34:38:39:40:44 SD: 4.1796 cents 23:24:26:27:30 x 31:35:36:39:40:42:46 SD: 4.5753 cents 24:25:27:28:31:32:33:36:37:41:42:44:48 SD: 2.6596 cents 26:27:29:30:33:35 x 39:40:45:46:47:52 SD: 4.4635 cents 27:28:30:32:35:36:37:41:42:46:47:49:54 SD: 3.9047 cents 28:29:32:33:36:37:38:42:44:48:49:51:56 SD: 3.4079 cents 29:30:33:34:37:39 x 44:45:50:51:53:58 SD: 3.6456 cents 30:31:34:35:39:40:41:45:47:51:53:54:60 SD: 3.1729 cents 31:32:35:36:40:41:42:47:48:53:54:56:62 SD: 2.6634 cents 32:33:36:37:41:43:44:48:50:55:56:58:64 SD: 2.5634 cents 42:44:47:49:54:56:57:63:65:72:74:76:84 SD: 2.1418 cents 48:50:54:56:62:64:65:72:75:82:84:87:96 SD: 1.4492 cents 56:58:63:65:72:75:76:84:87:96:98:102:112 SD: 1.2158 cents 72:75:81:84:93:96:98:108:112:123:126:131:144 SD: 1.1153 cents 78:81:88:91:100:104:106:117:121:134:137:142:156 SD: 1.0787 cents 80:83:90:93:103:107:109:120:124:137:140:145:160 SD: 0.9262 cents 88:91:99:103:113:117:120:132:137:151:154:160:176 SD: 0.8742 cents 102:106:115:119:131:136:139:153:159:175:179:185:204 SD: 0.7217 cents 108:112:122:126:139:144:147:162:168:185:189:196:216 SD: 0.6208 cents 136:141:153:159:175:181:185:204:212:233:238:247:272 SD: 0.5442 cents 144:149:162:168:185:192:196:216:224:247:252:261:288 SD: 0.3965 cents 168:174:189:196:216:224:229:252:261:288:294:305:336 SD: 0.3387 cents 192:199:216:224:247:256:261:288:299:329:336:348:384 SD: 0.3333 cents 216:224:243:252:278:288:294:324:336:370:378:392:432 SD: 0.1855 cents 360:373:405:420:463:480:490:540:560:617:630:653:720 SD: 0.1585 cents 432:448:486:504:555:576:588:648:672:741:756:784:864 SD: 0.1392 cents 480:498:540:560:617:640:653:720:747:823:840:871:960 SD: 0.1257 cents 504:523:567:588:648:672:686:756:784:864:882:915:1008 SD: 0.1059 cents