Scala analysis: cx5
Fifth 10/4 scale <10 17 24 29| epimorphic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 7/6 266.870906 septimal minor third 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 6: 35/24 653.184619 septimal semi-diminished fifth 7: 3/2 701.955001 perfect fifth 8: 12/7 933.129094 septimal major sixth 9: 7/4 968.825906 harmonic seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 8/7 231.1741 septimal whole tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 28/25 196.1985 middle second 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 36/35 48.7704 septimal diesis, 1/4-tone 8: 8/7 231.1741 septimal whole tone 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 28/25 196.198 cents middle second 1: 3 8/7 231.174 cents septimal whole tone 2: 2 15/14 119.443 cents major diatonic semitone 2: 6 7/6 266.871 cents septimal minor third 2: 2 288/245 279.944 cents 3: 1 343/288 302.568 cents 3: 4 6/5 315.641 cents minor third 3: 1 175/144 337.543 cents 3: 2 60/49 350.617 cents smaller approximation to neutral third 3: 2 4/3 498.045 cents perfect fourth 4: 4 5/4 386.314 cents major third 4: 2 49/36 533.742 cents Arabic lute acute fourth 4: 4 48/35 546.815 cents septimal semi-augmented fourth 5: 1 9/7 435.084 cents septimal major third, BP third 5: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 5: 4 10/7 617.488 cents Euler's tritone 5: 1 14/9 764.916 cents septimal minor sixth 6: 4 35/24 653.185 cents septimal semi-diminished fifth 6: 2 72/49 666.258 cents Arabic lute grave fifth 6: 4 8/5 813.686 cents minor sixth 7: 2 3/2 701.955 cents perfect fifth 7: 2 49/30 849.383 cents larger approximation to neutral sixth 7: 1 288/175 862.457 cents 7: 4 5/3 884.359 cents major sixth, BP sixth 7: 1 576/343 897.432 cents 8: 2 245/144 920.056 cents 8: 6 12/7 933.129 cents septimal major sixth 8: 2 28/15 1080.557 cents grave major seventh 9: 3 7/4 968.826 cents harmonic seventh 9: 1 25/14 1003.802 cents middle minor seventh 9: 2 48/25 1129.328 cents classic diminished octave 9: 2 35/18 1151.230 cents septimal semi-diminished octave 9: 2 96/49 1164.303 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 35.7 266.9 315.6 386.3 582.5 653.2 702.0 933.1 968.8 1200.0 35.7 : 231.2 279.9 350.6 546.8 617.5 666.3 897.4 933.1 1164.3 1200.0 266.9 : 48.8 119.4 315.6 386.3 435.1 666.3 702.0 933.1 968.8 1200.0 315.6 : 70.7 266.9 337.5 386.3 617.5 653.2 884.4 920.1 1151.2 1200.0 386.3 : 196.2 266.9 315.6 546.8 582.5 813.7 849.4 1080.6 1129.3 1200.0 582.5 : 70.7 119.4 350.6 386.3 617.5 653.2 884.4 933.1 1003.8 1200.0 653.2 : 48.8 279.9 315.6 546.8 582.5 813.7 862.5 933.1 1129.3 1200.0 702.0 : 231.2 266.9 498.0 533.7 764.9 813.7 884.4 1080.6 1151.2 1200.0 933.1 : 35.7 266.9 302.6 533.7 582.5 653.2 849.4 920.1 968.8 1200.0 968.8 : 231.2 266.9 498.0 546.8 617.5 813.7 884.4 933.1 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 231.1741 cents 384/343, 195.4773 cents 49/48, 35.6968 cents 2: 119.4428 .. 279.9445 cents 192/175, 160.5017 cents 15/16,-111.7313 cents 3: 302.5677 .. 498.0450 cents 384/343, 195.4773 cents 84035/82944, 22.6232 cents 4: 386.3137 .. 546.8154 cents 192/175, 160.5017 cents 15/16,-111.7313 cents 5: 435.0841 .. 764.9159 cents 98/81, 329.8318 cents 15/16,-111.7313 cents 6: 653.1846 .. 813.6863 cents 192/175, 160.5017 cents 15/16,-111.7313 cents 7: 701.9550 .. 897.4323 cents 384/343, 195.4773 cents 15/16,-111.7313 cents 8: 920.0555 .. 1080.5572 cents 192/175, 160.5017 cents 84035/82944, 22.6232 cents 9: 968.8259 .. 1164.3032 cents 384/343, 195.4773 cents 15/16,-111.7313 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 3.361645 Largest / Average step : 1.926451 Largest / Smallest step : 6.476043 Median interval of one step : 25/24, 70.6724 cents, amount: 2 Most common interval of one step : 8/7, 231.1741 cents, amount: 3 Least squares average step : 111.66607 cents, oct.: 1116.66070 cents Scale is not proper Step pattern alph. order: ABCDEDCBAB Step pattern size order : AEBCDCBEAE Scale is a Constant Structure, by a margin of 22.62324 cents Scale diversity : 1.456887 Lumma stability : 0.097200 Lumma impropriety factor : 0.453722 Rothenberg efficiency : 0.366587 redundancy: 0.633413 Efficiency x scale size : 3.665873 Number of different interval sizes : 36 = 4.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1728/1715, 13.0736 cents Most common intervals : 7/6, 266.8709 cents & inv., amount: 6 Most common triad is 0.0 266.871 933.129 cents, amount: 2 Number of recognisable fifths : 2, average 701.9550 cents Scale contains a complete diamond : 3 7 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 30.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 9-10 -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.018185 Average absolute harmonicity : 0.185244 Specific harmonicity : 0.121891 Fundamental : 1/1680, -10.7142 octaves, 0.1557 Hz. Guide tone : 2940, 11.5216 octaves, 769179.162 Hz. Exponens Consonantiae : 4.939200E+06, 22.23585 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 119.5, average 11.95000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.48972, average 0.84897 Sum of Tenney's harmonic distance : 16.69180, average 1.66918 Vogel's harmonic complexity : 21.60000 Wille's k value : 857 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 158.19355, average 2.87625 Lattice compactness (without 2's) : 93.29304, average 1.69624 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.90000 17 1 3: -1 .. 1 0.00000 6 1 5: -1 .. 1 0.00000 4 2 7: -1 .. 2 0.50000 7 6 Average exponent except 2's : 5 / 10 = 0.50000 Average absolute exponent except 2's: 17 / 10 = 1.70000 Scale is weakly epimorphic with val: <10 15 21 27| Scale is weakly epimorphic with val: <10 15 22 31| Scale is weakly epimorphic with val: <10 15 23 31| Scale is weakly epimorphic with val: <10 15 24 27| Scale is weakly epimorphic with val: <10 16 21 29| Scale is weakly epimorphic with val: <10 16 22 27| Scale is weakly epimorphic with val: <10 16 24 27| Scale is weakly epimorphic with val: <10 16 25 29| Scale is weakly epimorphic with val: <10 17 21 25| Scale is weakly epimorphic with val: <10 17 23 29| Scale is JI-epimorphic with val: <10 17 24 29| Scale is weakly epimorphic with val: <10 18 22 31| Scale is weakly epimorphic with val: <10 18 23 27| Scale is weakly epimorphic with val: <10 18 25 27|
FIT/MODE
10: 0 2 1 0 2 0 1 2 0 2 N T3 SD: 29.8604 c. M: 53.1846 c. 11: 0 2 1 1 1 1 0 3 0 2 N SD: 35.2809 c. M:-50.0499 c. 12: 0 3 0 1 2 1 0 2 1 2 N SD: 27.1559 c. M:-46.8154 c. 13: 0 3 0 1 2 1 0 3 0 3 N SD: 30.5699 c. M: 55.8012 c. 15: 0 3 1 1 2 1 1 3 0 3 N SD: 20.0220 c. M: 35.6968 c. 18: 1 3 1 1 3 1 1 3 1 3 N D3 SD: 19.7574 c. M:-31.3783 c. 19: 0 4 1 1 3 1 1 4 0 4 N SD: 17.0645 c. M: 35.6968 c. 22: 1 4 1 1 4 1 1 4 1 4 N D3 SD: 10.5203 c. M:-18.8486 c. 24: 1 4 1 2 4 1 1 5 0 5 N SD: 13.7113 c. M: 18.8259 c. 26: 1 5 1 1 5 1 1 5 1 5 N D3 SD: 10.5216 c. M:-17.4878 c. 27: 1 5 1 2 4 2 1 5 1 5 N SD: 8.0783 c. M:-13.6863 c. 31: 1 6 1 2 5 2 1 6 1 6 N SD: 3.6625 c. M: 5.9639 c. 68: 2 13 3 4 11 4 3 13 2 13 N SD: 1.8939 c. M:-3.9274 c. 72: 2 14 3 4 12 4 3 14 2 14 N SD: 1.8683 c. M: 3.1846 c. 99: 3 19 4 6 16 6 4 19 3 19 N SD: 0.8641 c. M:-1.5651 c. 171: 5 33 7 10 28 10 7 33 5 33 N SD: 0.3333 c. M: 0.6091 c. 270: 8 52 11 16 44 16 11 52 8 52 N SD: 0.2042 c. M:-0.3530 c. 441: 13 85 18 26 72 26 18 85 13 85 N SD: 0.1644 c. M: 0.3227 c. 643: 19 124 26 38 105 38 26 124 19 124 N SD: 0.1711 c. M: 0.2447 c. 711: 21 137 29 42 116 42 29 137 21 137 N SD: 0.1625 c. M: 0.2538 c. 814: 24 157 33 48 133 48 33 157 24 157 N SD: 0.1788 c. M: 0.3160 c. 836: 25 161 34 49 137 49 34 161 25 161 N SD: 0.1419 c. M:-0.2629 c. 913: 27 176 37 54 149 54 37 176 27 176 N SD: 0.1414 c. M: 0.2559 c. 935: 28 180 38 55 153 55 38 180 28 180 N SD: 0.1182 c. M:-0.2390 c. 1007: 30 194 41 59 165 59 41 194 30 194 N SD: 0.1231 c. M: 0.2164 c. 1106: 33 213 45 65 181 65 45 213 33 213 N SD: 0.0699 c. M:-0.1280 c. 1277: 38 246 52 75 209 75 52 246 38 246 N SD: 0.0618 c. M:-0.1033 c. 1376: 41 265 56 81 225 81 56 265 41 265 N SD: 0.0457 c. M:-0.0799 c. 1547: 46 298 63 91 253 91 63 298 46 298 N SD: 0.0365 c. M:-0.0665 c. 1578: 47 304 64 93 258 93 64 304 47 304 N SD: 0.0384 c. M: 0.0539 c. 1749: 52 337 71 103 286 103 71 337 52 337 N SD: 0.0326 c. M: 0.0682 c. 2019: 60 389 82 119 330 119 82 389 60 389 N SD: 0.0260 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 x 3 x x 4 S SD: 0.0000 cents 3 x x x x 4 x x 5 x 6 S SD: 32.5120 cents 4 x x x 5 x x 6 x 7:8 S SD: 0.0000 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 24.3823 cents 6 x 7 x x 8 x 9:10:11:12 S SD: 21.0815 cents 7 x 8 x 9:10 x 11:12 x 14 S SD: 17.7657 cents 8 x 9 x 10:11 x 12 x 14:16 S SD: 11.7108 cents 9 x x 11 x x 13:14:15:16:18 SD: 15.2475 cents 10 x x 12:13:14 x 15:17:18:20 SD: 12.1209 cents 11:12:13 x 14:15:16:17:19 x 22 SD: 17.5095 cents 12:13:14 x 15:17 x 18 x 21:24 SD: 14.9852 cents 13:14:15 x 16:18:19:20:22:23:26 SD: 12.5806 cents 14:15:16:17:18:20 x 21:24:25:28 SD: 12.9255 cents 15:16 x 18:19:21:22:23 x 26:30 SD: 11.2685 cents 16:17 x 19:20:22:23:24:27:28:32 SD: 9.5983 cents 17:18:20 x 21:24:25:26:29:30:34 SD: 8.9328 cents 18:19:21:22:23:25:26:27:31:32:36 SD: 8.4155 cents 19:20:22:23:24:27:28:29 x 33:38 SD: 8.3308 cents 20:21:23:24:25:28:29:30:34:35:40 SD: 5.7510 cents 21:22 x 25:26:29:31:32:36:37:42 SD: 7.3391 cents 22:23:26 x 28:31:32:33:38:39:44 SD: 7.0185 cents 23:24:27:28:29:32:34:35:39:40:46 SD: 6.4546 cents 24:25:28:29:30:34:35:36:41:42:48 SD: 4.2695 cents 27:28 x 32:34:38:39:41:46:47:54 SD: 5.4178 cents 28:29:33:34:35:39:41:42:48:49:56 SD: 3.8530 cents 31:32:36:37:39:43:45:47:53:54:62 SD: 3.7358 cents 32:33:37:38:40:45:47:48:55:56:64 SD: 3.3320 cents 35:36:41:42:44:49:51:53:60:61:70 SD: 2.5286 cents 40:41:47:48:50:56:58:60:69:70:80 SD: 2.0404 cents 48:49:56:58:60:67:70:72:82:84:96 SD: 1.4368 cents 60:61:70:72:75:84:88:90:103:105:120 SD: 1.2378 cents 80:82:93:96:100:112:117:120:137:140:160 SD: 1.0759 cents 85:87:99:102:106:119:124:128:146:149:170 SD: 1.0591 cents 92:94:107:110:115:129:134:138:158:161:184 SD: 0.9618 cents 96:98:112:115:120:134:140:144:165:168:192 SD: 0.7480 cents 100:102:117:120:125:140:146:150:171:175:200 SD: 0.7006 cents 136:139:159:163:170:190:198:204:233:238:272 SD: 0.6700 cents 140:143:163:168:175:196:204:210:240:245:280 SD: 0.3940 cents 192:196:224:230:240:269:280:288:329:336:384 SD: 0.3357 cents 240:245:280:288:300:336:350:360:411:420:480 SD: 0.1804 cents 336:343:392:403:420:470:490:504:576:588:672 SD: 0.1705 cents 340:347:397:408:425:476:496:510:583:595:680 SD: 0.1675 cents 384:392:448:461:480:538:560:576:658:672:768 SD: 0.1670 cents 480:490:560:576:600:672:700:720:823:840:960 SD: 0.0301 cents