Scala analysis: pris
Optimized (15/14)^3 (16/15)^4 (21/20)^3 (25/24)^2 scale.
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: 28/25 196.198479 middle second 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 28/15 1080.557192 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 21/20 84.4672 minor semitone 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 21/20 84.4672 minor semitone 11: 16/15 111.7313 minor diatonic semitone 12: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 21/20 84.467 cents minor semitone 1: 4 16/15 111.731 cents minor diatonic semitone 1: 3 15/14 119.443 cents major diatonic semitone 2: 2 35/32 155.140 cents septimal neutral second 2: 1 10/9 182.404 cents minor whole tone 2: 1 125/112 190.115 cents classic augmented semitone 2: 3 28/25 196.198 cents middle second 2: 1 9/8 203.910 cents major whole tone 2: 4 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 1 75/64 274.582 cents classic augmented second 3: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 5 6/5 315.641 cents minor third 3: 1 128/105 342.905 cents septimal neutral third 4: 1 56/45 378.602 cents septimal narrow major third 4: 7 5/4 386.314 cents major third 4: 3 32/25 427.373 cents classic diminished fourth 4: 1 9/7 435.084 cents septimal major third, BP third 5: 2 21/16 470.781 cents narrow fourth 5: 6 4/3 498.045 cents perfect fourth 5: 2 75/56 505.757 cents marvelous fourth 5: 1 168/125 511.840 cents 5: 1 48/35 546.815 cents septimal semi-augmented fourth 6: 5 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: 5 10/7 617.488 cents Euler's tritone 7: 1 35/24 653.185 cents septimal semi-diminished fifth 7: 1 125/84 688.160 cents 7: 2 112/75 694.243 cents marvelous fifth 7: 6 3/2 701.955 cents perfect fifth 7: 2 32/21 729.219 cents wide fifth 8: 1 14/9 764.916 cents septimal minor sixth 8: 3 25/16 772.627 cents classic augmented fifth 8: 7 8/5 813.686 cents minor sixth 8: 1 45/28 821.398 cents septimale wide minor sixth 9: 1 105/64 857.095 cents septimal neutral sixth 9: 5 5/3 884.359 cents major sixth, BP sixth 9: 2 42/25 898.153 cents quasi-equal major sixth 9: 1 128/75 925.418 cents diminished seventh 9: 3 12/7 933.129 cents septimal major sixth 10: 4 7/4 968.826 cents harmonic seventh 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 3 25/14 1003.802 cents middle minor seventh 10: 1 224/125 1009.885 cents 10: 1 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 64/35 1044.860 cents septimal neutral seventh 11: 3 28/15 1080.557 cents grave major seventh 11: 4 15/8 1088.269 cents classic major seventh 11: 3 40/21 1115.533 cents acute major seventh 11: 2 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.72727 = 52/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 196.2 266.9 386.3 498.0 582.5 702.0 813.7 884.4 968.8 1080.6 1200.0 111.7 : 84.5 155.1 274.6 386.3 470.8 590.2 702.0 772.6 857.1 968.8 1088.3 1200.0 196.2 : 70.7 190.1 301.8 386.3 505.8 617.5 688.2 772.6 884.4 1003.8 1115.5 1200.0 266.9 : 119.4 231.2 315.6 435.1 546.8 617.5 702.0 813.7 933.1 1044.9 1129.3 1200.0 386.3 : 111.7 196.2 315.6 427.4 498.0 582.5 694.2 813.7 925.4 1009.9 1080.6 1200.0 498.0 : 84.5 203.9 315.6 386.3 470.8 582.5 702.0 813.7 898.2 968.8 1088.3 1200.0 582.5 : 119.4 231.2 301.8 386.3 498.0 617.5 729.2 813.7 884.4 1003.8 1115.5 1200.0 702.0 : 111.7 182.4 266.9 378.6 498.0 609.8 694.2 764.9 884.4 996.1 1080.6 1200.0 813.7 : 70.7 155.1 266.9 386.3 498.0 582.5 653.2 772.6 884.4 968.8 1088.3 1200.0 884.4 : 84.5 196.2 315.6 427.4 511.8 582.5 702.0 813.7 898.2 1017.6 1129.3 1200.0 968.8 : 111.7 231.2 342.9 427.4 498.0 617.5 729.2 813.7 933.1 1044.9 1115.5 1200.0 1080.6: 119.4 231.2 315.6 386.3 505.8 617.5 702.0 821.4 933.1 1003.8 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 119.4428 cents 36/35, 48.7704 cents 25/24, 70.6724 cents 2: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 3: 266.8709 .. 342.9054 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 5: 470.7809 .. 546.8154 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/48, 35.6968 cents 7: 653.1846 .. 729.2191 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 9: 857.0946 .. 933.1291 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 10: 968.8259 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1129.3276 cents 36/35, 48.7704 cents 49/48, 35.6968 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 : 15/14, 119.4428 cents Average / Smallest step : 1.414979 Largest / Average step : 1.194428 Largest / Smallest step : 1.690091 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 : 98.75706 cents, oct.: 1185.08466 cents Scale is strictly proper Step pattern alph. order: ABCDABDACBAD Step pattern size order : CBADCBDCABCD Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.445012 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.415261 Rothenberg efficiency : 0.307167 redundancy: 0.692833 Efficiency x scale size : 3.686003 Number of different interval sizes : 52 = 4.72727 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.72727 = 52/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 3136/3125, 6.0832 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 7 Number of recognisable fifths : 9, average 698.7086 cents Number of appreciable fifths : 8, average 700.0271 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 10 Formal octave complements present : 5 = 41.6667% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Limited inverse transpositions with margin 76.0345 cents: 11 -- Rational properties -- Prime limit : 7 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.024498 Average absolute harmonicity : 0.183247 Specific harmonicity : 0.141104 Fundamental : 1/300, -8.2288 octaves, 0.8721 Hz. Guide tone : 1680, 10.7142 octaves, 439530.950 Hz. Exponens Consonantiae : 5.040000E+05, 18.94306 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 104.0, average 8.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.33657, average 0.77805 Sum of Tenney's harmonic distance : 18.70058, average 1.55838 Vogel's harmonic complexity : 15.91667 Wille's k value : 262 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 225.39714, average 2.88971 Lattice compactness (without 2's) : 122.03083, average 1.56450 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 0.66667 20 1 3: -1 .. 1 -0.33333 6 2 5: -2 .. 1 -0.33333 8 4 7: 0 .. 1 0.41667 5 5 Average exponent except 2's :-3 / 12 =-0.25000 Average absolute exponent except 2's: 19 / 12 = 1.58333 Scale is weakly epimorphic with val: <12 19 25 34| 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: 17.1566 c. M:-33.1291 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 1 2 2 1 2 2 1 1 2 2 P D3 SD: 10.7225 c. M: 21.4575 c. 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 10.7388 c. M:-21.9833 c. Jubilee-12 24: 2 2 1 3 2 2 2 2 2 1 3 2 P T3 SD: 13.2347 c. M:-19.4428 c. 27: 2 2 2 3 2 2 3 2 2 2 2 3 SP D3 SD: 11.9703 c. M: 22.8424 c. 29: 3 2 1 3 3 2 3 3 1 2 3 3 P SD: 11.4264 c. M: 18.5950 c. 31: 3 2 2 3 3 2 3 3 2 2 3 3 SP D3 SD: 3.5269 c. M:-5.9639 c. Fokker 12-tone 53: 5 4 3 5 5 4 5 5 3 4 5 5 SP SD: 3.9601 c. M:-7.5751 c. 68: 6 5 4 7 6 5 7 6 4 5 6 7 SP SD: 2.9625 c. M: 5.8489 c. 72: 7 5 4 7 7 5 7 7 4 5 7 7 SP SD: 2.5553 c. M:-4.9354 c. Smith's Prism 84: 8 6 5 8 8 6 8 8 5 6 8 8 SP SD: 2.8221 c. M:-5.1571 c. 87: 8 6 5 9 8 6 9 8 5 6 8 9 SP SD: 2.6590 c. M: 4.8019 c. 94: 9 6 6 9 9 7 9 9 5 7 9 9 SP SD: 3.0710 c. M:-4.7218 c. 99: 9 7 6 10 9 7 10 9 6 7 9 10 SP SD: 1.4124 c. M: 2.6404 c. 130: 12 9 8 13 12 9 13 12 8 9 12 13 SP SD: 1.1521 c. M: 2.3523 c. 140: 13 10 8 14 13 10 14 13 8 10 13 14 SP SD: 0.7862 c. M: 1.5016 c. 171: 16 12 10 17 16 12 17 16 10 12 16 17 SP SD: 0.2833 c. M:-0.5494 c. 441: 41 31 26 44 41 31 44 41 26 31 41 44 SP SD: 0.1609 c. M: 0.2851 c. 612: 57 43 36 61 57 43 61 57 36 43 57 61 SP SD: 0.1134 c. M: 0.2042 c. 935: 87 66 55 93 87 66 93 87 55 66 87 93 SP SD: 0.0983 c. M:-0.1652 c. 966: 90 68 57 96 90 68 96 90 57 68 90 96 SP SD: 0.1095 c. M:-0.2098 c. 1106: 103 78 65 110 103 78 110 103 65 78 103 110 SP SD: 0.0834 c. M:-0.1849 c. 1236: 115 87 73 123 115 87 123 115 73 87 115 123 SP SD: 0.0759 c. M:-0.1194 c. 1376: 128 97 81 137 128 97 137 128 81 97 128 137 SP SD: 0.0551 c. M: 0.1034 c. 1407: 131 99 83 140 131 99 140 131 83 99 131 140 SP SD: 0.0437 c. M:-0.0801 c. 1547: 144 109 91 154 144 109 154 144 91 109 144 154 SP SD: 0.0368 c. M: 0.0665 c. 1578: 147 111 93 157 147 111 157 147 93 111 147 157 SP SD: 0.0373 c. M:-0.0558 c. 2019: 188 142 119 201 188 142 201 188 119 142 188 201 SP SD: 0.0296 c. M: 0.0618 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: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.7943 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 5.1990 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.0804 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 5.3216 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 10.0450 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.8821 cents 11:12 x 13:14:15 x 17 x 18:19:21:22 SD: 11.2247 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 4.4924 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 7.3153 cents 14:15:16 x 18:19:20:21:22:23:25:26:28 SD: 8.4886 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 5.9199 cents 16:17:18:19:20:21:22:24:26:27:28:30:32 S SD: 5.2726 cents 17:18:19:20:21:23:24:26:27:28:30:32:34 SD: 5.1287 cents 18:19:20:21:23:24:25:27:29:30:32:34:36 SD: 4.9044 cents 20:21:22:23:25:27:28:30:32:33:35:37:40 SD: 4.8184 cents 23:25:26:27:29:31:32:35:37:38:40:43:46 SD: 4.7059 cents 24:26:27:28:30:32:34:36:38:40:42:45:48 S SD: 3.3206 cents 28:30:31:33:35:37:39:42:45:47:49:52:56 SD: 3.0925 cents 30:32:34:35:38:40:42:45:48:50:53:56:60 SD: 2.9046 cents 32:34:36:37:40:43:45:48:51:53:56:60:64 SD: 2.3726 cents 40:43:45:47:50:53:56:60:64:67:70:75:80 SD: 2.1158 cents 42:45:47:49:53:56:59:63:67:70:74:78:84 SD: 2.0553 cents 48:51:54:56:60:64:67:72:77:80:84:90:96 SD: 1.2126 cents 60:64:67:70:75:80:84:90:96:100:105:112:120 SD: 0.4300 cents 132:141:148:154:165:176:185:198:211:220:231:246:264 SD: 0.4053 cents 168:179:188:196:210:224:235:252:269:280:294:314:336 SD: 0.3185 cents 180:192:202:210:225:240:252:270:288:300:315:336:360 SD: 0.2860 cents 192:205:215:224:240:256:269:288:307:320:336:358:384 SD: 0.2585 cents 240:256:269:280:300:320:336:360:384:400:420:448:480 SD: 0.1073 cents 300:320:336:350:375:400:420:450:480:500:525:560:600 S SD: 0.0000 cents