Scala analysis: even12b
second maximally even {15/14,16/15,21/20,25/24} scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 28/25 196.198479 middle second 3: 6/5 315.641287 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: 63/40 786.422194 narrow minor sixth 9: 42/25 898.153480 quasi-equal major 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: 21/20 84.4672 minor semitone 2: 16/15 111.7313 minor diatonic semitone 3: 15/14 119.4428 major diatonic semitone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 15/14 119.4428 major diatonic semitone 8: 21/20 84.4672 minor semitone 9: 16/15 111.7313 minor diatonic semitone 10: 25/24 70.6724 classic chromatic semitone, minor chroma 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: 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 10/9 182.404 cents minor whole tone 2: 2 125/112 190.115 cents classic augmented semitone 2: 4 28/25 196.198 cents middle second 2: 2 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 1 189/160 288.377 cents 3: 4 25/21 301.847 cents BP second, quasi-equal minor third 3: 1 448/375 307.930 cents 3: 4 6/5 315.641 cents minor third 4: 6 5/4 386.314 cents major third 4: 2 63/50 400.108 cents quasi-equal major third 4: 2 80/63 413.578 cents wide major third 4: 2 32/25 427.373 cents classic diminished fourth 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: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 2 45/32 590.224 cents diatonic tritone 6: 2 64/45 609.776 cents 2nd tritone 6: 4 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: 2 25/16 772.627 cents classic augmented fifth 8: 2 63/40 786.422 cents narrow minor sixth 8: 2 100/63 799.892 cents quasi-equal minor sixth 8: 6 8/5 813.686 cents minor sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 1 375/224 892.070 cents 9: 4 42/25 898.153 cents quasi-equal major sixth 9: 1 320/189 911.623 cents 9: 2 12/7 933.129 cents septimal major sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 4 25/14 1003.802 cents middle minor seventh 10: 2 224/125 1009.885 cents 10: 2 9/5 1017.596 cents just minor seventh, BP 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: 5 Average number of different intervals per interval class: 4.54545 = 50/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.5 196.2 315.6 386.3 498.0 582.5 702.0 786.4 898.2 968.8 1088.3 1200.0 84.5 : 111.7 231.2 301.8 413.6 498.0 617.5 702.0 813.7 884.4 1003.8 1115.5 1200.0 196.2 : 119.4 190.1 301.8 386.3 505.8 590.2 702.0 772.6 892.1 1003.8 1088.3 1200.0 315.6 : 70.7 182.4 266.9 386.3 470.8 582.5 653.2 772.6 884.4 968.8 1080.6 1200.0 386.3 : 111.7 196.2 315.6 400.1 511.8 582.5 702.0 813.7 898.2 1009.9 1129.3 1200.0 498.0 : 84.5 203.9 288.4 400.1 470.8 590.2 702.0 786.4 898.2 1017.6 1088.3 1200.0 582.5 : 119.4 203.9 315.6 386.3 505.8 617.5 702.0 813.7 933.1 1003.8 1115.5 1200.0 702.0 : 84.5 196.2 266.9 386.3 498.0 582.5 694.2 813.7 884.4 996.1 1080.6 1200.0 786.4 : 111.7 182.4 301.8 413.6 498.0 609.8 729.2 799.9 911.6 996.1 1115.5 1200.0 898.2 : 70.7 190.1 301.8 386.3 498.0 617.5 688.2 799.9 884.4 1003.8 1088.3 1200.0 968.8 : 119.4 231.2 315.6 427.4 546.8 617.5 729.2 813.7 933.1 1017.6 1129.3 1200.0 1088.3: 111.7 196.2 307.9 427.4 498.0 609.8 694.2 813.7 898.2 1009.9 1080.6 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: 182.4037 .. 231.1741 cents 36/35, 48.7704 cents 28/27, 62.9609 cents 3: 266.8709 .. 315.6413 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 5: 470.7809 .. 546.8154 cents 256/245, 76.0345 cents 525/512, 43.4083 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: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 525/512, 43.4083 cents 9: 884.3587 .. 933.1291 cents 36/35, 48.7704 cents 25/24, 70.6724 cents 10: 968.8259 .. 1017.5963 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1129.3276 cents 36/35, 48.7704 cents 28/27, 62.9609 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 : 98.92615 cents, oct.: 1187.11384 cents Scale is strictly proper Step pattern alph. order: ABCDBACABDCB Step pattern size order : BCDACBDBCADC Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.370514 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.531846 Rothenberg efficiency : 0.297499 redundancy: 0.702501 Efficiency x scale size : 3.569986 Number of different interval sizes : 50 = 4.54545 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.54545 = 50/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 3136/3125, 6.0832 cents 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 10 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval class 1 Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 6-7 -- Rational properties -- Prime limit : 7 Odd number limit : 375 (O: 375 U: 375) Highest odd numerator or denominator: 63 Scale harmonicity : 0.023537 Average absolute harmonicity : 0.174470 Specific harmonicity : 0.127605 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 7.560000E+05, 19.52803 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 172.5, average 14.37500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.13591, average 0.92799 Sum of Tenney's harmonic distance : 21.89786, average 1.82482 Vogel's harmonic complexity : 18.00000 Wille's k value : 562 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 229.50746, average 2.94240 Lattice compactness (without 2's) : 138.09254, average 1.77042 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.50000 20 1 3: -1 .. 2 0.50000 8 2 5: -2 .. 1 -0.50000 10 3 7: 0 .. 1 0.50000 6 6 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 24 / 12 = 2.00000 Scale is weakly epimorphic with val: <12 17 25 35| Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 20 26 31| Scale is weakly epimorphic with val: <12 20 26 33| Scale is weakly epimorphic with val: <12 20 26 35| Scale is weakly epimorphic with val: <12 20 26 37|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.8395 c. M:-31.1741 c. Twelve-tone Chromatic (1/11-comma) 19: 1 2 2 1 2 1 2 1 2 1 2 2 P D3 SD: 14.5422 c. M: 28.5275 c. 24: 2 2 2 2 2 2 2 2 2 1 3 2 P T3 SD: 11.8355 c. M: 18.8259 c. 27: 2 2 3 2 2 2 3 2 2 2 2 3 SP D3 SD: 11.4520 c. M: 21.6020 c. 29: 2 3 3 1 3 2 3 2 3 1 3 3 P SD: 9.8205 c. M: 17.1018 c. 31: 2 3 3 2 3 2 3 2 3 2 3 3 SP D3 SD: 5.6378 c. M: 12.2286 c. 41: 3 4 4 2 4 3 4 3 4 2 4 4 SP SD: 5.0398 c. M:-9.1636 c. 43: 3 4 4 3 4 3 4 3 4 3 4 4 SP D3 SD: 4.6459 c. M: 8.6645 c. 53: 4 5 5 3 5 4 5 4 5 3 5 5 SP SD: 4.6002 c. M:-7.5751 c. 56: 4 5 6 3 5 4 6 4 5 3 6 5 SP SD: 4.1070 c. M:-6.4349 c. 68: 5 6 7 4 6 5 7 5 6 4 7 6 SP SD: 3.6178 c. M:-7.6955 c. 72: 5 7 7 4 7 5 7 5 7 4 7 7 SP SD: 2.5160 c. M: 4.9354 c. 84: 6 8 8 5 8 6 8 6 8 5 8 8 SP SD: 2.1077 c. M:-3.8015 c. 87: 6 8 9 5 8 6 9 6 8 5 9 8 SP SD: 1.9421 c. M: 3.3087 c. 99: 7 9 10 6 9 7 10 7 9 6 10 9 SP SD: 1.3536 c. M:-2.6404 c. 130: 9 12 13 8 12 9 13 9 12 8 13 12 SP SD: 1.4693 c. M: 2.7689 c. 140: 10 13 14 8 13 10 14 10 13 8 14 13 SP SD: 1.1178 c. M:-2.1492 c. 171: 12 16 17 10 16 12 17 12 16 10 17 16 SP SD: 0.2975 c. M: 0.5494 c. 441: 31 41 44 26 41 31 44 31 41 26 44 41 SP SD: 0.1392 c. M: 0.2801 c. 612: 43 57 61 36 57 43 61 43 57 36 61 57 SP SD: 0.1089 c. M: 0.1985 c. 795: 56 74 79 47 74 56 79 56 74 47 79 74 SP SD: 0.1023 c. M:-0.2307 c. 966: 68 90 96 57 90 68 96 68 90 57 96 90 SP SD: 0.0773 c. M:-0.1182 c. 1236: 87 115 123 73 115 87 123 87 115 73 123 115 SP SD: 0.0675 c. M: 0.1073 c. 1407: 99 131 140 83 131 99 140 99 131 83 140 131 SP SD: 0.0450 c. M: 0.0763 c. 1578: 111 147 157 93 147 111 157 111 147 93 157 147 SP SD: 0.0500 c. M: 0.1104 c. 1988: 140 185 198 117 185 140 198 140 185 117 198 185 SP SD: 0.0468 c. M:-0.0969 c. 2019: 142 188 201 119 188 142 201 142 188 119 201 188 SP SD: 0.0502 c. M: 0.0923 c. 2159: 152 201 215 127 201 152 215 152 201 127 215 201 SP SD: 0.0343 c. M:-0.0604 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: 4.5983 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: 11.1748 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 10.6491 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.3734 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.8660 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.3786 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.3437 cents 11 x 12:13:14:15 x x 17:18:19:21:22 SD: 11.0538 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 7.8453 cents 13:14:15 x 16:17:18 x 20:22:23:24:26 S SD: 9.8406 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 8.3930 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 5.5304 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 4.3891 cents 24:25:27:29:30:32:34:36:38:40:42:45:48 SD: 2.7473 cents 35:37:39:42:44:47:49:53:55:59:61:66:70 SD: 2.5441 cents 40:42:45:48:50:53:56:60:63:67:70:75:80 SD: 1.1900 cents 60:63:67:72:75:80:84:90:95:101:105:113:120 SD: 1.1205 cents 75:79:84:90:94:100:105:113:118:126:131:141:150 SD: 1.0063 cents 80:84:90:96:100:107:112:120:126:134:140:150:160 SD: 0.8947 cents 84:88:94:101:105:112:118:126:132:141:147:158:168 SD: 0.8806 cents 100:105:112:120:125:133:140:150:158:168:175:188:200 SD: 0.6979 cents 120:126:134:144:150:160:168:180:189:202:210:225:240 SD: 0.5164 cents 144:151:161:173:180:192:202:216:227:242:252:270:288 SD: 0.4768 cents 160:168:179:192:200:213:224:240:252:269:280:300:320 SD: 0.2973 cents 200:210:224:240:250:267:280:300:315:336:350:375:400 SD: 0.1802 cents 240:252:269:288:300:320:336:360:378:403:420:450:480 SD: 0.1290 cents 360:378:403:432:450:480:504:540:567:605:630:675:720 SD: 0.0860 cents 560:588:627:672:700:747:784:840:882:941:980:1050:1120 SD: 0.0849 cents 600:630:672:720:750:800:840:900:945:1008:1050:1125:1200 S SD: 0.0000 cents