Scala analysis: meande12
chord-based detempering of 7-limit meantone
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: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 21/16 470.780907 narrow fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 14/9 764.915905 septimal minor sixth 9: 5/3 884.358713 major sixth, BP 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: 15/14 119.4428 major diatonic semitone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 15/14 119.4428 major diatonic semitone 5: 21/20 84.4672 minor semitone 6: 16/15 111.7313 minor diatonic semitone 7: 15/14 119.4428 major diatonic semitone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 15/14 119.4428 major diatonic semitone 10: 21/20 84.4672 minor semitone 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 28/27 62.961 cents Archytas' 1/3-tone 1: 3 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 5 15/14 119.443 cents major diatonic semitone 2: 4 10/9 182.404 cents minor whole tone 2: 2 28/25 196.198 cents middle second 2: 4 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 1 32/27 294.135 cents Pythagorean minor third 3: 2 25/21 301.847 cents BP second, quasi-equal minor third 3: 5 6/5 315.641 cents minor third 3: 1 135/112 323.353 cents septimal wide minor third 4: 3 56/45 378.602 cents septimal narrow major third 4: 4 5/4 386.314 cents major third 4: 1 63/50 400.108 cents quasi-equal major third 4: 1 80/63 413.578 cents wide major third 4: 3 9/7 435.084 cents septimal major third, BP third 5: 1 21/16 470.781 cents narrow fourth 5: 8 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 5: 2 27/20 519.551 cents acute fourth 6: 1 112/81 561.006 cents 6: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 5 10/7 617.488 cents Euler's tritone 6: 1 81/56 638.994 cents 7: 2 40/27 680.449 cents grave fifth 7: 1 112/75 694.243 cents marvelous fifth 7: 8 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 8: 3 14/9 764.916 cents septimal minor sixth 8: 1 63/40 786.422 cents narrow minor sixth 8: 1 100/63 799.892 cents quasi-equal minor sixth 8: 4 8/5 813.686 cents minor sixth 8: 3 45/28 821.398 cents septimale wide minor sixth 9: 1 224/135 876.647 cents narrow septimal major 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 27/16 905.865 cents Pythagorean major sixth 9: 3 12/7 933.129 cents septimal major sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 25/14 1003.802 cents middle minor seventh 10: 4 9/5 1017.596 cents just minor seventh, BP seventh 11: 5 28/15 1080.557 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 3 40/21 1115.533 cents acute major seventh 11: 2 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.36364 = 48/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 84.5 203.9 266.9 386.3 470.8 582.5 702.0 764.9 884.4 968.8 1088.3 1200.0 84.5 : 119.4 182.4 301.8 386.3 498.0 617.5 680.4 799.9 884.4 1003.8 1115.5 1200.0 203.9 : 63.0 182.4 266.9 378.6 498.0 561.0 680.4 764.9 884.4 996.1 1080.6 1200.0 266.9 : 119.4 203.9 315.6 435.1 498.0 617.5 702.0 821.4 933.1 1017.6 1137.0 1200.0 386.3 : 84.5 196.2 315.6 378.6 498.0 582.5 702.0 813.7 898.2 1017.6 1080.6 1200.0 470.8 : 111.7 231.2 294.1 413.6 498.0 617.5 729.2 813.7 933.1 996.1 1115.5 1200.0 582.5 : 119.4 182.4 301.8 386.3 505.8 617.5 702.0 821.4 884.4 1003.8 1088.3 1200.0 702.0 : 63.0 182.4 266.9 386.3 498.0 582.5 702.0 764.9 884.4 968.8 1080.6 1200.0 764.9 : 119.4 203.9 323.4 435.1 519.6 639.0 702.0 821.4 905.9 1017.6 1137.0 1200.0 884.4 : 84.5 203.9 315.6 400.1 519.6 582.5 702.0 786.4 898.2 1017.6 1080.6 1200.0 968.8 : 119.4 231.2 315.6 435.1 498.0 617.5 702.0 813.7 933.1 996.1 1115.5 1200.0 1088.3: 111.7 196.2 315.6 378.6 498.0 582.5 694.2 813.7 876.6 996.1 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 119.4428 cents 405/392, 56.4819 cents 28/27, 62.9609 cents 2: 182.4037 .. 231.1741 cents 36/35, 48.7704 cents 28/27, 62.9609 cents 3: 266.8709 .. 323.3528 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 4: 378.6022 .. 435.0841 cents 405/392, 56.4819 cents 6272/6075, 55.2494 cents 5: 470.7809 .. 519.5513 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 6: 561.0059 .. 638.9941 cents 6561/6272, 77.9882 cents 2240/2187, 41.4546 cents 7: 680.4487 .. 729.2191 cents 36/35, 48.7704 cents 2240/2187, 41.4546 cents 8: 764.9159 .. 821.3978 cents 405/392, 56.4819 cents 49/48, 35.6968 cents 9: 876.6472 .. 933.1291 cents 405/392, 56.4819 cents 6272/6075, 55.2494 cents 10: 968.8259 .. 1017.5963 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 11: 1080.5572 .. 1137.0391 cents 405/392, 56.4819 cents 28/27, 62.9609 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 : 15/14, 119.4428 cents Average / Smallest step : 1.588287 Largest / Average step : 1.194428 Largest / Smallest step : 1.897095 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Most common interval of one step : 15/14, 119.4428 cents, amount: 5 Least squares average step : 98.05937 cents, oct.: 1176.71239 cents Scale is strictly proper Step pattern alph. order: ABCBADBCBABD Step pattern size order : BDADBCDADBDC Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.412644 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.490032 Rothenberg efficiency : 0.338510 redundancy: 0.661490 Efficiency x scale size : 4.062121 Number of different interval sizes : 48 = 4.36364 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.36364 = 48/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 225/224, 7.7115 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 9, average 701.0982 cents Best fifths form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 10 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 8.3333% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 7 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 21 Scale harmonicity : 0.025805 Average absolute harmonicity : 0.173661 Specific harmonicity : 0.145505 Fundamental : 1/720, -9.4919 octaves, 0.3634 Hz. Guide tone : 630, 9.2992 octaves, 164824.106 Hz. Exponens Consonantiae : 4.536000E+05, 18.79106 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 101.0, average 8.41667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.13937, average 0.84495 Sum of Tenney's harmonic distance : 19.35725, average 1.61310 Vogel's harmonic complexity : 18.08333 Wille's k value : 472 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 213.27120, average 2.73425 Lattice compactness (without 2's) : 137.88289, average 1.76773 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.33333 20 1 3: -2 .. 2 0.16667 10 2 5: -1 .. 1 0.08333 5 3 7: 0 .. 1 0.50000 6 6 Average exponent except 2's : 9 / 12 = 0.75000 Average absolute exponent except 2's: 21 / 12 = 1.75000 Scale is weakly epimorphic with val: <12 17 26 37| 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: 20.9956 c. M:-35.0841 c. Twelve-tone Chromatic (1/11-comma) 16: 1 2 1 1 1 2 1 1 2 1 2 1 P D3 SD: 20.5723 c. M:-36.7313 c. 17: 1 2 1 1 2 1 2 1 2 1 1 2 P M ME SD: 20.3515 c. M: 33.3725 c. 19: 1 2 1 2 1 2 2 1 2 1 2 2 P M ME SD: 15.0414 c. M: 28.6756 c. 20: 1 2 1 2 2 2 2 1 2 1 2 2 P D3 S SD: 18.0732 c. M: 26.8709 c. 22: 2 2 1 2 2 2 2 1 2 2 2 2 P D3 S SD: 12.7119 c. M:-24.6237 c. 23: 2 2 1 2 2 2 2 2 2 2 2 2 SP M ME SD: 14.1881 c. M: 23.6941 c. 24: 2 2 1 3 1 3 2 1 3 1 3 2 P T3 SD: 14.2278 c. M: 20.7809 c. 25: 2 2 2 2 2 2 3 1 2 2 3 2 P D3 SD: 12.6788 c. M:-21.1291 c. 27: 2 3 1 3 2 2 3 1 3 2 3 2 P SD: 11.8548 c. M:-22.8424 c. 28: 2 3 1 3 2 3 2 2 3 2 2 3 SP D3 SD: 11.6550 c. M:-17.4878 c. 29: 2 3 1 3 2 3 3 1 3 2 3 3 P SD: 12.5626 c. M: 20.0883 c. 30: 2 3 2 3 2 3 3 1 3 2 3 3 P D3 SD: 10.4115 c. M:-18.0450 c. 31: 2 3 2 3 2 3 3 2 3 2 3 3 SP M ME SD: 5.6728 c. M: 10.3616 c. 41: 3 4 2 4 3 4 4 2 4 3 4 4 SP SD: 3.7108 c. M: 6.3099 c. 53: 4 5 3 5 4 5 5 3 5 4 5 5 SP SD: 3.7983 c. M:-6.1671 c. 72: 5 7 4 7 5 7 7 4 7 5 7 7 SP SD: 2.5829 c. M: 4.9354 c. 94: 7 9 5 9 7 9 9 5 9 7 9 9 SP SD: 2.6886 c. M:-4.8945 c. 99: 7 10 5 10 7 9 10 5 10 7 10 9 SP SD: 1.3631 c. M:-2.6404 c. 130: 9 13 7 13 9 12 13 7 13 9 13 12 SP SD: 1.0070 c. M:-1.7951 c. 171: 12 17 9 17 12 16 17 9 17 12 17 16 SP SD: 0.3276 c. M: 0.6055 c. 441: 31 44 23 44 31 41 44 23 44 31 44 41 SP SD: 0.1485 c. M: 0.2901 c. 612: 43 61 32 61 43 57 61 32 61 43 61 57 SP SD: 0.1342 c. M: 0.2100 c. 783: 55 78 41 78 55 73 78 41 78 55 78 73 SP SD: 0.1589 c. M: 0.2828 c. 836: 59 83 44 83 59 78 83 44 83 59 83 78 SP SD: 0.1532 c. M:-0.2629 c. 935: 66 93 49 93 66 87 93 49 93 66 93 87 SP SD: 0.1328 c. M:-0.2387 c. 1053: 74 105 55 105 74 98 105 55 105 74 105 98 SP SD: 0.1307 c. M: 0.2435 c. 1065: 75 106 56 106 75 99 106 56 106 75 106 99 SP SD: 0.1344 c. M:-0.2050 c. 1106: 78 110 58 110 78 103 110 58 110 78 110 103 SP SD: 0.0806 c. M:-0.1621 c. 1236: 87 123 65 123 87 115 123 65 123 87 123 115 SP SD: 0.0815 c. M:-0.1326 c. 1277: 90 127 67 127 90 119 127 67 127 90 127 119 SP SD: 0.0644 c. M:-0.1060 c. 1407: 99 140 74 140 99 131 140 74 140 99 140 131 SP SD: 0.0554 c. M:-0.1161 c. 1547: 109 154 81 154 109 144 154 81 154 109 154 144 SP SD: 0.0563 c. M:-0.0978 c. 1677: 118 167 88 167 118 156 167 88 167 118 167 156 SP SD: 0.0548 c. M:-0.1034 c. 1718: 121 171 90 171 121 160 171 90 171 121 171 160 SP SD: 0.0440 c. M: 0.0747 c. 1848: 130 184 97 184 130 172 184 97 184 130 184 172 SP SD: 0.0329 c. M:-0.0569 c. 2019: 142 201 106 201 142 188 201 106 201 142 201 188 SP SD: 0.0359 c. M: 0.0690 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: 9.0880 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: 16.8946 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 7.9180 cents 7 x 8 x x 9:10 x 11 x 12:13:14 S SD: 10.2006 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 6.7248 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.9948 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 10.3077 cents 11 x 12:13:14 x 15 x 17:18:19:21:22 SD: 10.5453 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 7.3165 cents 13:14 x 15:16:17:18 x 20:22:23:24:26 S SD: 7.4545 cents 14:15:16 x x 18:20:21:22:23:25:26:28 SD: 8.3014 cents 15:16:17:18:19:20:21 x 23:25:26:28:30 SD: 6.7473 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 4.4517 cents 17:18:19:20:21:22:24 x 26:28:30:32:34 S SD: 5.2312 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 5.1600 cents 20:21 x 23:25:26:28:30:31:33:35:38:40 SD: 3.8159 cents 23:24:26:27:29:30:32:35:36:38:40:43:46 SD: 3.5977 cents 24:25:27:28:30:32:34:36:37:40:42:45:48 SD: 3.3276 cents 25:26:28:29:31:33:35:38:39:42:44:47:50 SD: 3.3146 cents 32:34:36:37:40:42:45:48:50:53:56:60:64 SD: 2.4967 cents 40:42:45:47:50:53:56:60:62:67:70:75:80 SD: 1.9258 cents 48:50:54:56:60:63:67:72:75:80:84:90:96 SD: 1.3854 cents 64:67:72:75:80:84:90:96:100:107:112:120:128 SD: 1.2753 cents 72:76:81:84:90:95:101:108:112:120:126:135:144 SD: 1.1140 cents 80:84:90:93:100:105:112:120:124:133:140:150:160 SD: 0.8144 cents 96:101:108:112:120:126:134:144:149:160:168:180:192 SD: 0.6088 cents 120:126:135:140:150:158:168:180:187:200:210:225:240 SD: 0.5247 cents 144:151:162:168:180:189:202:216:224:240:252:270:288 SD: 0.3439 cents 160:168:180:187:200:210:224:240:249:267:280:300:320 SD: 0.3207 cents 240:252:270:280:300:315:336:360:373:400:420:450:480 SD: 0.1289 cents 480:504:540:560:600:630:672:720:747:800:840:900:960 SD: 0.0644 cents