Scala analysis: meandin
inverted detempered 7-limit meantone
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 8/7 231.174094 septimal whole tone 3: 6/5 315.641287 minor third 4: 9/7 435.084095 septimal major third, BP third 5: 4/3 498.044999 perfect fourth 6: 10/7 617.487807 Euler's tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 12/7 933.129094 septimal major sixth 10: 9/5 1017.596288 just minor seventh, BP seventh 11: 27/14 1137.039096 septimal major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 1: 15/14 119.4428 major diatonic semitone 2: 16/15 111.7313 minor diatonic semitone 3: 21/20 84.4672 minor semitone 4: 15/14 119.4428 major diatonic semitone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 15/14 119.4428 major diatonic semitone 7: 21/20 84.4672 minor semitone 8: 16/15 111.7313 minor diatonic semitone 9: 15/14 119.4428 major diatonic semitone 10: 21/20 84.4672 minor semitone 11: 15/14 119.4428 major diatonic semitone 12: 28/27 62.9609 Archytas' 1/3-tone
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 : 119.4 231.2 315.6 435.1 498.0 617.5 702.0 813.7 933.1 1017.6 1137.0 1200.0 119.4 : 111.7 196.2 315.6 378.6 498.0 582.5 694.2 813.7 898.2 1017.6 1080.6 1200.0 231.2 : 84.5 203.9 266.9 386.3 470.8 582.5 702.0 786.4 905.9 968.8 1088.3 1200.0 315.6 : 119.4 182.4 301.8 386.3 498.0 617.5 702.0 821.4 884.4 1003.8 1115.5 1200.0 435.1 : 63.0 182.4 266.9 378.6 498.0 582.5 702.0 764.9 884.4 996.1 1080.6 1200.0 498.0 : 119.4 203.9 315.6 435.1 519.6 639.0 702.0 821.4 933.1 1017.6 1137.0 1200.0 617.5 : 84.5 196.2 315.6 400.1 519.6 582.5 702.0 813.7 898.2 1017.6 1080.6 1200.0 702.0 : 111.7 231.2 315.6 435.1 498.0 617.5 729.2 813.7 933.1 996.1 1115.5 1200.0 813.7 : 119.4 203.9 323.4 386.3 505.8 617.5 702.0 821.4 884.4 1003.8 1088.3 1200.0 933.1 : 84.5 203.9 266.9 386.3 498.0 582.5 702.0 764.9 884.4 968.8 1080.6 1200.0 1017.6: 119.4 182.4 301.8 413.6 498.0 617.5 680.4 799.9 884.4 996.1 1115.5 1200.0 1137.0: 63.0 182.4 294.1 378.6 498.0 561.0 680.4 764.9 876.6 996.1 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 : 102.10605 cents, oct.: 1225.27261 cents Scale is strictly proper Step pattern alph. order: ABCADACBACAD Step pattern size order : DCBDADBCDBDA 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 Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 7 Formal octave complements present : 3 = 25.0000% 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 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 7 and 8 combined -- Rational properties -- Prime limit : 7 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 27 Scale harmonicity : 0.026488 Average absolute harmonicity : 0.178471 Specific harmonicity : 0.146854 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 1080, 10.0768 octaves, 282555.611 Hz. Exponens Consonantiae : 2.268000E+05, 17.79106 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 95.0, average 7.91667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.40342, average 0.78362 Sum of Tenney's harmonic distance : 19.10737, average 1.59228 Vogel's harmonic complexity : 15.41667 Wille's k value : 202 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 203.70488, average 2.61160 Lattice compactness (without 2's) : 139.45281, average 1.78786 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.83333 16 1 3: -1 .. 3 0.83333 12 2 5: -1 .. 1 -0.08333 5 3 7: -1 .. 0 -0.50000 6 6 Average exponent except 2's : 3 / 12 = 0.25000 Average absolute exponent except 2's: 23 / 12 = 1.91667 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: 22.5559 c. M: 37.0391 c. Twelve-tone Chromatic (1/11-comma) 14: 1 2 1 1 1 1 1 1 2 1 1 1 P D3 S SD: 22.2616 c. M: 42.2577 c. 15: 2 1 1 1 1 2 1 1 2 1 1 1 P D3 SD: 22.0460 c. M:-40.5572 c. 19: 2 2 1 2 1 2 1 2 2 1 2 1 P M ME SD: 9.8606 c. M:-21.4575 c. 22: 2 2 2 2 1 2 2 2 2 2 2 1 P D3 S SD: 10.4007 c. M:-18.7673 c. Hexachordal 27: 3 2 2 3 1 3 2 2 3 2 3 1 P SD: 9.6735 c. M:-18.5165 c. 31: 3 3 2 3 2 3 2 3 3 2 3 2 SP M ME SD: 6.7182 c. M: 14.4585 c. 33: 3 3 3 3 2 3 2 3 4 2 3 2 P D3 SD: 9.5409 c. M: 13.6863 c. 37: 4 3 3 3 2 4 3 3 4 2 4 2 SP SD: 8.4848 c. M: 13.4625 c. 38: 4 3 3 4 2 4 2 4 4 2 4 2 P D3 S SD: 8.2098 c. M:-14.2393 c. 39: 4 3 3 4 2 4 3 3 4 3 4 2 SP SD: 7.6912 c. M: 15.7895 c. 41: 4 4 3 4 2 4 3 4 4 3 4 2 SP SD: 3.9793 c. M:-6.7940 c. 53: 5 5 4 5 3 5 4 5 5 4 5 3 SP SD: 3.8391 c. M: 6.2353 c. 58: 6 5 4 6 3 6 4 5 6 4 6 3 SP SD: 3.4616 c. M: 6.7897 c. 72: 7 7 5 7 4 7 5 7 7 5 7 4 SP SD: 2.0068 c. M: 3.7058 c. 99: 10 9 7 10 5 10 7 9 10 7 10 5 SP SD: 1.1881 c. M:-2.3548 c. 130: 13 12 9 13 7 13 9 12 13 9 13 7 SP SD: 1.1807 c. M: 2.2117 c. 152: 15 14 11 15 8 15 11 14 15 11 15 8 SP SD: 1.0797 c. M: 2.2267 c. 171: 17 16 12 17 9 17 12 16 17 12 17 9 SP SD: 0.2032 c. M:-0.4049 c. 441: 44 41 31 44 23 44 31 41 44 31 44 23 SP SD: 0.1897 c. M:-0.3759 c. 612: 61 57 43 61 32 61 43 57 61 43 61 32 SP SD: 0.1386 c. M:-0.2158 c. 783: 78 73 55 78 41 78 55 73 78 55 78 41 SP SD: 0.1265 c. M:-0.2435 c. 935: 93 87 66 93 49 93 66 87 93 66 93 49 SP SD: 0.0972 c. M: 0.1616 c. 1106: 110 103 78 110 58 110 78 103 110 78 110 58 SP SD: 0.0719 c. M: 0.1280 c. 1277: 127 119 90 127 67 127 90 119 127 90 127 67 SP SD: 0.0646 c. M: 0.1033 c. 1407: 140 131 99 140 74 140 99 131 140 99 140 74 SP SD: 0.0759 c. M: 0.1521 c. 1448: 144 135 102 144 76 144 102 135 144 102 144 76 SP SD: 0.0681 c. M:-0.1259 c. 1547: 154 144 109 154 81 154 109 144 154 109 154 81 SP SD: 0.0638 c. M:-0.1296 c. 1677: 167 156 118 167 88 167 118 156 167 118 167 88 SP SD: 0.0481 c. M: 0.0906 c. 1718: 171 160 121 171 90 171 121 160 171 121 171 90 SP SD: 0.0559 c. M:-0.0987 c. 1848: 184 172 130 184 97 184 130 172 184 130 184 97 SP SD: 0.0348 c. M: 0.0638 c. 2019: 201 188 142 201 106 201 142 188 201 142 201 106 SP SD: 0.0320 c. M: 0.0629 c. 2190: 218 204 154 218 115 218 154 204 218 154 218 115 SP SD: 0.0372 c. M: 0.0620 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 7 x x 8 S SD: 15.1096 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.9951 cents 6 x 7 x x 8 x 9 x 10:11 x 12 S SD: 11.3797 cents 7 x 8 x 9 x 10 x 11:12:13 x 14 S SD: 8.9220 cents 8 x 9 x 10:11 x 12:13:14 x 15:16 S SD: 12.7065 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 11.2594 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 6.7399 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 8.8301 cents 12:13:14 x 15:16:17:18:19:21:22:23:24 SD: 7.5818 cents 13:14:15:16:17 x 19:20:21:22:23:25:26 SD: 8.2848 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 4.1850 cents 16:17:18:19 x 21:23:24:26:27:29:31:32 SD: 5.6134 cents 18:19:21:22:23:24:26:27:29:31:32:35:36 SD: 5.4666 cents 20:21:23:24:26:27:29:30:32:34:36:39:40 SD: 4.8651 cents 21:23:24:25:27:28:30:32:34:36:38:41:42 SD: 4.8131 cents 24:26:27:29:31:32:34:36:38:41:43:46:48 SD: 3.7924 cents 25:27:29:30:32:33:36:38:40:43:45:48:50 SD: 3.7506 cents 26:28:30:31:33:35:37:39:42:45:47:50:52 SD: 3.6540 cents 28:30:32:34:36:37:40:42:45:48:50:54:56 SD: 2.5147 cents 30:32:34:36:39:40:43:45:48:51:54:58:60 SD: 2.4953 cents 40:43:46:48:51:53:57:60:64:69:72:77:80 SD: 2.0794 cents 42:45:48:50:54:56:60:63:67:72:76:81:84 SD: 1.4443 cents 56:60:64:67:72:75:80:84:90:96:101:108:112 SD: 1.0453 cents 70:75:80:84:90:93:100:105:112:120:126:135:140 SD: 0.5162 cents 126:135:144:151:162:168:180:189:202:216:227:243:252 SD: 0.3666 cents 140:150:160:168:180:187:200:210:224:240:252:270:280 SD: 0.2574 cents 210:225:240:252:270:280:300:315:336:360:378:405:420 S SD: 0.0000 cents