Scala analysis: mean441
7-limit JI meantone, 441-et detempered
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16384/15309 117.489087 2: 262144/234375 193.849002 3: 1225/1024 310.279241 two (septimal neutral second) 4: 5/4 386.313714 major third 5: 8192/6125 503.407045 6: 65536/46875 580.162716 7: 6125/4096 696.592955 8: 8/5 813.686286 minor sixth 9: 2048/1225 889.720759 10: 234375/131072 1006.150998 11: 15309/8192 1082.510913 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16384/15309 117.4891 1: 16384/15309 117.4891 2: 81648/78125 76.3599 3: 287109375/268435456 116.4302 4: 256/245 76.0345 septimal minor semitone 5: 32768/30625 117.0933 6: 392/375 76.7557 7: 287109375/268435456 116.4302 8: 32768/30625 117.0933 9: 256/245 76.0345 septimal minor semitone 10: 287109375/268435456 116.4302 11: 81648/78125 76.3599 12: 16384/15309 117.4891
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/245 76.034 cents septimal minor semitone 1: 2 81648/78125 76.360 cents 1: 1 392/375 76.756 cents 1: 3 287109375/268435456 116.430 cents 1: 2 32768/30625 117.093 cents 1: 2 16384/15309 117.489 cents 2: 2 1171875/1048576 192.465 cents 2: 2 18753525/16777216 192.790 cents 2: 2 8388608/7503125 193.128 cents 2: 1 37515625/33554432 193.186 cents 2: 3 262144/234375 193.849 cents 2: 1 9375/8192 233.524 cents 2: 1 268435456/234365481 234.978 cents 3: 2 76545/65536 268.825 cents 3: 1 67108864/57421875 269.883 cents 3: 3 1875/1568 309.558 cents 3: 4 1225/1024 310.279 cents two (septimal neutral second) 3: 2 311.33809 cents 4: 2 2187/1750 385.918 cents 4: 5 5/4 386.314 cents major third 4: 1 387.69800 cents 4: 1 425.98828 cents 4: 1 32/25 427.373 cents classic diminished fourth 4: 2 2800/2187 427.768 cents 5: 1 20412/15625 462.674 cents 5: 1 717609375/536870912 502.348 cents 5: 2 1435546875/10737418 502.744 cents 5: 4 8192/6125 503.407 cents 5: 2 20480/15309 503.803 cents 5: 2 12544/9375 504.128 cents 6: 2 93767625/67108864 579.104 cents 6: 1 2097152/1500625 579.442 cents 6: 3 65536/46875 580.163 cents 6: 3 46875/32768 619.837 cents 6: 1 1500625/1048576 620.558 cents 6: 2 134217728/93767625 620.896 cents 7: 2 9375/6272 695.872 cents 7: 2 15309/10240 696.197 cents 7: 4 6125/4096 696.593 cents 7: 2 697.25605 cents 7: 1 1073741824/71760937 697.652 cents 7: 1 15625/10206 737.326 cents 8: 2 2187/1400 772.232 cents 8: 1 25/16 772.627 cents classic augmented fifth 8: 1 774.01172 cents 8: 1 812.30200 cents 8: 5 8/5 813.686 cents minor sixth 8: 2 3500/2187 814.082 cents 9: 2 888.66191 cents 9: 4 2048/1225 889.721 cents 9: 3 3136/1875 890.442 cents 9: 1 57421875/33554432 930.117 cents 9: 2 131072/76545 931.175 cents 10: 1 234365481/134217728 965.022 cents 10: 1 16384/9375 966.476 cents 10: 3 234375/131072 1006.151 cents 10: 1 67108864/37515625 1006.814 cents 10: 2 7503125/4194304 1006.872 cents 10: 2 33554432/18753525 1007.210 cents 10: 2 2097152/1171875 1007.535 cents 11: 2 15309/8192 1082.511 cents 11: 2 30625/16384 1082.907 cents 11: 3 536870912/287109375 1083.570 cents 11: 1 375/196 1123.244 cents 11: 2 78125/40824 1123.640 cents 11: 2 245/128 1123.966 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 117.5 193.8 310.3 386.3 503.4 580.2 696.6 813.7 889.7 1006.2 1082.5 1200.0 117.5 : 76.4 192.8 268.8 385.9 462.7 579.1 696.2 772.2 888.7 965.0 1082.5 1200.0 193.8 : 116.4 192.5 309.6 386.3 502.7 619.8 695.9 812.3 888.7 1006.2 1123.6 1200.0 310.3 : 76.0 193.1 269.9 386.3 503.4 579.4 695.9 772.2 889.7 1007.2 1083.6 1200.0 386.3 : 117.1 193.8 310.3 427.4 503.4 619.8 696.2 813.7 931.2 1007.5 1124.0 1200.0 503.4 : 76.8 193.2 310.3 386.3 502.7 579.1 696.6 814.1 890.4 1006.9 1082.9 1200.0 580.2 : 116.4 233.5 309.6 426.0 502.3 619.8 737.3 813.7 930.1 1006.2 1123.2 1200.0 696.6 : 117.1 193.1 309.6 385.9 503.4 620.9 697.3 813.7 889.7 1006.8 1083.6 1200.0 813.7 : 76.0 192.5 268.8 386.3 503.8 580.2 696.6 772.6 889.7 966.5 1082.9 1200.0 889.7 : 116.4 192.8 310.3 427.8 504.1 620.6 696.6 813.7 890.4 1006.9 1124.0 1200.0 1006.2: 76.4 193.8 311.3 387.7 504.1 580.2 697.3 774.0 890.4 1007.5 1083.6 1200.0 1082.5: 117.5 235.0 311.3 427.8 503.8 620.9 697.7 814.1 931.2 1007.2 1123.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.0345 .. 117.4891 cents 2240/2187, 41.4546 cents 256/245, 76.0345 cents 2: 192.4647 .. 234.9782 cents 42.51346 cents 74.97562 cents 3: 268.8246 .. 311.3381 cents 42.51346 cents 33.84645 cents 4: 385.9180 .. 427.7683 cents 4900000/4782969, 41.8504 cents 74.57987 cents 5: 462.6736 .. 504.1282 cents 2240/2187, 41.4546 cents 1594323/1562500, 34.9053 cents 6: 579.1039 .. 620.8961 cents 41.79227 cents 74.97562 cents 7: 695.8718 .. 737.3264 cents 2240/2187, 41.4546 cents 74.97562 cents 8: 772.2317 .. 814.0820 cents 4900000/4782969, 41.8504 cents 1594323/1562500, 34.9053 cents 9: 888.6619 .. 931.1754 cents 42.51346 cents 74.57987 cents 10: 965.0218 .. 1007.5353 cents 42.51346 cents 33.84645 cents 11: 1082.5109 .. 1123.9655 cents 2240/2187, 41.4546 cents 74.97562 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 256/245, 76.0345 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16384/15309, 117.4891 cents Average / Smallest step : 1.315193 Largest / Average step : 1.174891 Largest / Smallest step : 1.545208 Median interval of one step : 287109375/268435456, 116.4302 cents, amount: 3 Most common interval of one step : 287109375/268435456, 116.4302 cents, amount: 3 Least squares average step : 99.60238 cents, oct.: 1195.22860 cents Scale is strictly proper Step pattern alph. order: ABCDEFCEDCBA Step pattern size order : FBDAECDEADBF Scale is a Constant Structure, by a margin of 33.84645 cents Scale diversity : 1.234397 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.615529 Rothenberg efficiency : 0.253072 redundancy: 0.746928 Efficiency x scale size : 3.036869 Number of different interval sizes : 66 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.00000 = 6 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.05810 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 5 Number of recognisable fifths : 11, average 696.6067 cents Best fifths form a closed circle Scale contains a complete diamond : 1 5 6125 Formal octave complements present : 11 = 91.6667% Limited inverse transpositions with margin 41.4546 cents: 7 -- Rational properties -- Prime limit : 7 Odd number limit : too high to compute Highest odd numerator or denominator: 234375 Scale harmonicity : 0.004924 Average absolute harmonicity : 0.117059 Fundamental : too low to compute Guide tone : too high to compute Exponens Consonantiae : 2.408350E+30, 100.92589 octaves Euler's gradus suavitatis : 144 Sum of Mann's harmonic distance : 529828.0, average 44152.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 38.92908, average 3.24409 Sum of Tenney's harmonic distance : 78.06298, average 6.50525 Vogel's harmonic complexity : too high to compute Wille's k value : too high to compute Wilson's harmonic complexity : 140 Rectangular lattice diameter : 32 Triangular lattice diameter : 16 Lattice compactness : 1237.97953, average 15.87153 Lattice compactness (without 2's) : 471.63005, average 6.04654 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -17 .. 18 1.83333 130 1 3: -7 .. 7 -0.08333 17 5: -7 .. 7 -0.50000 32 5 7: -2 .. 2 0.00000 10 6 Average exponent except 2's :-7 / 12 =-0.58333 Average absolute exponent except 2's: 59 / 12 = 4.91667
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.8677 c. M:-19.8373 c. Twelve-tone Chromatic (1/11-comma) 19: 2 1 2 1 2 1 2 2 1 2 1 2 P M ME SD: 6.5072 c. M: 11.7417 c. Genus diatonico-chromaticum, Yasser's Supradiatonic inverse 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 0.7147 c. M:-1.3601 c. Genus diatonico-chromaticum 112: 11 7 11 7 11 7 11 11 7 11 7 11 SP M DE SD: 0.7025 c. M: 1.5913 c. 143: 14 9 14 9 14 9 14 14 9 14 9 14 SP M DE SD: 0.5005 c. M: 1.1417 c. 174: 17 11 17 11 17 11 17 17 11 17 11 17 SP M DE SD: 0.4078 c. M: 0.8524 c. 205: 20 13 20 13 20 13 20 20 13 20 13 20 SP M DE SD: 0.3757 c. M: 0.6783 c. 236: 23 15 23 15 23 15 23 23 15 23 15 23 SP M DE SD: 0.3744 c. M: 0.6287 c. 441: 43 28 43 28 43 28 43 43 28 43 28 43 SP M DE SD: 0.3725 c. M: 0.6517 c. 503: 49 32 49 32 49 32 49 49 32 49 32 49 SP M DE SD: 0.3796 c. M: 0.6084 c. 550: 54 35 53 35 54 35 53 54 35 53 35 54 SP SD: 0.3699 c. M: 0.5930 c. 581: 57 37 56 37 57 37 56 57 37 56 37 57 SP SD: 0.3417 c. M:-0.5516 c. 612: 60 39 59 39 60 39 59 60 39 59 39 60 SP SD: 0.3203 c. M:-0.5145 c. 643: 63 41 62 41 63 41 62 63 41 62 41 63 SP SD: 0.3049 c. M: 0.4814 c. 662: 65 42 64 42 65 42 64 65 42 64 42 65 SP SD: 0.3002 c. M:-0.5204 c. 674: 66 43 65 43 66 43 65 66 43 65 43 66 SP SD: 0.2945 c. M: 0.4870 c. 693: 68 44 67 44 68 44 67 68 44 67 44 68 SP SD: 0.2737 c. M:-0.4891 c. 724: 71 46 70 46 71 46 70 71 46 70 46 71 SP SD: 0.2526 c. M: 0.4604 c. 755: 74 48 73 48 74 48 73 74 48 73 48 74 SP SD: 0.2365 c. M:-0.4340 c. 786: 77 50 76 50 77 50 76 77 50 76 50 77 SP SD: 0.2251 c. M:-0.4097 c. 817: 80 52 79 52 80 52 79 80 52 79 52 80 SP SD: 0.2179 c. M: 0.3873 c. 848: 83 54 82 54 83 54 82 83 54 82 54 83 SP SD: 0.2145 c. M: 0.3736 c. 879: 86 56 85 56 86 56 85 86 56 85 56 86 SP SD: 0.2142 c. M: 0.3816 c. 898: 88 57 87 57 88 57 87 88 57 87 57 88 SP SD: 0.2100 c. M:-0.3791 c. 929: 91 59 90 59 91 59 90 91 59 90 59 91 SP SD: 0.1996 c. M: 0.3604 c. 947: 93 60 92 60 92 61 92 92 60 92 60 93 SP SD: 0.2329 c. M:-0.3567 c. 960: 94 61 93 61 94 61 93 94 61 93 61 94 SP SD: 0.1927 c. M:-0.3430 c. 978: 96 62 95 62 95 63 95 95 62 95 62 96 SP SD: 0.2185 c. M:-0.3396 c. 991: 97 63 96 63 97 63 96 97 63 96 63 97 SP SD: 0.1889 c. M: 0.3266 c. 1022: 100 65 99 65 100 65 99 100 65 99 65 100 SP SD: 0.1877 c. M: 0.3112 c. 1053: 103 67 102 67 103 67 102 103 67 102 67 103 SP SD: 0.1889 c. M: 0.3077 c. 1063: 104 68 103 67 104 68 103 104 67 103 68 104 SP SD: 0.1826 c. M:-0.3184 c. 1094: 107 70 106 69 107 70 106 107 69 106 70 107 SP SD: 0.1718 c. M:-0.3009 c. 1121: 110 71 109 71 109 72 109 109 71 109 71 110 SP SD: 0.1828 c. M: 0.2848 c. 1125: 110 72 109 71 110 72 109 110 71 109 72 110 SP SD: 0.1639 c. M:-0.2843 c. 1152: 113 73 112 73 112 74 112 112 73 112 73 113 SP SD: 0.1724 c. M: 0.2820 c. 1156: 113 74 112 73 113 74 112 113 73 112 74 113 SP SD: 0.1587 c. M:-0.2686 c. 1187: 116 76 115 75 116 76 115 116 75 115 76 116 SP SD: 0.1559 c. M: 0.2538 c. 1206: 118 77 117 76 118 77 117 118 76 117 77 118 SP SD: 0.1495 c. M: 0.2441 c. 1237: 121 79 120 78 121 79 120 121 78 120 79 121 SP SD: 0.1391 c. M: 0.2183 c. 1268: 124 81 123 80 124 81 123 124 80 123 81 124 SP SD: 0.1313 c. M: 0.1938 c. 1299: 127 83 126 82 127 83 126 127 82 126 83 127 SP SD: 0.1259 c. M: 0.1705 c. 1330: 130 85 129 84 130 85 129 130 84 129 85 130 SP SD: 0.1231 c. M:-0.1959 c. 1361: 133 87 132 86 133 87 132 133 86 132 87 133 SP SD: 0.1226 c. M:-0.2224 c. 1442: 141 92 140 91 141 92 140 141 91 140 92 141 SP SD: 0.1204 c. M: 0.1833 c. 1473: 144 94 143 93 144 94 143 144 93 143 94 144 SP SD: 0.1168 c. M:-0.1775 c. 1504: 147 96 146 95 147 96 146 147 95 146 96 147 SP SD: 0.1153 c. M:-0.2019 c. 1702: 167 108 165 108 166 109 165 166 108 165 108 167 SP SD: 0.1135 c. M:-0.2547 c. 1733: 170 110 168 110 169 111 168 169 110 168 110 170 SP SD: 0.1052 c. M:-0.2259 c. 1764: 173 112 171 112 172 113 171 172 112 171 112 173 SP SD: 0.0985 c. M:-0.1980 c. 1795: 176 114 174 114 175 115 174 175 114 174 114 176 SP SD: 0.0934 c. M:-0.1711 c. 1826: 179 116 177 116 178 117 177 178 116 177 116 179 SP SD: 0.0900 c. M:-0.1451 c. 1857: 182 118 180 118 181 119 180 181 118 180 118 182 SP SD: 0.0882 c. M:-0.1281 c. 1888: 185 120 183 120 184 121 183 184 120 183 120 185 SP SD: 0.0882 c. M:-0.1339 c. 1907: 187 121 185 121 186 122 185 186 121 185 121 187 SP SD: 0.0821 c. M:-0.1826 c. 1938: 190 123 188 123 189 124 188 189 123 188 123 190 SP SD: 0.0763 c. M:-0.1580 c. 1969: 193 125 191 125 192 126 191 192 125 191 125 193 SP SD: 0.0721 c. M:-0.1341 c. 2000: 196 127 194 127 195 128 194 195 127 194 127 196 SP SD: 0.0697 c. M:-0.1109 c. 2031: 199 129 197 129 198 130 197 198 129 197 129 199 SP SD: 0.0691 c. M:-0.0969 c. 2174: 213 138 211 138 212 139 211 212 138 211 138 213 SP SD: 0.0682 c. M: 0.1048 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: 2.6810 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.5277 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.4271 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 2.5711 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2336 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.8881 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 6.9695 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.6721 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1452 cents 11:12 x 13:14:15 x 16 x 18:20:21:22 S SD: 10.8369 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 6.8978 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.4369 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.6905 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.1099 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.5627 cents 25:27:28:30:31:33:35:37:40:42:45:47:50 SD: 3.3628 cents 27:29:30:32:34:36:38:40:43:45:48:50:54 SD: 3.1814 cents 30:32:34:36:38:40:42:45:48:50:54:56:60 SD: 3.0458 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.6371 cents 40:43:45:48:50:54:56:60:64:67:72:75:80 SD: 2.1397 cents 42:45:47:50:53:56:59:63:67:70:75:78:84 SD: 2.1212 cents 45:48:50:54:56:60:63:67:72:75:80:84:90 SD: 1.8197 cents 52:56:58:62:65:70:73:78:83:87:93:97:104 SD: 1.6809 cents 56:60:63:67:70:75:78:84:90:94:100:105:112 SD: 1.5098 cents 57:61:64:68:71:76:80:85:91:95:102:107:114 SD: 1.4588 cents 60:64:67:72:75:80:84:90:96:100:107:112:120 SD: 1.1399 cents 68:73:76:81:85:91:95:102:109:114:122:127:136 SD: 1.1309 cents 75:80:84:90:94:100:105:112:120:125:134:140:150 SD: 1.0642 cents 83:89:93:99:104:111:116:124:133:139:148:155:166 SD: 0.8648 cents 85:91:95:102:106:114:119:127:136:142:152:159:170 SD: 0.7568 cents 101:108:113:121:126:135:141:151:162:169:181:189:202 SD: 0.6910 cents 113:121:126:135:141:151:158:169:181:189:202:211:226 SD: 0.6063 cents 127:136:142:152:159:170:178:190:203:212:227:237:254 SD: 0.5714 cents 128:137:143:153:160:171:179:191:205:214:229:239:256 SD: 0.4526 cents 143:153:160:171:179:191:200:214:229:239:256:267:286 SD: 0.4035 cents 168:180:188:201:210:225:235:251:269:281:300:314:336 SD: 0.3830 cents 184:197:206:220:230:246:257:275:294:308:329:344:368 SD: 0.3632 cents 204:218:228:244:255:273:285:305:326:341:365:381:408 SD: 0.3527 cents 228:244:255:273:285:305:319:341:365:381:408:426:456 SD: 0.2294 cents 311:333:348:372:389:416:435:465:498:520:556:581:622 SD: 0.1978 cents 372:398:416:445:465:498:520:556:595:622:665:695:744 SD: 0.1791 cents 397:425:444:475:496:531:555:594:635:664:710:742:794 SD: 0.1462 cents 412:441:461:493:515:551:576:616:659:689:737:770:824 SD: 0.1136 cents 515:551:576:616:644:689:720:770:824:861:921:962:1030 SD: 0.1092 cents 525:562:587:628:656:702:734:785:840:878:939:981:1050 SD: 0.1090 cents