Scala analysis: lemba
Lemba temperament (4 down, 3 up)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 90.924 cents 90.924290 2: 139.951 cents 139.950640 3: 230.875 cents 230.874930 4: 279.901 cents 279.901280 5: 370.826 cents 370.825570 6: 461.750 cents 461.749850 7: 510.776 cents 510.776210 8: 601.700 cents 601.700490
SHOW/INTERVAL
0: 90.9243 cents 90.9243 1: 90.9243 cents 90.9243 2: 49.0264 cents 49.0264 3: 90.9243 cents 90.9243 4: 49.0264 cents 49.0264 5: 90.9243 cents 90.9243 6: 90.9243 cents 90.9243 7: 49.0264 cents 49.0264 8: 90.9243 cents 90.9243
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 49.02635 cents 1: 5 90.92429 cents 2: 6 139.95064 cents 2: 2 181.84857 cents 3: 1 188.97699 cents 3: 7 230.87493 cents 4: 4 279.90128 cents 4: 4 321.79921 cents 5: 7 370.82557 cents 5: 1 412.72350 cents 6: 2 419.85192 cents 6: 6 461.74985 cents 7: 5 510.77621 cents 7: 3 552.67414 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 90.9 140.0 230.9 279.9 370.8 461.7 510.8 601.7 90.9 : 49.0 140.0 189.0 279.9 370.8 419.9 510.8 601.7 140.0: 90.9 140.0 230.9 321.8 370.8 461.7 552.7 601.7 230.9: 49.0 140.0 230.9 279.9 370.8 461.7 510.8 601.7 279.9: 90.9 181.8 230.9 321.8 412.7 461.7 552.7 601.7 370.8: 90.9 140.0 230.9 321.8 370.8 461.7 510.8 601.7 461.7: 49.0 140.0 230.9 279.9 370.8 419.9 510.8 601.7 510.8: 90.9 181.8 230.9 321.8 370.8 461.7 552.7 601.7 601.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.0264 .. 90.9243 cents 41.89794 cents 49.02635 cents 2: 139.9506 .. 181.8486 cents 41.89793 cents 49.02635 cents 3: 188.9770 .. 230.8749 cents 41.89794 cents 7.12842 cents 4: 279.9013 .. 321.7992 cents 41.89793 cents 49.02635 cents 5: 370.8256 .. 412.7235 cents 41.89793 cents 49.02636 cents 6: 419.8519 .. 461.7498 cents 41.89793 cents 7.12842 cents 7: 510.7762 .. 552.6741 cents 41.89793 cents 49.02636 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 49.02635 cents, class 1 Average step (divided formal octave): 75.2126 cents Largest one step interval : 90.92429 cents Average / Smallest step : 1.534125 Largest / Average step : 1.208898 Largest / Smallest step : 1.854600 Median interval of one step : 90.92429 cents, amount: 5 Most common interval of one step : 90.92429 cents, amount: 5 Least squares average step : 74.49372 cents, oct.: 595.94980 cents Scale is strictly proper Scale has Myhill's property chromas: 41.89794 cents and 7.12841 cents, ratio: 5.877600 generators: 3 of 230.87493 cents and 5 of 370.82556 cents ET pair of linear temperament : 26&146 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 675-tone equal temperament with octave 601.700 cents degrees: 102 157 259 314 416 518 573 675 generators: 259 and 416 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABA Step pattern size order : LSLSLLSL Scale is a Constant Structure, by a margin of 7.12842 cents Scale diversity : 0.683518 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.512572 Rothenberg efficiency : 0.750000 redundancy: 0.250000 Efficiency x scale size : 6.000000 Number of different interval sizes : 14 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 7.12842 cents Most common intervals : 230.87493 cents & inv., amount: 7 Scale is a chain of 4 triads 0.0 90.924 370.826 cents Most common triad is 0.0 230.875 370.826 cents, amount: 6 Number of recognisable fifths : 0 Number of recognisable fourths : 5, average 510.7762 cents Best major thirds form a closed circle Formal octave complements present : 7 = 87.5000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 12.2824 c. M:-20.9490 c. 13: 2 1 2 1 2 2 1 2 P M ME SD: 1.2860 c. M: 2.1934 c. Mnarian 47: 7 4 7 4 7 7 4 7 SP M DE SD: 1.0235 c. M:-1.7458 c. 60: 9 5 9 5 9 9 5 9 SP M DE SD: 0.5231 c. M:-0.8923 c. 73: 11 6 11 6 11 11 6 11 SP M DE SD: 0.2010 c. M:-0.3428 c. 86: 13 7 13 7 13 13 7 13 SP M DE SD: 0.0238 c. M: 0.0406 c. 417: 63 34 63 34 63 63 34 63 SP M DE SD: 0.0156 c. M:-0.0265 c. 503: 76 41 76 41 76 76 41 76 SP M DE SD: 0.0088 c. M:-0.0151 c. 589: 89 48 89 48 89 89 48 89 SP M DE SD: 0.0041 c. M:-0.0069 c. 675: 102 55 102 55 102 102 55 102 SP M DE SD: 0.0005 c. M:-0.0009 c. 2111: 319 172 319 172 319 319 172 319 SP M DE SD: 0.0005 c. M: 0.0008 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 598.2995 cents 2 x x x x x x x 3 S SD: 100.2545 cents 3 x x x x x x 4 x S SD: 12.7312 cents 4 x x x x 5 x x 6 S SD: 50.7219 cents 5 x x x 6 x x x 7 S SD: 20.2826 cents 6 x x x 7 x x 8 x S SD: 9.1087 cents 7 x x 8 x x 9 x 10 S SD: 10.3301 cents 8 x x 9 x 10 x 11 x S SD: 17.0314 cents 9 x 10 x x 11 x 12:13 S SD: 15.2724 cents 10 x 11 x 12 x 13 x 14 S SD: 12.0675 cents 11 x 12 x 13 x 14:15:16 S SD: 14.2135 cents 12 x 13 x 14:15 x 16:17 S SD: 4.7973 cents 13 x 14:15 x 16:17 x 18 S SD: 8.9991 cents 14 x 15:16 x 17:18:19:20 S SD: 8.9839 cents 15:16 x 17:18:19 x 20:21 S SD: 10.4321 cents 16:17 x 18:19:20:21 x 23 SD: 7.9263 cents 17:18 x 19:20:21:22:23:24 S SD: 6.3503 cents 18:19:20 x 21:22 x 24:25 S SD: 10.2437 cents 19:20:21:22 x 24:25:26:27 S SD: 9.0718 cents 20:21:22:23:24:25:26:27:28 H SD: 6.6279 cents 21:22:23:24:25:26:27:28:30 S SD: 5.6193 cents 22:23:24:25:26:27:29:30:31 SD: 5.2646 cents 25:26:27 x 29:31:33:34:35 SD: 6.8425 cents 26:27:28:30:31:32:34:35:37 SD: 5.4691 cents 28 x 30:32:33:35:37:38:40 SD: 5.8599 cents 29 x 31:33:34:36:38:39:41 SD: 3.8647 cents 33:35:36:38:39:41:43:44:47 SD: 3.5557 cents 34:36:37:39:40:42:44:46:48 SD: 3.0452 cents 46:48:50:53:54:57:60:62:65 SD: 3.0026 cents 49:52:53:56:58:61:64:66:69 SD: 2.7444 cents 50:53:54:57:59:62:65:67:71 SD: 2.1988 cents 55:58:60:63:65:68:72:74:78 SD: 2.0581 cents 56:59:61:64:66:69:73:75:79 SD: 1.9543 cents 58:61:63:66:68:72:76:78:82 SD: 1.5581 cents 72:76:78:82:85:89:94:97:102 SD: 1.4851 cents 75:79:81:86:88:93:98:101:106 SD: 1.3971 cents 91:96:99:104:107:113:119:122:129 SD: 1.1046 cents 96:101:104:110:113:119:125:129:136 SD: 1.0125 cents 108:114:117:123:127:134:141:145:153 SD: 0.8959 cents 131:138:142:150:154:162:171:176:185 SD: 0.8008 cents 147:155:159:168:173:182:192:197:208 SD: 0.7830 cents 154:162:167:176:181:191:201:207:218 SD: 0.5092 cents 204:215:221:233:240:253:266:274:289 SD: 0.4862 cents 222:234:241:254:261:275:290:298:314 SD: 0.4695 cents 238:251:258:272:280:295:311:320:337 SD: 0.3871 cents 239:252:259:273:281:296:312:321:338 SD: 0.2793 cents 330:348:358:377:388:409:431:443:467 SD: 0.2643 cents 370:390:401:423:435:458:483:497:524 SD: 0.2533 cents 393:414:426:449:462:487:513:528:556 SD: 0.1977 cents 428:451:464:489:503:530:559:575:606 SD: 0.1487 cents