Scala analysis: zeus7b
A distributionally even scale in zeus temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 157.111 cents 157.111000 2: 314.222 cents 314.222000 3: 471.333 cents 471.333000 4: 812.140 cents 812.140000 5: 969.251 cents 969.251000 6: 1126.362 cents 1126.362000 7: 1200.172 cents 1200.172000
SHOW/INTERVAL
0: 73.8100 cents 73.8100 1: 157.1110 cents 157.1110 2: 157.1110 cents 157.1110 3: 157.1110 cents 157.1110 4: 340.8070 cents 340.8070 5: 157.1110 cents 157.1110 6: 157.1110 cents 157.1110 7: 73.8100 cents 73.8100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 73.81000 cents 1: 5 157.11100 cents 1: 1 340.80700 cents 2: 2 230.92100 cents 2: 3 314.22200 cents 2: 2 497.91800 cents 3: 3 388.03200 cents 3: 1 471.33300 cents 3: 3 655.02900 cents 4: 3 545.14300 cents 4: 1 728.83900 cents 4: 3 812.14000 cents 5: 2 702.25400 cents 5: 3 885.95000 cents 5: 2 969.25100 cents 6: 1 859.36500 cents 6: 5 1043.06100 cents 6: 1 1126.36200 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 157.1 314.2 471.3 812.1 969.3 1126.4 1200.2 157.1 : 157.1 314.2 655.0 812.1 969.3 1043.1 1200.2 314.2 : 157.1 497.9 655.0 812.1 885.9 1043.1 1200.2 471.3 : 340.8 497.9 655.0 728.8 885.9 1043.1 1200.2 812.1 : 157.1 314.2 388.0 545.1 702.3 859.4 1200.2 969.3 : 157.1 230.9 388.0 545.1 702.3 1043.1 1200.2 1126.4: 73.8 230.9 388.0 545.1 885.9 1043.1 1200.2 1200.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.8100 .. 340.8070 cents 266.99700 cents 73.81000 cents 2: 230.9210 .. 497.9180 cents 266.99700 cents -109.88600 cents 3: 388.0320 .. 655.0290 cents 266.99700 cents -109.88600 cents 4: 545.1430 .. 812.1400 cents 266.99700 cents -109.88600 cents 5: 702.2540 .. 969.2510 cents 266.99700 cents -109.88600 cents 6: 859.3650 .. 1126.3620 cents 266.99700 cents -109.88600 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 73.81000 cents, class 1 Average step (divided formal octave): 171.4531 cents Largest one step interval : 340.80700 cents Average / Smallest step : 2.322899 Largest / Average step : 1.987756 Largest / Smallest step : 4.617355 Median interval of one step : 157.11100 cents, amount: 5 Most common interval of one step : 157.11100 cents, amount: 5 Least squares average step : 181.81246 cents, oct.: 1272.68725 cents Scale is not proper Scale has trivalence property Step pattern alph. order: AAABAAC Step pattern size order : MMMLMMS Scale is a Constant Structure, by a margin of 26.58500 cents Scale diversity : 1.440781 Lumma stability : 0.122999 Lumma impropriety factor : 0.457793 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 26.58500 cents Most common intervals : 157.11100 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 655.029 1043.061 cents Most common triad is 0.0 157.111 1043.061 cents, amount: 3 Number of recognisable fifths : 2, average 702.2540 cents Number of recognisable fourths : 2, average 497.9180 cents Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
7: 1 1 1 2 1 1 0 N T3 SD: 44.5620 c. M:-73.8100 c. 9: 1 1 1 3 1 1 1 N M DE I SD: 42.8835 c. M: 71.2757 c. 10: 1 2 1 3 1 1 1 N SD: 30.5980 c. M: 46.2072 c. 12: 2 1 2 3 2 1 1 N SD: 25.7862 c. M:-42.9177 c. 14: 2 2 1 4 2 2 1 N SD: 27.5985 c. M: 42.7001 c. 15: 2 2 2 4 2 2 1 N T3 SD: 7.4146 c. M: 12.0253 c. 31: 4 4 4 9 4 4 2 N T3 SD: 3.5181 c. M: 6.7503 c. 46: 6 6 6 13 6 6 3 N T3 SD: 2.6902 c. M: 4.4621 c. 77: 10 10 10 22 10 10 5 N T3 SD: 2.6630 c. M: 4.1232 c. 84: 11 11 11 24 11 11 5 N T3 SD: 1.5189 c. M:-2.3712 c. 99: 13 13 13 28 13 13 6 N T3 SD: 0.8304 c. M:-1.4620 c. 130: 17 17 17 37 17 17 8 N T3 SD: 0.2619 c. M: 0.4963 c. 229: 30 30 30 65 30 30 14 N T3 SD: 0.2741 c. M:-0.4370 c. 275: 36 36 36 78 36 36 17 N T3 SD: 0.2520 c. M: 0.3873 c. 359: 47 47 47 102 47 47 22 N T3 SD: 0.1634 c. M:-0.2619 c. 405: 53 53 53 115 53 53 25 N T3 SD: 0.1656 c. M: 0.2747 c. 489: 64 64 64 139 64 64 30 N T3 SD: 0.1483 c. M:-0.2464 c. 504: 66 66 66 143 66 66 31 N T3 SD: 0.0924 c. M:-0.1631 c. 634: 83 83 83 180 83 83 39 N T3 SD: 0.0226 c. M: 0.0362 c. 1398: 183 183 183 397 183 183 86 N T3 SD: 0.0137 c. M: 0.0208 c. 2032: 266 266 266 577 266 266 125 N T3 SD: 0.0119 c. M: 0.0195 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.1720 cents 2 x x x 3 x x 4 S SD: 55.0926 cents 3 x x 4:5 x x 6 S SD: 25.6669 cents 4 x 5 x 6:7 x 8 S SD: 32.9186 cents 5 x 6:7:8:9 x 10 S SD: 24.2508 cents 6 x 7:8:10 x x 12 S SD: 22.5987 cents 7:8 x 9:11:12:13:14 SD: 18.2353 cents 8:9:10:11:13:14:15:16 SD: 18.0939 cents 9:10:11:12:14:16:17:18 S SD: 11.1080 cents 10:11:12:13:16:18:19:20 SD: 7.7288 cents 19:21:23:25:30:33:36:38 SD: 5.6907 cents 20:22:24:26:32:35:38:40 SD: 3.4697 cents 32:35:38:42:51:56:61:64 SD: 2.8598 cents 35:38:42:46:56:61:67:70 SD: 2.4161 cents 44:48:53:58:70:77:84:88 SD: 2.3488 cents 45:49:54:59:72:79:86:90 SD: 1.7797 cents 55:60:66:72:88:96:105:110 SD: 1.7129 cents 60:66:72:79:96:105:115:120 SD: 1.3648 cents 64:70:77:84:102:112:123:128 SD: 1.3439 cents 80:88:96:105:128:140:153:160 SD: 1.2916 cents 84:92:101:110:134:147:161:168 SD: 1.0789 cents 85:93:102:112:136:149:163:170 SD: 1.0299 cents 95:104:114:125:152:166:182:190 SD: 0.7664 cents 105:115:126:138:168:184:201:210 SD: 0.5779 cents 147:161:176:193:235:257:282:294 SD: 0.5182 cents 156:171:187:205:249:273:299:312 SD: 0.5160 cents 157:172:188:206:251:275:301:314 SD: 0.4185 cents 192:210:230:252:307:336:368:384 SD: 0.3807 cents 201:220:241:264:321:352:385:402 SD: 0.3468 cents 252:276:302:331:403:441:483:504 SD: 0.2101 cents 316:346:379:415:505:553:606:632 SD: 0.1919 cents 336:368:403:441:537:588:644:672 SD: 0.1517 cents 441:483:529:579:705:772:845:882 SD: 0.1493 cents 473:518:567:621:756:828:907:946 SD: 0.1361 cents 528:578:633:693:844:924:1012:1056 SD: 0.1276 cents 578:633:693:759:924:1012:1108:1156 SD: 0.0933 cents 588:644:705:772:940:1029:1127:1176 SD: 0.0865 cents