Scala analysis: zeus8
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: 655.029 cents 655.029000 5: 812.140 cents 812.140000 6: 969.251 cents 969.251000 7: 1126.362 cents 1126.362000 8: 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: 183.6960 cents 183.6960 5: 157.1110 cents 157.1110 6: 157.1110 cents 157.1110 7: 157.1110 cents 157.1110 8: 73.8100 cents 73.8100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 73.81000 cents 1: 6 157.11100 cents 1: 1 183.69600 cents 2: 2 230.92100 cents 2: 4 314.22200 cents 2: 2 340.80700 cents 3: 3 388.03200 cents 3: 2 471.33300 cents 3: 3 497.91800 cents 4: 4 545.14300 cents 4: 4 655.02900 cents 5: 3 702.25400 cents 5: 2 728.83900 cents 5: 3 812.14000 cents 6: 2 859.36500 cents 6: 4 885.95000 cents 6: 2 969.25100 cents 7: 1 1016.47600 cents 7: 6 1043.06100 cents 7: 1 1126.36200 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.85714 = 20/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 157.1 314.2 471.3 655.0 812.1 969.3 1126.4 1200.2 157.1 : 157.1 314.2 497.9 655.0 812.1 969.3 1043.1 1200.2 314.2 : 157.1 340.8 497.9 655.0 812.1 885.9 1043.1 1200.2 471.3 : 183.7 340.8 497.9 655.0 728.8 885.9 1043.1 1200.2 655.0 : 157.1 314.2 471.3 545.1 702.3 859.4 1016.5 1200.2 812.1 : 157.1 314.2 388.0 545.1 702.3 859.4 1043.1 1200.2 969.3 : 157.1 230.9 388.0 545.1 702.3 885.9 1043.1 1200.2 1126.4: 73.8 230.9 388.0 545.1 728.8 885.9 1043.1 1200.2 1200.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.8100 .. 183.6960 cents 109.88600 cents 73.81000 cents 2: 230.9210 .. 340.8070 cents 109.88600 cents 47.22500 cents 3: 388.0320 .. 497.9180 cents 109.88600 cents 47.22500 cents 4: 545.1430 .. 655.0290 cents 109.88600 cents 47.22500 cents 5: 702.2540 .. 812.1400 cents 109.88600 cents 47.22500 cents 6: 859.3650 .. 969.2510 cents 109.88600 cents 47.22500 cents 7: 1016.4760 .. 1126.3620 cents 109.88600 cents 47.22500 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 73.81000 cents, class 1 Average step (divided formal octave): 150.0215 cents Largest one step interval : 183.69600 cents Average / Smallest step : 2.032536 Largest / Average step : 1.224464 Largest / Smallest step : 2.488768 Median interval of one step : 157.11100 cents, amount: 6 Most common interval of one step : 157.11100 cents, amount: 6 Least squares average step : 157.75385 cents, oct.: 1262.03082 cents Scale is strictly proper Scale is 3-distributional even Step pattern alph. order: AAABAAAC Step pattern size order : MMMLMMMS Scale is a Constant Structure, by a margin of 47.22500 cents Scale diversity : 1.376761 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.359090 Rothenberg efficiency : 0.546429 redundancy: 0.453571 Efficiency x scale size : 4.371429 Number of different interval sizes : 20 = 2.85714 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.85714 = 20/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 26.58500 cents Most common intervals : 157.11100 cents & inv., amount: 6 Most common triad is 0.0 157.111 1043.061 cents, amount: 4 Number of recognisable fifths : 3, average 702.2540 cents Number of recognisable fourths : 3, average 497.9180 cents Scale contains two identical disjunct tetrachords Formal octave complements present : 1 = 12.5000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 47.6399 c. M: 76.2115 c. 9: 1 1 1 2 1 1 1 1 P M ME SD: 40.3278 c. M: 71.2757 c. 10: 1 1 2 1 2 1 1 1 N D3 SD: 40.2738 c. M: 74.1876 c. 11: 1 2 1 2 1 2 1 1 P D3 SD: 30.5040 c. M: 48.3942 c. 13: 2 1 2 2 2 1 2 1 P D3 SD: 25.3278 c. M: 46.0418 c. 15: 2 2 2 2 2 2 2 1 SP M ME SD: 8.7175 c. M: 14.9373 c. 31: 4 4 4 5 4 4 4 2 SP D3 SD: 3.4720 c. M: 6.7503 c. 46: 6 6 6 7 6 6 6 3 SP D3 SD: 2.6992 c. M: 4.4621 c. 77: 10 10 10 12 10 10 10 5 SP D3 SD: 2.4948 c. M: 4.1232 c. 84: 11 11 11 13 11 11 11 5 SP D3 SD: 1.6212 c. M:-2.3712 c. Zeus8tri 99: 13 13 13 15 13 13 13 6 SP D3 SD: 0.7889 c. M:-1.4620 c. Zeus8tri 130: 17 17 17 20 17 17 17 8 SP D3 SD: 0.2920 c. M: 0.4963 c. 229: 30 30 30 35 30 30 30 14 SP D3 SD: 0.2582 c. M:-0.4370 c. 275: 36 36 36 42 36 36 36 17 SP D3 SD: 0.2730 c. M: 0.3897 c. 359: 47 47 47 55 47 47 47 22 SP D3 SD: 0.1712 c. M:-0.2619 c. 405: 53 53 53 62 53 53 53 25 SP D3 SD: 0.1606 c. M: 0.2747 c. 504: 66 66 66 77 66 66 66 31 SP D3 SD: 0.1060 c. M: 0.1732 c. 634: 83 83 83 97 83 83 83 39 SP D3 SD: 0.0265 c. M: 0.0455 c. 1398: 183 183 183 214 183 183 183 86 SP D3 SD: 0.0128 c. M: 0.0208 c. 2032: 266 266 266 311 266 266 266 125 SP D3 SD: 0.0121 c. M: 0.0195 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.1720 cents 2 x x x 3 x x x 4 S SD: 23.4632 cents 3 x x 4 x 5 x x 6 S SD: 25.6669 cents 4 x 5 x 6 x 7 x 8 S SD: 21.5051 cents 5 x 6 x 7:8:9 x 10 S SD: 17.4360 cents 6 x 7:8:9:10 x x 12 S SD: 20.3699 cents 7:8 x 9:10:11:12:13:14 S SD: 16.5247 cents 9:10:11:12:13:14:16:17:18 S SD: 9.9882 cents 10:11:12:13:15:16:18:19:20 SD: 8.9522 cents 13:14:16:17:19:21:23:25:26 SD: 7.5337 cents 15:16:18:20:22:24:26:29:30 SD: 7.2389 cents 19:21:23:25:28:30:33:36:38 SD: 5.3793 cents 20:22:24:26:29:32:35:38:40 SD: 3.3734 cents 32:35:38:42:47:51:56:61:64 SD: 2.8244 cents 35:38:42:46:51:56:61:67:70 SD: 2.1529 cents 45:49:54:59:66:72:79:86:90 SD: 1.8520 cents 52:57:62:68:76:83:91:100:104 SD: 1.7195 cents 55:60:66:72:80:88:96:105:110 SD: 1.6959 cents 60:66:72:79:88:96:105:115:120 SD: 1.5592 cents 61:67:73:80:89:98:107:117:122 SD: 1.4411 cents 65:71:78:85:95:104:114:125:130 SD: 1.3600 cents 74:81:89:97:108:118:130:142:148 SD: 1.2390 cents 80:88:96:105:117:128:140:153:160 SD: 1.1945 cents 84:92:101:110:123:134:147:161:168 SD: 1.1467 cents 85:93:102:112:124:136:149:163:170 SD: 0.9149 cents 95:104:114:125:139:152:166:182:190 SD: 0.8272 cents 96:105:115:126:140:153:168:184:192 SD: 0.7673 cents 105:115:126:138:153:168:184:201:210 SD: 0.6493 cents 115:126:138:151:168:184:201:220:230 SD: 0.6193 cents 135:148:162:177:197:216:236:259:270 SD: 0.5949 cents 137:150:164:180:200:219:240:263:274 SD: 0.5400 cents 156:171:187:205:228:249:273:299:312 SD: 0.5135 cents 157:172:188:206:229:251:275:301:314 SD: 0.4131 cents 192:210:230:252:280:307:336:368:384 SD: 0.4051 cents 211:231:253:277:308:337:369:404:422 SD: 0.3634 cents 241:264:289:316:352:385:422:462:482 SD: 0.3561 cents 252:276:302:331:368:403:441:483:504 SD: 0.1946 cents 326:357:391:428:476:521:571:625:652 SD: 0.1761 cents 422:462:506:554:616:675:739:809:844 SD: 0.1738 cents 441:483:529:579:644:705:772:845:882 SD: 0.1453 cents 518:567:621:680:756:828:907:993:1036 SD: 0.1350 cents 528:578:633:693:771:844:924:1012:1056 SD: 0.1225 cents 578:633:693:759:844:924:1012:1108:1156 SD: 0.0944 cents