Scala analysis: zeus7
A distributionally even scale in zeus temperament, aabacab
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: 388.032 cents 388.032000 3: 545.143 cents 545.143000 4: 702.254 cents 702.254000 5: 933.175 cents 933.175000 6: 1090.286 cents 1090.286000 7: 1200.172 cents 1200.172000
SHOW/INTERVAL
0: 109.8860 cents 109.8860 1: 157.1110 cents 157.1110 2: 230.9210 cents 230.9210 3: 157.1110 cents 157.1110 4: 157.1110 cents 157.1110 5: 230.9210 cents 230.9210 6: 157.1110 cents 157.1110 7: 109.8860 cents 109.8860
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 109.88600 cents 1: 4 157.11100 cents 1: 2 230.92100 cents 2: 2 266.99700 cents 2: 1 314.22200 cents 2: 4 388.03200 cents 3: 1 424.10800 cents 3: 2 497.91800 cents 3: 4 545.14300 cents 4: 4 655.02900 cents 4: 2 702.25400 cents 4: 1 776.06400 cents 5: 4 812.14000 cents 5: 1 885.95000 cents 5: 2 933.17500 cents 6: 2 969.25100 cents 6: 4 1043.06100 cents 6: 1 1090.28600 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 : 157.1 388.0 545.1 702.3 933.2 1090.3 1200.2 157.1 : 230.9 388.0 545.1 776.1 933.2 1043.1 1200.2 388.0 : 157.1 314.2 545.1 702.3 812.1 969.3 1200.2 545.1 : 157.1 388.0 545.1 655.0 812.1 1043.1 1200.2 702.3 : 230.9 388.0 497.9 655.0 885.9 1043.1 1200.2 933.2 : 157.1 267.0 424.1 655.0 812.1 969.3 1200.2 1090.3: 109.9 267.0 497.9 655.0 812.1 1043.1 1200.2 1200.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 109.8860 .. 230.9210 cents 121.03500 cents 109.88600 cents 2: 266.9970 .. 388.0320 cents 121.03500 cents 36.07600 cents 3: 424.1080 .. 545.1430 cents 121.03500 cents 36.07600 cents 4: 655.0290 .. 776.0640 cents 121.03500 cents 109.88600 cents 5: 812.1400 .. 933.1750 cents 121.03500 cents 36.07600 cents 6: 969.2510 .. 1090.2860 cents 121.03500 cents 36.07600 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 109.88600 cents, class 1 Average step (divided formal octave): 171.4531 cents Largest one step interval : 230.92100 cents Average / Smallest step : 1.560282 Largest / Average step : 1.346846 Largest / Smallest step : 2.101460 Median interval of one step : 157.11100 cents, amount: 4 Most common interval of one step : 157.11100 cents, amount: 4 Least squares average step : 178.47439 cents, oct.: 1249.32075 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAABAC Step pattern size order : MLMMLMS Scale is a Constant Structure, by a margin of 36.07600 cents Scale diversity : 1.439234 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.394912 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 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 : 36.07600 cents Number of recognisable fifths : 2, average 702.2540 cents Number of recognisable fourths : 2, average 497.9180 cents Scale contains two identical conjunct tetrachords Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 Inversional symmetry on intervals : 6-7 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 43.1156 c. M: 75.9093 c. Lebeng 9: 1 2 1 1 2 1 1 P M ME S SD: 19.4832 c. M: 35.4918 c. Pelog Saptanada: Sunda 15: 2 3 2 2 3 2 1 P T3 S SD: 18.1827 c. M:-29.8745 c. 21: 3 4 3 2 4 3 2 SP T3 SD: 15.5253 c. M:-26.3675 c. 22: 3 4 3 3 4 3 2 SP T3 S SD: 4.8257 c. M:-6.9385 c. 31: 4 6 4 4 6 4 3 SP T3 S SD: 3.7766 c. M: 6.2597 c. 46: 6 9 6 6 9 6 4 SP T3 S SD: 3.6142 c. M:-6.0900 c. 53: 7 10 7 7 10 7 5 SP T3 S SD: 2.6149 c. M: 4.7401 c. 68: 9 13 9 9 13 9 6 SP T3 S SD: 2.4480 c. M:-3.9885 c. 77: 10 15 10 10 15 10 7 SP T3 S SD: 1.1836 c. M:-2.0240 c. 99: 13 19 13 13 19 13 9 SP T3 S SD: 0.5156 c. M:-0.8771 c. Zeus7tri 130: 17 25 17 17 25 17 12 SP T3 S SD: 0.5392 c. M: 0.8991 c. 207: 27 40 27 27 40 27 19 SP T3 S SD: 0.4108 c. M: 0.7042 c. 229: 30 44 30 30 44 30 21 SP T3 S SD: 0.1594 c. M: 0.2902 c. 328: 43 63 43 43 63 43 30 SP T3 S SD: 0.1659 c. M:-0.2857 c. 405: 53 78 53 53 78 53 37 SP T3 S SD: 0.1667 c. M:-0.2921 c. 535: 70 103 70 70 103 70 49 SP T3 S SD: 0.0572 c. M: 0.0973 c. 634: 83 122 83 83 122 83 58 SP T3 S SD: 0.0554 c. M:-0.0911 c. 764: 100 147 100 100 147 100 70 SP T3 S SD: 0.0463 c. M: 0.0774 c. 863: 113 166 113 113 166 113 79 SP T3 S SD: 0.0276 c. M:-0.0483 c. 1398: 183 269 183 183 269 183 128 SP T3 S SD: 0.0051 c. M: 0.0074 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: 0.1725 cents 3 x x 4 x 5 x 6 S SD: 22.6109 cents 4 x 5 x 6:7 x 8 S SD: 8.9235 cents 5 x 6:7:8 x 9:10 S SD: 31.2012 cents 6:7 x 8:9:10:11:12 S SD: 22.5606 cents 7:8:9:10:11:12:13:14 H SD: 20.0594 cents 8:9:10:11:12:14:15:16 S SD: 8.4593 cents 16:18:20:22:24:27:30:32 S SD: 7.8001 cents 18:20:23:25:27:31:34:36 SD: 7.4157 cents 19:21:24:26:29:33:36:38 SD: 6.6902 cents 20:22:25:27:30:34:38:40 SD: 5.2855 cents 22:24:28:30:33:38:41:44 SD: 5.1603 cents 24:26:30:33:36:41:45:48 SD: 2.9477 cents 32:35:40:44:48:55:60:64 SD: 1.1868 cents 76:83:95:104:114:130:143:152 SD: 1.1040 cents 84:92:105:115:126:144:158:168 SD: 0.5898 cents 116:127:145:159:174:199:218:232 SD: 0.4275 cents 178:195:223:244:267:305:334:356 SD: 0.3903 cents 210:230:263:288:315:360:394:420 SD: 0.3612 cents 230:252:288:315:345:394:432:460 SD: 0.3498 cents 252:276:315:345:378:432:473:504 SD: 0.3207 cents 262:287:328:359:393:449:492:524 SD: 0.2114 cents 294:322:368:403:441:504:552:588 SD: 0.1718 cents 430:471:538:589:645:737:807:860 SD: 0.1381 cents 462:506:578:633:693:792:867:924 SD: 0.1094 cents 546:598:683:748:819:936:1025:1092 SD: 0.1021 cents