Scala analysis: zeus7a
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: 702.254 cents 702.254000 5: 859.365 cents 859.365000 6: 1016.476 cents 1016.476000 7: 1200.172 cents 1200.172000
SHOW/INTERVAL
0: 183.6960 cents 183.6960 1: 157.1110 cents 157.1110 2: 157.1110 cents 157.1110 3: 157.1110 cents 157.1110 4: 230.9210 cents 230.9210 5: 157.1110 cents 157.1110 6: 157.1110 cents 157.1110 7: 183.6960 cents 183.6960
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 157.11100 cents 1: 1 183.69600 cents 1: 1 230.92100 cents 2: 3 314.22200 cents 2: 2 340.80700 cents 2: 2 388.03200 cents 3: 1 471.33300 cents 3: 3 497.91800 cents 3: 3 545.14300 cents 4: 3 655.02900 cents 4: 3 702.25400 cents 4: 1 728.83900 cents 5: 2 812.14000 cents 5: 2 859.36500 cents 5: 3 885.95000 cents 6: 1 969.25100 cents 6: 1 1016.47600 cents 6: 5 1043.06100 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 : 157.1 314.2 471.3 702.3 859.4 1016.5 1200.2 157.1 : 157.1 314.2 545.1 702.3 859.4 1043.1 1200.2 314.2 : 157.1 388.0 545.1 702.3 885.9 1043.1 1200.2 471.3 : 230.9 388.0 545.1 728.8 885.9 1043.1 1200.2 702.3 : 157.1 314.2 497.9 655.0 812.1 969.3 1200.2 859.4 : 157.1 340.8 497.9 655.0 812.1 1043.1 1200.2 1016.5: 183.7 340.8 497.9 655.0 886.0 1043.1 1200.2 1200.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 157.1110 .. 230.9210 cents 73.81000 cents 157.11100 cents 2: 314.2220 .. 388.0320 cents 73.81000 cents 83.30100 cents 3: 471.3330 .. 545.1430 cents 73.81000 cents 83.30100 cents 4: 655.0290 .. 728.8390 cents 73.81000 cents 109.88600 cents 5: 812.1400 .. 885.9500 cents 73.81000 cents 83.30100 cents 6: 969.2510 .. 1043.0610 cents 73.81000 cents 83.30100 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 157.11100 cents, class 1 Average step (divided formal octave): 171.4531 cents Largest one step interval : 230.92100 cents Average / Smallest step : 1.091287 Largest / Average step : 1.346846 Largest / Smallest step : 1.469795 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 : 170.03896 cents, oct.: 1190.27275 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AAABAAC Step pattern size order : SSSLSSM Scale is a Constant Structure, by a margin of 83.30100 cents Scale diversity : 1.336664 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.631003 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 0.0 545.143 1043.061 cents Most common triad is 0.0 157.111 1043.061 cents, amount: 3 Number of recognisable fifths : 3, average 702.2540 cents Number of recognisable fourths : 3, average 497.9180 cents Best fifths form a closed circle Best major thirds 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% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.7268 c. M:-43.0264 c. Lebeng 12: 2 1 2 2 2 1 2 P M ME I SD: 26.1915 c. M:-42.9177 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 13: 2 1 2 3 1 2 2 P D3 SD: 24.9895 c. M: 37.2592 c. 15: 2 2 2 3 2 2 2 SP M ME I SD: 14.2866 c. M:-23.6731 c. Miller's Porcupine-7 20: 3 2 3 4 2 3 3 SP D3 SD: 14.6622 c. M:-22.9148 c. 22: 3 3 3 4 3 3 3 SP M ME I SD: 13.2661 c. M:-20.0362 c. Minor quasi-equal Heptatonic, Miller's Porcupine-7 24: 3 3 3 5 3 3 4 SP T3 SD: 12.3084 c. M: 21.2685 c. 26: 3 4 3 5 4 3 4 SP T3 SD: 11.5357 c. M: 18.6296 c. 28: 4 3 4 5 4 4 4 SP T3 SD: 10.8981 c. M: 16.4414 c. 31: 4 4 4 6 4 4 5 SP T3 SD: 6.0434 c. M: 9.8801 c. 38: 5 5 5 7 5 5 6 SP T3 SD: 4.4965 c. M: 7.4176 c. 46: 6 6 6 9 6 6 7 SP T3 SD: 1.3676 c. M:-2.1948 c. 84: 11 11 11 16 11 11 13 SP T3 SD: 1.3768 c. M: 2.1537 c. 99: 13 13 13 19 13 13 15 SP T3 SD: 1.1579 c. M:-1.8518 c. 130: 17 17 17 25 17 17 20 SP T3 SD: 0.5688 c. M: 0.9458 c. 176: 23 23 23 34 23 23 27 SP T3 SD: 0.4205 c. M: 0.8110 c. 229: 30 30 30 44 30 30 35 SP T3 SD: 0.2010 c. M:-0.3503 c. 359: 47 47 47 69 47 47 55 SP T3 SD: 0.1256 c. M: 0.2035 c. 405: 53 53 53 78 53 53 62 SP T3 SD: 0.0786 c. M: 0.1544 c. 634: 83 83 83 122 83 83 97 SP T3 SD: 0.0443 c. M:-0.0735 c. 993: 130 130 130 191 130 130 152 SP T3 SD: 0.0247 c. M: 0.0386 c. 1398: 183 183 183 269 183 183 214 SP T3 SD: 0.0141 c. M: 0.0213 c. 2032: 266 266 266 391 266 266 311 SP T3 SD: 0.0072 c. M:-0.0120 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: 12.1940 cents 4 x 5 x 6 x 7:8 S SD: 21.6042 cents 5 x 6:7 x 8:9:10 S SD: 24.0422 cents 6 x 7:8:9:10:11:12 S SD: 11.3798 cents 7:8 x 9 x 12:13:14 S SD: 24.7309 cents 8:9:10:11:12:13:14:16 S SD: 18.3005 cents 9:10:11:12:14:15:16:18 S SD: 12.3068 cents 10:11:12:13:15:16:18:20 SD: 7.0643 cents 19:21:23:25:29:31:34:38 SD: 5.8194 cents 20:22:24:26:30:33:36:40 SD: 2.9152 cents 40:44:48:53:60:66:72:80 SD: 2.7658 cents 42:46:50:55:63:69:76:84 SD: 2.3849 cents 44:48:53:58:66:72:79:88 SD: 2.0698 cents 50:55:60:66:75:82:90:100 SD: 1.8127 cents 54:59:65:71:81:89:97:108 SD: 1.4594 cents 64:70:77:84:96:105:115:128 SD: 0.9907 cents 84:92:101:110:126:138:151:168 SD: 0.9611 cents 86:94:103:113:129:141:155:172 SD: 0.8858 cents 96:105:115:126:144:158:173:192 SD: 0.7414 cents 106:116:127:139:159:174:191:212 SD: 0.6017 cents 146:160:175:192:219:240:263:292 SD: 0.5999 cents 156:171:187:205:234:256:281:312 SD: 0.5540 cents 160:175:192:210:240:263:288:320 SD: 0.4196 cents 210:230:252:276:315:345:378:420 SD: 0.3722 cents 230:252:276:302:345:378:414:460 SD: 0.3206 cents 252:276:302:331:378:414:453:504 SD: 0.2465 cents 316:346:379:415:474:519:568:632 SD: 0.2264 cents 336:368:403:441:504:552:604:672 SD: 0.2149 cents 358:392:429:470:537:588:644:716 SD: 0.1594 cents 412:451:494:541:618:677:741:824 SD: 0.1232 cents 422:462:506:554:633:693:759:844 SD: 0.1209 cents 588:644:705:772:882:966:1058:1176 SD: 0.1002 cents