Scala analysis: archytas8
A distributionally even scale in archytas (64/63 planar) temperament, abacbabc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 121.030 cents 121.030000 2: 392.380 cents 392.380000 3: 489.440 cents 489.440000 4: 610.470 cents 610.470000 5: 707.530 cents 707.530000 6: 978.880 cents 978.880000 7: 1099.910 cents 1099.910000 8: 1196.970 cents 1196.970000
SHOW/INTERVAL
0: 97.0600 cents 97.0600 1: 121.0300 cents 121.0300 2: 271.3500 cents 271.3500 3: 97.0600 cents 97.0600 4: 121.0300 cents 121.0300 5: 97.0600 cents 97.0600 6: 271.3500 cents 271.3500 7: 121.0300 cents 121.0300 8: 97.0600 cents 97.0600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 97.06000 cents 1: 3 121.03000 cents 1: 2 271.35000 cents 2: 4 218.09000 cents 2: 2 368.41000 cents 2: 2 392.38000 cents 3: 1 315.15000 cents 3: 1 339.12000 cents 3: 6 489.44000 cents 4: 4 586.50000 cents 4: 4 610.47000 cents 5: 6 707.53000 cents 5: 1 857.85000 cents 5: 1 881.82000 cents 6: 2 804.59000 cents 6: 2 828.56000 cents 6: 4 978.88000 cents 7: 2 925.62000 cents 7: 3 1075.94000 cents 7: 3 1099.91000 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 : 121.0 392.4 489.4 610.5 707.5 978.9 1099.9 1197.0 121.0 : 271.3 368.4 489.4 586.5 857.8 978.9 1075.9 1197.0 392.4 : 97.1 218.1 315.1 586.5 707.5 804.6 925.6 1197.0 489.4 : 121.0 218.1 489.4 610.5 707.5 828.6 1099.9 1197.0 610.5 : 97.1 368.4 489.4 586.5 707.5 978.9 1075.9 1197.0 707.5 : 271.4 392.4 489.4 610.5 881.8 978.9 1099.9 1197.0 978.9 : 121.0 218.1 339.1 610.5 707.5 828.6 925.6 1197.0 1099.9: 97.1 218.1 489.4 586.5 707.5 804.6 1075.9 1197.0 1197.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.0600 .. 271.3500 cents 174.29000 cents 97.06000 cents 2: 218.0900 .. 392.3800 cents 174.29000 cents -53.26000 cents 3: 315.1500 .. 489.4400 cents 174.29000 cents -77.23000 cents 4: 586.5000 .. 610.4700 cents 23.97000 cents 97.06000 cents 5: 707.5300 .. 881.8200 cents 174.29000 cents 97.06000 cents 6: 804.5900 .. 978.8800 cents 174.29000 cents -77.23000 cents 7: 925.6200 .. 1099.9100 cents 174.29000 cents -53.26000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 97.06000 cents, class 1 Average step (divided formal octave): 149.6212 cents Largest one step interval : 271.35000 cents Average / Smallest step : 1.541534 Largest / Average step : 1.813579 Largest / Smallest step : 2.795693 Median interval of one step : 121.03000 cents, amount: 3 Least squares average step : 154.42181 cents, oct.: 1235.37451 cents Scale is not proper Scale is 3-distributional even Step pattern alph. order: ABCACBAC Step pattern size order : MLSMSLMS Scale is a Constant Structure, by a margin of 29.29000 cents Scale diversity : 1.330712 Lumma stability : 0.324352 Lumma impropriety factor : 0.218034 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 : 23.97000 cents Most common intervals : 489.44000 cents & inv., amount: 6 Most common triad is 0.0 489.440 707.530 cents, amount: 4 Number of recognisable fifths : 6, average 707.5300 cents Number of recognisable fourths : 6, average 489.4400 cents Formal octave complements present : 3 = 37.5000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 174.2900 cents: 4 Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties --
FIT/MODE
8: 0 2 1 1 0 2 1 1 N B D3 SD: 76.1185 c. M: 121.0300 c. 9: 1 2 1 1 0 2 1 1 N D3 SD: 35.9952 c. M:-54.5133 c. 10: 1 2 1 1 1 2 1 1 P B ME SD: 17.4886 c. M: 33.2890 c. 12: 1 3 1 1 1 3 1 1 N B DE SD: 12.0735 c. M: 21.2825 c. Tcherepnin Octatonic mode 1 22: 2 5 2 2 2 5 2 2 N B DE SD: 8.3978 c. M: 12.2145 c. 27: 3 6 2 3 2 6 3 2 N D3 SD: 6.8935 c. M:-11.9667 c. 37: 4 8 3 4 3 8 4 3 N D3 SD: 5.1235 c. M:-8.3722 c. 39: 4 9 3 4 3 9 4 3 N D3 SD: 3.5123 c. M:-6.6100 c. 49: 5 11 4 5 4 11 5 4 N D3 SD: 1.0436 c. M: 1.7616 c. 110: 11 25 9 11 9 25 11 9 N D3 SD: 0.7491 c. M: 1.3330 c. 137: 14 31 11 14 11 31 14 11 N D3 SD: 0.7590 c. M:-1.2881 c. 149: 15 34 12 15 12 34 15 12 N D3 SD: 0.7429 c. M:-1.2544 c. 159: 16 36 13 16 13 36 16 13 N D3 SD: 0.5459 c. M: 0.9181 c. 198: 20 45 16 20 16 45 20 16 N D3 SD: 0.3110 c. M:-0.5647 c. 247: 25 56 20 25 20 56 25 20 N D3 SD: 0.0959 c. M:-0.1486 c. 604: 61 137 49 61 49 137 61 49 N D3 SD: 0.0761 c. M: 0.1440 c. 653: 66 148 53 66 53 148 66 53 N D3 SD: 0.0617 c. M: 0.1111 c. 851: 86 193 69 86 69 193 86 69 N D3 SD: 0.0449 c. M:-0.0755 c. 900: 91 204 73 91 73 204 91 73 N D3 SD: 0.0209 c. M: 0.0398 c. 1147: 116 260 93 116 93 260 116 93 N D3 SD: 0.0124 c. M:-0.0236 c. 1998: 202 453 162 202 162 453 202 162 N D3 SD: 0.0138 c. M:-0.0234 c. 2047: 207 464 166 207 166 464 207 166 N D3 SD: 0.0115 c. M: 0.0193 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 3.0300 cents 2 x x x x 3 x x 4 S SD: 3.1726 cents 3 x x 4 x x 5 x 6 S SD: 31.6535 cents 4 x 5 x x 6:7 x 8 S SD: 3.3368 cents 5 x 6 x 7:8:9 x 10 S SD: 27.8910 cents 6 x x 8 x 9 x 11:12 SD: 12.9163 cents 7:8:9 x 10:11:12:13:14 S SD: 21.4390 cents 8:9:10 x 11:12:14:15:16 S SD: 14.7646 cents 9:10:11:12:13:14:16:17:18 S SD: 12.5914 cents 10:11 x 13:14:15:18:19:20 SD: 10.7123 cents 12:13:15:16:17:18:21:23:24 SD: 4.5297 cents 16:17:20:21:23:24:28:30:32 SD: 4.3968 cents 24:26:30:32:34:36:42:45:48 SD: 3.4261 cents 28:30:35:37:40:42:49:53:56 SD: 2.1671 cents 43:46:54:57:61:65:76:81:86 SD: 1.6954 cents 54:58:68:72:77:81:95:102:108 SD: 1.6918 cents 55:59:69:73:78:83:97:104:110 SD: 1.1579 cents 71:76:89:94:101:107:125:134:142 SD: 0.7990 cents 83:89:104:110:118:125:146:157:166 SD: 0.7300 cents 125:134:157:166:178:188:220:236:250 SD: 0.5669 cents 168:180:211:223:239:253:296:317:335 SD: 0.5220 cents 178:191:223:236:253:268:313:336:355 SD: 0.5211 cents 180:193:226:239:256:271:317:340:359 SD: 0.4153 cents 196:210:246:260:279:295:345:370:391 SD: 0.3130 cents 208:223:261:276:296:313:366:393:415 SD: 0.2797 cents 220:236:276:292:313:331:387:415:439 SD: 0.2603 cents 275:295:345:365:391:414:484:519:549 SD: 0.2129 cents 291:312:365:386:414:438:512:549:581 SD: 0.1728 cents 303:325:380:402:431:456:533:572:605 SD: 0.1621 cents 471:505:591:625:670:709:829:889:940 SD: 0.1475 cents 499:535:626:662:710:751:878:942:996 SD: 0.1195 cents 551:591:691:731:784:829:970:1040:1100 SD: 0.0876 cents