Scala analysis: archytas7_tuning-math_19356_19356
A distributionally even scale in archytas (64/63 planar) temperament, abacabc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 174.290 cents 174.290000 2: 392.380 cents 392.380000 3: 489.440 cents 489.440000 4: 707.530 cents 707.530000 5: 881.820 cents 881.820000 6: 978.880 cents 978.880000 7: 1196.970 cents 1196.970000
SHOW/INTERVAL
0: 218.0900 cents 218.0900 1: 174.2900 cents 174.2900 2: 218.0900 cents 218.0900 3: 97.0600 cents 97.0600 4: 218.0900 cents 218.0900 5: 174.2900 cents 174.2900 6: 97.0600 cents 97.0600 7: 218.0900 cents 218.0900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 97.06000 cents 1: 2 174.29000 cents 1: 3 218.09000 cents 2: 1 271.35000 cents 2: 3 315.15000 cents 2: 3 392.38000 cents 3: 5 489.44000 cents 3: 1 533.24000 cents 3: 1 610.47000 cents 4: 1 586.50000 cents 4: 1 663.73000 cents 4: 5 707.53000 cents 5: 3 804.59000 cents 5: 3 881.82000 cents 5: 1 925.62000 cents 6: 3 978.88000 cents 6: 2 1022.68000 cents 6: 2 1099.91000 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 : 174.3 392.4 489.4 707.5 881.8 978.9 1197.0 174.3 : 218.1 315.2 533.2 707.5 804.6 1022.7 1197.0 392.4 : 97.1 315.1 489.4 586.5 804.6 978.9 1197.0 489.4 : 218.1 392.4 489.4 707.5 881.8 1099.9 1197.0 707.5 : 174.3 271.4 489.4 663.7 881.8 978.9 1197.0 881.8 : 97.1 315.2 489.4 707.5 804.6 1022.7 1197.0 978.9 : 218.1 392.4 610.5 707.5 925.6 1099.9 1197.0 1197.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.0600 .. 218.0900 cents 121.03000 cents 97.06000 cents 2: 271.3500 .. 392.3800 cents 121.03000 cents 53.26000 cents 3: 489.4400 .. 610.4700 cents 121.03000 cents 97.06000 cents 4: 586.5000 .. 707.5300 cents 121.03000 cents -23.97000 cents 5: 804.5900 .. 925.6200 cents 121.03000 cents 97.06000 cents 6: 978.8800 .. 1099.9100 cents 121.03000 cents 53.26000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 97.06000 cents, class 1 Average step (divided formal octave): 170.9957 cents Largest one step interval : 218.09000 cents Average / Smallest step : 1.761753 Largest / Average step : 1.275412 Largest / Smallest step : 2.246961 Median interval of one step : 174.29000 cents, amount: 2 Most common interval of one step : 218.09000 cents, amount: 3 Least squares average step : 170.84757 cents, oct.: 1195.93300 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : MLSLMSL Scale is a Constant Structure, by a margin of 23.97000 cents Scale diversity : 1.455277 Lumma stability : 0.413344 Lumma impropriety factor : 0.020026 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 : 23.97000 cents Most common intervals : 489.44000 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 392.380 707.530 cents Most common triad is 0.0 489.440 707.530 cents, amount: 3 Number of recognisable fifths : 5, average 707.5300 cents Number of recognisable fourths : 5, average 489.4400 cents Best minor thirds form a closed circle Formal octave complements present : 3 = 42.8571% 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: 30.6993 c. M: 50.3886 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 30.9381 c. M: 54.5930 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 14.3959 c. M:-25.2050 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 15: 2 3 1 3 2 1 3 N T3 SD: 11.6909 c. M: 21.3040 c. 22: 3 4 2 4 3 2 4 P T3 SD: 7.3993 c. M: 11.5259 c. Murchhana Hrishyaka 27: 4 5 2 5 4 2 5 N T3 SD: 3.6904 c. M:-6.6100 c. 49: 7 9 4 9 7 4 9 N T3 SD: 1.8393 c. M: 3.2943 c. 61: 9 11 5 11 9 5 11 N T3 SD: 1.4300 c. M:-2.3121 c. 76: 11 14 6 14 11 6 14 N T3 SD: 1.2894 c. M: 2.4045 c. 88: 13 16 7 16 13 7 16 N T3 SD: 1.5292 c. M:-2.5351 c. 110: 16 20 9 20 16 9 20 N T3 SD: 0.3660 c. M: 0.6444 c. 247: 36 45 20 45 36 20 45 N T3 SD: 0.1038 c. M:-0.1672 c. 357: 52 65 29 65 52 29 65 N T3 SD: 0.0834 c. M:-0.1543 c. 543: 79 99 44 99 79 44 99 N T3 SD: 0.0901 c. M: 0.1452 c. 604: 88 110 49 110 88 49 110 N T3 SD: 0.0634 c. M:-0.1030 c. 790: 115 144 64 144 115 64 144 N T3 SD: 0.0491 c. M: 0.0919 c. 900: 131 164 73 164 131 73 164 N T3 SD: 0.0365 c. M: 0.0644 c. 1147: 167 209 93 209 167 93 209 N T3 SD: 0.0093 c. M: 0.0153 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 3.0300 cents 2 x x x 3 x x 4 S SD: 3.1726 cents 3 x x 4 x 5 x 6 S SD: 3.1565 cents 4 x 5 x 6 x 7:8 S SD: 3.3368 cents 5 x 6:7 x 8:9:10 S SD: 28.7761 cents 6:7 x 8:9:10:11:12 S SD: 19.4792 cents 7:8:9 x 11 x 12:14 SD: 22.6107 cents 8:9:10:11:12:13:14:16 S SD: 11.5965 cents 9:10:11:12:14:15:16:18 S SD: 10.8490 cents 10:11 x 13:15:17:18:20 SD: 10.8297 cents 12:13:15:16:18:20:21:24 SD: 5.5959 cents 18:20:23:24:27:30:32:36 SD: 5.5435 cents 20:22:25:27:30:33:35:40 SD: 5.3297 cents 21:23:26:28:32:35:37:42 SD: 5.2631 cents 24:27:30:32:36:40:42:48 S SD: 4.8149 cents 27:30:34:36:41:45:48:54 SD: 3.8919 cents 28:31:35:37:42:47:49:56 SD: 3.0324 cents 36:40:45:48:54:60:63:72 S SD: 2.5733 cents 39:43:49:52:59:65:69:78 SD: 2.4226 cents 46:51:58:61:69:77:81:92 SD: 2.2172 cents 47:52:59:62:71:78:83:94 SD: 2.0675 cents 55:61:69:73:83:92:97:110 SD: 1.7352 cents 59:65:74:78:89:98:104:118 SD: 1.5995 cents 67:74:84:89:101:112:118:134 SD: 1.3475 cents 74:82:93:98:111:123:130:148 SD: 1.3443 cents 83:92:104:110:125:138:146:166 SD: 0.8756 cents 95:105:119:126:143:158:167:190 SD: 0.6848 cents 113:125:142:150:170:188:199:226 SD: 0.6560 cents 162:179:203:215:244:270:285:323 SD: 0.6536 cents 172:190:216:228:259:286:303:343 SD: 0.6313 cents 178:197:223:236:268:296:313:355 SD: 0.5854 cents 180:199:226:239:271:300:317:359 SD: 0.5703 cents 188:208:236:249:283:313:331:375 SD: 0.5409 cents 196:217:246:260:295:326:345:391 SD: 0.3976 cents 208:230:261:276:313:346:366:415 SD: 0.2349 cents 303:335:380:402:456:504:533:605 SD: 0.2218 cents 358:396:449:475:539:596:630:715 SD: 0.1950 cents 471:521:591:625:709:784:829:940 SD: 0.1669 cents 527:583:661:699:793:877:928:1052 SD: 0.1505 cents 539:596:676:715:811:897:949:1076 SD: 0.1032 cents