Scala analysis: xen18-erlich-tetracot-06
1L 5s MOS for Tetracot, L=318.48, s=176.11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 176.110 cents 176.110000 2: 352.220 cents 352.220000 3: 670.700 cents 670.700000 4: 846.810 cents 846.810000 5: 1022.920 cents 1022.920000 6: 1199.030 cents 1199.030000
SHOW/INTERVAL
0: 176.1100 cents 176.1100 1: 176.1100 cents 176.1100 2: 176.1100 cents 176.1100 3: 318.4800 cents 318.4800 4: 176.1100 cents 176.1100 5: 176.1100 cents 176.1100 6: 176.1100 cents 176.1100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 176.11000 cents 1: 1 318.48000 cents 2: 4 352.22000 cents 2: 2 494.59000 cents 3: 3 528.33000 cents 3: 3 670.70000 cents 4: 2 704.44000 cents 4: 4 846.81000 cents 5: 1 880.55000 cents 5: 5 1022.92000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 176.1 352.2 670.7 846.8 1022.9 1199.0 176.1 : 176.1 494.6 670.7 846.8 1022.9 1199.0 352.2 : 318.5 494.6 670.7 846.8 1022.9 1199.0 670.7 : 176.1 352.2 528.3 704.4 880.5 1199.0 846.8 : 176.1 352.2 528.3 704.4 1022.9 1199.0 1022.9: 176.1 352.2 528.3 846.8 1022.9 1199.0 1199.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 176.1100 .. 318.4800 cents 142.37000 cents 176.11000 cents 2: 352.2200 .. 494.5900 cents 142.37000 cents 33.74000 cents 3: 528.3300 .. 670.7000 cents 142.37000 cents 33.74000 cents 4: 704.4400 .. 846.8100 cents 142.37000 cents 33.74000 cents 5: 880.5500 .. 1022.9200 cents 142.37000 cents 33.74000 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 176.11000 cents, class 1 Average step (divided formal octave): 199.8383 cents Largest one step interval : 318.48000 cents Average / Smallest step : 1.134736 Largest / Average step : 1.593688 Largest / Smallest step : 1.808415 Median interval of one step : 176.11000 cents, amount: 5 Most common interval of one step : 176.11000 cents, amount: 5 Least squares average step : 204.27110 cents, oct.: 1225.62659 cents Scale is strictly proper Scale has Myhill's property chromas: 142.37000 cents and 33.74000 cents, ratio: 4.219621 generators: 1 of 176.11000 cents and 5 of 1022.92000 cents ET pair of linear temperament : 34&143 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1137-tone equal temperament with octave 1199.030 cents degrees: 167 334 636 803 970 1137 generators: 167 and 970 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAA Step pattern size order : SSLSSS Scale is a Constant Structure, by a margin of 33.74000 cents Scale diversity : 1.199530 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.406312 Rothenberg efficiency : 0.777778 redundancy: 0.222222 Efficiency x scale size : 4.666667 Number of different interval sizes : 10 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 33.74000 cents Most common intervals : 176.11000 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 352.220 1022.920 cents Number of recognisable fifths : 2, average 704.4400 cents Number of recognisable fourths : 2, average 494.5900 cents Formal octave complements present : 5 = 83.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 5-6 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 42.2249 c. M: 71.1850 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 1 2 1 1 1 P M ME SD: 8.5773 c. M:-14.4600 c. 20: 3 3 5 3 3 3 SP M DE SD: 6.6634 c. M: 11.2335 c. 27: 4 4 7 4 4 4 SP M DE SD: 2.7121 c. M: 4.5722 c. 34: 5 5 9 5 5 5 SP M DE SD: 0.3878 c. M: 0.6538 c. 109: 16 16 29 16 16 16 SP M DE SD: 0.1879 c. M:-0.3168 c. 143: 21 21 38 21 21 21 SP M DE SD: 0.0510 c. M:-0.0860 c. 177: 26 26 47 26 26 26 SP M DE SD: 0.0333 c. M: 0.0561 c. 320: 47 47 85 47 47 47 SP M DE SD: 0.0044 c. M:-0.0074 c. 817: 120 120 217 120 120 120 SP M DE SD: 0.0038 c. M: 0.0064 c. 1137: 167 167 302 167 167 167 SP M DE SD: 0.0015 c. M: 0.0025 c. 1457: 214 214 387 214 214 214 SP M DE SD: 0.0002 c. M: 0.0003 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.9700 cents 2 x x 3 x x 4 S SD: 15.6350 cents 3 x 4 x 5 x 6 S SD: 50.1949 cents 4 x 5:6 x 7:8 S SD: 17.7946 cents 5 x 6:7:8:9:10 S SD: 20.2401 cents 6 x 7:9:10:11:12 SD: 20.3680 cents 8:9:10:12:13:14:16 S SD: 12.7788 cents 9:10:11:13:15:16:18 SD: 9.6538 cents 16:18:20:24:26:29:32 SD: 9.1239 cents 17:19:21:25:28:31:34 SD: 5.4039 cents 19:21:23:28:31:34:38 SD: 4.4408 cents 26:29:32:38:42:47:52 SD: 4.3698 cents 27:30:33:40:44:49:54 SD: 2.5777 cents 36:40:44:53:59:65:72 SD: 1.9462 cents 57:63:70:84:93:103:114 SD: 0.8133 cents 93:103:114:137:152:168:186 SD: 0.6675 cents 133:147:163:196:217:240:266 SD: 0.5500 cents 159:176:195:234:259:287:318 SD: 0.5235 cents 160:177:196:236:261:289:320 SD: 0.4901 cents 186:206:228:274:303:336:372 SD: 0.4158 cents 195:216:239:287:318:352:390 SD: 0.3585 cents 222:246:272:327:362:401:444 SD: 0.3542 cents 252:279:309:371:411:455:504 SD: 0.2796 cents 279:309:342:411:455:504:558 SD: 0.2508 cents 328:363:402:483:535:592:656 SD: 0.2488 cents 355:393:435:523:579:641:710 SD: 0.1759 cents 514:569:630:757:838:928:1027 SD: 0.1757 cents 541:599:663:797:882:977:1081 SD: 0.1659 cents 550:609:674:810:897:993:1099 SD: 0.1475 cents 598:662:733:881:975:1080:1195 SD: 0.1432 cents