Scala analysis: xen18-erlich-tetracot-07
6L 1s MOS for Tetracot, L=176.11, s=142.37
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: 528.330 cents 528.330000 4: 670.700 cents 670.700000 5: 846.810 cents 846.810000 6: 1022.920 cents 1022.920000 7: 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: 176.1100 cents 176.1100 4: 142.3700 cents 142.3700 5: 176.1100 cents 176.1100 6: 176.1100 cents 176.1100 7: 176.1100 cents 176.1100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 142.37000 cents 1: 6 176.11000 cents 2: 2 318.48000 cents 2: 5 352.22000 cents 3: 3 494.59000 cents 3: 4 528.33000 cents 4: 4 670.70000 cents 4: 3 704.44000 cents 5: 5 846.81000 cents 5: 2 880.55000 cents 6: 6 1022.92000 cents 6: 1 1056.66000 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 7 0.0 : 176.1 352.2 528.3 670.7 846.8 1022.9 1199.0 176.1 : 176.1 352.2 494.6 670.7 846.8 1022.9 1199.0 352.2 : 176.1 318.5 494.6 670.7 846.8 1022.9 1199.0 528.3 : 142.4 318.5 494.6 670.7 846.8 1022.9 1199.0 670.7 : 176.1 352.2 528.3 704.4 880.5 1056.7 1199.0 846.8 : 176.1 352.2 528.3 704.4 880.5 1022.9 1199.0 1022.9: 176.1 352.2 528.3 704.4 846.8 1022.9 1199.0 1199.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 142.3700 .. 176.1100 cents 33.74000 cents 142.37000 cents 2: 318.4800 .. 352.2200 cents 33.74000 cents 142.37000 cents 3: 494.5900 .. 528.3300 cents 33.74000 cents 142.37000 cents 4: 670.7000 .. 704.4400 cents 33.74000 cents 142.37000 cents 5: 846.8100 .. 880.5500 cents 33.74000 cents 142.37000 cents 6: 1022.9200 .. 1056.6600 cents 33.74000 cents 142.37000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 142.37000 cents, class 1 Average step (divided formal octave): 171.2900 cents Largest one step interval : 176.11000 cents Average / Smallest step : 1.203133 Largest / Average step : 1.028139 Largest / Smallest step : 1.236988 Median interval of one step : 176.11000 cents, amount: 6 Most common interval of one step : 176.11000 cents, amount: 6 Least squares average step : 170.80800 cents, oct.: 1195.65600 cents Scale is strictly proper Scale has Myhill's property chromas: 33.74000 cents and 108.63000 cents, ratio: 3.219621 generators: 1 of 176.11000 cents and 6 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: 167 334 501 636 803 970 1137 generators: 167 and 970 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAA Step pattern size order : LLLSLLL Scale is a Constant Structure, by a margin of 142.37000 cents Scale diversity : 1.166858 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.831164 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 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: 6 Scale is a chain of 3 triads 0.0 528.330 1022.920 cents Most common triad is 0.0 176.110 1022.920 cents, amount: 5 Number of recognisable fifths : 3, average 704.4400 cents Number of recognisable fourths : 3, average 494.5900 cents Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 7 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 9.6400 c. M: 14.4600 c. Lebeng 20: 3 3 3 2 3 3 3 SP M ME I SD: 7.4890 c. M: 11.2335 c. 27: 4 4 4 3 4 4 4 SP M ME I SD: 3.0481 c. M: 4.5722 c. 34: 5 5 5 4 5 5 5 SP M ME I SD: 0.4359 c. M: 0.6538 c. 109: 16 16 16 13 16 16 16 SP M DE I SD: 0.2112 c. M: 0.3168 c. 143: 21 21 21 17 21 21 21 SP M DE I SD: 0.0573 c. M: 0.0860 c. 177: 26 26 26 21 26 26 26 SP M DE I SD: 0.0374 c. M: 0.0561 c. 320: 47 47 47 38 47 47 47 SP M DE I SD: 0.0049 c. M: 0.0074 c. 817: 120 120 120 97 120 120 120 SP M DE I SD: 0.0042 c. M: 0.0064 c. 1137: 167 167 167 135 167 167 167 SP M DE I SD: 0.0017 c. M: 0.0025 c. 1457: 214 214 214 173 214 214 214 SP M DE I SD: 0.0002 c. M: 0.0003 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.9700 cents 2 x x x 3 x x 4 S SD: 15.6350 cents 3 x x 4 x 5 x 6 S SD: 16.0832 cents 4 x 5 x 6 x 7:8 S SD: 17.7946 cents 5 x 6:7 x 8:9:10 S SD: 14.6972 cents 6 x 7:8:9:10:11:12 S SD: 17.7080 cents 7:8:9 x 10:11:13:14 SD: 23.1225 cents 8:9:10:11:12:13:14:16 S SD: 11.4349 cents 9:10:11:12:13:15:16:18 SD: 9.3375 cents 16:18:20:22:24:26:29:32 SD: 8.4820 cents 17:19:21:23:25:28:31:34 SD: 4.6869 cents 19:21:23:26:28:31:34:38 SD: 4.3462 cents 26:29:32:35:38:42:47:52 SD: 4.2272 cents 27:30:33:37:40:44:49:54 SD: 3.2990 cents 30:33:37:41:44:49:54:60 SD: 3.1654 cents 36:40:44:49:53:59:65:72 SD: 1.8386 cents 57:63:70:77:84:93:103:114 SD: 1.2968 cents 67:74:82:91:99:109:121:134 SD: 1.2158 cents 76:84:93:103:112:124:137:152 SD: 0.7746 cents 84:93:103:114:124:137:152:168 SD: 0.7678 cents 93:103:114:126:137:152:168:186 SD: 0.6809 cents 129:143:158:175:190:210:233:258 SD: 0.6095 cents 159:176:195:216:234:259:287:318 SD: 0.5378 cents 160:177:196:217:236:261:289:320 SD: 0.4347 cents 205:227:251:278:302:334:370:410 SD: 0.4168 cents 216:239:265:293:318:352:390:432 SD: 0.4071 cents 222:246:272:301:327:362:401:444 SD: 0.3548 cents 252:279:309:342:371:411:455:504 SD: 0.2450 cents 319:353:391:433:470:520:576:638 SD: 0.2380 cents 328:363:402:445:483:535:592:656 SD: 0.2151 cents 412:456:505:559:607:672:744:824 SD: 0.1625 cents 541:599:663:734:797:882:977:1081 SD: 0.1438 cents 577:639:707:783:850:941:1042:1153 SD: 0.1417 cents