Scala analysis: quasi_6-EDO
Emulation of 6-EDO
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 352/273 440.009373 3: 63/44 621.417966 4: 21/13 830.253246 5: 39/22 991.164720 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 44/39 208.8353 1: 8/7 231.1741 septimal whole tone 2: 44/39 208.8353 3: 17199/15488 181.4086 4: 44/39 208.8353 5: 169/154 160.9115 6: 44/39 208.8353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 169/154 160.911 cents 1: 1 17199/15488 181.409 cents 1: 3 44/39 208.835 cents 1: 1 8/7 231.174 cents septimal whole tone 2: 2 26/21 369.747 cents 2: 2 441/352 390.244 cents 2: 2 352/273 440.009 cents 3: 1 10647/7744 551.155 cents 3: 1 88/63 578.582 cents 3: 1 147/104 599.079 cents 3: 1 208/147 600.921 cents 3: 1 63/44 621.418 cents 3: 1 15488/10647 648.845 cents 4: 2 273/176 759.991 cents 4: 2 704/441 809.756 cents 4: 2 21/13 830.253 cents 5: 1 7/4 968.826 cents harmonic seventh 5: 3 39/22 991.165 cents 5: 1 30976/17199 1018.591 cents 5: 1 308/169 1039.089 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 231.2 440.0 621.4 830.3 991.2 1200.0 231.2 : 208.8 390.2 599.1 760.0 968.8 1200.0 440.0 : 181.4 390.2 551.2 760.0 991.2 1200.0 621.4 : 208.8 369.7 578.6 809.8 1018.6 1200.0 830.3 : 160.9 369.7 600.9 809.8 991.2 1200.0 991.2 : 208.8 440.0 648.8 830.3 1039.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 160.9115 .. 231.1741 cents 176/169, 70.2626 cents 169/154, 160.9115 cents 2: 369.7468 .. 440.0094 cents 176/169, 70.2626 cents 13/12, 138.5727 cents 3: 551.1553 .. 648.8447 cents 119939072/113358609, 97.6893 cents 2906631/2725888, 111.1460 cents 4: 759.9906 .. 830.2532 cents 176/169, 70.2626 cents 2906631/2725888, 111.1460 cents 5: 968.8259 .. 1039.0885 cents 176/169, 70.2626 cents 13/12, 138.5727 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 169/154, 160.9115 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.242919 Largest / Average step : 1.155870 Largest / Smallest step : 1.436654 Median interval of one step : 44/39, 208.8353 cents, amount: 3 Most common interval of one step : 44/39, 208.8353 cents, amount: 3 Least squares average step : 202.77234 cents, oct.: 1216.63407 cents Scale is strictly proper Step pattern alph. order: ABCBDB Step pattern size order : DCBCAC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 111.14597 cents Scale diversity : 1.357938 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.684384 Rothenberg efficiency : 0.450000 redundancy: 0.550000 Efficiency x scale size : 2.700000 Number of different interval sizes : 20 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 21632/21609, 1.8417 cents Most common intervals : 44/39, 208.8353 cents & inv., amount: 3 Most common triad is 0.0 208.835 1039.089 cents, amount: 1 Number of recognisable fifths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 16.6667% Limited inverse transpositions with margin 70.2626 cents: 1 2 -- Rational properties -- Prime limit : 13 Odd number limit : 17199 (O: 17199 U: 17199) Highest odd numerator or denominator: 273 Scale harmonicity : 0.008603 Average absolute harmonicity : 0.195261 Specific harmonicity : 0.050252 Fundamental : 1/12012, -13.5522 octaves, 0.0218 Hz. Guide tone : 288288, 18.1372 octaves, 75423510.969 Hz. Exponens Consonantiae : 3.462915E+09, 31.68934 octaves Euler's gradus suavitatis : 70 Sum of Mann's harmonic distance : 422.5, average 70.41667 Mersenne's string divisions : 416096250 Sum of van Prooijen's expressibility: 7.99389, average 1.33231 Sum of Tenney's harmonic distance : 15.84437, average 2.64073 Vogel's harmonic complexity : 34.50000 Wille's k value : 8599 Wilson's harmonic complexity : 71 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 76.79834, average 3.65706 Lattice compactness (without 2's) : 43.77051, average 2.08431 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 5 1.00000 12 1 3: -1 .. 2 0.50000 5 7: -1 .. 1 0.00000 4 1 11: -1 .. 1 -0.16667 3 1 13: -1 .. 1 -0.16667 3 3 Average exponent except 2's : 1 / 6 = 0.16667 Average absolute exponent except 2's: 15 / 6 = 2.50000 Scale is weakly epimorphic with val: <6 9 15 20 22| Scale is weakly epimorphic with val: <6 9 16 21 21| Scale is JI-epimorphic with val: <6 9 17 20 22| Scale is weakly epimorphic with val: <6 9 17 21 21| Scale is weakly epimorphic with val: <6 9 19 21 21| Scale is weakly epimorphic with val: <6 10 15 22 23| Scale is JI-epimorphic with val: <6 10 17 22 23| Scale is weakly epimorphic with val: <6 11 15 20 22| Scale is weakly epimorphic with val: <6 11 16 19 23| Scale is weakly epimorphic with val: <6 11 17 19 23| Scale is weakly epimorphic with val: <6 11 19 19 23| Scale is weakly epimorphic with val: <6 11 19 20 22|
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 25.8992 c. M: 40.0094 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 10: 2 2 1 2 1 2 P D3 SD: 23.1016 c. M:-39.9906 c. 11: 2 2 2 2 1 2 SP M ME SD: 22.9888 c. M:-42.4740 c. Schulter Hexatonic 13: 3 2 2 2 2 2 SP M ME SD: 25.0173 c. M:-45.7490 c. 16: 3 3 2 3 2 3 SP D3 SD: 12.1488 c. M: 21.4180 c. 17: 3 3 3 3 2 3 SP M ME SD: 13.7348 c. M: 19.4094 c. 19: 4 3 3 3 3 3 SP M ME SD: 13.0868 c. M:-21.4575 c. 22: 4 4 3 4 3 4 SP D3 SD: 12.0685 c. M: 21.4180 c. 25: 5 4 4 4 4 4 SP M ME SD: 10.2899 c. M:-16.8353 c. 27: 5 5 4 5 3 5 SP SD: 8.9541 c. M:-14.1912 c. 30: 6 5 5 5 4 5 SP T3 SD: 9.9687 c. M:-18.5820 c. 33: 6 6 5 6 4 6 SP SD: 7.2716 c. M: 12.9923 c. 35: 7 6 5 6 5 6 SP SD: 5.6739 c. M:-8.8259 c. 41: 8 7 6 7 6 7 SP SD: 5.5805 c. M: 10.7411 c. 46: 9 8 7 8 6 8 SP SD: 3.3513 c. M:-4.6690 c. 52: 10 9 8 9 7 9 SP SD: 1.0712 c. M:-1.6590 c. 120: 23 21 18 21 16 21 SP SD: 0.8954 c. M: 1.4180 c. 166: 32 29 25 29 22 29 SP SD: 0.6832 c. M:-1.0721 c. 172: 33 30 26 30 23 30 SP SD: 0.5112 c. M: 0.9415 c. 218: 42 38 33 38 29 38 SP SD: 0.4977 c. M:-0.9394 c. 224: 43 39 34 39 30 39 SP SD: 0.4492 c. M: 0.8170 c. 311: 60 54 47 54 42 54 SP SD: 0.3758 c. M: 0.6713 c. 338: 65 59 51 59 45 59 SP SD: 0.3862 c. M: 0.6322 c. 357: 69 62 54 62 48 62 SP SD: 0.4192 c. M:-0.7587 c. 363: 70 63 55 63 49 63 SP SD: 0.3537 c. M:-0.5708 c. 390: 75 68 59 68 52 68 SP SD: 0.3165 c. M:-0.5160 c. 425: 82 74 64 74 57 74 SP SD: 0.2667 c. M:-0.4612 c. 431: 83 75 65 75 58 75 SP SD: 0.3197 c. M: 0.5549 c. 442: 85 77 67 77 59 77 SP SD: 0.3171 c. M:-0.5160 c. 477: 92 83 72 83 64 83 SP SD: 0.1523 c. M:-0.2724 c. 529: 102 92 80 92 71 92 SP SD: 0.1182 c. M:-0.2059 c. 649: 125 113 98 113 87 113 SP SD: 0.0838 c. M: 0.1545 c. 701: 135 122 106 122 94 122 SP SD: 0.0423 c. M: 0.0757 c. 1178: 227 205 178 205 158 205 SP SD: 0.0397 c. M:-0.0653 c. 1230: 237 214 186 214 165 214 SP SD: 0.0349 c. M:-0.0548 c. 1879: 362 327 284 327 252 327 SP SD: 0.0156 c. M: 0.0244 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 40.2685 cents 3 x 4 x 5 x 6 S SD: 26.4481 cents 4 x 5:6 x 7:8 S SD: 24.8350 cents 5:6 x 7:8:9:10 S SD: 19.6178 cents 7:8:9:10:11:12:14 S SD: 12.5709 cents 13:15:17:19:21:23:26 SD: 7.7234 cents 14:16:18:20:23:25:28 SD: 5.4051 cents 21:24:27:30:34:37:42 SD: 2.1569 cents 44:50:57:63:71:78:88 SD: 2.1544 cents 49:56:63:70:79:87:98 SD: 1.2739 cents 62:71:80:89:100:110:124 SD: 1.0865 cents 76:87:98:109:123:135:152 SD: 1.0447 cents 83:95:107:119:134:147:166 SD: 0.6626 cents 127:145:164:182:205:225:254 SD: 0.6436 cents 132:151:170:189:213:234:264 SD: 0.5337 cents 141:161:182:202:228:250:282 SD: 0.5277 cents 162:185:209:232:262:287:324 SD: 0.4786 cents 169:193:218:242:273:300:338 SD: 0.4661 cents 176:201:227:252:284:312:352 SD: 0.3840 cents 190:217:245:272:307:337:380 SD: 0.2614 cents 211:241:272:302:341:374:422 SD: 0.2511 cents 252:288:325:361:407:447:504 SD: 0.2445 cents 273:312:352:391:441:484:546 SD: 0.0881 cents 567:648:731:812:916:1005:1134 SD: 0.0790 cents