Scala analysis: quasi_8-EDO
Emulation of 8-EDO
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 13/11 289.209719 tridecimal minor third 3: 352/273 440.009373 4: 63/44 621.417966 5: 264/169 772.217620 6: 22/13 910.790281 tridecimal major sixth 7: 24/13 1061.427339 tridecimal neutral seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 3872/3549 150.7997 4: 17199/15488 181.4086 5: 3872/3549 150.7997 6: 13/12 138.5727 tridecimal 2/3-tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone 8: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 13/12 138.573 cents tridecimal 2/3-tone 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 3872/3549 150.800 cents 1: 1 17199/15488 181.409 cents 2: 4 13/11 289.210 cents tridecimal minor third 2: 2 968/819 289.372 cents 2: 2 63/52 332.208 cents 3: 2 169/132 427.782 cents 3: 1 156/121 439.847 cents 3: 2 352/273 440.009 cents 3: 2 21/16 470.781 cents narrow fourth 3: 1 2904/2197 483.008 cents 4: 2 169/121 578.419 cents two (tridecimal minor third) 4: 2 88/63 578.582 cents 4: 2 63/44 621.418 cents 4: 2 242/169 621.581 cents 5: 1 2197/1452 716.992 cents 5: 2 32/21 729.219 cents wide fifth 5: 2 273/176 759.991 cents 5: 1 121/78 760.153 cents 5: 2 264/169 772.218 cents 6: 2 104/63 867.792 cents 6: 2 819/484 910.628 cents 6: 4 22/13 910.790 cents tridecimal major sixth 7: 1 30976/17199 1018.591 cents 7: 2 3549/1936 1049.200 cents 7: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 7: 3 24/13 1061.427 cents tridecimal neutral seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 150.6 289.2 440.0 621.4 772.2 910.8 1061.4 1200.0 150.6 : 138.6 289.4 470.8 621.6 760.2 910.8 1049.4 1200.0 289.2 : 150.8 332.2 483.0 621.6 772.2 910.8 1061.4 1200.0 440.0 : 181.4 332.2 470.8 621.4 760.0 910.6 1049.2 1200.0 621.4 : 150.8 289.4 440.0 578.6 729.2 867.8 1018.6 1200.0 772.2 : 138.6 289.2 427.8 578.4 717.0 867.8 1049.2 1200.0 910.8 : 150.6 289.2 439.8 578.4 729.2 910.6 1061.4 1200.0 1061.4: 138.6 289.2 427.8 578.6 760.0 910.8 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 181.4086 cents 3969/3872, 42.8359 cents 13/12, 138.5727 cents 2: 289.2097 .. 332.2082 cents 693/676, 42.9985 cents 1408/1323, 107.8011 cents 3: 427.7824 .. 483.0079 cents 383328/371293, 55.2255 cents 2197/2079, 95.5741 cents 4: 578.4194 .. 621.5806 cents 29282/28561, 43.1611 cents 371293/351384, 95.4115 cents 5: 716.9921 .. 772.2176 cents 383328/371293, 55.2255 cents 371293/351384, 95.4115 cents 6: 867.7918 .. 910.7903 cents 693/676, 42.9985 cents 2197/2079, 95.5741 cents 7: 1018.5914 .. 1061.4273 cents 3969/3872, 42.8359 cents 1408/1323, 107.8011 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 17199/15488, 181.4086 cents Average / Smallest step : 1.082465 Largest / Average step : 1.209391 Largest / Smallest step : 1.309123 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Most common interval of one step : 13/12, 138.5727 cents, amount: 3 Least squares average step : 151.42440 cents, oct.: 1211.39520 cents Scale is strictly proper Step pattern alph. order: ABCDCBAB Step pattern size order : BACDCABA Scale is a Constant Structure, by a margin of 95.41154 cents Scale diversity : 1.244427 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.728932 Rothenberg efficiency : 0.387500 redundancy: 0.612500 Efficiency x scale size : 3.100000 Number of different interval sizes : 28 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 10648/10647, 0.1626 cents Most common intervals : 13/11, 289.2097 cents & inv., amount: 4 Number of recognisable fifths : 1, average 716.9921 cents Number of appreciable fifths : 0 Best fifths form a closed circle Scale contains a complete diamond : 11 13 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 3 = 37.5000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties -- Prime limit : 13 Odd number limit : 17199 (O: 17199 U: 17199) Highest odd numerator or denominator: 273 Scale harmonicity : 0.007226 Average absolute harmonicity : 0.148557 Specific harmonicity : 0.044983 Fundamental : 1/156156, -17.2526 octaves, 0.0017 Hz. Guide tone : 288288, 18.1372 octaves, 75423510.969 Hz. Exponens Consonantiae : 4.501790E+10, 35.38978 octaves Euler's gradus suavitatis : 82 Sum of Mann's harmonic distance : 643.5, average 80.43750 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.84661, average 1.35583 Sum of Tenney's harmonic distance : 22.60245, average 2.82531 Vogel's harmonic complexity : 45.62500 Wille's k value : 111793 Wilson's harmonic complexity : 84 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 121.06990, average 3.36305 Lattice compactness (without 2's) : 75.54887, average 2.09858 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 5 1.62500 17 1 3: -1 .. 2 0.50000 6 7: -1 .. 1 0.00000 2 11: -1 .. 1 0.00000 6 2 13: -2 .. 1 -0.50000 6 5 Average exponent except 2's : 0 / 8 = 0.00000 Average absolute exponent except 2's: 20 / 8 = 2.50000 Scale is weakly epimorphic with val: <8 12 21 25 27| Scale is weakly epimorphic with val: <8 12 21 25 31| Scale is weakly epimorphic with val: <8 12 22 25 27| Scale is weakly epimorphic with val: <8 12 22 27 29| Scale is weakly epimorphic with val: <8 12 22 29 31| Scale is weakly epimorphic with val: <8 12 22 31 33| Scale is weakly epimorphic with val: <8 12 23 26 33| Scale is JI-epimorphic with val: <8 12 23 27 29| Scale is weakly epimorphic with val: <8 12 23 27 33| Scale is weakly epimorphic with val: <8 12 24 26 29| Scale is weakly epimorphic with val: <8 12 24 26 33| Scale is weakly epimorphic with val: <8 12 24 30 31| Scale is weakly epimorphic with val: <8 13 20 26 28| Scale is weakly epimorphic with val: <8 13 20 26 32| Scale is weakly epimorphic with val: <8 13 21 25 30| Scale is weakly epimorphic with val: <8 13 21 26 28| Scale is weakly epimorphic with val: <8 13 21 28 30| Scale is weakly epimorphic with val: <8 13 21 30 32| Scale is weakly epimorphic with val: <8 13 22 25 28| Scale is JI-epimorphic with val: <8 13 22 28 30| = patent Scale is weakly epimorphic with val: <8 13 23 27 30| Scale is weakly epimorphic with val: <8 13 23 31 32| Scale is weakly epimorphic with val: <8 13 24 25 30| Scale is weakly epimorphic with val: <8 13 24 30 32| Scale is weakly epimorphic with val: <8 13 24 31 32| Scale is weakly epimorphic with val: <8 14 20 25 27| Scale is weakly epimorphic with val: <8 14 20 26 27| Scale is weakly epimorphic with val: <8 14 20 26 31| Scale is weakly epimorphic with val: <8 14 20 27 29| Scale is weakly epimorphic with val: <8 14 20 29 31| Scale is weakly epimorphic with val: <8 14 20 31 33| Scale is weakly epimorphic with val: <8 14 21 26 29| Scale is JI-epimorphic with val: <8 14 21 29 31| Scale is weakly epimorphic with val: <8 14 22 28 31| Scale is weakly epimorphic with val: <8 14 23 26 31| Scale is weakly epimorphic with val: <8 14 23 31 33| Scale is weakly epimorphic with val: <8 14 24 25 31| Scale is weakly epimorphic with val: <8 14 24 26 29| Scale is weakly epimorphic with val: <8 14 24 26 33| Scale is weakly epimorphic with val: <8 14 24 27 33|
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 13.3042 c. M: 22.2176 c. 17: 2 2 2 3 2 2 2 2 SP M ME SD: 9.1688 c. M: 16.4800 c. 25: 3 3 3 4 3 3 3 3 SP M ME SD: 4.5420 c. M: 8.0094 c. 33: 4 4 4 5 4 4 4 4 SP M ME SD: 4.7090 c. M: 8.5813 c. 54: 7 6 7 8 7 6 7 6 SP SD: 3.5896 c. M:-5.5602 c. 62: 8 7 8 9 8 7 8 7 SP SD: 2.8367 c. M:-5.1519 c. 71: 9 8 9 11 9 8 9 8 SP SD: 2.8268 c. M:-5.2472 c. 79: 10 9 10 12 10 9 10 9 SP SD: 1.3222 c. M:-2.4659 c. 87: 11 10 11 13 11 10 11 10 SP SD: 0.7446 c. M:-1.3699 c. 112: 14 13 14 17 14 13 14 13 SP SD: 0.5089 c. M: 0.7890 c. 191: 24 22 24 29 24 22 24 22 SP SD: 0.3382 c. M:-0.5716 c. 199: 25 23 25 30 25 23 25 23 SP SD: 0.2247 c. M: 0.3583 c. 303: 38 35 38 46 38 35 38 35 SP SD: 0.2070 c. M: 0.4054 c. 390: 49 45 49 59 49 45 49 45 SP SD: 0.0817 c. M:-0.1322 c. 589: 74 68 74 89 74 68 74 68 SP SD: 0.0731 c. M:-0.1269 c. 892: 112 103 112 135 112 103 112 103 SP SD: 0.0553 c. M:-0.1067 c. 979: 123 113 123 148 123 113 123 113 SP SD: 0.0625 c. M:-0.1290 c. 1091: 137 126 137 165 137 126 137 126 SP SD: 0.0516 c. M: 0.0820 c. 1481: 186 171 186 224 186 171 186 171 SP SD: 0.0460 c. M:-0.0719 c. 1871: 235 216 235 283 235 216 235 216 SP SD: 0.0483 c. M:-0.0845 c. 1983: 249 229 249 300 249 229 249 229 SP SD: 0.0484 c. M: 0.0699 c. 2373: 298 274 298 359 298 274 298 274 SP SD: 0.0468 c. M:-0.0738 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 35.1313 cents 3 x x 4 x x 5 x 6 S SD: 21.2571 cents 4 x x 5 x 6:7 x 8 S SD: 26.4436 cents 5 x 6 x 7:8 x 9:10 S SD: 15.3011 cents 6 x 7:8 x 9:10:11:12 S SD: 16.3708 cents 7 x 8:9:10:11:12:13:14 S SD: 9.1674 cents 8:9 x 10:11:13:14:15:16 SD: 19.8926 cents 9:10:11:12:13:14:15:17:18 SD: 12.6965 cents 10:11:12:13:14:16:17:18:20 S SD: 9.9396 cents 11:12:13:14:16:17:19:20:22 SD: 7.4446 cents 18:20:21:23:26:28:30:33:36 SD: 6.7099 cents 20:22:24:26:29:31:34:37:40 SD: 5.3631 cents 21:23:25:27:30:33:36:39:42 SD: 3.8660 cents 32:35:38:41:46:50:54:59:64 SD: 2.1124 cents 44:48:52:57:63:69:74:81:88 SD: 1.9812 cents 45:49:53:58:64:70:76:83:90 SD: 1.9747 cents 55:60:65:71:79:86:93:102:110 SD: 1.2551 cents 65:71:77:84:93:102:110:120:130 SD: 1.2523 cents 76:83:90:98:109:119:129:140:152 SD: 1.1306 cents 77:84:91:99:110:120:130:142:154 SD: 1.0949 cents 97:106:115:125:139:152:164:179:194 SD: 1.0766 cents 98:107:116:126:140:153:166:181:196 SD: 0.9132 cents 100:109:118:129:143:156:169:185:200 SD: 0.7793 cents 111:121:131:143:159:173:188:205:222 SD: 0.6648 cents 121:132:143:156:173:189:205:223:242 SD: 0.5449 cents 153:167:181:197:219:239:259:282:306 SD: 0.5349 cents 155:169:183:200:222:242:262:286:310 SD: 0.4253 cents 176:192:208:227:252:275:298:325:352 SD: 0.1488 cents 429:468:507:553:614:670:726:792:858 SD: 0.1156 cents 539:588:637:695:772:842:912:995:1078 SD: 0.0812 cents