Scala analysis: met24-quasi_8-EDO_Cup
Emulation of 8-EDO
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 150.000 cents 150.000000 2: 289.453 cents 289.453120 3: 439.453 cents 439.453120 4: 622.266 cents 622.265620 5: 772.266 cents 772.265620 6: 911.719 cents 911.718750 7: 1061.719 cents 1061.718750 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 138.2813 cents 138.2813 1: 150.0000 cents 150.0000 2: 139.4531 cents 139.4531 3: 150.0000 cents 150.0000 4: 182.8125 cents 182.8125 5: 150.0000 cents 150.0000 6: 139.4531 cents 139.4531 7: 150.0000 cents 150.0000 8: 138.2813 cents 138.2813
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 138.28125 cents 1: 2 139.45312 cents 1: 4 150.00000 cents 1: 1 182.81250 cents 2: 2 288.28125 cents 2: 4 289.45312 cents 2: 2 332.81250 cents 3: 2 427.73438 cents 3: 1 438.28125 cents 3: 2 439.45312 cents 3: 2 472.26562 cents 3: 1 482.81250 cents 4: 4 577.73438 cents 4: 4 622.26562 cents 5: 1 717.18750 cents 5: 2 727.73438 cents 5: 2 760.54688 cents 5: 1 761.71875 cents 5: 2 772.26562 cents 6: 2 867.18750 cents 6: 4 910.54688 cents 6: 2 911.71875 cents 7: 1 1017.18750 cents 7: 4 1050.00000 cents 7: 2 1060.54688 cents 7: 1 1061.71875 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.71429 = 26/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 150.0 289.5 439.5 622.3 772.3 911.7 1061.7 1200.0 150.0 : 139.5 289.5 472.3 622.3 761.7 911.7 1050.0 1200.0 289.5 : 150.0 332.8 482.8 622.3 772.3 910.5 1060.5 1200.0 439.5 : 182.8 332.8 472.3 622.3 760.5 910.5 1050.0 1200.0 622.3 : 150.0 289.5 439.5 577.7 727.7 867.2 1017.2 1200.0 772.3 : 139.5 289.5 427.7 577.7 717.2 867.2 1050.0 1200.0 911.7 : 150.0 288.3 438.3 577.7 727.7 910.5 1060.5 1200.0 1061.7: 138.3 288.3 427.7 577.7 760.5 910.5 1050.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.2813 .. 182.8125 cents 44.53125 cents 138.28125 cents 2: 288.2813 .. 332.8125 cents 44.53125 cents 105.46875 cents 3: 427.7344 .. 482.8125 cents 55.07812 cents 94.92188 cents 4: 577.7344 .. 622.2656 cents 44.53124 cents 94.92188 cents 5: 717.1875 .. 772.2656 cents 55.07812 cents 94.92188 cents 6: 867.1875 .. 911.7187 cents 44.53125 cents 94.92188 cents 7: 1017.1875 .. 1061.7188 cents 44.53125 cents 105.46875 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 138.28125 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 182.81250 cents Average / Smallest step : 1.084746 Largest / Average step : 1.218750 Largest / Smallest step : 1.322034 Median interval of one step : 150.00000 cents, amount: 4 Most common interval of one step : 150.00000 cents, amount: 4 Least squares average step : 151.47059 cents, oct.: 1211.76470 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 128 247 375 531 659 778 906 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 983 of 1151.953 cents and inv. generated superset size: 197 = 189 more = 2462.500% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABAD Step pattern size order : CBCDCBCA Scale is a Constant Structure, by a margin of 94.92188 cents Scale diversity : 1.248976 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.722656 Rothenberg efficiency : 0.421429 redundancy: 0.578571 Efficiency x scale size : 3.371429 Number of different interval sizes : 26 = 3.71429 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 3.71429 = 26/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 1.17187 cents Number of recognisable fifths : 1, average 717.1875 cents Number of appreciable fifths : 0 Scale contains two identical disjunct tetrachords Best fifths form a closed circle Formal octave complements present : 1 = 12.5000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 13.6411 c. M: 22.2656 c. 17: 2 2 2 3 2 2 2 2 SP M ME SD: 8.7520 c. M: 15.9237 c. 25: 3 3 3 4 3 3 3 3 SP M ME SD: 4.2960 c. M: 7.4531 c. 33: 4 4 4 5 4 4 4 4 SP M ME SD: 4.7675 c. M: 8.6293 c. 54: 7 6 7 8 7 6 7 6 SP SD: 3.7305 c. M:-5.5556 c. 58: 7 7 7 9 7 7 7 7 SP M DE SD: 4.2466 c. M: 6.7484 c. 62: 8 7 8 9 8 7 8 7 SP SD: 3.1807 c. M:-5.7082 c. 71: 9 8 9 11 9 8 9 8 SP SD: 2.6433 c. M:-5.1992 c. 79: 10 9 10 12 10 9 10 9 SP SD: 1.3287 c. M:-2.4179 c. 87: 11 10 11 13 11 10 11 10 SP SD: 1.1853 c. M:-1.9262 c. 104: 13 12 13 16 13 12 13 12 SP SD: 0.6469 c. M: 0.9916 c. 112: 14 13 14 17 14 13 14 13 SP SD: 0.6591 c. M: 1.0045 c. 191: 24 22 24 29 24 22 24 22 SP SD: 0.4736 c. M:-0.7853 c. 216: 27 25 27 33 27 25 27 25 SP SD: 0.4152 c. M: 0.6076 c. 295: 37 34 37 45 37 34 37 34 SP SD: 0.4122 c. M: 0.6396 c. 328: 41 38 41 50 41 38 41 38 SP SD: 0.4569 c. M: 0.7431 c. 399: 50 46 50 61 50 46 50 46 SP SD: 0.4373 c. M: 0.7313 c. 407: 51 47 51 62 51 47 51 47 SP SD: 0.3554 c. M: 0.6622 c. 513: 64 60 64 78 64 60 64 59 SP SD: 0.3628 c. M:-0.6054 c. 538: 67 63 67 82 67 63 67 62 SP SD: 0.3783 c. M: 0.5576 c. 544: 68 63 68 83 68 63 68 63 SP SD: 0.4332 c. M: 0.6893 c. 559: 70 65 70 85 70 65 70 64 SP SD: 0.5166 c. M:-0.8931 c. 563: 70 66 70 86 70 66 70 65 SP SD: 0.4742 c. M: 0.7993 c. 567: 71 66 71 86 71 66 71 65 SP SD: 0.4548 c. M:-0.7585 c. 584: 73 68 73 89 73 68 73 67 SP SD: 0.3742 c. M:-0.6100 c. 592: 74 69 74 90 74 69 74 68 SP SD: 0.3030 c. M:-0.4434 c. 617: 77 72 77 94 77 72 77 71 SP SD: 0.2344 c. M:-0.4368 c. 696: 87 81 87 106 87 81 87 80 SP SD: 0.2153 c. M:-0.3502 c. 704: 88 82 88 107 88 82 88 81 SP SD: 0.1993 c. M:-0.3196 c. 721: 90 84 90 110 90 84 90 83 SP SD: 0.1768 c. M:-0.3478 c. 729: 91 85 91 111 91 85 91 84 SP SD: 0.1668 c. M:-0.2588 c. 800: 100 93 100 122 100 93 100 92 SP SD: 0.1845 c. M:-0.2813 c. 808: 101 94 101 123 101 94 101 93 SP SD: 0.1110 c. M:-0.1624 c. 833: 104 97 104 127 104 97 104 96 SP SD: 0.1086 c. M: 0.1801 c. 912: 114 106 114 139 114 106 114 105 SP SD: 0.0809 c. M:-0.1234 c. 920: 115 107 115 140 115 107 115 106 SP SD: 0.0731 c. M:-0.1121 c. 1024: 128 119 128 156 128 119 128 118 SP SD: 0.0000 c. M:-0.0000 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: 35.1553 cents 3 x x 4 x x 5 x 6 S SD: 21.5550 cents 4 x x 5 x 6:7 x 8 S SD: 26.2543 cents 5 x 6 x 7:8 x 9:10 S SD: 15.3995 cents 6 x 7:8 x 9:10:11:12 S SD: 16.4889 cents 7 x 8:9:10:11:12:13:14 S SD: 9.1484 cents 8:9 x 10:11:13:14:15:16 SD: 19.8923 cents 9:10:11:12:13:14:15:17:18 SD: 12.7457 cents 10:11:12:13:14:16:17:18:20 S SD: 10.0153 cents 11:12:13:14:16:17:19:20:22 SD: 7.3204 cents 18:20:21:23:26:28:30:33:36 SD: 6.7879 cents 20:22:24:26:29:31:34:37:40 SD: 5.3210 cents 21:23:25:27:30:33:36:39:42 SD: 3.7797 cents 32:35:38:41:46:50:54:59:64 SD: 2.0779 cents 46:50:54:59:66:72:78:85:92 SD: 2.0633 cents 53:58:63:68:76:83:90:98:106 SD: 1.9715 cents 55:60:65:71:79:86:93:102:110 SD: 1.2130 cents 66:72:78:85:95:103:112:122:132 SD: 1.2028 cents 76:83:90:98:109:119:129:140:152 SD: 1.0638 cents 98:107:116:126:140:153:166:181:196 SD: 0.9206 cents 100:109:118:129:143:156:169:185:200 SD: 0.8655 cents 110:120:130:142:158:172:186:203:220 SD: 0.7696 cents 111:121:131:143:159:173:188:205:222 SD: 0.6215 cents 121:132:143:156:173:189:205:223:242 SD: 0.6077 cents 143:156:169:184:205:223:242:264:286 SD: 0.5775 cents 153:167:181:197:219:239:259:283:306 SD: 0.5494 cents 155:169:183:200:222:242:262:286:310 SD: 0.5389 cents 166:181:196:214:238:259:281:307:332 SD: 0.5310 cents 169:184:200:218:242:264:286:312:338 SD: 0.4900 cents 176:192:208:227:252:275:298:325:352 SD: 0.1981 cents 363:396:429:468:520:567:615:670:726 SD: 0.1847 cents 384:419:454:495:550:600:650:709:768 SD: 0.1645 cents 488:532:577:629:699:762:826:901:976 SD: 0.1604 cents 495:540:585:638:709:773:838:914:990 SD: 0.1249 cents 599:653:708:772:858:936:1014:1106:1198 SD: 0.1105 cents