Scala analysis: arrow1
"Arrow I" well-temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93.750 cents 93.750000 2: 196.875 cents 196.875000 3: 294.141 cents 294.140630 4: 391.406 cents 391.406250 5: 498.047 cents 498.046880 6: 591.797 cents 591.796900 7: 698.438 cents 698.437500 8: 795.703 cents 795.703130 9: 892.969 cents 892.968750 10: 996.094 cents 996.093750 11: 1089.844 cents 1089.843800 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 110.1562 cents 110.1562 1: 93.7500 cents 93.7500 2: 103.1250 cents 103.1250 3: 97.2656 cents 97.2656 4: 97.2656 cents 97.2656 5: 106.6406 cents 106.6406 6: 93.7500 cents 93.7500 7: 106.6406 cents 106.6406 8: 97.2656 cents 97.2656 9: 97.2656 cents 97.2656 10: 103.1250 cents 103.1250 11: 93.7501 cents 93.7501 12: 110.1562 cents 110.1562
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 93.75000 cents 1: 4 97.26563 cents 1: 2 103.12500 cents 1: 2 106.64063 cents 1: 1 110.15620 cents 2: 2 194.53125 cents 2: 2 196.87500 cents 2: 4 200.39063 cents 2: 4 203.90625 cents 3: 2 294.14063 cents 3: 5 297.65625 cents 3: 2 301.17188 cents 3: 3 307.03125 cents 4: 2 391.40625 cents 4: 2 394.92190 cents 4: 2 400.78125 cents 4: 6 404.29688 cents 5: 6 498.04688 cents 5: 5 501.56250 cents 5: 1 503.90625 cents 6: 2 591.79690 cents 6: 2 595.31250 cents 6: 2 598.82813 cents 6: 2 601.17187 cents 6: 2 604.68750 cents 6: 2 608.20310 cents 7: 1 696.09375 cents 7: 5 698.43750 cents 7: 6 701.95313 cents 8: 6 795.70313 cents 8: 2 799.21875 cents 8: 2 805.07810 cents 8: 2 808.59375 cents 9: 3 892.96875 cents 9: 2 898.82812 cents 9: 5 902.34375 cents 9: 2 905.85937 cents 10: 4 996.09375 cents 10: 4 999.60937 cents 10: 2 1003.12500 cents 10: 2 1005.46875 cents 11: 1 1089.84380 cents 11: 2 1093.35937 cents 11: 2 1096.87500 cents 11: 4 1102.73437 cents 11: 3 1106.25000 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.18182 = 46/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 93.8 196.9 294.1 391.4 498.0 591.8 698.4 795.7 893.0 996.1 1089.8 1200.0 93.8 : 103.1 200.4 297.7 404.3 498.0 604.7 702.0 799.2 902.3 996.1 1106.3 1200.0 196.9 : 97.3 194.5 301.2 394.9 501.6 598.8 696.1 799.2 893.0 1003.1 1096.9 1200.0 294.1 : 97.3 203.9 297.7 404.3 501.6 598.8 702.0 795.7 905.9 999.6 1102.7 1200.0 391.4 : 106.6 200.4 307.0 404.3 501.6 604.7 698.4 808.6 902.3 1005.5 1102.7 1200.0 498.0 : 93.8 200.4 297.7 394.9 498.0 591.8 702.0 795.7 898.8 996.1 1093.4 1200.0 591.8 : 106.6 203.9 301.2 404.3 498.0 608.2 702.0 805.1 902.3 999.6 1106.2 1200.0 698.4 : 97.3 194.5 297.7 391.4 501.6 595.3 698.4 795.7 893.0 999.6 1093.4 1200.0 795.7 : 97.3 200.4 294.1 404.3 498.0 601.2 698.4 795.7 902.3 996.1 1102.7 1200.0 893.0 : 103.1 196.9 307.0 400.8 503.9 601.2 698.4 805.1 898.8 1005.5 1102.7 1200.0 996.1 : 93.8 203.9 297.7 400.8 498.0 595.3 702.0 795.7 902.3 999.6 1096.9 1200.0 1089.8: 110.2 203.9 307.0 404.3 501.6 608.2 702.0 808.6 905.9 1003.1 1106.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.7500 .. 110.1562 cents 16.40620 cents 93.75000 cents 2: 194.5312 .. 203.9062 cents 9.37500 cents 84.37505 cents 3: 294.1406 .. 307.0312 cents 12.89062 cents 90.23438 cents 4: 391.4063 .. 404.2969 cents 12.89063 cents 84.37500 cents 5: 498.0469 .. 503.9063 cents 5.85937 cents 93.75000 cents 6: 591.7969 .. 608.2031 cents 16.40620 cents 87.89065 cents 7: 696.0937 .. 701.9531 cents 5.85938 cents 87.89065 cents 8: 795.7031 .. 808.5937 cents 12.89062 cents 93.75000 cents 9: 892.9687 .. 905.8594 cents 12.89062 cents 84.37500 cents 10: 996.0938 .. 1005.4687 cents 9.37500 cents 90.23438 cents 11: 1089.8438 .. 1106.2500 cents 16.40620 cents 84.37505 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 93.75000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 110.15620 cents Average / Smallest step : 1.066667 Largest / Average step : 1.101562 Largest / Smallest step : 1.174999 Median interval of one step : 97.26563 cents, amount: 4 Most common interval of one step : 97.26563 cents, amount: 4 Least squares average step : 99.41106 cents, oct.: 1192.93271 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 80 168 251 334 425 505 596 679 762 850 930 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 639 of 748.828 cents and inv. generated superset size: 175 = 163 more = 1458.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCCDADCCBAE Step pattern size order : ACBBDADBBCAE Scale is a Constant Structure, by a margin of 84.37500 cents Scale diversity : 1.090232 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.890625 Rothenberg efficiency : 0.301623 redundancy: 0.698377 Efficiency x scale size : 3.619481 Number of different interval sizes : 46 = 4.18182 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 4.18182 = 46/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2.34374 cents Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 3 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 16.4062 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 5.8940 c. M:-10.1562 c. Twelve-tone Chromatic (1/11-comma) 53: 4 5 4 4 5 4 5 4 4 5 4 5 SP M ME SD: 4.4772 c. M: 9.9499 c. Schismic-12 54: 4 5 4 5 4 5 4 5 4 5 4 5 SP B ME SD: 5.9753 c. M: 9.5486 c. 55: 4 5 4 5 5 4 5 4 5 5 4 5 SP M ME SD: 5.3343 c. M: 10.5043 c. 62: 5 5 5 5 6 4 6 5 5 5 5 6 SP D3 SD: 5.2882 c. M: 11.1517 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.1316 c. M: 6.8149 c. 77: 6 7 6 6 7 6 7 6 6 7 6 7 SP M ME SD: 2.4835 c. M:-5.7224 c. 87: 7 7 7 7 8 7 8 7 7 7 7 8 SP D3 SD: 3.3980 c. M: 5.1994 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.2946 c. M:-5.3722 c. 90: 7 8 7 7 8 7 8 8 7 8 7 8 SP D3 SD: 3.5786 c. M: 5.1302 c. 91: 7 8 7 8 8 7 8 7 8 8 7 8 SP M ME SD: 3.4408 c. M:-6.1041 c. 98: 8 8 8 8 9 7 9 8 8 8 8 9 SP D3 SD: 2.4221 c. M: 4.2570 c. 101: 8 9 8 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.3607 c. M:-5.1052 c. 110: 9 9 9 9 10 8 10 9 9 9 9 10 SP D3 SD: 2.2138 c. M:-4.4318 c. 113: 9 10 9 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.5341 c. M:-4.8949 c. 118: 9 10 10 9 11 9 11 9 10 10 9 11 SP D3 SD: 2.4366 c. M: 4.9656 c. 122: 10 10 10 10 11 9 11 10 10 10 10 11 SP D3 SD: 2.2035 c. M:-4.6107 c. 130: 10 11 11 10 12 10 12 10 11 11 10 12 SP D3 SD: 1.9956 c. M: 3.7139 c. 140: 11 12 11 12 12 11 12 12 11 12 11 13 SP D3 SD: 1.9046 c. M: 4.1518 c. 142: 11 12 12 11 13 11 13 11 12 12 11 13 SP D3 SD: 1.7526 c. M:-2.9710 c. 152: 12 13 12 13 13 12 13 13 12 13 12 14 SP D3 SD: 1.7369 c. M: 3.7007 c. 154: 12 13 13 12 14 12 14 12 13 13 12 14 SP D3 SD: 1.6756 c. M:-3.1351 c. 160: 12 14 13 13 14 13 14 13 13 14 12 15 SP SD: 1.8504 c. M: 3.7500 c. 163: 13 14 13 13 15 12 15 13 13 14 13 15 SP SD: 1.7009 c. M: 2.8398 c. 164: 13 14 13 13 15 13 14 14 13 14 13 15 SP SD: 1.6857 c. M: 3.6014 c. 172: 13 15 14 14 15 14 15 14 14 15 13 16 SP SD: 1.5153 c. M: 3.0523 c. 175: 14 15 14 14 16 13 16 14 14 15 14 16 SP SD: 1.5114 c. M:-2.5245 c. 184: 14 16 15 15 16 15 16 15 15 16 14 17 SP SD: 1.3113 c. M: 2.4457 c. 196: 15 17 16 16 17 16 17 16 16 17 15 18 SP SD: 1.2340 c. M: 2.1285 c. 208: 16 18 17 17 18 17 18 17 17 18 16 19 SP SD: 1.2609 c. M:-2.4339 c. 217: 17 19 17 18 19 17 19 18 17 19 17 20 SP SD: 1.2410 c. M: 2.6462 c. 229: 18 20 18 19 20 18 20 19 18 20 18 21 SP SD: 1.1657 c. M:-2.2516 c. 240: 19 20 20 19 22 18 22 19 20 20 19 22 SP SD: 1.3880 c. M:-2.0313 c. 241: 19 21 19 20 21 19 21 20 19 21 19 22 SP SD: 1.1736 c. M:-2.2951 c. 246: 19 21 20 20 22 19 22 20 20 21 19 23 SP SD: 1.1770 c. M: 2.0389 c. 249: 19 22 20 20 22 20 22 20 20 22 19 23 SP SD: 1.1250 c. M: 2.1837 c. 254: 20 22 20 21 22 20 23 20 21 22 20 23 SP SD: 1.2207 c. M: 2.0023 c. 257: 20 22 21 21 23 20 23 20 21 22 20 24 SP SD: 1.2942 c. M:-1.9516 c. 258: 20 22 21 21 23 20 23 21 21 22 20 24 SP SD: 0.8844 c. M: 1.5262 c. 270: 21 23 22 22 24 21 24 22 22 23 21 25 SP SD: 0.6447 c. M: 1.3194 c. 282: 22 24 23 23 25 22 25 23 23 24 22 26 SP SD: 0.4828 c. M: 1.1303 c. 294: 23 25 24 24 26 23 26 24 24 25 23 27 SP SD: 0.4406 c. M: 0.9566 c. 347: 27 30 28 28 31 27 31 28 28 30 27 32 SP SD: 0.3854 c. M: 0.7497 c. 359: 28 31 29 29 32 28 32 29 29 31 28 33 SP SD: 0.2203 c. M: 0.4896 c. 371: 29 32 30 30 33 29 33 30 30 32 29 34 SP SD: 0.1835 c. M:-0.4296 c. 641: 50 55 52 52 57 50 57 52 52 55 50 59 SP SD: 0.1780 c. M: 0.3071 c. 653: 51 56 53 53 58 51 58 53 53 56 51 60 SP SD: 0.1043 c. M: 0.2441 c. 1000: 78 86 81 81 89 78 89 81 81 86 78 92 SP SD: 0.1415 c. M: 0.2438 c. 1012: 79 87 82 82 90 79 90 82 82 87 79 93 SP SD: 0.0699 c. M: 0.1205 c. 1024: 80 88 83 83 91 80 91 83 83 88 80 94 SP SD: 0.0000 c. M: 0.0001 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 1.7588 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.8700 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.9904 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.3054 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.2812 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.9365 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.3681 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0903 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3477 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.2353 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4697 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.2757 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.8197 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.1241 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.0987 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.9581 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 3.9780 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.4837 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.9616 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2274 cents 39:41:44:46:49:52:55:58:62:65:69:73:78 SD: 2.0909 cents 48:51:54:57:60:64:68:72:76:80:85:90:96 S SD: 1.8121 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.6934 cents 55:58:62:65:69:73:77:82:87:92:98:103:110 SD: 1.6137 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.4020 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.3468 cents 67:71:75:79:84:89:94:100:106:112:119:126:134 SD: 1.3310 cents 71:75:80:84:89:95:100:106:112:119:126:133:142 SD: 1.2620 cents 72:76:81:85:90:96:101:108:114:121:128:135:144 SD: 1.1894 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 1.0515 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 1.0383 cents 86:91:96:102:108:115:121:129:136:144:153:161:172 SD: 0.9560 cents 90:95:101:107:113:120:127:135:143:151:160:169:180 SD: 0.9111 cents 91:96:102:108:114:121:128:136:144:152:162:171:182 SD: 0.7273 cents 108:114:121:128:135:144:152:162:171:181:192:203:216 SD: 0.5689 cents 123:130:138:146:154:164:173:184:195:206:219:231:246 SD: 0.5115 cents 157:166:176:186:197:209:221:235:249:263:279:295:314 SD: 0.4663 cents 177:187:198:210:222:236:249:265:280:296:315:332:354 SD: 0.4496 cents 194:205:217:230:243:259:273:290:307:325:345:364:388 SD: 0.4321 cents 201:212:225:238:252:268:283:301:318:337:357:377:402 SD: 0.3428 cents 216:228:242:256:271:288:304:323:342:362:384:405:432 SD: 0.2443 cents 292:308:327:346:366:389:411:437:462:489:519:548:584 SD: 0.2296 cents 307:324:344:364:385:409:432:460:486:514:546:576:614 SD: 0.2250 cents 324:342:363:384:406:432:456:485:513:543:576:608:648 SD: 0.1100 cents