Scala analysis: xen18-schulter-archytan-1-3-12
1/3-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 177.301 cents 177.301220 2: 222.086 cents 222.086063 3: 266.871 cents 266.870906 4: 444.172 cents 444.172126 5: 488.957 cents 488.956969 6: 666.258 cents 666.258189 7: 711.043 cents 711.043031 8: 888.344 cents 888.344252 9: 933.129 cents 933.129094 10: 977.914 cents 977.913937 11: 1155.215 cents 1155.215157 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 44.7848 cents 44.7848 1: 177.3012 cents 177.3012 2: 44.7848 cents 44.7848 3: 44.7848 cents 44.7848 4: 177.3012 cents 177.3012 5: 44.7848 cents 44.7848 6: 177.3012 cents 177.3012 7: 44.7848 cents 44.7848 8: 177.3012 cents 177.3012 9: 44.7848 cents 44.7848 10: 44.7848 cents 44.7848 11: 177.3012 cents 177.3012 12: 44.7848 cents 44.7848
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 44.78484 cents 1: 5 177.30122 cents 2: 2 89.56969 cents 2: 10 222.08606 cents 3: 9 266.87091 cents 3: 3 399.38728 cents 4: 4 311.65575 cents 4: 8 444.17213 cents 5: 11 488.95697 cents 5: 1 621.47335 cents 6: 6 533.74181 cents 6: 6 666.25819 cents 7: 1 578.52665 cents 7: 11 711.04303 cents 8: 8 755.82787 cents 8: 4 888.34425 cents 9: 3 800.61272 cents 9: 9 933.12909 cents 10: 10 977.91394 cents 10: 2 1110.43031 cents 11: 5 1022.69878 cents 11: 7 1155.21516 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 8 9 10 11 12 0.0 : 177.3 222.1 266.9 444.2 489.0 666.3 711.0 888.3 933.1 977.9 1155.2 1200.0 177.3 : 44.8 89.6 266.9 311.7 489.0 533.7 711.0 755.8 800.6 977.9 1022.7 1200.0 222.1 : 44.8 222.1 266.9 444.2 489.0 666.3 711.0 755.8 933.1 977.9 1155.2 1200.0 266.9 : 177.3 222.1 399.4 444.2 621.5 666.3 711.0 888.3 933.1 1110.4 1155.2 1200.0 444.2 : 44.8 222.1 266.9 444.2 489.0 533.7 711.0 755.8 933.1 977.9 1022.7 1200.0 489.0 : 177.3 222.1 399.4 444.2 489.0 666.3 711.0 888.3 933.1 977.9 1155.2 1200.0 666.3 : 44.8 222.1 266.9 311.7 489.0 533.7 711.0 755.8 800.6 977.9 1022.7 1200.0 711.0 : 177.3 222.1 266.9 444.2 489.0 666.3 711.0 755.8 933.1 977.9 1155.2 1200.0 888.3 : 44.8 89.6 266.9 311.7 489.0 533.7 578.5 755.8 800.6 977.9 1022.7 1200.0 933.1 : 44.8 222.1 266.9 444.2 489.0 533.7 711.0 755.8 933.1 977.9 1155.2 1200.0 977.9 : 177.3 222.1 399.4 444.2 489.0 666.3 711.0 888.3 933.1 1110.4 1155.2 1200.0 1155.2: 44.8 222.1 266.9 311.7 489.0 533.7 711.0 755.8 933.1 977.9 1022.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.7848 .. 177.3012 cents 132.51638 cents 44.78484 cents 2: 89.5697 .. 222.0861 cents 132.51638 cents -87.73153 cents 3: 266.8709 .. 399.3873 cents 132.51638 cents 44.78484 cents 4: 311.6557 .. 444.1721 cents 132.51638 cents -87.73153 cents 5: 488.9570 .. 621.4733 cents 132.51638 cents 44.78484 cents 6: 533.7418 .. 666.2582 cents 132.51638 cents -87.73154 cents 7: 578.5267 .. 711.0430 cents 132.51638 cents -87.73154 cents 8: 755.8279 .. 888.3443 cents 132.51638 cents 44.78484 cents 9: 800.6127 .. 933.1291 cents 132.51638 cents -87.73154 cents 10: 977.9139 .. 1110.4303 cents 132.51638 cents 44.78484 cents 11: 1022.6988 .. 1155.2152 cents 132.51638 cents -87.73153 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 44.78484 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 177.30122 cents Average / Smallest step : 2.232898 Largest / Average step : 1.773012 Largest / Smallest step : 3.958956 Median interval of one step : 44.78484 cents, amount: 7 Most common interval of one step : 44.78484 cents, amount: 7 Least squares average step : 103.09205 cents, oct.: 1237.10459 cents Scale is not proper Scale has Myhill's property chromas: 132.51638 cents and 87.73153 cents, ratio: 1.510476 generators: 5 of 488.95697 cents and 7 of 711.04303 cents ET pair of linear temperament : 22&27 Scale is distributional even Scale is a mode of a 1313-tone equal temperament with octave 1200.000 cents degrees: 194 243 292 486 535 729 778 972 1021 1070 1264 1313 generators: 535 and 778 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : LSSLSLSLSSLS Scale is a Constant Structure, by a margin of 42.94669 cents Ratio Whole / Half tone : 4.958956 Scale diversity : 1.224253 Lumma stability : 0.223924 Lumma impropriety factor : 0.402869 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 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 : 42.94669 cents Most common intervals : 488.95697 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 44.785 711.043 cents Most common triad is 0.0 488.957 711.043 cents, amount: 10 Number of recognisable fifths : 11, average 711.0430 cents Scale contains two identical disjunct hexachords Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 2 0 1 1 1 2 0 2 0 1 2 0 N T3 SD: 27.6300 c. M:-44.7848 c. 13: 2 0 1 2 0 2 1 2 0 1 2 0 N SD: 26.5911 c. M:-44.7848 c. 14: 2 0 1 2 0 3 0 2 1 0 2 1 N SD: 31.0612 c. M: 60.3855 c. 15: 2 1 0 2 1 2 1 2 0 1 2 1 N D3 SD: 26.7656 c. M: 53.1291 c. 16: 2 1 0 3 0 3 0 3 0 1 2 1 N SD: 25.1479 c. M: 41.8709 c. 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 21.9960 c. M: 41.2854 c. Twelve-tone Chromatic (2/11-comma positive) 18: 3 0 1 3 0 3 1 2 1 1 2 1 N SD: 18.1189 c. M:-22.6988 c. 20: 3 0 1 3 1 3 1 3 0 1 3 1 N SD: 20.5554 c. M: 42.0861 c. 22: 3 1 1 3 1 3 1 3 1 1 3 1 N M DE SD: 8.3204 c. M: 15.6170 c. Twelve-tone Chromatic (1/3-comma positive) 27: 4 1 1 4 1 4 1 4 1 1 4 1 N M DE SD: 0.2902 c. M:-0.5446 c. Twelve-tone Chromatic (4/9-comma positive) 346: 51 13 13 51 13 51 13 51 13 13 51 13 N M DE SD: 0.2573 c. M: 0.4830 c. 373: 55 14 14 55 14 55 14 55 14 14 55 14 N M DE SD: 0.2177 c. M: 0.4086 c. 400: 59 15 15 59 15 59 15 59 15 15 59 15 N M DE SD: 0.1834 c. M: 0.3443 c. 427: 63 16 16 63 16 63 16 63 16 16 63 16 N M DE SD: 0.1535 c. M: 0.2880 c. 454: 67 17 17 67 17 67 17 67 17 17 67 17 N M DE SD: 0.1271 c. M: 0.2385 c. 481: 71 18 18 71 18 71 18 71 18 18 71 18 N M DE SD: 0.1037 c. M: 0.1946 c. 508: 75 19 19 75 19 75 19 75 19 19 75 19 N M DE SD: 0.0827 c. M: 0.1553 c. 535: 79 20 20 79 20 79 20 79 20 20 79 20 N M DE SD: 0.0639 c. M: 0.1200 c. 562: 83 21 21 83 21 83 21 83 21 21 83 21 N M DE SD: 0.0469 c. M: 0.0880 c. 589: 87 22 22 87 22 87 22 87 22 22 87 22 N M DE SD: 0.0314 c. M: 0.0590 c. 616: 91 23 23 91 23 91 23 91 23 23 91 23 N M DE SD: 0.0173 c. M: 0.0326 c. 643: 95 24 24 95 24 95 24 95 24 24 95 24 N M DE SD: 0.0044 c. M: 0.0083 c. 1313: 194 49 49 194 49 194 49 194 49 49 194 49 N M DE SD: 0.0016 c. M:-0.0030 c. 1956: 289 73 73 289 73 289 73 289 73 73 289 73 N M DE SD: 0.0004 c. M: 0.0007 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: 4.5440 cents 3 x x x x 4 x x 5 x x x 6 S SD: 3.3078 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 14.8172 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 25.7219 cents 6 x x 7 x 8 x 9:10 x 11 x 12 S SD: 12.1175 cents 7 x 8 x 9 x 10:11 x 12 x x 14 S SD: 14.5761 cents 8 x 9 x 10:11 x 12:13 x 14 x 16 S SD: 14.2989 cents 9:10 x 11 x 12:13:14:15 x 16 x 18 S SD: 12.9434 cents 10:11 x 12:13 x x 15 x 17:18:19:20 SD: 10.0274 cents 11:12 x 13:14:15:16:17:18:19 x 21:22 SD: 9.5261 cents 12:13 x 14 x 16 x 18:20 x 21:23:24 SD: 6.3720 cents 13:14 x 15:17 x 19:20 x 22:23:25:26 SD: 8.3153 cents 14 x 16 x 18:19 x 21:23:24:25:27:28 SD: 6.7236 cents 15 x 17:18:19:20:22:23:25:26 x 29:30 SD: 7.1656 cents 16 x 18:19 x 21 x 24:27 x 28:31:32 SD: 5.8302 cents 17:19 x 20:22:23:25:26:28:29:30:33:34 SD: 4.9626 cents 18:20 x 21:23:24:26:27:30:31:32:35:36 SD: 3.9503 cents 19:21 x 22 x 25:28:29:32 x 33:37:38 SD: 4.3586 cents 20:22:23 x 26:27:29:30:33:34:35:39:40 SD: 4.9335 cents 21:23:24:25:27:28:31:32:35:36:37:41:42 SD: 3.9879 cents 24 x 27:28:31:32:35:36:40:41:42:47:48 SD: 2.6844 cents 25:28 x 29:32:33:37:38:42:43:44:49:50 SD: 3.3770 cents 26:29 x 30:34 x 38:39:43:45:46:51:52 SD: 4.3358 cents 27:30:31:32:35:36:40:41:45:46:48:53:54 SD: 3.8501 cents 28:31:32:33:36:37:41:42:47:48:49:55:56 SD: 2.5986 cents 30:33:34:35:39:40:44:45:50:51:53:58:60 SD: 2.5406 cents 36:40:41:42:47:48:53:54:60:62:63:70:72 SD: 2.1948 cents 37:41:42:43:48:49:54:56:62:63:65:72:74 SD: 1.7853 cents 49:54:56:57:63:65:72:74:82:84:86:95:98 SD: 1.6413 cents 55:61:63:64:71:73:81:83:92:94:97:107:110 SD: 1.3897 cents 65:72:74:76:84:86:96:98:109:111:114:127:130 SD: 1.3248 cents 66:73:75:77:85:88:97:100:110:113:116:129:132 SD: 1.3081 cents 67:74:76:78:87:89:98:101:112:115:118:131:134 SD: 1.2693 cents 73:81:83:85:94:97:107:110:122:125:128:142:146 SD: 0.9801 cents 83:92:94:97:107:110:122:125:139:142:146:162:166 SD: 0.9047 cents 95:105:108:111:123:126:140:143:159:163:167:185:190 SD: 0.7618 cents 102:113:116:119:132:135:150:154:170:175:179:199:204 SD: 0.6707 cents 119:132:135:139:154:158:175:179:199:204:209:232:238 SD: 0.6596 cents 130:144:148:152:168:172:191:196:217:223:229:253:260 SD: 0.6073 cents 132:146:150:154:171:175:194:199:221:226:232:257:264 SD: 0.5916 cents 137:152:156:160:177:182:201:207:229:235:241:267:274 SD: 0.5714 cents 138:153:157:161:178:183:203:208:231:237:243:269:276 SD: 0.5593 cents 140:155:159:163:181:186:206:211:234:240:246:273:280 SD: 0.5132 cents 168:186:191:196:217:223:247:253:281:288:296:327:336 SD: 0.4322 cents 175:194:199:204:226:232:257:264:292:300:308:341:350 SD: 0.2936 cents 270:299:307:315:349:358:397:407:451:463:475:526:540 SD: 0.1512 cents 445:493:506:519:575:590:654:671:743:763:783:867:890 SD: 0.1305 cents 564:625:641:658:729:748:829:850:942:967:992:1099:1128 SD: 0.1202 cents