Scala analysis: xen18-schulter-archytan-1-2-12
1/2-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 209.109 cents 209.109327 2: 231.174 cents 231.174094 3: 253.239 cents 253.238860 4: 462.348 cents 462.348187 5: 484.413 cents 484.412953 6: 693.522 cents 693.522281 7: 715.587 cents 715.587047 8: 924.696 cents 924.696374 9: 946.761 cents 946.761140 10: 968.826 cents 968.825906 11: 1177.935 cents 1177.935234 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 22.0648 cents 22.0648 1: 209.1093 cents 209.1093 2: 22.0648 cents 22.0648 3: 22.0648 cents 22.0648 4: 209.1093 cents 209.1093 5: 22.0648 cents 22.0648 6: 209.1093 cents 209.1093 7: 22.0648 cents 22.0648 8: 209.1093 cents 209.1093 9: 22.0648 cents 22.0648 10: 22.0648 cents 22.0648 11: 209.1093 cents 209.1093 12: 22.0648 cents 22.0648
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 22.06477 cents 1: 5 209.10933 cents 2: 2 44.12953 cents 2: 10 231.17409 cents 3: 9 253.23886 cents 3: 3 440.28342 cents 4: 4 275.30363 cents 4: 8 462.34819 cents 5: 11 484.41295 cents 5: 1 671.45751 cents 6: 6 506.47772 cents 6: 6 693.52228 cents 7: 1 528.54249 cents 7: 11 715.58705 cents 8: 8 737.65181 cents 8: 4 924.69637 cents 9: 3 759.71658 cents 9: 9 946.76114 cents 10: 10 968.82591 cents 10: 2 1155.87047 cents 11: 5 990.89067 cents 11: 7 1177.93523 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 : 209.1 231.2 253.2 462.3 484.4 693.5 715.6 924.7 946.8 968.8 1177.9 1200.0 209.1 : 22.1 44.1 253.2 275.3 484.4 506.5 715.6 737.7 759.7 968.8 990.9 1200.0 231.2 : 22.1 231.2 253.2 462.3 484.4 693.5 715.6 737.7 946.8 968.8 1177.9 1200.0 253.2 : 209.1 231.2 440.3 462.3 671.5 693.5 715.6 924.7 946.8 1155.9 1177.9 1200.0 462.3 : 22.1 231.2 253.2 462.3 484.4 506.5 715.6 737.7 946.8 968.8 990.9 1200.0 484.4 : 209.1 231.2 440.3 462.3 484.4 693.5 715.6 924.7 946.8 968.8 1177.9 1200.0 693.5 : 22.1 231.2 253.2 275.3 484.4 506.5 715.6 737.7 759.7 968.8 990.9 1200.0 715.6 : 209.1 231.2 253.2 462.3 484.4 693.5 715.6 737.7 946.8 968.8 1177.9 1200.0 924.7 : 22.1 44.1 253.2 275.3 484.4 506.5 528.5 737.7 759.7 968.8 990.9 1200.0 946.8 : 22.1 231.2 253.2 462.3 484.4 506.5 715.6 737.7 946.8 968.8 1177.9 1200.0 968.8 : 209.1 231.2 440.3 462.3 484.4 693.5 715.6 924.7 946.8 1155.9 1177.9 1200.0 1177.9: 22.1 231.2 253.2 275.3 484.4 506.5 715.6 737.7 946.8 968.8 990.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.0648 .. 209.1093 cents 187.04456 cents 22.06477 cents 2: 44.1295 .. 231.1741 cents 187.04456 cents -164.97979 cents 3: 253.2389 .. 440.2834 cents 187.04456 cents 22.06477 cents 4: 275.3036 .. 462.3482 cents 187.04456 cents -164.97979 cents 5: 484.4130 .. 671.4575 cents 187.04456 cents 22.06477 cents 6: 506.4777 .. 693.5223 cents 187.04456 cents -164.97979 cents 7: 528.5425 .. 715.5870 cents 187.04456 cents -164.97980 cents 8: 737.6518 .. 924.6964 cents 187.04456 cents 22.06477 cents 9: 759.7166 .. 946.7611 cents 187.04456 cents -164.97979 cents 10: 968.8259 .. 1155.8705 cents 187.04456 cents 22.06477 cents 11: 990.8907 .. 1177.9352 cents 187.04456 cents -164.97979 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 22.06477 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 209.10933 cents Average / Smallest step : 4.532112 Largest / Average step : 2.091093 Largest / Smallest step : 9.477070 Median interval of one step : 22.06477 cents, amount: 7 Most common interval of one step : 22.06477 cents, amount: 7 Least squares average step : 104.36437 cents, oct.: 1252.37248 cents Scale is not proper Scale has Myhill's property chromas: 187.04456 cents and 164.97979 cents, ratio: 1.133742 generators: 5 of 484.41295 cents and 7 of 715.58705 cents ET pair of linear temperament : 52&109 Scale is distributional even Scale is a mode of a 1142-tone equal temperament with octave 1200.000 cents degrees: 199 220 241 440 461 660 681 880 901 922 1121 1142 generators: 461 and 681 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 22.06477 cents Ratio Whole / Half tone : 10.477070 Scale diversity : 0.943577 Lumma stability : 0.110324 Lumma impropriety factor : 0.705803 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 : 22.06477 cents Most common intervals : 484.41295 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 22.065 715.587 cents Most common triad is 0.0 484.413 715.587 cents, amount: 10 Number of recognisable fifths : 17, average 707.7995 cents Number of appreciable fifths : 6, average 693.5223 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 2 0 2 0 2 0 1 2 0 N T3 SD: 28.0507 c. M:-46.7611 c. 14: 2 1 0 2 1 2 0 3 0 0 3 0 N SD: 23.4562 c. M: 37.6808 c. 15: 3 0 0 3 0 3 0 3 0 0 3 0 N M DE SD: 18.8091 c. M:-35.3036 c. 17: 3 0 1 3 0 3 0 3 0 1 3 0 N SD: 19.0235 c. M:-31.7695 c. 18: 3 0 1 3 0 3 1 3 0 1 3 0 N SD: 18.9702 c. M: 31.1741 c. 19: 3 1 0 3 1 3 0 4 0 0 4 0 N SD: 17.2934 c. M:-22.6720 c. 22: 4 0 1 4 0 4 0 4 0 1 4 0 N SD: 15.3175 c. M:-28.5609 c. 23: 4 0 1 4 0 4 1 4 0 1 4 0 N SD: 14.5725 c. M: 22.4784 c. 27: 5 0 1 4 1 5 0 5 0 1 5 0 N SD: 12.6631 c. M:-22.0648 c. 28: 5 0 1 5 0 5 1 5 0 1 4 1 N SD: 12.4848 c. M: 20.7924 c. 29: 5 0 1 5 0 6 0 5 1 0 5 1 N SD: 14.9092 c. M: 29.2405 c. 30: 5 1 0 5 1 5 1 5 0 1 5 1 N D3 SD: 13.5252 c. M: 26.7611 c. 31: 5 1 0 6 0 6 0 6 0 1 5 1 N SD: 13.1020 c. M: 20.9808 c. 33: 6 0 1 6 0 6 1 5 1 1 5 1 N SD: 10.2428 c. M: 15.6055 c. 36: 6 1 1 6 1 6 0 7 0 1 6 1 N SD: 10.0042 c. M:-15.5870 c. 37: 6 1 1 6 1 6 1 6 1 1 6 1 N M DE SD: 8.8379 c. M: 16.5883 c. 38: 7 0 1 7 0 7 1 6 1 1 6 1 N SD: 8.5553 c. M:-11.9433 c. 42: 7 1 1 7 1 7 1 7 1 1 7 1 N M DE SD: 5.5466 c. M: 10.4107 c. 47: 8 1 1 8 1 8 1 8 1 1 8 1 N M DE SD: 2.9556 c. M: 5.5474 c. 52: 9 1 1 9 1 9 1 9 1 1 9 1 N M DE SD: 0.8628 c. M: 1.6195 c. 57: 10 1 1 10 1 10 1 10 1 1 10 1 N M DE SD: 0.8628 c. M:-1.6194 c. 109: 19 2 2 19 2 19 2 19 2 2 19 2 N M DE SD: 0.0396 c. M:-0.0743 c. 597: 104 11 11 104 11 104 11 104 11 11 104 11 N M DE SD: 0.0390 c. M: 0.0733 c. 706: 123 13 13 123 13 123 13 123 13 13 123 13 N M DE SD: 0.0269 c. M: 0.0505 c. 815: 142 15 15 142 15 142 15 142 15 15 142 15 N M DE SD: 0.0180 c. M: 0.0338 c. 924: 161 17 17 161 17 161 17 161 17 17 161 17 N M DE SD: 0.0112 c. M: 0.0210 c. 1033: 180 19 19 180 19 180 19 180 19 19 180 19 N M DE SD: 0.0059 c. M: 0.0110 c. 1142: 199 21 21 199 21 199 21 199 21 21 199 21 N M DE SD: 0.0015 c. M: 0.0029 c. 2393: 417 44 44 417 44 417 44 417 44 44 417 44 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 3 x x x x x 4 S SD: 4.2164 cents 3 x x x x 4 x x 5 x x x 6 S SD: 14.1930 cents 4 x x x 5 x 6 x x x 7 x 8 S SD: 19.1252 cents 5 x x 6 x 7 x 8 x x 9 x 10 S SD: 31.9497 cents 6 x x 7 x 8:9 x 10 x 11 x 12 S SD: 15.4165 cents 7 x 8 x 9 x 10:11:12 x x x 14 S SD: 17.5372 cents 8:9 x x 10:11:12 x x x 14 x 16 S SD: 16.9605 cents 9:10 x x x 12:13:14:15 x 16 x 18 S SD: 13.5081 cents 10:11 x 12:13 x 15 x 17 x 18 x 20 SD: 13.0867 cents 11:12 x 13:14:15:16:17 x 19 x x 22 SD: 14.2207 cents 12 x x 14 x 16:18 x 20 x 21 x 24 S SD: 7.5827 cents 13 x x 15:17 x 19:20:22 x 23 x 26 SD: 7.6035 cents 14 x 16 x 18:19:21 x 24 x 25 x 28 SD: 9.1127 cents 15:17 x x x 20:22:23 x 26 x x 30 SD: 7.0678 cents 16:18 x 19:21 x 24 x 27 x 28 x 32 SD: 7.1201 cents 17:19 x 20:22 x 25:26:29 x 30 x 34 SD: 6.3710 cents 18:20 x 21 x 24:27 x x 31:32 x 36 SD: 6.2777 cents 19:21 x 22 x 25:28:29:32:33 x x 38 SD: 6.5077 cents 20 x 23 x 26 x 30 x 34 x 35:39:40 SD: 3.9488 cents 21 x 24 x 27:28:31:32:36 x 37:41:42 SD: 5.0691 cents 22 x 25 x x 29:33 x x 38:39:43:44 SD: 4.5629 cents 23:26 x 27:30 x 34:35:39 x 40:45:46 SD: 4.3050 cents 24:27 x 28:31:32:36 x 41 x 42:47:48 SD: 3.6068 cents 25:28 x 29 x 33:37:38 x 43:44:49:50 SD: 3.1939 cents 26:29 x 30:34 x 39 x 44:45:46:51:52 SD: 3.8514 cents 27:30:31 x 35:36:40:41:46 x 47:53:54 SD: 3.9475 cents 28 x 32 x x 37:42 x 48 x 49:55:56 SD: 2.1626 cents 29 x 33:34:38 x 43:44:49:50:51:57:58 SD: 3.4299 cents 30:34 x 35:39:40:45 x 51:52:53:59:60 SD: 3.0854 cents 31:35 x 36:40:41:46:47:53 x 54:61:62 SD: 2.6864 cents 32:36 x 37:42 x 48 x x 55:56:63:64 SD: 2.1037 cents 33:37 x 38:43:44:49:50:56:57:58:65:66 SD: 2.3394 cents 34:38:39 x 44:45:51 x 58:59:60:67:68 SD: 3.0332 cents 35:39:40:41:46 x 52:53:60 x 61:69:70 SD: 3.4945 cents 36 x 41:42:47:48:54 x 61:62:63:71:72 SD: 2.5561 cents 37:42 x 43:48:49:55:56:63:64:65:73:74 SD: 1.8481 cents 38:43 x 44 x 50:57 x 65:66:67:75:76 SD: 2.3654 cents 39:44 x 45:51:52:58:59 x 67:68:77:78 SD: 2.0054 cents 40:45:46 x 52:53:60 x 68:69:70:79:80 SD: 1.8254 cents 41:46:47 x x 54:61:62:70:71:72:81:82 SD: 1.6436 cents 43 x 49:50:56:57:64:65:73:74:75:85:86 SD: 1.5910 cents 44 x 50:51:57:58:66:67:75:76:77:87:88 SD: 2.1795 cents 45:51 x 52:59:60:67:68:77:78:79:89:90 SD: 1.8428 cents 46:52 x 53:60:61:69:70:78:79:81:91:92 SD: 2.3008 cents 47:53:54 x 61:62:70:71:80:81:82:93:94 SD: 1.6316 cents 48:54:55:56:63 x 72:73:82:83:84:95:96 SD: 2.0398 cents 49:55:56:57:64:65:73:74:84:85:86:97:98 SD: 1.5742 cents 51 x 58:59:67 x 76:77:87:88:89:101:102 SD: 1.5575 cents 52:59 x 60:68:69:78:79:89:90:91:103:104 SD: 1.7358 cents 53:60 x 61:69:70:79:80:90:92:93:105:106 SD: 1.7342 cents 54:61:62:63 x 71:81:82:92:93:95:107:108 SD: 2.3184 cents 55:62:63:64:72:73:82:83:94:95:96:109:110 SD: 1.2758 cents 59:67 x 68:77:78:88:89:101:102:103:117:118 SD: 1.5885 cents 60:68:69 x 78:79:90:91:102:104:105:118:120 SD: 2.0809 cents 61:69:70:71:80:81:91:92:104:105:107:120:122 SD: 1.6126 cents 62:70:71:72:81:82:93:94:106:107:109:122:124 SD: 1.3411 cents 63:71:72:73:82:83:94:95:107:109:110:124:126 SD: 1.2551 cents 69:78:79:80:90:91:103:104:118:119:121:136:138 SD: 0.9886 cents 71:80:81:82:93:94:106:107:121:123:124:140:142 SD: 0.9493 cents 84:95:96:97:110:111:125:127:143:145:147:166:168 SD: 0.8450 cents 108:122:123:125:141:143:161:163:184:187:189:213:216 SD: 0.7463 cents 115:130:131:133:150:152:172:174:196:199:201:227:230 SD: 0.7443 cents 121:137:138:140:158:160:181:183:206:209:212:239:242 SD: 0.7443 cents 125:141:143:145:163:165:187:189:213:216:219:247:250 SD: 0.6615 cents 127:143:145:147:166:168:190:192:217:219:222:251:254 SD: 0.6378 cents 133:150:152:154:174:176:199:201:227:230:233:263:266 SD: 0.5196 cents 140:158:160:162:183:185:209:212:239:242:245:276:280 SD: 0.4052 cents 195:220:223:226:255:258:291:295:333:337:341:385:390 SD: 0.3416 cents 203:229:232:235:265:269:303:307:346:351:355:401:406 SD: 0.3313 cents 235:265:269:272:307:311:351:355:401:406:411:464:470 SD: 0.3104 cents 266:300:304:308:347:352:397:402:454:460:466:525:532 SD: 0.3069 cents 272:307:311:315:355:360:406:411:464:470:476:537:544 SD: 0.1867 cents 405:457:463:469:529:536:605:612:691:700:709:800:810 SD: 0.1844 cents 412:465:471:477:538:545:615:623:703:712:721:814:824 SD: 0.1156 cents 477:538:545:552:623:631:712:721:814:824:835:942:954 SD: 0.1137 cents