Scala analysis: xen13-rapoport-13tet-diatonic
13-tet diatonic scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92.000 cents 92.000000 2: 185.000 cents 185.000000 3: 277.000 cents 277.000000 4: 462.000 cents 462.000000 5: 554.000 cents 554.000000 6: 646.000 cents 646.000000 7: 831.000 cents 831.000000 8: 923.000 cents 923.000000 9: 1015.000 cents 1015.000000 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 185.0000 cents 185.0000 1: 92.0000 cents 92.0000 2: 93.0000 cents 93.0000 3: 92.0000 cents 92.0000 4: 185.0000 cents 185.0000 5: 92.0000 cents 92.0000 6: 92.0000 cents 92.0000 7: 185.0000 cents 185.0000 8: 92.0000 cents 92.0000 9: 92.0000 cents 92.0000 10: 185.0000 cents 185.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 92.00000 cents 1: 1 93.00000 cents 1: 3 185.00000 cents 2: 2 184.00000 cents 2: 2 185.00000 cents 2: 6 277.00000 cents 3: 1 277.00000 cents 3: 7 369.00000 cents 3: 2 370.00000 cents 4: 4 461.00000 cents 4: 4 462.00000 cents 4: 2 554.00000 cents 5: 1 553.00000 cents 5: 4 554.00000 cents 5: 4 646.00000 cents 5: 1 647.00000 cents 6: 2 646.00000 cents 6: 4 738.00000 cents 6: 4 739.00000 cents 7: 2 830.00000 cents 7: 7 831.00000 cents 7: 1 923.00000 cents 8: 6 923.00000 cents 8: 2 1015.00000 cents 8: 2 1016.00000 cents 9: 3 1015.00000 cents 9: 1 1107.00000 cents 9: 6 1108.00000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.11111 = 28/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 92.0 185.0 277.0 462.0 554.0 646.0 831.0 923.0 1015.0 1200.0 92.0 : 93.0 185.0 370.0 462.0 554.0 739.0 831.0 923.0 1108.0 1200.0 185.0 : 92.0 277.0 369.0 461.0 646.0 738.0 830.0 1015.0 1107.0 1200.0 277.0 : 185.0 277.0 369.0 554.0 646.0 738.0 923.0 1015.0 1108.0 1200.0 462.0 : 92.0 184.0 369.0 461.0 553.0 738.0 830.0 923.0 1015.0 1200.0 554.0 : 92.0 277.0 369.0 461.0 646.0 738.0 831.0 923.0 1108.0 1200.0 646.0 : 185.0 277.0 369.0 554.0 646.0 739.0 831.0 1016.0 1108.0 1200.0 831.0 : 92.0 184.0 369.0 461.0 554.0 646.0 831.0 923.0 1015.0 1200.0 923.0 : 92.0 277.0 369.0 462.0 554.0 739.0 831.0 923.0 1108.0 1200.0 1015.0: 185.0 277.0 370.0 462.0 647.0 739.0 831.0 1016.0 1108.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.0000 .. 185.0000 cents 93.00000 cents 92.00000 cents 2: 184.0000 .. 277.0000 cents 93.00000 cents -1.00000 cents 3: 277.0000 .. 370.0000 cents 93.00000 cents 1/1, 0.0000 cents 4: 461.0000 .. 554.0000 cents 93.00000 cents 91.00000 cents 5: 553.0000 .. 647.0000 cents 94.00000 cents -1.00000 cents 6: 646.0000 .. 739.0000 cents 93.00000 cents -1.00000 cents 7: 830.0000 .. 923.0000 cents 93.00000 cents 91.00000 cents 8: 923.0000 .. 1016.0000 cents 93.00000 cents 1/1, 0.0000 cents 9: 1015.0000 .. 1108.0000 cents 93.00000 cents -1.00000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 92.00000 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 185.00000 cents Average / Smallest step : 1.304348 Largest / Average step : 1.541667 Largest / Smallest step : 2.010870 Median interval of one step : 92.00000 cents, amount: 6 Most common interval of one step : 92.00000 cents, amount: 6 Least squares average step : 114.60519 cents, oct.: 1146.05195 cents Scale is not proper Scale is a mode of a 1187-tone equal temperament with octave 1200.000 cents degrees: 91 183 274 457 548 639 822 913 1004 1187 Least number of segments generator : 594 of 600.505 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 913 of 922.999 cents and inv. generated superset size: 12 = 2 more = 120.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACAACAAC Step pattern size order : SMSLSSLSSL Scale is not a Constant Structure Scale diversity : 1.121159 Lumma stability : 0.305000 Lumma impropriety factor : 0.003333 Rothenberg efficiency : 0.500635 redundancy: 0.499365 Efficiency x scale size : 5.006349 Number of different interval sizes : 22 = 2.44444 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.11111 = 28/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 0 Formal octave complements present : 7 = 70.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 6-7 -- Rational properties --
FIT/MODE
10: 0 1 1 1 1 1 1 1 1 2 N T3 SD: 73.6811 c. M: 111.0000 c. 11: 1 1 1 1 1 1 2 0 1 2 N D3 SD: 31.7700 c. M:-50.2727 c. 12: 1 1 1 2 1 0 2 1 1 2 N D3 SD: 28.6514 c. M: 46.0000 c. 13: 1 1 1 2 1 1 2 1 1 2 P M ME SD: 0.2676 c. M: 0.4615 c. Sephiroth-10 602: 46 47 46 93 46 46 93 46 46 93 N SD: 0.2658 c. M:-0.4585 c. 615: 47 48 47 95 47 47 95 47 47 95 N SD: 0.2545 c. M:-0.4390 c. 628: 48 49 48 97 48 48 97 48 48 97 N SD: 0.2437 c. M:-0.4204 c. 641: 49 50 49 99 49 49 99 49 49 99 N SD: 0.2333 c. M:-0.4025 c. 654: 50 51 50 101 50 50 101 50 50 101 N SD: 0.2234 c. M:-0.3853 c. 667: 51 52 51 103 51 51 103 51 51 103 N SD: 0.2138 c. M:-0.3688 c. 680: 52 53 52 105 52 52 105 52 52 105 N SD: 0.2046 c. M:-0.3529 c. 693: 53 54 53 107 53 53 107 53 53 107 N SD: 0.1958 c. M:-0.3377 c. 706: 54 55 54 109 54 54 109 54 54 109 N SD: 0.1872 c. M:-0.3229 c. 719: 55 56 55 111 55 55 111 55 55 111 N SD: 0.1790 c. M:-0.3088 c. 732: 56 57 56 113 56 56 113 56 56 113 N SD: 0.1711 c. M:-0.2951 c. 745: 57 58 57 115 57 57 115 57 57 115 N SD: 0.1634 c. M:-0.2819 c. 758: 58 59 58 117 58 58 117 58 58 117 N SD: 0.1560 c. M:-0.2691 c. 771: 59 60 59 119 59 59 119 59 59 119 N SD: 0.1489 c. M:-0.2568 c. 784: 60 61 60 121 60 60 121 60 60 121 N SD: 0.1420 c. M:-0.2449 c. 797: 61 62 61 123 61 61 123 61 61 123 N SD: 0.1353 c. M:-0.2334 c. 810: 62 63 62 125 62 62 125 62 62 125 N SD: 0.1288 c. M:-0.2222 c. 823: 63 64 63 127 63 63 127 63 63 127 N SD: 0.1226 c. M:-0.2114 c. 836: 64 65 64 129 64 64 129 64 64 129 N SD: 0.1165 c. M:-0.2010 c. 849: 65 66 65 131 65 65 131 65 65 131 N SD: 0.1106 c. M:-0.1908 c. 862: 66 67 66 133 66 66 133 66 66 133 N SD: 0.1049 c. M:-0.1810 c. 875: 67 68 67 135 67 67 135 67 67 135 N SD: 0.0994 c. M:-0.1714 c. 888: 68 69 68 137 68 68 137 68 68 137 N SD: 0.0940 c. M:-0.1622 c. 901: 69 70 69 139 69 69 139 69 69 139 N SD: 0.0888 c. M:-0.1532 c. 914: 70 71 70 141 70 70 141 70 70 141 N SD: 0.0837 c. M:-0.1444 c. 927: 71 72 71 143 71 71 143 71 71 143 N SD: 0.0788 c. M:-0.1359 c. 940: 72 73 72 145 72 72 145 72 72 145 N SD: 0.0740 c. M:-0.1277 c. 953: 73 74 73 147 73 73 147 73 73 147 N SD: 0.0694 c. M:-0.1196 c. 966: 74 75 74 149 74 74 149 74 74 149 N SD: 0.0648 c. M:-0.1118 c. 979: 75 76 75 151 75 75 151 75 75 151 N SD: 0.0604 c. M:-0.1042 c. 992: 76 77 76 153 76 76 153 76 76 153 N SD: 0.0561 c. M:-0.0968 c. 1005: 77 78 77 155 77 77 155 77 77 155 N SD: 0.0519 c. M:-0.0896 c. 1018: 78 79 78 157 78 78 157 78 78 157 N SD: 0.0478 c. M:-0.0825 c. 1031: 79 80 79 159 79 79 159 79 79 159 N SD: 0.0439 c. M:-0.0757 c. 1044: 80 81 80 161 80 80 161 80 80 161 N SD: 0.0400 c. M:-0.0690 c. 1057: 81 82 81 163 81 81 163 81 81 163 N SD: 0.0362 c. M:-0.0624 c. 1070: 82 83 82 165 82 82 165 82 82 165 N SD: 0.0325 c. M:-0.0561 c. 1083: 83 84 83 167 83 83 167 83 83 167 N SD: 0.0289 c. M:-0.0499 c. 1096: 84 85 84 169 84 84 169 84 84 169 N SD: 0.0254 c. M:-0.0438 c. 1109: 85 86 85 171 85 85 171 85 85 171 N SD: 0.0220 c. M:-0.0379 c. 1122: 86 87 86 173 86 86 173 86 86 173 N SD: 0.0186 c. M:-0.0321 c. 1135: 87 88 87 175 87 87 175 87 87 175 N SD: 0.0153 c. M:-0.0264 c. 1148: 88 89 88 177 88 88 177 88 88 177 N SD: 0.0121 c. M:-0.0209 c. 1161: 89 90 89 179 89 89 179 89 89 179 N SD: 0.0090 c. M:-0.0155 c. 1174: 90 91 90 181 90 90 181 90 90 181 N SD: 0.0059 c. M:-0.0102 c. 1187: 91 92 91 183 91 91 183 91 91 183 N SD: 0.0029 c. M:-0.0051 c. 1200: 92 93 92 185 92 92 185 92 92 185 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 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 4 S SD: 27.9775 cents 3 x x x 4 x x x 5 x 6 S SD: 17.6144 cents 4 x x x 5 x 6 x 7 x 8 S SD: 26.1718 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 10.2227 cents 6 x x 7:8 x 9 x 10:11:12 S SD: 14.1488 cents 7 x x 8:9 x 10:11:12:13:14 S SD: 13.7827 cents 8 x 9 x 10:11:12:13:14 x 16 S SD: 15.2630 cents 9 x 10:11:12 x 13 x 15:16:18 SD: 12.9379 cents 10 x 11:12:13:14:15:16:17:18:20 S SD: 8.7651 cents 11 x 12:13:14:15:16:18:19:20:22 S SD: 7.8657 cents 12 x 13:14:16 x 17:19:20:22:24 SD: 12.0781 cents 13:14 x 15:17:18:19:21:22:23:26 SD: 6.3641 cents 14:15 x 16:18:19:20:23:24:25:28 SD: 8.6557 cents 15:16:17:18:20:21:22:24:26:27:30 S SD: 8.0324 cents 16:17:18:19:21:22:23:26:27:29:32 SD: 4.4063 cents 24:25:27:28:31:33:35:39:41:43:48 SD: 3.8328 cents 29:31:32:34:38:40:42:47:49:52:58 SD: 3.3085 cents 33:35:37:39:43:45:48:53:56:59:66 SD: 3.1361 cents 34:36:38:40:44:47:49:55:58:61:68 SD: 2.4572 cents 35:37:39:41:46:48:51:57:60:63:70 SD: 2.2990 cents 50:53:56:59:65:69:73:81:85:90:100 SD: 2.2275 cents 51:54:57:60:67:70:74:82:87:92:102 SD: 1.9742 cents 52:55:58:61:68:72:76:84:89:93:104 SD: 1.9620 cents 53:56:59:62:69:73:77:86:90:95:106 SD: 1.3425 cents 69:73:77:81:90:95:100:112:118:124:138 SD: 1.2870 cents 71:75:79:83:93:98:103:115:121:128:142 SD: 1.1963 cents 75:79:83:88:98:103:109:121:128:135:150 SD: 1.1916 cents 88:93:98:103:115:121:128:142:150:158:176 SD: 0.7860 cents 108:114:120:127:141:149:157:175:184:194:216 SD: 0.7558 cents 109:115:121:128:142:150:158:176:186:196:218 SD: 0.7516 cents 115:121:128:135:150:158:167:186:196:207:230 SD: 0.6731 cents 132:139:147:155:172:182:192:213:225:237:264 SD: 0.6719 cents 133:140:148:156:174:183:193:215:227:239:266 SD: 0.5659 cents 143:151:159:168:187:197:208:231:244:257:286 SD: 0.5374 cents 167:176:186:196:218:230:243:270:285:300:334 SD: 0.4684 cents 183:193:204:215:239:252:266:296:312:329:366 SD: 0.4316 cents 186:196:207:218:243:256:270:301:317:334:372 SD: 0.4089 cents 196:207:218:230:256:270:285:317:334:352:392 SD: 0.3962 cents 203:214:226:238:265:280:295:328:346:365:406 SD: 0.3651 cents 241:254:268:283:315:332:350:389:411:433:482 SD: 0.3556 cents 255:269:284:299:333:351:370:412:435:458:510 SD: 0.3438 cents 258:272:287:303:337:355:375:417:440:464:516 SD: 0.3061 cents 276:291:307:324:360:380:401:446:470:496:552 SD: 0.2785 cents 292:308:325:343:381:402:424:472:498:525:584 SD: 0.2732 cents 294:310:327:345:384:405:427:475:501:528:588 SD: 0.1791 cents 409:431:455:480:534:563:594:661:697:735:818 SD: 0.1635 cents 477:503:531:560:623:657:693:771:813:857:954 SD: 0.1435 cents 513:541:571:602:670:706:745:829:874:922:1026 SD: 0.1392 cents 549:579:611:644:717:756:797:887:936:987:1098 SD: 0.1382 cents 586:618:652:688:765:807:851:947:999:1053:1172 SD: 0.1176 cents