Scala analysis: asbru
Modified bifrost
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 89.602 cents 89.601917 2: 200.000 cents 200.000000 3: 310.398 cents 310.398083 4: 400.000 cents 400.000000 5: 510.398 cents 510.398083 6: 589.602 cents 589.601917 7: 700.000 cents 700.000000 8: 800.000 cents 800.000000 9: 900.000 cents 900.000000 10: 1010.398 cents 1010.398083 11: 1089.602 cents 1089.601917 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 110.3981 cents 110.3981 1: 89.6019 cents 89.6019 2: 110.3981 cents 110.3981 3: 110.3981 cents 110.3981 4: 89.6019 cents 89.6019 5: 110.3981 cents 110.3981 6: 79.2038 cents 79.2038 7: 110.3981 cents 110.3981 8: 100.0000 cents 100.0000 9: 100.0000 cents 100.0000 10: 110.3981 cents 110.3981 11: 79.2038 cents 79.2038 12: 110.3981 cents 110.3981
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 79.20383 cents 1: 2 89.60192 cents 1: 2 100.00000 cents 1: 6 110.39808 cents 2: 4 189.60192 cents 2: 5 200.00000 cents 2: 2 210.39808 cents 2: 1 220.79617 cents 3: 2 279.20383 cents 3: 2 289.60192 cents 3: 2 300.00000 cents 3: 6 310.39808 cents 4: 6 389.60192 cents 4: 3 400.00000 cents 4: 3 420.79617 cents 5: 2 489.60192 cents 5: 8 500.00000 cents 5: 2 510.39808 cents 6: 1 579.20383 cents 6: 4 589.60192 cents 6: 2 600.00000 cents 6: 4 610.39808 cents 6: 1 620.79617 cents 7: 2 689.60192 cents 7: 8 700.00000 cents 7: 2 710.39808 cents 8: 3 779.20383 cents 8: 3 800.00000 cents 8: 6 810.39808 cents 9: 6 889.60192 cents 9: 2 900.00000 cents 9: 2 910.39808 cents 9: 2 920.79617 cents 10: 1 979.20383 cents 10: 2 989.60192 cents 10: 5 1000.00000 cents 10: 4 1010.39808 cents 11: 6 1089.60192 cents 11: 2 1100.00000 cents 11: 2 1110.39808 cents 11: 2 1120.79617 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.72727 = 41/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 89.6 200.0 310.4 400.0 510.4 589.6 700.0 800.0 900.0 1010.4 1089.6 1200.0 89.6 : 110.4 220.8 310.4 420.8 500.0 610.4 710.4 810.4 920.8 1000.0 1110.4 1200.0 200.0 : 110.4 200.0 310.4 389.6 500.0 600.0 700.0 810.4 889.6 1000.0 1089.6 1200.0 310.4 : 89.6 200.0 279.2 389.6 489.6 589.6 700.0 779.2 889.6 979.2 1089.6 1200.0 400.0 : 110.4 189.6 300.0 400.0 500.0 610.4 689.6 800.0 889.6 1000.0 1110.4 1200.0 510.4 : 79.2 189.6 289.6 389.6 500.0 579.2 689.6 779.2 889.6 1000.0 1089.6 1200.0 589.6 : 110.4 210.4 310.4 420.8 500.0 610.4 700.0 810.4 920.8 1010.4 1120.8 1200.0 700.0 : 100.0 200.0 310.4 389.6 500.0 589.6 700.0 810.4 900.0 1010.4 1089.6 1200.0 800.0 : 100.0 210.4 289.6 400.0 489.6 600.0 710.4 800.0 910.4 989.6 1100.0 1200.0 900.0 : 110.4 189.6 300.0 389.6 500.0 610.4 700.0 810.4 889.6 1000.0 1100.0 1200.0 1010.4: 79.2 189.6 279.2 389.6 500.0 589.6 700.0 779.2 889.6 989.6 1089.6 1200.0 1089.6: 110.4 200.0 310.4 420.8 510.4 620.8 700.0 810.4 910.4 1010.4 1120.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 79.2038 .. 110.3981 cents 31.19425 cents 79.20383 cents 2: 189.6019 .. 220.7962 cents 31.19425 cents 79.20383 cents 3: 279.2038 .. 310.3981 cents 31.19425 cents 58.40767 cents 4: 389.6019 .. 420.7962 cents 31.19425 cents 79.20383 cents 5: 489.6019 .. 510.3981 cents 20.79617 cents 68.80575 cents 6: 579.2038 .. 620.7962 cents 41.59233 cents 68.80575 cents 7: 689.6019 .. 710.3981 cents 20.79617 cents 68.80575 cents 8: 779.2038 .. 810.3981 cents 31.19425 cents 68.80575 cents 9: 889.6019 .. 920.7962 cents 31.19425 cents 79.20383 cents 10: 979.2038 .. 1010.3981 cents 31.19425 cents 58.40767 cents 11: 1089.6019 .. 1120.7962 cents 31.19425 cents 79.20383 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 79.20383 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 110.39808 cents Average / Smallest step : 1.262565 Largest / Average step : 1.103981 Largest / Smallest step : 1.393848 Median interval of one step : 105.19904 cents, amount: 0 Most common interval of one step : 110.39808 cents, amount: 6 Least squares average step : 100.00000 cents, oct.: 1200.00000 cents Scale is strictly proper Scale is a mode of a 1500-tone equal temperament with octave 1200.000 cents degrees: 112 250 388 500 638 737 875 1000 1125 1263 1362 1500 Least number of segments generator : 751 of 600.800 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 773 of 618.400 cents and inv. generated superset size: 1001 = 989 more = 8341.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABCBDDBCB Step pattern size order : BDDBDADCCDAD Scale is a Constant Structure, by a margin of 58.40767 cents Scale diversity : 1.232788 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.722718 Rothenberg efficiency : 0.346185 redundancy: 0.653815 Efficiency x scale size : 4.154221 Number of different interval sizes : 41 = 3.72727 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 3.72727 = 41/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 10.39808 cents Most common intervals : 500.00000 cents & inv., amount: 8 Most common triad is 0.0 500.000 700.000 cents, amount: 5 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 31.1942 cents: 7 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 8 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.3526 c. M: 10.3981 c. Twelve-tone Chromatic (1/11-comma) 43: 3 4 4 3 4 3 4 3 4 4 3 4 SP M ME SD: 7.4555 c. M: 18.6047 c. Meantone Chromatic (1/5-comma) 45: 3 5 4 3 4 3 4 4 4 4 3 4 SP D3 SD: 6.4300 c. M:-13.3333 c. 51: 4 5 4 4 5 3 5 4 4 5 3 5 SP SD: 5.4561 c. M:-11.7647 c. 53: 4 5 5 4 5 3 5 4 5 5 3 5 SP SD: 5.7429 c. M:-10.3566 c. 55: 4 5 5 4 5 4 5 4 5 5 4 5 SP M ME SD: 6.2043 c. M: 14.5455 c. Meantone Chromatic (3/17-comma) 57: 4 6 5 4 5 4 5 5 5 5 4 5 SP D3 SD: 4.8054 c. M:-10.5263 c. 61: 5 5 6 4 6 4 6 5 5 5 4 6 SP SD: 5.7319 c. M:-8.7587 c. 63: 5 6 5 5 6 4 6 5 5 6 4 6 SP SD: 4.3907 c. M:-9.5238 c. 64: 5 6 6 4 6 4 6 6 5 6 4 6 SP SD: 5.3151 c. M:-8.3519 c. 65: 5 6 6 5 6 4 6 5 6 6 4 6 SP SD: 4.0520 c. M:-6.5250 c. 72: 5 7 7 5 7 4 7 6 6 7 4 7 SP S SD: 4.4326 c. M: 6.2686 c. 75: 6 7 6 6 7 5 7 6 6 7 5 7 SP SD: 4.0260 c. M:-8.0000 c. 76: 6 7 7 5 7 5 7 7 6 7 5 7 SP SD: 4.2983 c. M: 5.3914 c. 77: 6 7 7 6 7 5 7 6 7 7 5 7 SP SD: 3.2250 c. M:-5.1948 c. 84: 6 8 8 6 8 5 8 7 7 8 5 8 SP S SD: 2.7490 c. M: 3.8876 c. 89: 7 8 8 7 8 6 8 7 8 8 6 8 SP SD: 2.9628 c. M:-4.7801 c. 96: 7 9 9 7 9 6 9 8 8 9 6 9 SP S SD: 1.4863 c. M: 2.1019 c. 108: 8 10 10 8 10 7 10 9 9 10 7 10 SP S SD: 0.5042 c. M: 0.7130 c. 120: 9 11 11 9 11 8 11 10 10 11 8 11 SP S SD: 0.2815 c. M: 0.3981 c. 228: 17 21 21 17 21 15 21 19 19 21 15 21 SP S SD: 0.0907 c. M: 0.1282 c. 348: 26 32 32 26 32 23 32 29 29 32 23 32 SP S SD: 0.0377 c. M:-0.0533 c. 576: 43 53 53 43 53 38 53 48 48 53 38 53 SP S SD: 0.0131 c. M: 0.0186 c. 924: 69 85 85 69 85 61 85 77 77 85 61 85 SP S SD: 0.0060 c. M:-0.0085 c. 1500: 112 138 138 112 138 99 138 125 125 138 99 138 SP S SD: 0.0014 c. M: 0.0019 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: 0.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 6.6437 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.9527 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 3.5602 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.2929 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.7988 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.8782 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.5010 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 7.2791 cents 11 x 12:13:14:15 x 16:17:19:20:21:22 SD: 11.0955 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 8.1041 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 10.1268 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.7901 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.5757 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 4.2954 cents 22:23:25:26:28:30:31:33:35:37:39:41:44 SD: 4.2658 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.1846 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.3764 cents 34:36:38:41:43:46:48:51:54:57:61:64:68 SD: 2.1445 cents 41:43:46:49:52:55:58:61:65:69:73:77:82 SD: 2.0444 cents 42:44:47:50:53:56:59:63:67:71:75:79:84 SD: 1.9745 cents 50:53:56:60:63:67:70:75:79:84:90:94:100 SD: 1.5995 cents 56:59:63:67:71:75:79:84:89:94:100:105:112 SD: 1.3365 cents 72:76:81:86:91:97:101:108:114:121:129:135:144 SD: 0.9894 cents 76:80:85:91:96:102:107:114:121:128:136:143:152 SD: 0.9747 cents 81:85:91:97:102:109:114:121:129:136:145:152:162 SD: 0.9628 cents 82:86:92:98:103:110:115:123:130:138:147:154:164 SD: 0.8934 cents 91:96:102:109:115:122:128:136:144:153:163:171:182 SD: 0.8854 cents 96:101:108:115:121:129:135:144:152:161:172:180:192 SD: 0.7211 cents 97:102:109:116:122:130:136:145:154:163:174:182:194 SD: 0.7081 cents 116:122:130:139:146:156:163:174:184:195:208:218:232 SD: 0.5511 cents 131:138:147:157:165:176:184:196:208:220:235:246:262 SD: 0.4451 cents 169:178:190:202:213:227:238:253:268:284:303:317:338 SD: 0.4422 cents 170:179:191:203:214:228:239:255:270:286:305:319:340 SD: 0.4403 cents 172:181:193:206:217:231:242:258:273:289:308:323:344 SD: 0.4151 cents 189:199:212:226:238:254:266:283:300:318:339:355:378 SD: 0.3229 cents 204:215:229:244:257:274:287:306:324:343:366:383:408 SD: 0.2888 cents 245:258:275:293:309:329:344:367:389:412:439:460:490 SD: 0.2592 cents 269:283:302:322:339:361:378:403:427:452:482:505:538 SD: 0.2576 cents 285:300:320:341:359:383:401:427:452:479:511:535:570 SD: 0.2572 cents 301:317:338:360:379:404:423:451:478:506:540:565:602 SD: 0.2119 cents 342:360:384:409:431:459:481:512:543:575:613:642:684 SD: 0.2073 cents 377:397:423:451:475:506:530:565:598:634:676:707:754 SD: 0.1786 cents 434:457:487:519:547:583:610:650:689:730:778:814:868 SD: 0.1416 cents 530:558:595:634:668:712:745:794:841:891:950:995:1060 SD: 0.1409 cents 540:569:606:646:680:725:759:809:857:908:968:1013:1080 SD: 0.1349 cents 550:579:617:658:693:739:773:824:873:925:986:1032:1100 SD: 0.1336 cents 565:595:634:676:712:759:794:847:897:950:1013:1060:1130 SD: 0.1291 cents