Scala analysis: fifaug
Three circles of four (56/11)^(1/4) fifths with 11/7 as wolf
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 95.623 cents 95.623008 2: 113.131 cents 113.130973 3: 208.754 cents 208.753982 4: 304.377 cents 304.376991 5: 400.000 cents 400.000000 6: 495.623 cents 495.623008 7: 513.131 cents 513.130973 8: 608.754 cents 608.753982 9: 704.377 cents 704.376991 10: 800.000 cents 800.000000 11: 895.623 cents 895.623008 12: 913.131 cents 913.130973 13: 1008.754 cents 1008.753982 14: 1104.377 cents 1104.376991 15: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 95.6230 cents 95.6230 1: 95.6230 cents 95.6230 2: 17.5080 cents 17.5080 3: 95.6230 cents 95.6230 4: 95.6230 cents 95.6230 5: 95.6230 cents 95.6230 6: 95.6230 cents 95.6230 7: 17.5080 cents 17.5080 8: 95.6230 cents 95.6230 9: 95.6230 cents 95.6230 10: 95.6230 cents 95.6230 11: 95.6230 cents 95.6230 12: 17.5080 cents 17.5080 13: 95.6230 cents 95.6230 14: 95.6230 cents 95.6230 15: 95.6230 cents 95.6230
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 17.50796 cents 1: 12 95.62301 cents 2: 6 113.13097 cents 2: 9 191.24602 cents 3: 9 208.75398 cents 3: 6 286.86903 cents 4: 12 304.37699 cents 4: 3 382.49204 cents 5: 15 400.00000 cents 6: 3 417.50796 cents 6: 12 495.62301 cents 7: 6 513.13097 cents 7: 9 591.24602 cents 8: 9 608.75398 cents 8: 6 686.86903 cents 9: 12 704.37699 cents 9: 3 782.49203 cents 10: 15 800.00000 cents 11: 3 817.50797 cents 11: 12 895.62301 cents 12: 6 913.13097 cents 12: 9 991.24602 cents 13: 9 1008.75398 cents 13: 6 1086.86903 cents 14: 12 1104.37699 cents 14: 3 1182.49203 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.85714 = 13/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 95.6 113.1 208.8 304.4 400.0 495.6 513.1 608.8 704.4 800.0 895.6 913.1 1008.8 1104.4 1200.0 95.6 : 17.5 113.1 208.8 304.4 400.0 417.5 513.1 608.8 704.4 800.0 817.5 913.1 1008.8 1104.4 1200.0 113.1 : 95.6 191.2 286.9 382.5 400.0 495.6 591.2 686.9 782.5 800.0 895.6 991.2 1086.9 1182.5 1200.0 208.8 : 95.6 191.2 286.9 304.4 400.0 495.6 591.2 686.9 704.4 800.0 895.6 991.2 1086.9 1104.4 1200.0 304.4 : 95.6 191.2 208.8 304.4 400.0 495.6 591.2 608.8 704.4 800.0 895.6 991.2 1008.8 1104.4 1200.0 400.0 : 95.6 113.1 208.8 304.4 400.0 495.6 513.1 608.8 704.4 800.0 895.6 913.1 1008.8 1104.4 1200.0 495.6 : 17.5 113.1 208.8 304.4 400.0 417.5 513.1 608.8 704.4 800.0 817.5 913.1 1008.8 1104.4 1200.0 513.1 : 95.6 191.2 286.9 382.5 400.0 495.6 591.2 686.9 782.5 800.0 895.6 991.2 1086.9 1182.5 1200.0 608.8 : 95.6 191.2 286.9 304.4 400.0 495.6 591.2 686.9 704.4 800.0 895.6 991.2 1086.9 1104.4 1200.0 704.4 : 95.6 191.2 208.8 304.4 400.0 495.6 591.2 608.8 704.4 800.0 895.6 991.2 1008.8 1104.4 1200.0 800.0 : 95.6 113.1 208.8 304.4 400.0 495.6 513.1 608.8 704.4 800.0 895.6 913.1 1008.8 1104.4 1200.0 895.6 : 17.5 113.1 208.8 304.4 400.0 417.5 513.1 608.8 704.4 800.0 817.5 913.1 1008.8 1104.4 1200.0 913.1 : 95.6 191.2 286.9 382.5 400.0 495.6 591.2 686.9 782.5 800.0 895.6 991.2 1086.9 1182.5 1200.0 1008.8: 95.6 191.2 286.9 304.4 400.0 495.6 591.2 686.9 704.4 800.0 895.6 991.2 1086.9 1104.4 1200.0 1104.4: 95.6 191.2 208.8 304.4 400.0 495.6 591.2 608.8 704.4 800.0 895.6 991.2 1008.8 1104.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.5080 .. 95.6230 cents 78.11504 cents 17.50796 cents 2: 113.1310 .. 191.2460 cents 78.11504 cents 17.50796 cents 3: 208.7540 .. 286.8690 cents 78.11505 cents 17.50796 cents 4: 304.3770 .. 382.4920 cents 78.11504 cents 17.50796 cents 5: 400.0000 .. 400.0000 cents 1/1, 0.0000 cents 17.50797 cents 6: 417.5080 .. 495.6230 cents 78.11504 cents 17.50796 cents 7: 513.1310 .. 591.2460 cents 78.11504 cents 17.50797 cents 8: 608.7540 .. 686.8690 cents 78.11504 cents 17.50796 cents 9: 704.3770 .. 782.4920 cents 78.11504 cents 17.50796 cents 10: 800.0000 .. 800.0000 cents 1/1, 0.0000 cents 17.50797 cents 11: 817.5080 .. 895.6230 cents 78.11504 cents 17.50797 cents 12: 913.1310 .. 991.2460 cents 78.11505 cents 17.50797 cents 13: 1008.7540 .. 1086.8690 cents 78.11504 cents 17.50796 cents 14: 1104.3770 .. 1182.4920 cents 78.11504 cents 17.50796 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 17.50796 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 95.62301 cents Average / Smallest step : 4.569349 Largest / Average step : 1.195288 Largest / Smallest step : 5.461686 Median interval of one step : 95.62301 cents, amount: 12 Most common interval of one step : 95.62301 cents, amount: 12 Least squares average step : 78.48810 cents, oct.: 1177.32144 cents Scale is strictly proper Scale has 3 repeating blocks of 5 notes Blocks have Myhill's property chromas: 78.11504 cents and 60.60708 cents, ratio: 1.288877 generators: 1 of 95.62301 cents and 4 of 304.37699 cents ET pair of linear temperament : 63&138 Scale is distributional even Scale is a mode of a 891-tone equal temperament with octave 1200.000 cents degrees: 71 84 155 226 297 368 381 452 523 594 665 678 749 820 891 Least number of segments generator : 448 of 603.367 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 523 of 704.377 cents and inv. generated superset size: 599 = 584 more = 3993.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAAABAAAABAAA Step pattern size order : LSLLLLSLLLLSLLL Scale is a Constant Structure, by a margin of 17.50796 cents Scale diversity : 1.077521 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.218850 Number of different interval sizes : 26 = 1.85714 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.85714 = 13/7 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 17.50796 cents Most common intervals : 400.00000 cents & inv., amount: 15 Most common triad is 0.0 400.000 800.000 cents, amount: 15 Number of recognisable fifths : 18, average 698.5410 cents Number of appreciable fifths : 12, average 704.3770 cents Formal octave complements present : 9 = 60.0000% Limited transpositions : 5 10 Limited inverse transpositions : 3 8 13 Inversional symmetry on degrees : 4 9 14 Inversional symmetry on intervals : 1-2 6-7 11-12 -- Rational properties --
FIT/MODE
15: 1 0 2 1 1 1 0 2 1 1 1 0 2 1 1 N B D3 SD: 22.6368 c. M: 33.1310 c. 16: 1 1 1 1 1 2 0 1 1 2 1 0 1 2 1 N D3 SD: 21.6294 c. M:-36.8690 c. 17: 1 1 1 1 2 1 0 2 1 1 2 0 1 2 1 N D3 S SD: 19.3878 c. M:-28.0455 c. 19: 1 1 1 2 1 2 0 2 1 2 1 0 2 1 2 N D3 SD: 18.7915 c. M: 32.4651 c. 21: 2 0 2 1 2 2 0 2 1 2 2 0 2 1 2 N B D3 SD: 14.7693 c. M:-19.8174 c. 24: 2 0 2 2 2 2 0 2 2 2 2 0 2 2 2 P B DE S SD: 7.5812 c. M: 13.1310 c. 39: 3 1 3 3 3 3 1 3 3 3 3 1 3 3 3 SP B DE S SD: 5.7423 c. M:-9.9460 c. 46: 4 0 4 4 3 4 1 3 4 4 3 1 4 3 4 P S SD: 7.1001 c. M: 8.7831 c. 49: 4 1 4 3 4 4 1 4 4 4 4 0 4 4 4 N SD: 7.0223 c. M:-11.6542 c. 51: 4 1 4 4 4 4 1 4 4 4 4 1 4 4 4 SP B DE S SD: 2.6074 c. M:-4.5161 c. 63: 5 1 5 5 5 5 1 5 5 5 5 1 5 5 5 SP B DE S SD: 0.6667 c. M:-1.1547 c. 75: 6 1 6 6 6 6 1 6 6 6 6 1 6 6 6 SP B DE S SD: 0.6530 c. M: 1.1310 c. 138: 11 2 11 11 11 11 2 11 11 11 11 2 11 11 11 SP B DE S SD: 0.0505 c. M: 0.0875 c. 477: 38 7 38 38 38 38 7 38 38 38 38 7 38 38 38 SP B DE S SD: 0.0442 c. M:-0.0766 c. 615: 49 9 49 49 49 49 9 49 49 49 49 9 49 49 49 SP B DE S SD: 0.0230 c. M:-0.0398 c. 753: 60 11 60 60 60 60 11 60 60 60 60 11 60 60 60 SP B DE S SD: 0.0095 c. M:-0.0164 c. 891: 71 13 71 71 71 71 13 71 71 71 71 13 71 71 71 SP B DE S SD: 0.0002 c. M:-0.0003 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 1.2110 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 3.8406 cents 4 x x x x 5 x x x 6 x x x 7 x 8 S SD: 10.5695 cents 5 x x x 6 x x x 7 x 8 x x 9 x 10 S SD: 6.5758 cents 6 x x x 7 x 8 x x 9 x 10 x 11 x 12 S SD: 9.4199 cents 7 x x 8 x 9 x x 10 x 11 x 12 x 13:14 S SD: 8.5523 cents 8 x x 9 x 10 x 11 x 12:13 x x 14:15:16 S SD: 8.9888 cents 9 x x 10:11 x 12 x 13 x 14:15 x 16:17:18 S SD: 7.7440 cents 10 x x 11:12 x 13 x 14:15:16 x 17:18:19:20 S SD: 6.9228 cents 11 x 12 x 13:14 x 15:16 x 17:18:19:20:21:22 S SD: 9.1433 cents 12 x 13 x 14:15:16 x 17:18:19:20 x 21:23:24 SD: 6.1041 cents 13 x 14:15 x 16:17 x 18:20:21 x 22:23:25:26 SD: 9.2126 cents 14 x 15:16:17:18 x 19:20:21:22:23:24:25:27:28 SD: 6.0629 cents 15 x 16:17:18:19:20 x 21:23:24:25 x 27:28:30 SD: 4.7147 cents 16 x 17:18:19:20:21:22:23:24:25 x 27:29:30:32 SD: 5.0337 cents 17:18 x 19:20:21 x 23:24:26:27 x 29:30:32:34 SD: 5.3056 cents 18:19 x 20:21:23:24 x 26:27:29:30:31:32:34:36 SD: 5.5618 cents 19:20 x 21:23:24:25:26:27:29:30:32 x 34:36:38 SD: 5.0091 cents 20:21 x 23:24:25 x 27:28:30:32 x 34:36:38:40 SD: 4.2651 cents 21:22 x 24:25:26:28 x 30:32:33:35:36:38:40:42 SD: 4.6360 cents 22:23 x 25:26:28:29:30:31:33:35:37 x 39:42:44 SD: 4.0077 cents 23:24:25:26:27:29 x 31:33:35:37 x 39:41:44:46 SD: 4.8136 cents 24:25:26:27:29:30:32 x 34:36:38:40:41:43:45:48 SD: 3.6894 cents 25:26:27:28:30:32:33:34:36:38:40:42 x 45:47:50 SD: 4.5913 cents 26:27:28:29:31:33 x 35:37:39:41 x 44:47:49:52 SD: 3.5776 cents 27 x 29:30:32:34:36 x 38:41:43:45:46:48:51:54 SD: 3.4238 cents 28 x 30:32:33:35:37:38:40:42:44:47 x 50:53:56 SD: 3.4013 cents 29 x 31:33:35:37 x 39:41:44:46 x 49:52:55:58 SD: 3.3170 cents 30 x 32:34:36:38:40 x 43:45:48:50:51:54:57:60 SD: 2.3937 cents 31 x 33:35:37:39:41:42:44:47:49:52:53:56:59:62 SD: 2.4804 cents 32 x 34:36:38:40 x 43:45:48:51 x 54:57:61:64 SD: 2.6612 cents 33:35 x 37:39:42:44 x 47:50:52:55:56:59:62:66 SD: 2.8725 cents 34:36 x 38:41:43:45:46:48:51:54:57:58:61:64:68 SD: 2.5675 cents 35:37 x 39:42:44 x 47:50:53:56:59 x 63:66:70 SD: 2.9522 cents 36:38 x 41:43:45:48 x 51:54:57:60:61:64:68:72 SD: 2.2211 cents 38:40:41:43:45:48 x 51:54:57:60:64 x 68:72:76 SD: 2.0748 cents 39:41:42:44:46:49:52 x 55:59:62:65:66:70:74:78 SD: 2.4716 cents 40:42:43:45:48:50:53:54:57:60:63:67:68:72:76:80 SD: 2.2028 cents 41:43:44:46:49:52 x 55:58:62:65:69 x 73:78:82 SD: 2.3560 cents 42:44:45:47:50:53:56 x 60:63:67:70:71:75:79:84 SD: 2.1674 cents 44 x 47:50:52:55 x 59:63:66:70:74:75:79:83:88 SD: 2.3818 cents 45 x 48:51:54:57:60:61:64:68:71:75:76:81:85:90 SD: 2.1848 cents 46 x 49:52:55:58:61:62:65:69:73:77:78:82:87:92 SD: 1.2475 cents 47 x 50:53:56:59 x 63:67:71:75:79:80:84:89:94 SD: 1.5395 cents 48 x 51:54:57:60:64:65:68:72:76 x 81:86:91:96 SD: 1.8686 cents 49:52 x 55:58:62:65:66:70:74:78:82:83:88:93:98 SD: 1.8073 cents 50:53 x 56:60:63 x 67:71:75:79:84:85:90:95:100 SD: 1.8675 cents 51:54 x 58:61:64:68:69:72:77:81 x 86:91:97:102 SD: 2.1722 cents 52:55:56:59:62:66:69:70:74:78:83:87:88:93:98:104 SD: 1.7828 cents 53:56:57:60:63:67 x 71:75:80:84:89:90:95:100:106 SD: 1.5854 cents 54:57:58:61:64:68:72:73:77:81:86:91:92:97:102:108 SD: 1.5851 cents 55:58:59:62:66:69:73:74:78:83:87:92:93:98:104:110 SD: 1.5384 cents 56:59:60:63:67:71 x 75:80:84:89:94:95:100:106:112 SD: 1.4579 cents 57:60:61:64:68:72:76:77:81:86:90:96:97:102:108:114 SD: 1.4405 cents 58:61:62:65:69:73:77:78:82:87:92:97:98:104:110:116 SD: 1.3578 cents 59:62:63:67:70:74 x 79:84:89:94:99:100:106:112:118 SD: 1.7181 cents 61:64:65:69:73:77:81:82:87:92:97:102:103:109:115:122 SD: 1.4693 cents 62 x 66:70:74:78 x 83:88:93:98:104:105:111:117:124 SD: 1.0730 cents 63 x 67:71:75:79:84:85:90:95:100:106:107:113:119:126 SD: 1.3102 cents 64 x 68:72:76:81:85:86:91:96:102:107:108:115:121:128 SD: 1.4256 cents 65:69 x 73:77:82 x 87:92:98:103:109:110:116:123:130 SD: 1.6613 cents 66:70 x 74:79:83:88:89:94:99:105:111:112:118:125:132 SD: 1.2464 cents 68:72:73:77:81:86 x 91:97:102:108:114:115:122:129:136 SD: 1.3438 cents 69:73:74:78:82:87:92:93:98:104:110:116:117:124:131:138 SD: 1.1638 cents 71:75:76:80:85:89:95 x 101:107:113:119:120:127:134:142 SD: 1.3047 cents 72:76:77:81:86:91:96:97:102:108:114:121:122:129:136:144 SD: 0.8727 cents 80 x 85:90:95:101:107:108:114:120:127:134:136:143:151:160 SD: 1.3296 cents 81:86 x 91:97:102:108:109:115:122:129:136:137:145:153:162 SD: 1.1666 cents 84:89:90:95:100:106:112:113:119:126:133:141:142:150:159:168 SD: 0.9435 cents 85:90:91:96:101:107:113:114:121:128:135:143:144:152:161:170 SD: 0.8602 cents 87:92:93:98:104:110:116:117:124:131:138:146:147:156:165:174 SD: 0.8544 cents 88:93:94:99:105:111:117:118:125:132:140:148:149:158:167:176 SD: 0.8174 cents 93:98:99:105:111:117:124:125:132:140:148:156:158:167:176:186 SD: 0.8132 cents 102:108:109:115:122:129:136:137:145:153:162:171:173:183:193:204 SD: 0.7361 cents 104:110:111:117:124:131:138:140:148:156:165:174:176:186:197:208 SD: 0.6951 cents 109:115:116:123:130:137:145:147:155:164:173:183:185:195:206:218 SD: 0.6873 cents 118:125:126:133:141:149:157:159:168:177:187:198:200:211:223:236 SD: 0.6566 cents 119:126:127:134:142:150:158:160:169:179:189:200:202:213:225:238 SD: 0.5968 cents 124:131:132:140:148:156:165:167:176:186:197:208:210:222:235:248 SD: 0.5328 cents 147:155:157:166:175:185:196:198:209:221:233:247:249:263:278:294 SD: 0.5280 cents 157:166:168:177:187:198:209:211:223:236:249:263:266:281:297:314 SD: 0.4197 cents 177:187:189:200:211:223:236:238:252:266:281:297:300:317:335:354 SD: 0.3218 cents 211:223:225:238:252:266:281:284:300:317:335:354:358:378:399:422 SD: 0.3204 cents 223:236:238:252:266:281:297:300:317:335:354:374:378:399:422:446 SD: 0.2888 cents 235:248:251:265:280:296:313:316:334:353:373:394:398:421:445:470 SD: 0.2352 cents 281:297:300:317:335:354:374:378:399:422:446:471:476:503:532:562 SD: 0.1821 cents 353:373:377:398:421:445:470:475:502:530:560:592:598:632:668:706 SD: 0.1756 cents 354:374:378:399:422:446:471:476:503:532:562:594:600:634:670:708 SD: 0.1654 cents 443:468:473:500:528:558:590:596:630:665:703:743:751:793:838:886 SD: 0.1645 cents 444:469:474:501:529:559:591:597:631:667:705:745:752:795:840:888 SD: 0.1615 cents 446:471:476:503:532:562:594:600:634:670:708:748:756:799:844:892 SD: 0.1335 cents 458:484:489:517:546:577:610:616:651:688:727:768:776:820:867:916 SD: 0.1034 cents 531:561:567:599:633:669:707:714:755:798:843:891:900:951:1005:1062 SD: 0.0959 cents 577:610:616:651:688:727:768:776:820:867:916:968:978:1033:1092:1154 SD: 0.0881 cents