Scala analysis: hemifamcyc
Hemifamity cycle of thirds scale, nearest to proper
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 85.876 cents 85.875706 2: 180.791 cents 180.790960 3: 291.525 cents 291.525424 4: 386.441 cents 386.440678 5: 402.260 cents 402.259887 6: 497.175 cents 497.175141 7: 607.910 cents 607.909605 8: 702.825 cents 702.824859 9: 788.701 cents 788.700565 10: 883.616 cents 883.615819 11: 969.492 cents 969.491525 12: 994.350 cents 994.350282 13: 1105.085 cents 1105.084746 14: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 94.9153 cents 94.9153 1: 85.8757 cents 85.8757 2: 94.9153 cents 94.9153 3: 110.7345 cents 110.7345 4: 94.9153 cents 94.9153 5: 15.8192 cents 15.8192 6: 94.9153 cents 94.9153 7: 110.7345 cents 110.7345 8: 94.9153 cents 94.9153 9: 85.8757 cents 85.8757 10: 94.9153 cents 94.9153 11: 85.8757 cents 85.8757 12: 24.8588 cents 24.8588 13: 110.7345 cents 110.7345 14: 94.9153 cents 94.9153
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15.81921 cents 1: 1 24.85876 cents 1: 3 85.87571 cents 1: 6 94.91525 cents 1: 3 110.73446 cents 2: 3 110.73446 cents 2: 1 135.59322 cents 2: 5 180.79096 cents 2: 5 205.64972 cents 3: 2 205.64972 cents 3: 3 221.46893 cents 3: 1 230.50848 cents 3: 1 266.66667 cents 3: 2 275.70621 cents 3: 3 291.52542 cents 3: 2 300.56497 cents 4: 1 291.52542 cents 4: 7 316.38418 cents 4: 1 361.58192 cents 4: 5 386.44068 cents 5: 1 386.44068 cents 5: 4 402.25989 cents 5: 4 411.29944 cents 5: 1 427.11864 cents 5: 1 472.31638 cents 5: 2 481.35593 cents 5: 1 497.17514 cents 6: 9 497.17514 cents 6: 3 522.03390 cents 6: 1 567.23164 cents 6: 1 592.09040 cents 7: 2 583.05085 cents 7: 5 592.09040 cents 7: 5 607.90960 cents 7: 2 616.94915 cents 8: 1 607.90960 cents 8: 1 632.76836 cents 8: 3 677.96610 cents 8: 9 702.82486 cents 9: 1 702.82486 cents 9: 2 718.64407 cents 9: 1 727.68362 cents 9: 1 772.88135 cents 9: 4 788.70056 cents 9: 4 797.74011 cents 9: 1 813.55932 cents 10: 5 813.55932 cents 10: 1 838.41808 cents 10: 7 883.61582 cents 10: 1 908.47458 cents 11: 2 899.43503 cents 11: 3 908.47458 cents 11: 2 924.29379 cents 11: 1 933.33333 cents 11: 1 969.49153 cents 11: 3 978.53107 cents 11: 2 994.35028 cents 12: 5 994.35028 cents 12: 5 1019.20904 cents 12: 1 1064.40678 cents 12: 3 1089.26554 cents 13: 3 1089.26554 cents 13: 6 1105.08475 cents 13: 3 1114.12429 cents 13: 1 1175.14124 cents 13: 1 1184.18079 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.07692 = 66/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 85.9 180.8 291.5 386.4 402.3 497.2 607.9 702.8 788.7 883.6 969.5 994.4 1105.1 1200.0 85.9 : 94.9 205.6 300.6 316.4 411.3 522.0 616.9 702.8 797.7 883.6 908.5 1019.2 1114.1 1200.0 180.8 : 110.7 205.6 221.5 316.4 427.1 522.0 607.9 702.8 788.7 813.6 924.3 1019.2 1105.1 1200.0 291.5 : 94.9 110.7 205.6 316.4 411.3 497.2 592.1 678.0 702.8 813.6 908.5 994.4 1089.3 1200.0 386.4 : 15.8 110.7 221.5 316.4 402.3 497.2 583.1 607.9 718.6 813.6 899.4 994.4 1105.1 1200.0 402.3 : 94.9 205.6 300.6 386.4 481.4 567.2 592.1 702.8 797.7 883.6 978.5 1089.3 1184.2 1200.0 497.2 : 110.7 205.6 291.5 386.4 472.3 497.2 607.9 702.8 788.7 883.6 994.4 1089.3 1105.1 1200.0 607.9 : 94.9 180.8 275.7 361.6 386.4 497.2 592.1 678.0 772.9 883.6 978.5 994.4 1089.3 1200.0 702.8 : 85.9 180.8 266.7 291.5 402.3 497.2 583.1 678.0 788.7 883.6 899.4 994.4 1105.1 1200.0 788.7 : 94.9 180.8 205.6 316.4 411.3 497.2 592.1 702.8 797.7 813.6 908.5 1019.2 1114.1 1200.0 883.6 : 85.9 110.7 221.5 316.4 402.3 497.2 607.9 702.8 718.6 813.6 924.3 1019.2 1105.1 1200.0 969.5 : 24.9 135.6 230.5 316.4 411.3 522.0 616.9 632.8 727.7 838.4 933.3 1019.2 1114.1 1200.0 994.4 : 110.7 205.6 291.5 386.4 497.2 592.1 607.9 702.8 813.6 908.5 994.4 1089.3 1175.1 1200.0 1105.1: 94.9 180.8 275.7 386.4 481.4 497.2 592.1 702.8 797.7 883.6 978.5 1064.4 1089.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 15.8192 .. 110.7345 cents 94.91525 cents 15.81921 cents 2: 110.7345 .. 205.6497 cents 94.91526 cents -0.00000 cents 3: 205.6497 .. 300.5650 cents 94.91525 cents -0.00000 cents 4: 291.5254 .. 386.4407 cents 94.91525 cents -9.03955 cents 5: 386.4407 .. 497.1751 cents 110.73447 cents -0.00000 cents 6: 497.1751 .. 592.0904 cents 94.91526 cents -0.00000 cents 7: 583.0508 .. 616.9492 cents 33.89831 cents -9.03955 cents 8: 607.9096 .. 702.8249 cents 94.91525 cents -9.03955 cents 9: 702.8249 .. 813.5593 cents 110.73447 cents -0.00000 cents 10: 813.5593 .. 908.4746 cents 94.91526 cents -0.00000 cents 11: 899.4350 .. 994.3503 cents 94.91525 cents -9.03955 cents 12: 994.3503 .. 1089.2655 cents 94.91526 cents -0.00000 cents 13: 1089.2655 .. 1184.1808 cents 94.91525 cents -0.00000 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 15.81921 cents, class 1 Average step (divided formal octave): 85.7143 cents Largest one step interval : 110.73446 cents Average / Smallest step : 5.418367 Largest / Average step : 1.291902 Largest / Smallest step : 7.000000 Median interval of one step : 94.91525 cents, amount: 6 Most common interval of one step : 94.91525 cents, amount: 6 Least squares average step : 86.14511 cents, oct.: 1206.03156 cents Scale is not proper Scale is a mode of a 531-tone equal temperament with octave 1200.000 cents degrees: 38 80 129 171 178 220 269 311 349 391 429 440 489 531 Least number of segments generator : 268 of 605.650 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 511 of 1154.802 cents and inv. generated superset size: 81 = 67 more = 578.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCBDBCBABAECB Step pattern size order : CDEDADEDCDCBED Scale is not a Constant Structure Scale diversity : 1.383250 Lumma stability : 0.026365 Lumma impropriety factor : 0.030132 Number of different interval sizes : 54 = 4.15385 / class Number of one step interval sizes : 5 Highest interval variety : 7 Mean interval variety : 5.07692 = 66/13 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 9.03955 cents Most common intervals : 497.17514 cents & inv., amount: 10 Most common triad is 0.0 497.175 702.825 cents, amount: 7 Number of recognisable fifths : 12, average 705.4614 cents Number of appreciable fifths : 10, average 702.8249 cents Formal octave complements present : 3 = 21.4286% -- Rational properties --
FIT/MODE
14: 1 1 1 1 0 2 1 1 1 1 1 0 2 1 N B D3 SD: 29.0208 c. M: 59.4027 c. 15: 1 1 2 1 0 1 2 1 1 1 1 0 2 1 N SD: 18.3606 c. M: 34.3503 c. 17: 1 2 1 2 0 1 2 1 1 2 1 0 2 1 N D3 SD: 20.9796 c. M:-37.0887 c. 19: 1 2 2 1 0 2 2 1 1 2 1 1 1 2 N SD: 19.1933 c. M: 31.4005 c. 21: 1 2 2 2 0 1 2 2 2 1 2 0 2 2 N SD: 20.8653 c. M: 40.0323 c. 22: 1 2 2 2 0 2 2 2 1 2 2 0 2 2 N T3 SD: 15.7350 c. M: 31.3303 c. 24: 2 2 2 2 0 2 2 2 2 2 1 1 2 2 N T3 SD: 11.1535 c. M: 19.4915 c. 26: 2 2 2 2 1 2 2 2 2 2 2 1 2 2 SP B ME S SD: 10.4616 c. M:-21.0343 c. 27: 2 2 3 2 0 2 3 2 2 2 2 0 3 2 N G SD: 10.2400 c. M:-19.5857 c. 29: 2 2 3 2 1 2 3 2 2 2 2 1 3 2 P SD: 10.0933 c. M: 17.7674 c. 34: 2 3 3 3 0 3 3 3 2 3 2 1 3 3 N SD: 9.2598 c. M: 16.5503 c. 37: 3 3 3 3 0 3 4 3 2 3 3 1 3 3 N SD: 8.8907 c. M:-13.8036 c. 38: 3 3 3 3 1 3 3 3 3 3 3 0 4 3 N SD: 7.8054 c. M: 15.4029 c. 41: 3 3 4 3 1 3 4 3 3 3 3 1 4 3 P SD: 4.3656 c. M:-7.4962 c. 53: 4 4 5 4 1 4 5 4 4 4 4 1 5 4 P SD: 3.0163 c. M:-5.2873 c. 87: 6 7 8 7 1 7 8 7 6 7 6 2 8 7 N SD: 1.8775 c. M: 3.9743 c. 99: 7 8 9 8 1 8 9 8 7 8 7 2 9 8 N SD: 1.1891 c. M: 2.2599 c. 140: 10 11 13 11 2 11 13 11 10 11 10 3 13 11 N SD: 0.5227 c. M: 0.9201 c. 239: 17 19 22 19 3 19 22 19 17 19 17 5 22 19 N SD: 0.3344 c. M: 0.5862 c. 292: 21 23 27 23 4 23 27 23 21 23 21 6 27 23 N SD: 0.2737 c. M:-0.4798 c. 379: 27 30 35 30 5 30 35 30 27 30 27 8 35 30 N SD: 0.2589 c. M: 0.6261 c. 391: 28 31 36 31 5 31 36 31 28 31 28 8 36 31 N SD: 0.1872 c. M:-0.3294 c. 531: 38 42 49 42 7 42 49 42 38 42 38 11 49 42 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 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 3 x x x x x 4 S SD: 0.4349 cents 3 x x x x x 4 x x x 5 x x x 6 S SD: 0.3813 cents 4 x x x 5 x x x 6 x x 7 x x 8 S SD: 0.2757 cents 5 x x 6 x x x 7 x 8 x x 9 x 10 S SD: 9.7801 cents 6 x x 7 x x 8 x 9 x 10 x 11 x 12 S SD: 10.0503 cents 7 x 8 x x 9 x 10 x 11 x 12 x 13:14 S SD: 11.2330 cents 8 x 9 x 10 x 11 x 12 x 13:14 x 15:16 S SD: 9.3596 cents 9 x 10 x 11 x 12:13 x 14:15 x 16:17:18 S SD: 6.0212 cents 10 x 11:12 x x 13:14:15:16:17 x 18:19:20 S SD: 7.5836 cents 11 x 12:13 x 14:15:16 x 17:18:19:20:21:22 S SD: 8.6172 cents 12 x 13:14:15 x 16:17:18:19:20:21 x 23:24 SD: 4.9081 cents 13:14 x 15:16 x 17:18 x 21:22 x 23:25:26 SD: 10.3622 cents 14:15:16:17 x 18:19:20:21:22:23 x 25:27:28 SD: 8.1440 cents 15:16:17:18 x 19:20:21:23:24:25:26:27:28:30 SD: 6.2867 cents 16:17:18:19:20 x 21:23:24:25:27:28 x 30:32 SD: 4.6272 cents 17:18:19:20:21 x 23:24:26:27:28 x 30:32:34 SD: 4.9120 cents 18:19:20:21 x 23:24:26:27:28:30 x 32:34:36 SD: 4.2246 cents 19:20:21:22 x 24:25:27:29:30:32:33:34:36:38 SD: 4.5875 cents 20:21:22:24:25 x 27:28:30:32:33:35:36:38:40 SD: 4.5242 cents 21:22:23:25:26 x 28:30:32:33:35:37 x 40:42 SD: 3.7421 cents 22:23:24:26 x 28:29:31:33:35:37 x 39:42:44 SD: 4.1679 cents 23:24:26:27 x 29:31:33:35:36:38:40:41:44:46 SD: 4.5246 cents 24:25:27:28:30 x 32:34:36:38:40:42:43:45:48 SD: 3.4067 cents 25:26:28:30:31:32:33:36:38:39:42:44 x 47:50 SD: 4.9110 cents 26:27:29:31 x 33:35:37:39:41:43 x 46:49:52 SD: 3.0598 cents 27:28:30:32 x 34:36:38:41:43:45:47:48:51:54 SD: 3.1048 cents 28:29:31:33:35 x 37:40:42:44:47:49:50:53:56 SD: 2.7829 cents 30:32:33:36 x 38:40:43:45:47:50 x 53:57:60 SD: 3.7614 cents 31:33:34:37 x 39:41:44:47:49:52:54:55:59:62 SD: 3.4234 cents 32:34:36:38:40 x 43:45:48:50:53:56:57:61:64 SD: 3.4230 cents 33:35:37:39:41:42:44:47:50:52:55:58:59:62:66 SD: 2.8196 cents 34:36:38:40 x 43:45:48:51:54:57 x 60:64:68 SD: 2.8667 cents 35:37:39:41 x 44:47:50:53:55:58:61:62:66:70 SD: 2.7247 cents 36:38:40:43:45 x 48:51:54:57:60:63:64:68:72 SD: 1.5650 cents 38:40:42:45 x 48:51:54:57:60:63:67 x 72:76 SD: 1.7666 cents 39:41:43:46 x 49:52:55:59:62:65:68:69:74:78 SD: 2.2783 cents 40:42:44:47:50 x 53:57:60:63:67:70:71:76:80 SD: 1.9809 cents 42:44:47:50 x 53:56:60:63:66:70:74:75:80:84 SD: 2.1523 cents 43:45:48:51:54 x 57:61:65:68:72:75:76:81:86 SD: 2.1170 cents 44:46:49:52:55:56:59:63:66:69:73:77:78:83:88 SD: 2.0742 cents 45:47:50:53:56:57:60:64:68:71:75:79:80:85:90 SD: 1.5694 cents 46:48:51:54 x 58:61:65:69:73:77:81:82:87:92 SD: 2.2305 cents 47:49:52:56:59 x 63:67:71:74:78:82:83:89:94 SD: 2.2583 cents 48:50:53:57:60:61:64:68:72:76:80:84:85:91:96 SD: 1.7747 cents 50:53:56:59 x 63:67:71:75:79:83:88:89:95:100 SD: 2.1340 cents 51:54:57:60:64 x 68:72:77:80:85:89:91:97:102 SD: 2.3466 cents 52:55:58:62:65:66:69:74:78:82:87:91:92:98:104 SD: 1.8897 cents 53:56:59:63:66:67:71:75:80:84:88:93:94:100:106 SD: 1.7805 cents 54:57:60:64 x 68:72:77:81:85:90:95:96:102:108 SD: 1.1506 cents 55:58:61:65:69 x 73:78:83:87:92:96:98:104:110 SD: 1.4859 cents 57:60:63:67:71:72:76:81:86:90:95:100:101:108:114 SD: 1.3680 cents 58:61:64:69 x 73:77:82:87:91:97:102:103:110:116 SD: 1.7533 cents 59:62:65:70:74 x 79:84:89:93:98:103:105:112:118 SD: 1.6657 cents 60:63:67:71:75:76:80:85:90:95:100:105:107:114:120 SD: 1.2734 cents 62:65:69:73 x 78:83:88:93:98:103:109:110:117:124 SD: 1.3938 cents 63:66:70:75:79 x 84:90:95:99:105:110:112:119:126 SD: 1.5514 cents 64:67:71:76:80:81:85:91:96:101:107:112:114:121:128 SD: 1.0608 cents 66:69:73:78 x 83:88:94:99:104:110:116:117:125:132 SD: 1.1770 cents 70:74:78:83 x 88:93:99:105:110:117:123:124:133:140 SD: 1.6447 cents 71:75:79:84:89:90:95:101:107:112:118:124:126:134:142 SD: 1.3566 cents 72:76:80:85:90:91:96:102:108:114:120:126:128:136:144 SD: 0.9657 cents 74:78:82:88 x 93:99:105:111:117:123:130:131:140:148 SD: 1.3466 cents 75:79:83:89:94:95:100:107:113:118:125:131:133:142:150 SD: 1.1877 cents 76:80:84:90:95:96:101:108:114:120:127:133:135:144:152 SD: 0.8149 cents 78:82:87:92 x 98:104:111:117:123:130:137:139:148:156 SD: 1.2004 cents 80:84:89:95:100:101:107:114:120:126:133:140:142:151:160 SD: 0.9286 cents 81:85:90:96:101:102:108:115:122:128:135:142:144:153:162 SD: 0.7936 cents 82:86:91:97 x 103:109:116:123:129:137:144:146:155:164 SD: 1.1982 cents 83:87:92:98:104:105:111:118:125:131:138:145:147:157:166 SD: 1.0304 cents 84:88:93:99:105:106:112:119:126:132:140:147:149:159:168 SD: 0.9304 cents 86:90:95:102:108 x 115:122:129:136:143:151:153:163:172 SD: 1.3637 cents 87:91:97:103:109:110:116:124:131:137:145:152:155:165:174 SD: 1.1861 cents 88:92:98:104:110:111:117:125:132:139:147:154:156:167:176 SD: 0.9823 cents 92:97:102:109:115:116:123:131:138:145:153:161:163:174:184 SD: 0.7862 cents 99:104:110:117:124:125:132:141:149:156:165:173:176:187:198 SD: 0.7060 cents 100:105:111:118:125:126:133:142:150:158:167:175:178:189:200 SD: 0.7059 cents 116:122:129:137:145:146:155:165:174:183:193:203:206:220:232 SD: 0.6429 cents 120:126:133:142:150:151:160:170:180:189:200:210:213:227:240 SD: 0.5720 cents 135:142:150:160:169:170:180:192:203:213:225:236:240:256:270 SD: 0.5615 cents 152:160:169:180:190:192:203:216:228:240:253:266:270:288:304 SD: 0.4840 cents 153:161:170:181:191:193:204:217:230:241:255:268:272:290:306 SD: 0.4767 cents 156:164:173:185:195:197:208:222:234:246:260:273:277:295:312 SD: 0.4237 cents 180:189:200:213:225:227:240:256:270:284:300:315:320:341:360 SD: 0.2831 cents 252:265:280:298:315:318:336:358:378:397:420:441:448:477:504 SD: 0.2764 cents 256:269:284:303:320:323:341:364:384:404:426:448:455:485:512 SD: 0.2624 cents 272:286:302:322:340:343:362:386:408:429:453:476:483:515:544 SD: 0.2545 cents 300:315:333:355:375:378:400:426:450:473:500:525:533:568:600 SD: 0.2315 cents 316:332:351:374:395:399:421:449:474:498:526:553:561:598:632 SD: 0.2237 cents 317:333:352:375:396:400:422:450:476:500:528:555:563:600:634 SD: 0.2191 cents 336:353:373:398:420:424:448:477:504:530:560:588:597:636:672 SD: 0.2037 cents 371:390:412:439:464:468:494:527:557:585:618:649:659:702:742 SD: 0.1917 cents 392:412:435:464:490:495:522:557:588:618:653:686:696:742:784 SD: 0.1903 cents 393:413:436:465:491:496:524:558:590:620:655:688:698:744:786 SD: 0.1716 cents 409:430:454:484:511:516:545:581:614:645:681:716:726:774:818 SD: 0.1491 cents 473:497:525:560:591:597:630:672:710:746:788:828:840:896:946 SD: 0.1427 cents 508:534:564:601:635:641:677:722:762:801:846:889:902:962:1016 SD: 0.1273 cents 535:562:594:633:669:675:713:760:803:844:891:937:950:1013:1070 SD: 0.1060 cents 589:619:654:697:736:743:785:837:884:929:981:1031:1046:1115:1178 SD: 0.0821 cents