Scala analysis: 12root618phi
12 root of 0.61803 phi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 51.503 cents 51.502500 2: 103.005 cents 103.005000 3: 154.507 cents 154.507500 4: 206.010 cents 206.010000 5: 257.513 cents 257.512500 6: 309.015 cents 309.015000 7: 360.518 cents 360.517500 8: 412.020 cents 412.020000 9: 463.523 cents 463.522500 10: 515.025 cents 515.025000 11: 566.528 cents 566.527500 12: 618.030 cents 618.030000
SHOW/INTERVAL
0: 51.5025 cents 51.5025 1: 51.5025 cents 51.5025 2: 51.5025 cents 51.5025 3: 51.5025 cents 51.5025 4: 51.5025 cents 51.5025 5: 51.5025 cents 51.5025 6: 51.5025 cents 51.5025 7: 51.5025 cents 51.5025 8: 51.5025 cents 51.5025 9: 51.5025 cents 51.5025 10: 51.5025 cents 51.5025 11: 51.5025 cents 51.5025 12: 51.5025 cents 51.5025
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 51.50250 cents 2: 12 103.00500 cents 3: 12 154.50750 cents 4: 12 206.01000 cents 5: 12 257.51250 cents 6: 12 309.01500 cents 7: 12 360.51750 cents 8: 12 412.02000 cents 9: 12 463.52250 cents 10: 12 515.02500 cents 11: 12 566.52750 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 51.5 : 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 103.0: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 154.5: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 206.0: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 257.5: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 309.0: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 360.5: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 412.0: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 463.5: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 515.0: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 566.5: 51.5 103.0 154.5 206.0 257.5 309.0 360.5 412.0 463.5 515.0 566.5 618.0 618.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.5025 .. 51.5025 cents 1/1, 0.0000 cents 51.50250 cents 2: 103.0050 .. 103.0050 cents 1/1, 0.0000 cents 51.50250 cents 3: 154.5075 .. 154.5075 cents 1/1, 0.0000 cents 51.50250 cents 4: 206.0100 .. 206.0100 cents 1/1, 0.0000 cents 51.50250 cents 5: 257.5125 .. 257.5125 cents 1/1, 0.0000 cents 51.50250 cents 6: 309.0150 .. 309.0150 cents 1/1, 0.0000 cents 51.50250 cents 7: 360.5175 .. 360.5175 cents 1/1, 0.0000 cents 51.50250 cents 8: 412.0200 .. 412.0200 cents 1/1, 0.0000 cents 51.50250 cents 9: 463.5225 .. 463.5225 cents 1/1, 0.0000 cents 51.50250 cents 10: 515.0250 .. 515.0250 cents 1/1, 0.0000 cents 51.50250 cents 11: 566.5275 .. 566.5275 cents 1/1, 0.0000 cents 51.50250 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 51.50250 cents, class 1 Average step (divided formal octave): 51.5025 cents Largest one step interval : 51.50250 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 51.50250 cents, amount: 12 Most common interval of one step : 51.50250 cents, amount: 12 Least squares average step : 51.50250 cents, oct.: 618.03000 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 51.50250 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.083333 redundancy: 0.916667 Efficiency x scale size : 1.000000 Number of different interval sizes : 11 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0000 c. M: 0.0000 c. Twelve-tone Chromatic (1/11-comma)
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 581.9700 cents 2 x x x x x x x x x x x 3 S SD: 83.9250 cents 3 x x x x x x x x x 4 x x S SD: 16.9800 cents 4 x x x x x x x 5 x x x 6 S SD: 43.8868 cents 5 x x x x x 6 x x x x 7 x S SD: 8.6519 cents 6 x x x x 7 x x x x 8 x 9 S SD: 28.7118 cents 7 x x x 8 x x x 9 x x x 10 S SD: 11.3797 cents 8 x x x 9 x x x 10 x x 11 x S SD: 9.9808 cents 9 x x x 10 x x 11 x x 12 x 13 S SD: 9.2295 cents 10 x x 11 x x 12 x x 13 x 14 x S SD: 5.5692 cents 11 x x 12 x x 13 x 14 x 15 x 16 S SD: 8.6201 cents 12 x x 13 x 14 x x 15 x 16 x 17 S SD: 7.7885 cents 13 x 14 x x 15 x 16 x 17 x 18:19 S SD: 7.9312 cents 14 x 15 x 16 x x 17:18 x 19 x 20 S SD: 7.8477 cents 15 x 16 x 17 x 18 x 19 x 20:21 x S SD: 4.6714 cents 16 x 17 x 18 x 19 x 20:21 x 22:23 S SD: 4.9286 cents 17 x 18 x 19:20 x 21 x 22:23 x 24 S SD: 5.7138 cents 18 x 19 x 20:21 x 22:23 x 24:25:26 S SD: 5.1480 cents 19 x 20:21 x 22:23 x 24:25 x 26:27 S SD: 5.4180 cents 20 x 21:22 x 23:24 x 25:26:27:28:29 S SD: 5.4431 cents 21 x 22:23:24 x 25:26:27 x 28:29:30 S SD: 5.1686 cents 22:23 x 24:25 x 26:27:28:29:30 x 31 S SD: 5.7133 cents 23:24 x 25:26:27 x 28:29:30:31:32:33 S SD: 4.0517 cents 24:25 x 26:27:28:29 x 30:31:32:33:34 S SD: 5.3701 cents 25:26 x 27:28:29:30:31:32:33:34:35:36 S SD: 4.3243 cents 26:27:28 x 29:30:31:32:33:34:35:36:37 S SD: 3.2767 cents 27:28:29 x 30:31:32:33:34:35:36:37:39 SD: 5.2176 cents 28:29:30:31:32 x 33:34:36:37:38:39:40 S SD: 5.5958 cents 29:30:31:32:33:34:35:36:37:38:39:40:41 H SD: 3.8328 cents 30:31:32:33:34:35:36:37:38:39:40:42:43 S SD: 2.8031 cents 31:32:33:34:35:36:37:38:39:41:42:43:44 SD: 2.6938 cents 46:47:49:50:52:53:55:57:58:60:62:64:66 SD: 2.4398 cents 49:50:52:54:55:57:59:60:62:64:66:68:70 SD: 2.3488 cents 51:53:54:56:57:59:61:63:65:67:69:71:73 SD: 2.3483 cents 52:54:55:57:59:60:62:64:66:68:70:72:74 SD: 2.0170 cents 55:57:58:60:62:64:66:68:70:72:74:76:79 SD: 1.9043 cents 56:58:59:61:63:65:67:69:71:73:75:78:80 SD: 1.7758 cents 61:63:65:67:69:71:73:75:77:80:82:85:87 SD: 1.7001 cents 62:64:66:68:70:72:74:76:79:81:83:86:89 SD: 1.6182 cents 63:65:67:69:71:73:75:78:80:82:85:87:90 SD: 1.4398 cents 77:79:82:84:87:89:92:95:98:101:104:107:110 SD: 1.4267 cents 78:80:83:85:88:91:93:96:99:102:105:108:111 SD: 1.4259 cents 81:83:86:89:91:94:97:100:103:106:109:112:116 SD: 1.3776 cents 82:84:87:90:92:95:98:101:104:107:110:114:117 SD: 1.3600 cents 86:89:91:94:97:100:103:106:109:112:116:119:123 SD: 1.1525 cents 94:97:100:103:106:109:112:116:119:123:127:130:134 SD: 1.1414 cents 95:98:101:104:107:110:114:117:121:124:128:132:136 SD: 1.0134 cents 96:99:102:105:108:111:115:118:122:125:129:133:137 SD: 1.0117 cents 98:101:104:107:110:114:117:121:124:128:132:136:140 SD: 0.8748 cents 126:130:134:138:142:146:151:155:160:165:170:175:180 SD: 0.7847 cents 127:131:135:139:143:147:152:156:161:166:171:176:181 SD: 0.7674 cents 130:134:138:142:146:151:155:160:165:170:175:180:186 SD: 0.6959 cents 142:146:151:155:160:165:170:175:180:186:191:197:203 SD: 0.6747 cents 150:155:159:164:169:174:179:185:190:196:202:208:214 SD: 0.6712 cents 159:164:169:174:179:185:190:196:202:208:214:221:227 SD: 0.6613 cents 160:165:170:175:180:186:191:197:203:209:215:222:229 SD: 0.5806 cents 163:168:173:178:184:189:195:201:207:213:219:226:233 SD: 0.5648 cents 168:173:178:184:189:195:201:207:213:220:226:233:240 SD: 0.5323 cents 193:199:205:211:217:224:231:238:245:252:260:268:276 SD: 0.4831 cents 199:205:211:218:224:231:238:245:252:260:268:276:284 SD: 0.4776 cents 205:211:218:224:231:238:245:252:260:268:276:284:293 SD: 0.4737 cents 212:218:225:232:239:246:253:261:269:277:285:294:303 SD: 0.4709 cents 224:231:238:245:252:260:268:276:284:293:302:311:320 SD: 0.4238 cents 245:252:260:268:276:284:293:302:311:320:330:340:350 SD: 0.3538 cents 261:269:277:285:294:303:312:321:331:341:351:362:373 SD: 0.3419 cents 268:276:284:293:302:311:320:330:340:350:361:372:383 SD: 0.3292 cents 294:303:312:321:331:341:351:362:373:384:396:408:420 SD: 0.3246 cents 312:321:331:341:351:362:373:384:396:408:420:433:446 SD: 0.3132 cents 323:333:343:353:364:375:386:398:410:422:435:448:462 SD: 0.2633 cents 362:373:384:396:408:420:433:446:459:473:487:502:517 SD: 0.2551 cents 364:375:386:398:410:422:435:448:462:476:490:505:520 SD: 0.2305 cents 398:410:422:435:448:462:476:490:505:520:536:552:569 SD: 0.2182 cents 410:422:435:448:462:476:490:505:520:536:552:569:586 SD: 0.2156 cents 424:437:450:464:478:492:507:522:538:554:571:588:606 SD: 0.2140 cents 436:449:463:477:491:506:521:537:553:570:587:605:623 SD: 0.1692 cents 491:506:521:537:553:570:587:605:623:642:661:681:702 SD: 0.1600 cents 506:521:537:553:570:587:605:623:642:661:681:702:723 SD: 0.1562 cents 522:538:554:571:588:606:624:643:662:682:703:724:746 SD: 0.1482 cents 569:586:604:622:641:660:680:701:722:744:766:789:813 SD: 0.1404 cents 592:610:628:647:667:687:708:729:751:774:797:821:846 SD: 0.1368 cents