Scala analysis: 12throotofphi_tuning_97758_97761
12th root of phi tuning (Chris Vaisvil's idea)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 69.424 cents 69.424190 2: 138.848 cents 138.848380 3: 208.273 cents 208.272570 4: 277.697 cents 277.696770 5: 347.121 cents 347.120960 6: 416.545 cents 416.545150 7: 485.969 cents 485.969340 8: 555.394 cents 555.393530 9: 624.818 cents 624.817720 10: 694.242 cents 694.241910 11: 763.666 cents 763.666100 12: 833.090 cents 833.090300
SHOW/INTERVAL
0: 69.4242 cents 69.4242 1: 69.4242 cents 69.4242 2: 69.4242 cents 69.4242 3: 69.4242 cents 69.4242 4: 69.4242 cents 69.4242 5: 69.4242 cents 69.4242 6: 69.4242 cents 69.4242 7: 69.4242 cents 69.4242 8: 69.4242 cents 69.4242 9: 69.4242 cents 69.4242 10: 69.4242 cents 69.4242 11: 69.4242 cents 69.4242 12: 69.4242 cents 69.4242
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 69.42419 cents 2: 12 138.84838 cents 3: 12 208.27257 cents 4: 12 277.69677 cents 5: 12 347.12096 cents 6: 12 416.54515 cents 7: 12 485.96934 cents 8: 12 555.39353 cents 9: 12 624.81772 cents 10: 12 694.24191 cents 11: 12 763.66610 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 : 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 69.4 : 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 138.8: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 208.3: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 277.7: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 347.1: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 416.5: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 486.0: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 555.4: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 624.8: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 694.2: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 763.7: 69.4 138.8 208.3 277.7 347.1 416.5 486.0 555.4 624.8 694.2 763.7 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 69.4242 .. 69.4242 cents 1/1, 0.0000 cents 69.42419 cents 2: 138.8484 .. 138.8484 cents 1/1, 0.0000 cents 69.42419 cents 3: 208.2726 .. 208.2726 cents 1/1, 0.0000 cents 69.42419 cents 4: 277.6968 .. 277.6968 cents 1/1, 0.0000 cents 69.42420 cents 5: 347.1210 .. 347.1210 cents 1/1, 0.0000 cents 69.42419 cents 6: 416.5452 .. 416.5452 cents 1/1, 0.0000 cents 69.42419 cents 7: 485.9693 .. 485.9693 cents 1/1, 0.0000 cents 69.42419 cents 8: 555.3935 .. 555.3935 cents 1/1, 0.0000 cents 69.42419 cents 9: 624.8177 .. 624.8177 cents 1/1, 0.0000 cents 69.42419 cents 10: 694.2419 .. 694.2419 cents 1/1, 0.0000 cents 69.42419 cents 11: 763.6661 .. 763.6661 cents 1/1, 0.0000 cents 69.42419 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 69.42419 cents, class 1 Average step (divided formal octave): 69.4242 cents Largest one step interval : 69.42419 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 69.42419 cents, amount: 12 Most common interval of one step : 69.42419 cents, amount: 12 Least squares average step : 69.42419 cents, oct.: 833.09030 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 69.42419 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 : 12, average 694.2419 cents Number of recognisable fourths : 12, average 485.9693 cents Best minor thirds form a closed circle 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: 366.9097 cents 2 x x x x x x x x x 3 x x S SD: 7.7131 cents 3 x x x x x x 4 x x x x 5 S SD: 26.3357 cents 4 x x x x x 5 x x x 6 x x S SD: 15.5999 cents 5 x x x x 6 x x 7 x x x 8 S SD: 15.2858 cents 6 x x x 7 x x 8 x x 9 x 10 S SD: 13.5807 cents 7 x x 8 x x 9 x x 10 x 11 x S SD: 8.9314 cents 8 x x 9 x x 10 x 11 x 12 x 13 S SD: 6.5250 cents 9 x x 10 x 11 x 12 x 13 x 14:15 S SD: 9.9782 cents 10 x 11 x x 12 x 13:14 x 15 x 16 S SD: 10.3480 cents 11 x 12 x 13 x 14 x 15:16 x 17:18 S SD: 5.8257 cents 12 x 13 x 14 x 15:16 x 17:18:19 x S SD: 7.4637 cents 13 x 14 x 15:16 x 17:18:19 x 20:21 S SD: 6.9051 cents 14 x 15:16 x 17:18 x 19:20:21:22:23 S SD: 6.3257 cents 15 x 16:17 x 18:19:20:21 x 22:23:24 S SD: 7.5694 cents 16 x 17:18:19 x 20:21:22:23:24:25:26 S SD: 5.4118 cents 17:18 x 19:20:21:22 x 23:24:25:26:28 S SD: 8.1343 cents 18:19 x 20:21:22:23:24:25:26:27:28:29 S SD: 4.0767 cents 19:20:21 x 22:23:24:25:26:27:28:30:31 S SD: 6.1356 cents 20:21:22:23 x 24:25:26:28:29:30:31:32 S SD: 7.3264 cents 21:22:23:24:25:26:27:28:29:30:31:33:34 SD: 4.8596 cents 22:23:24:25:26:27:28:29:30:32:33:34:36 S SD: 3.7857 cents 23:24:25:26:27:28:29:30:32:33:34:36:37 S SD: 3.5681 cents 32:33:35:36:38:39:41:42:44:46:48:50:52 SD: 3.3025 cents 34:35:37:38:40:42:43:45:47:49:51:53:55 SD: 3.0157 cents 37:39:40:42:43:45:47:49:51:53:55:58:60 SD: 2.9922 cents 39:41:42:44:46:48:50:52:54:56:58:61:63 SD: 2.8811 cents 40:42:43:45:47:49:51:53:55:57:60:62:65 SD: 2.2993 cents 45:47:49:51:53:55:57:60:62:65:67:70:73 SD: 2.0360 cents 47:49:51:53:55:57:60:62:65:67:70:73:76 SD: 1.8245 cents 58:60:63:65:68:71:74:77:80:83:87:90:94 SD: 1.6978 cents 63:66:68:71:74:77:80:83:87:90:94:98:102 SD: 1.5001 cents 69:72:75:78:81:84:88:91:95:99:103:107:112 SD: 1.2529 cents 71:74:77:80:83:87:90:94:98:102:106:110:115 SD: 1.0905 cents 92:96:100:104:108:112:117:122:127:132:137:143:149 SD: 1.0160 cents 95:99:103:107:112:116:121:126:131:136:142:148:154 SD: 0.9201 cents 99:103:107:112:116:121:126:131:136:142:148:154:160 SD: 0.8434 cents 108:112:117:122:127:132:137:143:149:155:161:168:175 SD: 0.8365 cents 117:122:127:132:137:143:149:155:161:168:175:182:189 SD: 0.7053 cents 143:149:155:161:168:175:182:189:197:205:214:222:231 SD: 0.6435 cents 148:154:160:167:174:181:188:196:204:212:221:230:239 SD: 0.5818 cents 154:160:167:174:181:188:196:204:212:221:230:239:249 SD: 0.5565 cents 166:173:180:187:195:203:211:220:229:238:248:258:269 SD: 0.4438 cents 195:203:211:220:229:238:248:258:269:280:291:303:316 SD: 0.4252 cents 217:226:235:245:255:265:276:287:299:311:324:337:351 SD: 0.3650 cents 225:234:244:254:264:275:286:298:310:323:336:350:364 SD: 0.3023 cents 265:276:287:299:311:324:337:351:365:380:396:412:429 SD: 0.2344 cents 346:360:375:390:406:423:440:458:477:496:517:538:560 SD: 0.2233 cents 361:376:391:407:424:441:459:478:498:518:539:561:584 SD: 0.2121 cents 442:460:479:499:519:540:562:585:609:634:660:687:715 SD: 0.1869 cents 460:479:498:519:540:562:585:609:634:660:687:715:744 SD: 0.1623 cents 518:539:561:584:608:633:659:686:714:743:774:805:838 SD: 0.1484 cents 540:562:585:609:634:660:687:715:744:775:806:839:874 SD: 0.1392 cents 563:586:610:635:661:688:716:745:776:808:841:875:911 SD: 0.1191 cents