Scala analysis: kpnobl12
Keenan Pepper's "Noble Fifth" with chromatic/diatonic semitone = Phi (12)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 128.669 cents 128.669246 2: 208.191 cents 208.191213 3: 287.713 cents 287.713180 4: 416.382 cents 416.382426 5: 495.904 cents 495.904393 6: 624.574 cents 624.573639 7: 704.096 cents 704.095607 8: 832.765 cents 832.764852 9: 912.287 cents 912.286820 10: 991.809 cents 991.808787 11: 1120.478 cents 1120.478033 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 79.5220 cents 79.5220 1: 128.6692 cents 128.6692 2: 79.5220 cents 79.5220 3: 79.5220 cents 79.5220 4: 128.6692 cents 128.6692 5: 79.5220 cents 79.5220 6: 128.6692 cents 128.6692 7: 79.5220 cents 79.5220 8: 128.6692 cents 128.6692 9: 79.5220 cents 79.5220 10: 79.5220 cents 79.5220 11: 128.6692 cents 128.6692 12: 79.5220 cents 79.5220
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 79.52197 cents 1: 5 128.66925 cents 2: 2 159.04393 cents 2: 10 208.19121 cents 3: 9 287.71318 cents 3: 3 336.86046 cents 4: 4 367.23515 cents 4: 8 416.38243 cents 5: 11 495.90439 cents 5: 1 545.05167 cents 6: 6 575.42636 cents 6: 6 624.57364 cents 7: 1 654.94833 cents 7: 11 704.09561 cents 8: 8 783.61757 cents 8: 4 832.76485 cents 9: 3 863.13954 cents 9: 9 912.28682 cents 10: 10 991.80879 cents 10: 2 1040.95607 cents 11: 5 1071.33075 cents 11: 7 1120.47803 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 128.7 208.2 287.7 416.4 495.9 624.6 704.1 832.8 912.3 991.8 1120.5 1200.0 128.7 : 79.5 159.0 287.7 367.2 495.9 575.4 704.1 783.6 863.1 991.8 1071.3 1200.0 208.2 : 79.5 208.2 287.7 416.4 495.9 624.6 704.1 783.6 912.3 991.8 1120.5 1200.0 287.7 : 128.7 208.2 336.9 416.4 545.1 624.6 704.1 832.8 912.3 1041.0 1120.5 1200.0 416.4 : 79.5 208.2 287.7 416.4 495.9 575.4 704.1 783.6 912.3 991.8 1071.3 1200.0 495.9 : 128.7 208.2 336.9 416.4 495.9 624.6 704.1 832.8 912.3 991.8 1120.5 1200.0 624.6 : 79.5 208.2 287.7 367.2 495.9 575.4 704.1 783.6 863.1 991.8 1071.3 1200.0 704.1 : 128.7 208.2 287.7 416.4 495.9 624.6 704.1 783.6 912.3 991.8 1120.5 1200.0 832.8 : 79.5 159.0 287.7 367.2 495.9 575.4 654.9 783.6 863.1 991.8 1071.3 1200.0 912.3 : 79.5 208.2 287.7 416.4 495.9 575.4 704.1 783.6 912.3 991.8 1120.5 1200.0 991.8 : 128.7 208.2 336.9 416.4 495.9 624.6 704.1 832.8 912.3 1041.0 1120.5 1200.0 1120.5: 79.5 208.2 287.7 367.2 495.9 575.4 704.1 783.6 912.3 991.8 1071.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 79.5220 .. 128.6692 cents 49.14728 cents 79.52197 cents 2: 159.0439 .. 208.1912 cents 49.14728 cents 30.37469 cents 3: 287.7132 .. 336.8605 cents 49.14728 cents 79.52197 cents 4: 367.2351 .. 416.3824 cents 49.14728 cents 30.37469 cents 5: 495.9044 .. 545.0517 cents 49.14728 cents 79.52197 cents 6: 575.4264 .. 624.5736 cents 49.14728 cents 30.37469 cents 7: 654.9483 .. 704.0956 cents 49.14728 cents 30.37469 cents 8: 783.6176 .. 832.7649 cents 49.14728 cents 79.52197 cents 9: 863.1395 .. 912.2868 cents 49.14728 cents 30.37469 cents 10: 991.8088 .. 1040.9561 cents 49.14728 cents 79.52197 cents 11: 1071.3308 .. 1120.4780 cents 49.14728 cents 30.37469 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 79.52197 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 128.66925 cents Average / Smallest step : 1.257514 Largest / Average step : 1.286692 Largest / Smallest step : 1.618034 Median interval of one step : 79.52197 cents, amount: 7 Most common interval of one step : 79.52197 cents, amount: 7 Least squares average step : 101.14677 cents, oct.: 1213.76124 cents Scale is strictly proper Scale has Myhill's property chromas: 49.14728 cents and 30.37469 cents, ratio: 1.618034 generators: 5 of 495.90439 cents and 7 of 704.09561 cents ET pair of linear temperament : 12&17 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1343-tone equal temperament with octave 2/1 degrees: 144 233 322 466 555 699 788 932 1021 1110 1254 1343 generators: 555 and 788 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : LSSLSLSLSSLS Scale is a Constant Structure, by a margin of 30.37469 cents Ratio Whole / Half tone : 2.618034 Scale diversity : 1.216631 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.549483 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 30.37469 cents Most common intervals : 495.90439 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 79.522 704.096 cents Most common triad is 0.0 495.904 704.096 cents, amount: 10 Number of recognisable fifths : 11, average 704.0956 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.4564 c. M: 32.7649 c. Twelve-tone Chromatic (1/11-comma) 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 7.6155 c. M:-14.2940 c. Twelve-tone Chromatic (2/11-comma positive) 29: 3 2 2 3 2 3 2 3 2 2 3 2 SP M ME SD: 2.7591 c. M: 5.1786 c. Twelve-tone Chromatic (1/14-comma positive) 46: 5 3 3 5 3 5 3 5 3 3 5 3 SP M DE SD: 1.0750 c. M:-2.0178 c. Twelve-tone Chromatic (1/9-comma positive) 75: 8 5 5 8 5 8 5 8 5 5 8 5 SP M DE SD: 0.4075 c. M: 0.7649 c. Twelve-tone Chromatic (2/21-comma positive) 121: 13 8 8 13 8 13 8 13 8 8 13 8 SP M DE SD: 0.1561 c. M:-0.2930 c. Twelve-tone Chromatic (1/10-comma positive), Leapday-12 196: 21 13 13 21 13 21 13 21 13 13 21 13 SP M DE SD: 0.0596 c. M: 0.1118 c. 317: 34 21 21 34 21 34 21 34 21 21 34 21 SP M DE SD: 0.0228 c. M:-0.0427 c. 513: 55 34 34 55 34 55 34 55 34 34 55 34 SP M DE SD: 0.0087 c. M: 0.0163 c. 830: 89 55 55 89 55 89 55 89 55 55 89 55 SP M DE SD: 0.0033 c. M:-0.0062 c. 1343: 144 89 89 144 89 144 89 144 89 89 144 89 SP M DE SD: 0.0013 c. M: 0.0024 c. 2173: 233 144 144 233 144 233 144 233 144 144 233 144 SP M DE SD: 0.0005 c. M:-0.0009 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: 1.0703 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.3367 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.4767 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.9635 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.2250 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.3111 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.3738 cents 9 x 10:11 x 12:13:14 x 15:16:17:18 S SD: 10.6881 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 8.0378 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 8.4382 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1911 cents 13:14:15 x x 17:19:20:21:22:23:25:26 SD: 7.4188 cents 14:15:16:17:18:19:20:21:23:24:25:27:28 SD: 6.4556 cents 16:17:18:19:20:21:23:24:26:27:28:31:32 SD: 4.9040 cents 21:23:24:25:27:28:30:32:34:36:37:40:42 SD: 4.7006 cents 22:24:25:26:28:29:32:33:36:37:39:42:44 SD: 3.8190 cents 23:25:26:27:29:31:33:35:37:39:41:44:46 SD: 3.4670 cents 26:28:29:31:33:35:37:39:42:44:46:50:52 SD: 3.0797 cents 30:32:34:35:38:40:43:45:49:51:53:57:60 SD: 3.0060 cents 32:34:36:38:41:43:46:48:52:54:57:61:64 SD: 2.9728 cents 34:37:38:40:43:45:49:51:55:58:60:65:68 SD: 2.7704 cents 36:39:41:43:46:48:52:54:58:61:64:69:72 SD: 2.7674 cents 37:40:42:44:47:49:53:56:60:63:66:71:74 SD: 2.4483 cents 39:42:44:46:50:52:56:59:63:66:69:74:78 SD: 1.9002 cents 48:52:54:57:61:64:69:72:78:81:85:92:96 SD: 1.6229 cents 55:59:62:65:70:73:79:83:89:93:98:105:110 SD: 1.2907 cents 62:67:70:73:79:83:89:93:100:105:110:118:124 SD: 1.2532 cents 66:71:74:78:84:88:95:99:107:112:117:126:132 SD: 1.1238 cents 76:82:86:90:97:101:109:114:123:129:135:145:152 SD: 1.0105 cents 78:84:88:92:99:104:112:117:126:132:138:149:156 SD: 0.6170 cents 118:127:133:139:150:157:169:177:191:200:209:225:236 SD: 0.6013 cents 133:143:150:157:169:177:191:200:215:225:236:254:266 SD: 0.4586 cents 154:166:174:182:196:205:221:231:249:261:273:294:308 SD: 0.4104 cents 205:221:231:242:261:273:294:308:332:347:364:392:410 SD: 0.3800 cents 209:225:236:247:266:278:300:314:338:354:371:399:418 SD: 0.3635 cents 220:237:248:260:280:293:316:330:356:373:390:420:440 SD: 0.3618 cents 221:238:249:261:281:294:317:332:358:374:392:422:442 SD: 0.3220 cents 233:251:263:275:296:310:334:350:377:395:413:445:466 SD: 0.3153 cents 235:253:265:277:299:313:337:353:380:398:417:449:470 SD: 0.2973 cents 265:285:299:313:337:353:380:398:429:449:470:506:530 SD: 0.2788 cents 283:305:319:334:360:377:406:425:458:479:502:541:566 SD: 0.2173 cents 353:380:398:417:449:470:506:530:571:598:626:674:706 SD: 0.1762 cents 398:429:449:470:506:530:571:598:644:674:706:760:796 SD: 0.1615 cents 437:471:493:516:556:582:627:656:707:740:775:835:874 SD: 0.1450 cents 492:530:555:581:626:655:706:739:796:833:873:940:984 SD: 0.1411 cents 516:556:582:609:656:687:740:775:835:874:915:986:1032 SD: 0.1350 cents 548:590:618:647:697:730:786:823:887:928:972:1047:1096 SD: 0.1263 cents 570:614:643:673:725:759:818:856:922:965:1011:1089:1140 SD: 0.1097 cents