Scala analysis: 14_13-12
Temperament with just 14/13 apotome, close to Pepper Noble Fifth
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 128.298 cents 128.298240 2: 208.085 cents 208.085210 3: 287.872 cents 287.872180 4: 416.170 cents 416.170430 5: 495.957 cents 495.957390 6: 624.256 cents 624.255640 7: 704.043 cents 704.042610 8: 832.341 cents 832.340850 9: 912.128 cents 912.127820 10: 991.915 cents 991.914790 11: 1120.213 cents 1120.213030 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 79.7870 cents 79.7870 1: 128.2982 cents 128.2982 2: 79.7870 cents 79.7870 3: 79.7870 cents 79.7870 4: 128.2982 cents 128.2982 5: 79.7870 cents 79.7870 6: 128.2983 cents 128.2983 7: 79.7870 cents 79.7870 8: 128.2982 cents 128.2982 9: 79.7870 cents 79.7870 10: 79.7870 cents 79.7870 11: 128.2982 cents 128.2982 12: 79.7870 cents 79.7870
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 79.78697 cents 1: 5 128.29824 cents 2: 2 159.57394 cents 2: 10 208.08521 cents 3: 9 287.87218 cents 3: 3 336.38346 cents 4: 4 367.65915 cents 4: 8 416.17043 cents 5: 11 495.95739 cents 5: 1 544.46867 cents 6: 6 575.74437 cents 6: 6 624.25564 cents 7: 1 655.53133 cents 7: 11 704.04261 cents 8: 8 783.82958 cents 8: 4 832.34085 cents 9: 3 863.61655 cents 9: 9 912.12782 cents 10: 10 991.91479 cents 10: 2 1040.42606 cents 11: 5 1071.70176 cents 11: 7 1120.21303 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 : 128.3 208.1 287.9 416.2 496.0 624.3 704.0 832.3 912.1 991.9 1120.2 1200.0 128.3 : 79.8 159.6 287.9 367.7 496.0 575.7 704.0 783.8 863.6 991.9 1071.7 1200.0 208.1 : 79.8 208.1 287.9 416.2 496.0 624.3 704.0 783.8 912.1 991.9 1120.2 1200.0 287.9 : 128.3 208.1 336.4 416.2 544.5 624.3 704.0 832.3 912.1 1040.4 1120.2 1200.0 416.2 : 79.8 208.1 287.9 416.2 496.0 575.7 704.0 783.8 912.1 991.9 1071.7 1200.0 496.0 : 128.3 208.1 336.4 416.2 496.0 624.3 704.0 832.3 912.1 991.9 1120.2 1200.0 624.3 : 79.8 208.1 287.9 367.7 496.0 575.7 704.0 783.8 863.6 991.9 1071.7 1200.0 704.0 : 128.3 208.1 287.9 416.2 496.0 624.3 704.0 783.8 912.1 991.9 1120.2 1200.0 832.3 : 79.8 159.6 287.9 367.7 496.0 575.7 655.5 783.8 863.6 991.9 1071.7 1200.0 912.1 : 79.8 208.1 287.9 416.2 496.0 575.7 704.0 783.8 912.1 991.9 1120.2 1200.0 991.9 : 128.3 208.1 336.4 416.2 496.0 624.3 704.0 832.3 912.1 1040.4 1120.2 1200.0 1120.2: 79.8 208.1 287.9 367.7 496.0 575.7 704.0 783.8 912.1 991.9 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 79.7870 .. 128.2982 cents 48.51127 cents 79.78697 cents 2: 159.5739 .. 208.0852 cents 48.51127 cents 31.27570 cents 3: 287.8722 .. 336.3835 cents 48.51128 cents 79.78697 cents 4: 367.6591 .. 416.1704 cents 48.51128 cents 31.27569 cents 5: 495.9574 .. 544.4687 cents 48.51128 cents 79.78696 cents 6: 575.7444 .. 624.2556 cents 48.51127 cents 31.27570 cents 7: 655.5313 .. 704.0426 cents 48.51128 cents 31.27569 cents 8: 783.8296 .. 832.3409 cents 48.51127 cents 79.78697 cents 9: 863.6166 .. 912.1278 cents 48.51127 cents 31.27570 cents 10: 991.9148 .. 1040.4261 cents 48.51127 cents 79.78697 cents 11: 1071.7018 .. 1120.2130 cents 48.51127 cents 31.27570 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 79.78696 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 128.29824 cents Average / Smallest step : 1.253338 Largest / Average step : 1.282982 Largest / Smallest step : 1.608010 Median interval of one step : 79.78697 cents, amount: 7 Most common interval of one step : 79.78697 cents, amount: 7 Least squares average step : 101.13193 cents, oct.: 1213.58316 cents Scale is strictly proper Scale has Myhill's property chromas: 48.51127 cents and 31.27570 cents, ratio: 1.551085 generators: 5 of 495.95739 cents and 7 of 704.04261 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 1113-tone equal temperament with octave 2/1 degrees: 119 193 267 386 460 579 653 772 846 920 1039 1113 generators: 460 and 653 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 31.27569 cents Ratio Whole / Half tone : 2.608011 Scale diversity : 1.217187 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.555313 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 : 31.27569 cents Most common intervals : 495.95739 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 79.787 704.043 cents Most common triad is 0.0 495.957 704.043 cents, amount: 10 Number of recognisable fifths : 11, average 704.0426 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: 17.2305 c. M: 32.3409 c. Twelve-tone Chromatic (1/11-comma) 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 7.8414 c. M:-14.7180 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: 2.5332 c. M: 4.7546 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: 1.3009 c. M:-2.4418 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: 0.1816 c. M: 0.3409 c. Twelve-tone Chromatic (2/21-comma positive) 196: 21 13 13 21 13 21 13 21 13 13 21 13 SP M DE SD: 0.1663 c. M:-0.3122 c. 271: 29 18 18 29 18 29 18 29 18 18 29 18 SP M DE SD: 0.0700 c. M:-0.1315 c. 346: 37 23 23 37 23 37 23 37 23 23 37 23 SP M DE SD: 0.0155 c. M:-0.0291 c. 767: 82 51 51 82 51 82 51 82 51 51 82 51 SP M DE SD: 0.0038 c. M: 0.0071 c. 1113: 119 74 74 119 74 119 74 119 74 74 119 74 SP M DE SD: 0.0022 c. M:-0.0042 c. 1880: 201 125 125 201 125 201 125 201 125 125 201 125 SP M DE SD: 0.0002 c. M: 0.0004 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: 1.0438 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.2825 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.4501 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.8679 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.2066 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.2630 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.3529 cents 9 x 10:11 x 12:13:14 x 15:16:17:18 S SD: 10.6706 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 8.0274 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 8.4631 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.1611 cents 13:14:15 x x 17:19:20:21:22:23:25:26 SD: 7.4467 cents 14:15:16:17:18:19:20:21:23:24:25:27:28 SD: 6.4656 cents 16:17:18:19:20:21:23:24:26:27:28:31:32 SD: 4.8994 cents 21:23:24:25:27:28:30:32:34:36:37:40:42 SD: 4.7270 cents 22:24:25:26:28:29:32:33:36:37:39:42:44 SD: 3.8635 cents 23:25:26:27:29:31:33:35:37:39:41:44:46 SD: 3.4693 cents 26:28:29:31:33:35:37:39:42:44:46:50:52 SD: 3.0603 cents 30:32:34:35:38:40:43:45:49:51:53:57:60 SD: 3.0115 cents 32:34:36:38:41:43:46:48:52:54:57:61:64 SD: 2.9562 cents 34:37:38:40:43:45:49:51:55:58:60:65:68 SD: 2.7963 cents 36:39:41:43:46:48:52:54:58:61:64:69:72 SD: 2.7826 cents 37:40:42:44:47:49:53:56:60:63:66:71:74 SD: 2.4655 cents 39:42:44:46:50:52:56:59:63:66:69:74:78 SD: 1.9025 cents 40:43:45:47:51:53:57:60:65:68:71:76:80 SD: 1.8989 cents 48:52:54:57:61:64:69:72:78:81:85:92:96 SD: 1.6513 cents 54:58:61:64:69:72:77:81:87:91:96:103:108 SD: 1.6374 cents 55:59:62:65:70:73:79:83:89:93:98:105:110 SD: 1.2781 cents 62:67:70:73:79:83:89:93:100:105:110:118:124 SD: 1.2524 cents 66:71:74:78:84:88:95:99:107:112:117:126:132 SD: 1.1359 cents 76:82:86:90:97:101:109:114:123:129:135:145:152 SD: 1.0275 cents 78:84:88:92:99:104:112:117:126:132:138:149:156 SD: 0.6085 cents 118:127:133:139:150:157:169:177:191:200:209:225:236 SD: 0.5925 cents 133:143:150:157:169:177:191:200:215:225:236:254:266 SD: 0.4368 cents 154:166:174:182:196:205:221:231:249:261:273:294:308 SD: 0.4246 cents 195:210:220:230:248:260:280:293:315:330:346:372:390 SD: 0.4192 cents 199:214:224:235:253:265:285:299:322:337:353:380:398 SD: 0.4101 cents 209:225:236:247:266:278:300:314:338:354:371:399:418 SD: 0.3638 cents 221:238:249:261:281:294:317:332:357:374:392:422:442 SD: 0.2964 cents 235:253:265:278:299:313:337:353:380:398:417:449:470 SD: 0.2865 cents 265:285:299:313:337:353:380:398:429:449:470:506:530 SD: 0.2647 cents 283:305:319:334:360:377:406:425:458:479:502:541:566 SD: 0.2524 cents 287:309:324:339:365:382:412:431:464:486:509:548:574 SD: 0.2369 cents 313:337:353:370:398:417:449:470:506:530:555:598:626 SD: 0.1899 cents 353:380:398:417:449:470:506:530:571:598:626:674:706 SD: 0.1375 cents 431:464:486:509:548:574:618:647:697:730:764:823:862 SD: 0.1212 cents 548:590:618:647:697:730:786:823:886:928:972:1047:1096 SD: 0.1006 cents