Scala analysis: xen15-oconnell-golden-section-9
9-note scale in 25 parts of Golden Section
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.971 cents 99.970836 2: 199.942 cents 199.941671 3: 266.589 cents 266.588895 4: 366.560 cents 366.559730 5: 466.531 cents 466.530566 6: 566.501 cents 566.501402 7: 633.149 cents 633.148625 8: 733.119 cents 733.119461 9: 833.090 cents 833.090296
SHOW/INTERVAL
0: 99.9708 cents 99.9708 1: 99.9708 cents 99.9708 2: 99.9708 cents 99.9708 3: 66.6472 cents 66.6472 4: 99.9708 cents 99.9708 5: 99.9708 cents 99.9708 6: 99.9708 cents 99.9708 7: 66.6472 cents 66.6472 8: 99.9708 cents 99.9708 9: 99.9708 cents 99.9708
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 66.64722 cents 1: 7 99.97084 cents 2: 4 166.61806 cents 2: 5 199.94167 cents 3: 6 266.58890 cents 3: 3 299.91251 cents 4: 8 366.55973 cents 4: 1 399.88334 cents 5: 1 433.20695 cents 5: 8 466.53057 cents 6: 3 533.17779 cents 6: 6 566.50140 cents 7: 5 633.14862 cents 7: 4 666.47224 cents 8: 7 733.11946 cents 8: 2 766.44307 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 0.0 : 100.0 199.9 266.6 366.6 466.5 566.5 633.1 733.1 833.1 100.0: 100.0 166.6 266.6 366.6 466.5 533.2 633.1 733.1 833.1 199.9: 66.6 166.6 266.6 366.6 433.2 533.2 633.1 733.1 833.1 266.6: 100.0 199.9 299.9 366.6 466.5 566.5 666.5 766.4 833.1 366.6: 100.0 199.9 266.6 366.6 466.5 566.5 666.5 733.1 833.1 466.5: 100.0 166.6 266.6 366.6 466.5 566.5 633.1 733.1 833.1 566.5: 66.6 166.6 266.6 366.6 466.5 533.2 633.1 733.1 833.1 633.1: 100.0 199.9 299.9 399.9 466.5 566.5 666.5 766.4 833.1 733.1: 100.0 199.9 299.9 366.6 466.5 566.5 666.5 733.1 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.6472 .. 99.9708 cents 33.32361 cents 66.64722 cents 2: 166.6181 .. 199.9417 cents 33.32361 cents 66.64722 cents 3: 266.5889 .. 299.9125 cents 33.32361 cents 66.64722 cents 4: 366.5597 .. 399.8833 cents 33.32361 cents 66.64722 cents 5: 433.2070 .. 466.5306 cents 33.32361 cents 33.32361 cents 6: 533.1778 .. 566.5014 cents 33.32361 cents 66.64722 cents 7: 633.1486 .. 666.4722 cents 33.32361 cents 66.64722 cents 8: 733.1195 .. 766.4431 cents 33.32361 cents 66.64722 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 66.64722 cents, class 1 Average step (divided formal octave): 92.5656 cents Largest one step interval : 99.97084 cents Average / Smallest step : 1.388889 Largest / Average step : 1.080000 Largest / Smallest step : 1.500000 Median interval of one step : 99.97084 cents, amount: 7 Most common interval of one step : 99.97084 cents, amount: 7 Least squares average step : 92.25379 cents, oct.: 830.28410 cents Scale is strictly proper Scale has Myhill's property chromas: 33.32361 cents and 33.32361 cents, ratio: 1.000000 generators: 4 of 366.55973 cents and 5 of 466.53057 cents Scale is maximally even in 25-tone equal temperament ET pair of linear temperament : 16&25 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 25-tone equal temperament with octave 833.090 cents degrees: 3 6 8 11 14 17 19 22 25 generators: 11 and 14 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAA Step pattern size order : LLSLLLSLL Interval vector is [ 0 2 7 0 4 5 0 6 3 0 8 1 ] Scale is a Constant Structure, by a margin of 33.32361 cents Scale diversity : 1.003885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.680000 Rothenberg efficiency : 0.740741 redundancy: 0.259259 Efficiency x scale size : 6.666667 Number of different interval sizes : 16 = 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 : 33.32361 cents Most common intervals : 366.55973 cents & inv., amount: 8 Scale is a chain of 4 triads 0.0 366.560 733.119 cents Most common triad is 0.0 366.560 466.531 cents, amount: 7 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Formal octave complements present : 9 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.5601 c. M: 14.8105 c. Pelog Nawanada: Sunda 16: 2 2 1 2 2 2 1 2 2 P M ME I SD: 5.3776 c. M:-8.3309 c. Superolympian 25: 3 3 2 3 3 3 2 3 3 SP M ME I SD: 0.0000 c. M: 0.0000 c. Superolympian
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 366.9097 cents 2 x x x x x x x 3 x S SD: 31.1645 cents 3 x x x x 4 x x x 5 S SD: 30.0899 cents 4 x x x 5 x x x 6 x S SD: 18.4489 cents 5 x x 6 x x 7 x x 8 S SD: 18.3757 cents 6 x x 7 x 8 x x 9:10 S SD: 16.9428 cents 7 x 8 x x 9 x 10:11 x S SD: 17.0427 cents 8 x 9 x 10 x 11 x 12:13 S SD: 8.1561 cents 9 x 10 x 11:12 x 13:14:15 S SD: 12.1553 cents 10 x 11:12 x 13:14 x 15:16 S SD: 12.2276 cents 11 x 12:13 x 14:15:16:17:18 S SD: 12.1737 cents 12:13 x 14:15:16 x 17:18:19 S SD: 11.2144 cents 13:14 x 15:16:17:18:19:20:21 S SD: 5.5322 cents 14:15:16 x 17:18:19:20:21:23 SD: 10.1632 cents 15:16:17:18:19:20:21:22:23:24 H SD: 9.4374 cents 16:17:18:19:20:21:22:23:24:26 S SD: 5.7585 cents 23:24:26:27:28:30:32:33:35:37 SD: 4.8638 cents 29:31:33:34:36:38:40:42:44:47 SD: 3.9151 cents 31:33:35:36:38:41:43:45:47:50 SD: 3.6358 cents 32:34:36:37:40:42:44:46:49:52 SD: 3.5337 cents 34:36:38:40:42:45:47:49:52:55 SD: 2.8699 cents 42:44:47:49:52:55:58:61:64:68 SD: 2.8519 cents 46:49:52:54:57:60:64:66:70:74 SD: 2.8513 cents 47:50:53:55:58:62:65:68:72:76 SD: 2.2698 cents 48:51:54:56:59:63:67:69:73:78 SD: 2.2108 cents 49:52:55:57:61:64:68:71:75:79 SD: 2.0552 cents 55:58:62:64:68:72:76:79:84:89 SD: 1.6532 cents 65:69:73:76:80:85:90:94:99:105 SD: 1.3816 cents 68:72:76:79:84:89:94:98:104:110 SD: 1.3488 cents 84:89:94:98:104:110:117:121:128:136 SD: 1.1484 cents 97:103:109:113:120:127:135:140:148:157 SD: 0.9215 cents 114:121:128:133:141:149:158:164:174:184 SD: 0.8302 cents 131:139:147:153:162:172:182:189:200:212 SD: 0.7626 cents 132:140:148:154:163:173:183:190:202:214 SD: 0.7304 cents 139:147:156:162:172:182:193:200:212:225 SD: 0.6699 cents 149:158:167:174:184:195:207:215:228:241 SD: 0.6690 cents 152:161:171:177:188:199:211:219:232:246 SD: 0.6150 cents 165:175:185:192:204:216:229:238:252:267 SD: 0.5836 cents 181:192:203:211:224:237:251:261:276:293 SD: 0.5235 cents 186:197:209:217:230:244:258:268:284:301 SD: 0.4616 cents 204:216:229:238:252:267:283:294:312:330 SD: 0.3235 cents 288:305:323:336:356:377:399:415:440:466 SD: 0.3157 cents 301:319:338:351:372:394:418:434:460:487 SD: 0.2888 cents 317:336:356:370:392:415:440:457:484:513 SD: 0.2592 cents 336:356:377:392:415:440:466:484:513:544 SD: 0.2416 cents 385:408:432:449:476:504:534:555:588:623 SD: 0.1284 cents 589:624:661:687:728:771:817:849:900:953 SD: 0.1156 cents