Scala analysis: gldspec
The golden spectrum
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.271 cents 99.270890 2: 198.542 cents 198.541780 3: 267.639 cents 267.638810 4: 366.910 cents 366.909700 5: 466.181 cents 466.180590 6: 565.451 cents 565.451480 7: 634.549 cents 634.548520 8: 733.819 cents 733.819410 9: 833.090 cents 833.090300 10: 932.361 cents 932.361190 11: 1100.729 cents 1100.729110 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 99.2709 cents 99.2709 1: 99.2709 cents 99.2709 2: 99.2709 cents 99.2709 3: 69.0970 cents 69.0970 4: 99.2709 cents 99.2709 5: 99.2709 cents 99.2709 6: 99.2709 cents 99.2709 7: 69.0970 cents 69.0970 8: 99.2709 cents 99.2709 9: 99.2709 cents 99.2709 10: 99.2709 cents 99.2709 11: 168.3679 cents 168.3679 12: 99.2709 cents 99.2709
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 69.09703 cents 1: 9 99.27089 cents 1: 1 168.36792 cents 2: 4 168.36792 cents 2: 6 198.54178 cents 2: 2 267.63881 cents 3: 6 267.63881 cents 3: 3 297.81267 cents 3: 3 366.90970 cents 4: 8 366.90970 cents 4: 4 466.18059 cents 5: 1 436.00674 cents 5: 6 466.18059 cents 5: 2 535.27763 cents 5: 3 565.45148 cents 6: 2 535.27763 cents 6: 4 565.45148 cents 6: 4 634.54852 cents 6: 2 664.72237 cents 7: 3 634.54852 cents 7: 2 664.72238 cents 7: 6 733.81941 cents 7: 1 763.99326 cents 8: 4 733.81941 cents 8: 8 833.09030 cents 9: 3 833.09030 cents 9: 3 902.18733 cents 9: 6 932.36119 cents 10: 2 932.36119 cents 10: 6 1001.45822 cents 10: 4 1031.63208 cents 11: 1 1031.63208 cents 11: 9 1100.72911 cents 11: 2 1130.90297 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09091 = 34/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 99.3 198.5 267.6 366.9 466.2 565.5 634.5 733.8 833.1 932.4 1100.7 1200.0 99.3 : 99.3 168.4 267.6 366.9 466.2 535.3 634.5 733.8 833.1 1001.5 1100.7 1200.0 198.5 : 69.1 168.4 267.6 366.9 436.0 535.3 634.5 733.8 902.2 1001.5 1100.7 1200.0 267.6 : 99.3 198.5 297.8 366.9 466.2 565.5 664.7 833.1 932.4 1031.6 1130.9 1200.0 366.9 : 99.3 198.5 267.6 366.9 466.2 565.5 733.8 833.1 932.4 1031.6 1100.7 1200.0 466.2 : 99.3 168.4 267.6 366.9 466.2 634.5 733.8 833.1 932.4 1001.5 1100.7 1200.0 565.5 : 69.1 168.4 267.6 366.9 535.3 634.5 733.8 833.1 902.2 1001.5 1100.7 1200.0 634.5 : 99.3 198.5 297.8 466.2 565.5 664.7 764.0 833.1 932.4 1031.6 1130.9 1200.0 733.8 : 99.3 198.5 366.9 466.2 565.5 664.7 733.8 833.1 932.4 1031.6 1100.7 1200.0 833.1 : 99.3 267.6 366.9 466.2 565.5 634.5 733.8 833.1 932.4 1001.5 1100.7 1200.0 932.4 : 168.4 267.6 366.9 466.2 535.3 634.5 733.8 833.1 902.2 1001.5 1100.7 1200.0 1100.7: 99.3 198.5 297.8 366.9 466.2 565.5 664.7 733.8 833.1 932.4 1031.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 69.0970 .. 168.3679 cents 99.27089 cents 69.09703 cents 2: 168.3679 .. 267.6388 cents 99.27089 cents 1/1, 0.0000 cents 3: 267.6388 .. 366.9097 cents 99.27089 cents 1/1, 0.0000 cents 4: 366.9097 .. 466.1806 cents 99.27089 cents 1/1, 0.0000 cents 5: 436.0067 .. 565.4515 cents 129.44474 cents -30.17385 cents 6: 535.2776 .. 664.7224 cents 129.44474 cents -30.17385 cents 7: 634.5485 .. 763.9933 cents 129.44474 cents -30.17385 cents 8: 733.8194 .. 833.0903 cents 99.27089 cents -30.17385 cents 9: 833.0903 .. 932.3612 cents 99.27089 cents 1/1, 0.0000 cents 10: 932.3612 .. 1031.6321 cents 99.27089 cents 1/1, 0.0000 cents 11: 1031.6321 .. 1130.9030 cents 99.27089 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 69.09703 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 168.36792 cents Average / Smallest step : 1.447240 Largest / Average step : 1.683679 Largest / Smallest step : 2.436688 Median interval of one step : 99.27089 cents, amount: 9 Most common interval of one step : 99.27089 cents, amount: 9 Least squares average step : 95.58825 cents, oct.: 1147.05898 cents Scale is not proper Scale is a mode of a 1233-tone equal temperament with octave 2/1 degrees: 102 204 275 377 479 581 652 754 856 958 1131 1233 Least number of segments generator : 617 of 600.487 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 856 of 833.090 cents and inv. generated superset size: 12 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAAACA Step pattern size order : MMSMMMSMMMLM Scale is not a Constant Structure Scale diversity : 1.210227 Lumma stability : 0.115162 Lumma impropriety factor : 0.100580 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 : 3 Highest interval variety : 4 Mean interval variety : 3.09091 = 34/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 30.17385 cents Most common intervals : 366.90970 cents & inv., amount: 11 Scale has Generated (pseudo-Myhill) property, generator: 833.090 cents and inv. Most common triad is 0.0 366.910 833.090 cents, amount: 10 Number of recognisable fifths : 0 Formal octave complements present : 11 = 91.6667% Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 10-11 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 0 1 1 1 2 1 N T3 SD: 27.3287 c. M:-34.5485 c. 13: 1 1 1 1 1 1 1 1 1 1 2 1 P M ME SD: 8.0961 c. M: 13.9264 c. 23: 2 2 1 2 2 2 1 2 2 2 3 2 N G SD: 5.9029 c. M:-10.1539 c. 36: 3 3 2 3 3 3 2 3 3 3 5 3 N G SD: 0.8477 c. M:-1.4582 c. 85: 7 7 5 7 7 7 5 7 7 7 12 7 N G SD: 0.5201 c. M: 0.8947 c. 121: 10 10 7 10 10 10 7 10 10 10 17 10 N G SD: 0.1132 c. M: 0.1947 c. 157: 13 13 9 13 13 13 9 13 13 13 22 13 N G SD: 0.1072 c. M:-0.1843 c. 278: 23 23 16 23 23 23 16 23 23 23 39 23 N G SD: 0.0113 c. M:-0.0194 c. 677: 56 56 39 56 56 56 39 56 56 56 95 56 N G SD: 0.0110 c. M: 0.0189 c. 955: 79 79 55 79 79 79 55 79 79 79 134 79 N G SD: 0.0045 c. M: 0.0077 c. 1233: 102 102 71 102 102 102 71 102 102 102 173 102 N G SD: 0.0009 c. M: 0.0016 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 x 3 x x x 4 S SD: 15.9322 cents 3 x x x x 4 x x x x 5 x 6 S SD: 19.2053 cents 4 x x x 5 x x x 6 x 7 x 8 S SD: 13.0421 cents 5 x x 6 x x 7 x x 8 x 9:10 S SD: 19.8825 cents 6 x x 7 x 8 x x 9 x 10:11:12 S SD: 13.9184 cents 7 x 8 x x 9 x 10:11 x 12:13:14 S SD: 10.6283 cents 8 x 9 x 10 x 11 x 12:13:14:15:16 S SD: 7.0275 cents 9 x 10 x 11:12 x 13:14 x 15:17:18 SD: 8.7783 cents 10 x 11:12 x 13:14 x 15:16:17:19:20 SD: 8.2798 cents 11 x 12:13 x 14:15:16:17:18:19:21:22 SD: 8.6352 cents 12:13 x 14:15:16 x 17:18:19:21:23:24 SD: 9.1329 cents 13:14 x 15:16:17:18:19:20:21:22:25:26 SD: 5.3050 cents 14:15:16 x 17:18:19:20:21:23:24:26:28 SD: 7.9160 cents 15:16:17:18:19:20:21:22:23:24:26:28:30 S SD: 7.4149 cents 16:17:18:19:20:21:22:23:24:26:27:30:32 S SD: 4.9430 cents 18:19:20:21:22:24:25:26:28:29:31:34:36 SD: 4.4118 cents 23:24:26:27:28:30:32:33:35:37:39:43:46 SD: 4.2406 cents 25:26:28:29:31:33:35:36:38:40:43:47:50 SD: 3.9137 cents 29:31:33:34:36:38:40:42:44:47:50:55:58 SD: 3.1787 cents 31:33:35:36:38:41:43:45:47:50:53:59:62 SD: 3.0451 cents 32:34:36:37:40:42:44:46:49:52:55:60:64 SD: 2.9065 cents 34:36:38:40:42:45:47:49:52:55:58:64:68 SD: 2.2245 cents 42:44:47:49:52:55:58:61:64:68:72:79:84 SD: 2.0816 cents 47:50:53:55:58:62:65:68:72:76:81:89:94 SD: 1.9386 cents 49:52:55:57:61:64:68:71:75:79:84:93:98 SD: 1.6626 cents 52:55:58:61:64:68:72:75:79:84:89:98:104 SD: 1.5702 cents 55:58:62:64:68:72:76:79:84:89:94:104:110 SD: 1.3817 cents 65:69:73:76:80:85:90:94:99:105:111:123:130 SD: 1.1662 cents 72:76:81:84:89:94:100:104:110:116:123:136:144 SD: 1.1190 cents 81:86:91:95:100:106:112:117:124:131:139:153:162 SD: 1.0071 cents 83:88:93:97:103:109:115:120:127:134:142:157:166 SD: 0.9863 cents 84:89:94:98:104:110:116:121:128:136:144:159:168 SD: 0.8914 cents 97:103:109:113:120:127:134:140:148:157:166:183:194 SD: 0.8215 cents 101:107:113:118:125:132:140:146:154:163:173:191:202 SD: 0.7587 cents 115:122:129:134:142:151:159:166:176:186:197:217:230 SD: 0.7565 cents 119:126:133:139:147:156:165:172:182:193:204:225:238 SD: 0.7446 cents 131:139:147:153:162:171:182:189:200:212:224:247:262 SD: 0.7216 cents 132:140:148:154:163:173:183:190:202:214:226:249:264 SD: 0.6238 cents 133:141:149:155:164:174:184:192:203:215:228:251:266 SD: 0.6099 cents 149:158:167:174:184:195:207:215:228:241:255:281:298 SD: 0.5386 cents 156:165:175:182:193:204:216:225:238:252:267:295:312 SD: 0.5211 cents 165:175:185:193:204:216:229:238:252:267:283:312:330 SD: 0.4788 cents 174:184:195:203:215:228:241:251:266:282:298:329:348 SD: 0.4452 cents 191:202:214:223:236:250:265:276:292:309:327:361:382 SD: 0.4094 cents 199:211:223:232:246:260:276:287:304:322:341:376:398 SD: 0.4005 cents 204:216:229:238:252:267:283:294:312:330:350:385:408 SD: 0.3614 cents 220:233:247:257:272:288:305:317:336:356:377:415:440 SD: 0.3237 cents 233:247:261:272:288:305:323:336:356:377:399:440:466 SD: 0.2539 cents 288:305:323:336:356:377:399:416:440:466:493:544:576 SD: 0.2520 cents 305:323:342:356:377:399:423:440:466:494:523:576:610 SD: 0.2123 cents 377:399:423:440:466:493:523:544:576:610:646:712:754 SD: 0.2123 cents 388:411:435:453:480:508:538:560:593:628:665:733:776 SD: 0.1827 cents 411:435:461:480:508:538:570:593:628:665:704:776:822 SD: 0.1520 cents 479:507:537:559:592:627:664:691:732:775:821:905:958 SD: 0.1274 cents 492:521:552:574:608:644:682:710:752:796:843:929:984 SD: 0.1186 cents 576:610:646:672:712:754:798:831:880:932:987:1088:1152 SD: 0.1132 cents