Scala analysis: Golden_MOS_04
period Phi, generator 4th successive golden section of Phi, Bobro
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63.692 cents 63.691660 2: 149.464 cents 149.463660 3: 213.155 cents 213.155320 4: 298.927 cents 298.927320 5: 362.619 cents 362.618980 6: 448.391 cents 448.390980 7: 512.083 cents 512.082640 8: 597.855 cents 597.854640 9: 661.546 cents 661.546300 10: 747.318 cents 747.318300 11: 833.090 cents 833.090300
SHOW/INTERVAL
0: 85.7720 cents 85.7720 1: 63.6917 cents 63.6917 2: 85.7720 cents 85.7720 3: 63.6917 cents 63.6917 4: 85.7720 cents 85.7720 5: 63.6917 cents 63.6917 6: 85.7720 cents 85.7720 7: 63.6917 cents 63.6917 8: 85.7720 cents 85.7720 9: 63.6917 cents 63.6917 10: 85.7720 cents 85.7720 11: 85.7720 cents 85.7720
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 63.69166 cents 1: 6 85.77200 cents 2: 10 149.46366 cents 2: 1 171.54400 cents 3: 4 213.15532 cents 3: 7 235.23566 cents 4: 9 298.92732 cents 4: 2 321.00766 cents 5: 3 362.61898 cents 5: 8 384.69932 cents 6: 8 448.39098 cents 6: 3 470.47132 cents 7: 2 512.08264 cents 7: 9 534.16298 cents 8: 7 597.85464 cents 8: 4 619.93498 cents 9: 1 661.54630 cents 9: 10 683.62664 cents 10: 6 747.31830 cents 10: 5 769.39864 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 0.0 : 63.7 149.5 213.2 298.9 362.6 448.4 512.1 597.9 661.5 747.3 833.1 63.7 : 85.8 149.5 235.2 298.9 384.7 448.4 534.2 597.9 683.6 769.4 833.1 149.5: 63.7 149.5 213.2 298.9 362.6 448.4 512.1 597.9 683.6 747.3 833.1 213.2: 85.8 149.5 235.2 298.9 384.7 448.4 534.2 619.9 683.6 769.4 833.1 298.9: 63.7 149.5 213.2 298.9 362.6 448.4 534.2 597.9 683.6 747.3 833.1 362.6: 85.8 149.5 235.2 298.9 384.7 470.5 534.2 619.9 683.6 769.4 833.1 448.4: 63.7 149.5 213.2 298.9 384.7 448.4 534.2 597.9 683.6 747.3 833.1 512.1: 85.8 149.5 235.2 321.0 384.7 470.5 534.2 619.9 683.6 769.4 833.1 597.9: 63.7 149.5 235.2 298.9 384.7 448.4 534.2 597.9 683.6 747.3 833.1 661.5: 85.8 171.5 235.2 321.0 384.7 470.5 534.2 619.9 683.6 769.4 833.1 747.3: 85.8 149.5 235.2 298.9 384.7 448.4 534.2 597.9 683.6 747.3 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.6917 .. 85.7720 cents 22.08034 cents 63.69166 cents 2: 149.4637 .. 171.5440 cents 22.08034 cents 63.69166 cents 3: 213.1553 .. 235.2357 cents 22.08034 cents 41.61132 cents 4: 298.9273 .. 321.0077 cents 22.08034 cents 63.69166 cents 5: 362.6190 .. 384.6993 cents 22.08034 cents 41.61132 cents 6: 448.3910 .. 470.4713 cents 22.08034 cents 63.69166 cents 7: 512.0826 .. 534.1630 cents 22.08034 cents 41.61132 cents 8: 597.8546 .. 619.9350 cents 22.08034 cents 63.69166 cents 9: 661.5463 .. 683.6266 cents 22.08034 cents 41.61132 cents 10: 747.3183 .. 769.3986 cents 22.08034 cents 63.69166 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 63.69166 cents, class 1 Average step (divided formal octave): 75.7355 cents Largest one step interval : 85.77200 cents Average / Smallest step : 1.189096 Largest / Average step : 1.132521 Largest / Smallest step : 1.346676 Median interval of one step : 85.77200 cents, amount: 6 Most common interval of one step : 85.77200 cents, amount: 6 Least squares average step : 74.42637 cents, oct.: 818.69008 cents Scale is strictly proper Scale has Myhill's property chromas: 22.08034 cents and 41.61132 cents, ratio: 1.884542 generators: 2 of 149.46366 cents and 683.62664 cents ET pair of linear temperament : 11&28 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 981-tone equal temperament with octave 833.090 cents degrees: 75 176 251 352 427 528 603 704 779 880 981 generators: 176 and 805 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABB Step pattern size order : SLSLSLSLSLL Scale is a Constant Structure, by a margin of 41.61132 cents Scale diversity : 0.941279 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.734959 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 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 : 22.08034 cents Most common intervals : 149.46366 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 149.464 298.927 cents Most common triad is 0.0 149.464 683.627 cents, amount: 9 Number of recognisable fifths : 0 Number of recognisable fourths : 2, average 512.0826 cents Number of appreciable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 9.0909% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions : 9 Inversional symmetry on degrees : 10 Inversional symmetry on intervals : 4-5 -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.8754 c. M:-20.0730 c. 19: 1 2 2 2 1 2 2 2 1 2 2 P M ME S SD: 11.7840 c. M: 19.8448 c. 20: 2 2 1 2 2 2 1 2 2 2 2 P D3 S SD: 11.2792 c. M:-19.6174 c. 21: 2 2 1 3 1 2 2 2 2 2 2 P D3 S SD: 10.8385 c. M:-18.4404 c. 23: 2 2 2 2 2 2 2 3 1 3 2 SP D3 S SD: 9.5454 c. M:-17.9078 c. 24: 2 2 2 3 1 3 2 2 2 3 2 P D3 SD: 9.5577 c. M:-16.3478 c. 25: 2 2 2 3 2 2 2 3 2 2 3 SP M ME S SD: 9.8679 c. M: 16.1692 c. 26: 2 3 2 2 2 3 2 3 2 2 3 SP D3 S SD: 8.5809 c. M:-11.3343 c. 28: 2 3 2 3 2 3 2 3 2 3 3 SP M ME S SD: 4.1267 c. M: 6.9753 c. Machine-11 39: 3 4 3 4 3 4 3 4 3 4 4 SP M ME S SD: 0.3867 c. M:-0.6537 c. Machine-11 184: 14 19 14 19 14 19 14 19 14 19 19 SP M DE S SD: 0.3001 c. M: 0.5073 c. 223: 17 23 17 23 17 23 17 23 17 23 23 SP M DE S SD: 0.1800 c. M: 0.3042 c. 262: 20 27 20 27 20 27 20 27 20 27 27 SP M DE S SD: 0.0956 c. M: 0.1616 c. 301: 23 31 23 31 23 31 23 31 23 31 31 SP M DE S SD: 0.0331 c. M: 0.0560 c. 340: 26 35 26 35 26 35 26 35 26 35 35 SP M DE S SD: 0.0150 c. M:-0.0254 c. 641: 49 66 49 66 49 66 49 66 49 66 66 SP M DE S SD: 0.0076 c. M: 0.0128 c. 981: 75 101 75 101 75 101 75 101 75 101 101 SP M DE S SD: 0.0003 c. M:-0.0004 c.
FIT/HARMONIC
1 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 3 x x S SD: 40.4087 cents 3 x x x x x x 4 x x x 5 S SD: 26.5777 cents 4 x x x x 5 x x x 6 x x S SD: 23.4217 cents 5 x x x 6 x x x 7 x x 8 S SD: 9.9513 cents 6 x x x 7 x x 8 x 9 x 10 S SD: 18.5169 cents 7 x x 8 x x 9 x 10 x 11 x S SD: 11.5228 cents 8 x x 9 x 10 x 11 x 12 x 13 S SD: 12.4491 cents 9 x x 10 x 11 x 12 x 13:14:15 S SD: 11.7067 cents 10 x 11 x 12 x 13 x 14:15 x 16 S SD: 8.8185 cents 11 x 12 x 13 x 14:15 x 16:17:18 S SD: 6.7819 cents 12 x 13 x 14:15 x 16:17:18 x 19 S SD: 10.0739 cents 13 x 14:15 x 16:17 x 18:19:20:21 S SD: 6.9942 cents 14 x 15:16 x 17:18:19:20:21:22:23 S SD: 8.8406 cents 15 x 16:17:18 x 19:20:21:22:23:24 S SD: 7.1256 cents 16:17 x 18:19:20:21:22:23 x 25:26 SD: 8.6163 cents 17:18 x 19:20:21:22:23:24:25:26:28 S SD: 5.6927 cents 18:19 x 20:21:22:23:24:25:26:28:29 S SD: 7.5557 cents 19:20:21 x 23 x 25:26:27:28:29:31 SD: 7.4767 cents 20:21:22:23:24:25:26:27:28:29:31:32 SD: 5.3856 cents 21:22:23:24:25:26:27:28:30:31:32:34 S SD: 4.0473 cents 26:27:28:29:31:32:34:35:37:38:40:42 SD: 3.5624 cents 30:31:33:34:36:37:39:40:42:44:46:49 SD: 3.3637 cents 31:32:34:35:37:38:40:42:44:45:48:50 SD: 2.9464 cents 37:38:40:42:44:46:48:50:52:54:57:60 S SD: 2.8632 cents 43:45:47:49:51:53:56:58:61:63:66:70 SD: 2.4745 cents 44:46:48:50:52:54:57:59:62:64:68:71 SD: 2.3462 cents 47:49:51:53:56:58:61:63:66:69:72:76 SD: 1.8394 cents 52:54:57:59:62:64:67:70:73:76:80:84 SD: 1.8315 cents 53:55:58:60:63:65:69:71:75:78:82:86 SD: 1.8059 cents 54:56:59:61:64:67:70:73:76:79:83:87 SD: 1.7471 cents 55:57:60:62:65:68:71:74:78:81:85:89 SD: 1.7266 cents 68:71:74:77:81:84:88:91:96:100:105:110 SD: 1.5382 cents 75:78:82:85:89:92:97:101:106:110:115:121 SD: 1.4196 cents 76:79:83:86:90:94:98:102:107:111:117:123 SD: 1.3758 cents 78:81:85:88:93:96:101:105:110:114:120:126 SD: 0.9484 cents 99:103:108:112:118:122:128:133:140:145:152:160 SD: 0.9086 cents 107:111:117:121:127:132:139:144:151:157:165:173 SD: 0.7808 cents 131:136:143:148:156:162:170:176:185:192:202:212 SD: 0.7194 cents 133:138:145:150:158:164:172:179:188:195:205:215 SD: 0.6282 cents 155:161:169:175:184:191:201:208:219:227:239:251 SD: 0.5639 cents 159:165:173:180:189:196:206:214:225:233:245:257 SD: 0.5330 cents 180:187:196:204:214:222:233:242:254:264:277:291 SD: 0.5273 cents 185:192:202:209:220:228:240:249:261:271:285:299 SD: 0.5181 cents 189:196:206:214:225:233:245:254:267:277:291:306 SD: 0.3542 cents 244:253:266:276:290:301:316:328:345:358:376:395 SD: 0.3227 cents 267:277:291:302:317:329:346:359:377:391:411:432 SD: 0.2385 cents 322:334:351:364:383:397:417:433:455:472:496:521 SD: 0.2085 cents 398:413:434:450:473:491:516:535:562:583:613:644 SD: 0.1742 cents 456:473:497:516:542:562:591:613:644:668:702:738 SD: 0.1483 cents 511:530:557:578:607:630:662:687:722:749:787:827 SD: 0.1284 cents 589:611:642:666:700:726:763:792:832:863:907:953 SD: 0.0990 cents