Scala analysis: Golden_MOS_03
period Phi, generator third 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: 110.007 cents 110.007340 2: 235.774 cents 235.774410 3: 345.782 cents 345.781750 4: 471.549 cents 471.548820 5: 581.556 cents 581.556160 6: 707.323 cents 707.323230 7: 833.090 cents 833.090300
SHOW/INTERVAL
0: 125.7671 cents 125.7671 1: 110.0073 cents 110.0073 2: 125.7671 cents 125.7671 3: 110.0073 cents 110.0073 4: 125.7671 cents 125.7671 5: 110.0073 cents 110.0073 6: 125.7671 cents 125.7671 7: 125.7671 cents 125.7671
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 110.00734 cents 1: 4 125.76707 cents 2: 6 235.77441 cents 2: 1 251.53414 cents 3: 2 345.78175 cents 3: 5 361.54148 cents 4: 5 471.54882 cents 4: 2 487.30855 cents 5: 1 581.55616 cents 5: 6 597.31589 cents 6: 4 707.32323 cents 6: 3 723.08296 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 0.0 : 110.0 235.8 345.8 471.5 581.6 707.3 833.1 110.0: 125.8 235.8 361.5 471.5 597.3 723.1 833.1 235.8: 110.0 235.8 345.8 471.5 597.3 707.3 833.1 345.8: 125.8 235.8 361.5 487.3 597.3 723.1 833.1 471.5: 110.0 235.8 361.5 471.5 597.3 707.3 833.1 581.6: 125.8 251.5 361.5 487.3 597.3 723.1 833.1 707.3: 125.8 235.8 361.5 471.5 597.3 707.3 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 110.0073 .. 125.7671 cents 15.75973 cents 110.00734 cents 2: 235.7744 .. 251.5341 cents 15.75973 cents 110.00734 cents 3: 345.7818 .. 361.5415 cents 15.75973 cents 94.24761 cents 4: 471.5488 .. 487.3085 cents 15.75973 cents 110.00734 cents 5: 581.5562 .. 597.3159 cents 15.75973 cents 94.24761 cents 6: 707.3232 .. 723.0830 cents 15.75973 cents 110.00734 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 110.00734 cents, class 1 Average step (divided formal octave): 119.0129 cents Largest one step interval : 125.76707 cents Average / Smallest step : 1.081863 Largest / Average step : 1.056752 Largest / Smallest step : 1.143261 Median interval of one step : 125.76707 cents, amount: 4 Most common interval of one step : 125.76707 cents, amount: 4 Least squares average step : 117.77464 cents, oct.: 824.42245 cents Scale is strictly proper Scale has Myhill's property chromas: 15.75973 cents and 94.24761 cents, ratio: 5.980281 generators: 2 of 235.77441 cents and 597.31589 cents ET pair of linear temperament : 46&53 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 2325-tone equal temperament with octave 833.090 cents degrees: 307 658 965 1316 1623 1974 2325 generators: 658 and 1667 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABB Step pattern size order : SLSLSLL Scale is a Constant Structure, by a margin of 94.24761 cents Scale diversity : 1.057779 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.886497 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 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 : 15.75973 cents Most common intervals : 235.77441 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 235.774 471.549 cents Most common triad is 0.0 235.774 597.316 cents, amount: 5 Number of recognisable fifths : 4, average 707.3232 cents Number of recognisable fourths : 2, average 487.3085 cents 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 = 14.2857% 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 transpositions with margin 15.7597 cents: 1 2 3 4 5 6 Limited inverse transpositions : 5 Inversional symmetry on degrees : 6 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 8.1175 c. M:-13.5083 c. Lebeng 27: 4 4 3 4 4 4 4 SP M ME S SD: 7.9876 c. M:-13.4134 c. 31: 4 5 4 5 4 4 5 SP M ME S SD: 7.2907 c. M:-12.1810 c. Neutral Hypophrygian 32: 4 5 4 5 4 5 5 SP M ME S SD: 5.2921 c. M: 8.8066 c. 39: 5 6 5 6 5 6 6 SP M ME S SD: 2.8852 c. M: 4.8013 c. 46: 6 7 6 7 6 7 7 SP M ME S SD: 1.2109 c. M: 2.0151 c. 53: 7 8 7 8 7 8 8 SP M ME S SD: 0.0211 c. M:-0.0352 c. 1371: 181 207 181 207 181 207 207 SP M DE S SD: 0.0202 c. M: 0.0336 c. 1424: 188 215 188 215 188 215 215 SP M DE S SD: 0.0187 c. M: 0.0310 c. 1477: 195 223 195 223 195 223 223 SP M DE S SD: 0.0172 c. M: 0.0287 c. 1530: 202 231 202 231 202 231 231 SP M DE S SD: 0.0159 c. M: 0.0265 c. 1583: 209 239 209 239 209 239 239 SP M DE S SD: 0.0147 c. M: 0.0244 c. 1636: 216 247 216 247 216 247 247 SP M DE S SD: 0.0135 c. M: 0.0225 c. 1689: 223 255 223 255 223 255 255 SP M DE S SD: 0.0124 c. M: 0.0207 c. 1742: 230 263 230 263 230 263 263 SP M DE S SD: 0.0114 c. M: 0.0190 c. 1795: 237 271 237 271 237 271 271 SP M DE S SD: 0.0104 c. M: 0.0174 c. 1848: 244 279 244 279 244 279 279 SP M DE S SD: 0.0095 c. M: 0.0159 c. 1901: 251 287 251 287 251 287 287 SP M DE S SD: 0.0087 c. M: 0.0144 c. 1954: 258 295 258 295 258 295 295 SP M DE S SD: 0.0079 c. M: 0.0131 c. 2007: 265 303 265 303 265 303 303 SP M DE S SD: 0.0071 c. M: 0.0118 c. 2060: 272 311 272 311 272 311 311 SP M DE S SD: 0.0064 c. M: 0.0106 c. 2113: 279 319 279 319 279 319 319 SP M DE S SD: 0.0057 c. M: 0.0095 c. 2166: 286 327 286 327 286 327 327 SP M DE S SD: 0.0050 c. M: 0.0084 c. 2219: 293 335 293 335 293 335 335 SP M DE S SD: 0.0044 c. M: 0.0073 c. 2272: 300 343 300 343 300 343 343 SP M DE S SD: 0.0038 c. M: 0.0063 c. 2325: 307 351 307 351 307 351 351 SP M DE S SD: 0.0032 c. M: 0.0054 c. 2378: 314 359 314 359 314 359 359 SP M DE S SD: 0.0027 c. M: 0.0045 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 366.9097 cents 2 x x x x x 3 x S SD: 5.3682 cents 3 x x x 4 x x 5 S SD: 28.8552 cents 4 x x 5 x x 6 x S SD: 20.4430 cents 5 x x 6 x 7 x 8 S SD: 11.9530 cents 6 x 7 x 8 x 9:10 S SD: 16.4437 cents 7 x 8 x 9:10 x 11 S SD: 18.0314 cents 8 x 9:10 x 11:12:13 S SD: 12.0941 cents 9 x 10:11:12:13:14:15 S SD: 18.6564 cents 10:11 x 12:13:14:15:16 S SD: 11.3527 cents 11:12:13 x 14:15:17:18 SD: 18.2129 cents 12:13:14:15:16:17:18:19 H SD: 11.0889 cents 13:14:15:16:17:18:20:21 S SD: 7.1907 cents 18:19:21:22:24:25:27:29 SD: 6.6846 cents 22:23:25:27:29:31:33:36 SD: 6.3575 cents 26:28:30:32:34:36:39:42 S SD: 4.7014 cents 28:30:32:34:37:39:42:45 SD: 3.3552 cents 32:34:37:39:42:45:48:52 SD: 2.9921 cents 42:45:48:51:55:59:63:68 SD: 2.4831 cents 45:48:52:55:59:63:68:73 SD: 2.4715 cents 48:51:55:59:63:67:72:78 SD: 2.2977 cents 55:59:63:67:72:77:83:89 SD: 2.0452 cents 60:64:69:73:79:84:90:97 SD: 1.6573 cents 63:67:72:77:83:88:95:102 SD: 1.3779 cents 76:81:87:93:100:106:114:123 SD: 1.3515 cents 77:82:88:94:101:108:116:125 SD: 1.2799 cents 90:96:103:110:118:126:135:146 SD: 1.1691 cents 95:101:109:116:125:133:143:154 SD: 0.9615 cents 105:112:120:128:138:147:158:170 SD: 0.8693 cents 123:131:141:150:162:172:185:199 SD: 0.8501 cents 137:146:157:167:180:192:206:222 SD: 0.7219 cents 150:160:172:183:197:210:226:243 SD: 0.5962 cents 185:197:212:226:243:259:278:299 SD: 0.4979 cents 186:198:213:227:244:260:280:301 SD: 0.4867 cents 198:211:227:242:260:277:298:320 SD: 0.3963 cents 226:241:259:276:297:316:340:366 SD: 0.3939 cents 240:256:275:293:315:336:361:388 SD: 0.3797 cents 275:293:315:336:361:385:414:445 SD: 0.2717 cents 303:323:347:370:398:424:456:490 SD: 0.2412 cents 335:357:384:409:440:469:504:542 SD: 0.1795 cents 521:555:597:636:684:729:784:843 SD: 0.1169 cents