Metallic MOS: Difference between revisions
Cmloegcmluin (talk | contribs) |
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To compute the <span><math>L{:}s</math></span> sequence, we depleted terms of the generator’s continued fraction. By doing the opposite — gradually building up the generator’s continued fraction by incrementing terms — we can determine the path our generator takes through the Stern-Brocot tree. | To compute the <span><math>L{:}s</math></span> sequence, we depleted terms of the generator’s continued fraction. By doing the opposite — gradually building up the generator’s continued fraction by incrementing terms — we can determine the path our generator takes through the Stern-Brocot tree. | ||
We’ll use the example of the golden generator, with continued fraction [0; 2, 1] : | We’ll use the example of the golden generator, with continued fraction <span><math>[0; 2, 1]</math></span>: | ||
<math> | <math> | ||
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</math> | </math> | ||
If we look at the path that the generator ≈ 0.381966 takes through the scale tree — which intervals it crosses between as it goes — we’ll see that they are precisely the intervals bounded by these ratios, in this order. | If we look at the path that the generator <span><math>≈ 0.381966</math></span> takes through the scale tree — which intervals it crosses between as it goes — we’ll see that they are precisely the intervals bounded by these ratios, in this order. | ||
=== Application: finding tree level === | === Application: finding tree level === | ||