Metallic MOS: Difference between revisions
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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. | 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. | ||
Perhaps an even better way to approach the problem is to consider the terms of the continued fraction as map directions through the scale tree: each term represents a count of steps one should go in one direction, left or right, before switching directions. We start at <span><math>\frac11</math></span>, going left twice to <span><math>\frac12</math></span> and then to <span><math>\frac13</math></span>. Then we go right once to <span><math>\frac25</math></span>. Then we go left once to <span><math>\frac38</math></span>, and right once to <span><math>\frac{5}{13}</math></span>, and we can continue onwards. | |||
=== Application: finding tree level === | === Application: finding tree level === | ||