Diamond tradeoff: Difference between revisions
ArrowHead294 (talk | contribs) m Writing \frac without brackets in LaTeX is bad practice. |
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Reading the columns from <math>G</math>, the first one {{vector|1 0 0}} confirms our period of 2/1, and the second column {{vector|-1 1 0}} gives our generator 3/2. Which is unsurprising. In cents, that's {{nowrap|1200 | Reading the columns from <math>G</math>, the first one {{vector|1 0 0}} confirms our period of 2/1, and the second column {{vector|-1 1 0}} gives our generator 3/2. Which is unsurprising. In cents, that's {{nowrap|1200 × log<sub>2</sub>(3/2) ≈ 701.955{{cent}}}}. The next unchanged interval will give a more interesting result. | ||
==== Second diamond extrema ==== | ==== Second diamond extrema ==== | ||
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This tells us our generator is <math>\monzo{0 & 0 & \frac{1}{4}}</math>, or 5<sup>{{frac|1|4}}</sup>. In cents, that's {{nowrap|1200 | This tells us our generator is <math>\monzo{0 & 0 & \frac{1}{4}}</math>, or 5<sup>{{frac|1|4}}</sup>. In cents, that's {{nowrap|1200 × log<sub>2</sub>(5<sup>{{frac|1|4}}</sup>) ≈ 696.578{{c}}}}. | ||
==== Third diamond extrema ==== | ==== Third diamond extrema ==== | ||
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This tells us our generator is <math>\monzo{\frac{1}{3} & -\frac{1}{3} & \frac{1}{3}}</math>, or expressed another way, ({{frac|10|3}})<sup>{{frac|1|3}}</sup>. In cents, that's {{nowrap|1200 | This tells us our generator is <math>\monzo{\frac{1}{3} & -\frac{1}{3} & \frac{1}{3}}</math>, or expressed another way, ({{frac|10|3}})<sup>{{frac|1|3}}</sup>. In cents, that's {{nowrap|1200 × log<sub>2</sub>(({{frac|10|3}})<sup>{{frac|1|3}}</sup>) ≈ 694.786{{c}}}}. | ||
==== Determining the final range ==== | ==== Determining the final range ==== | ||