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== Conversion == | == Conversion == | ||
=== Ratio to cents === | === Ratio to cents === | ||
To find the size ''s'' of an interval in cents from its ratio '' | To find the size ''s'' of an interval in cents from its ratio ''r'', calculate the [[log2|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply it by 1200. | ||
<math>\displaystyle s = 1200\log_2 ( | <math>\displaystyle s = 1200 \cdot \log_2 (r)</math> | ||
For example, the size in cents of a just perfect fifth is 1200⋅log<sub>2</sub>(3/2) ≈ 1200 × 0.584 ≈ 701.955 cents. | |||
If your pocket calculator has no <code>log2</code> key, but does have a <code>log</code> (log<sub>10</sub>) or <code>ln</code> (log<sub>''e''</sub>) key, you can key it this way: | If your pocket calculator has no <code>log2</code> key, but does have a <code>log</code> (log<sub>10</sub>) or <code>ln</code> (log<sub>''e''</sub>) key, you can key it this way: | ||