Cent: Difference between revisions

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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 ''c'', you have to calculate the [[log2|binary logarithm]] (log<sub>2</sub>) of its [[frequency ratio]], and multiply this by 1200.
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 (c)</math>
<math>\displaystyle s = 1200 \cdot \log_2 (r)</math>


Example (just perfect fifth): log<sub>2</sub>(3/2) × 1200 ≈ 0.584 × 1200 ≈ 701.955 cents.
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: