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Example (just perfect fifth): log<sub>2</sub>2</sub>(3/2) × 1200 ≈ 0.584 × 1200 ≈ 701.955 cents. | Example (just perfect fifth): log<sub>2</sub>2</sub>(3/2) × 1200 ≈ 0.584 × 1200 ≈ 701.955 cents. | ||
If your pocket calculator has no | 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: | ||
(frequency ratio) log ÷ 2 log = | <code>(frequency ratio)</code> <code>log</code> <code>÷</code> <code>2</code> <code>log</code> <code>=</code> | ||
This makes use of the property of logarithms that log<sub>2</sub>(''x'') = log<sub>''n''</sub>(''x'') / log<sub>''n''</sub>(2). | |||
For scientific calculators, the order of buttons may be different, and a right parenthesis may be needed. | For scientific calculators, the order of buttons may be different, and a right parenthesis may be needed. | ||
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=== Monzo to cents === | === Monzo to cents === | ||
To find the size ''s'' of a just interval in cents from its [[monzo]] '''m''' = {{monzo| m<sub>1</sub> m<sub>2</sub> m<sub>3</sub> … }}, left-multiply '''m''' by the [[just tuning map]] in cents ''T''<sub>''J''</sub> = {{val| 1200.000 1901.955 2786.314 … }} | To find the size ''s'' of a just interval in cents from its [[monzo]] '''m''' = {{monzo| ''m''<sub>1</sub> ''m''<sub>2</sub> ''m''<sub>3</sub> … }}, left-multiply '''m''' by the [[just tuning map]] in cents ''T''<sub>''J''</sub> = {{val| 1200.000 1901.955 2786.314 … }} | ||
<math>\displaystyle s = T_J \cdot \vec m</math> | <math>\displaystyle s = T_J \cdot \vec m</math> | ||
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[[Category:Elementary math]] | [[Category:Elementary math]] | ||
[[Category:Terms]] | [[Category:Terms]] | ||