Editing Musical note (section)

==== Logarithmic scale ====
[[File:frequency vs name.svg|right|[[Logarithmic plot]] of frequency in [[hertz]] versus pitch of a [[chromatic scale]] starting on [[middle C]]. Each subsequent note has a pitch equal to the frequency of the prior note's pitch multiplied by {{radic|2|12}}.|thumb|228x228px]]The [[base-2 logarithm]] of the above frequency–pitch relation conveniently results in a linear relationship with <math>h</math> or <math>v</math>:
:<math>\begin{align}
\log_{2}(f) &= \tfrac{h}{12} + \log_{2}(\text{440 Hz})\\
&= v + \log_{2}(\text{440 Hz})
\end{align}</math>

When dealing specifically with intervals (rather than absolute frequency), the constant <math>\log_{2}(\text{440 Hz})</math> can be conveniently ignored, because the ''difference'' between any two frequencies <math>f_1</math> and <math>f_2</math> in this logarithmic scale simplifies to:
:<math>\begin{align}
\log_{2}(f_1) - \log_{2}(f_2) &= \tfrac{h_1}{12} - \tfrac{h_2}{12}\\
&= v_1 - v_2 \,.
\end{align}</math>

[[cent (music)|Cents]] are a convenient unit for humans to express finer divisions of this logarithmic scale that are {{fraction|1|100{{sup|th}}}} of an equally-[[Musical temperament|tempered]] semitone. Since one semitone equals 100&nbsp;[[cent (music)|cents]], one octave equals 12&nbsp;⋅&nbsp;100&nbsp;cents&nbsp;=&nbsp;1200&nbsp;cents. Cents correspond to a ''difference'' in this logarithmic scale, however in the regular linear scale of frequency, adding 1 cent corresponds to ''multiplying'' a frequency by {{radic|2|1200}}&nbsp;(≅&nbsp;{{val|1.000578}}).