Chromatic Music Scale

An octave is a sequence of 12 notes, given by the recurrence relation:

$\begin{eqnarray*} f_{x+1} = f_{x} * \sqrt[12]{2^{x}} \end{eqnarray*}$

with $x:\mathbb{N}\mapsto[0,11]$ and starting from the note $A$ with $f_{0}=440Hz$ .

The following table is an octave table (sequence of pitches) with notes corresponding to frequencies. Each successive frequency is determined by multiplying the previously obtained frequency with $\sqrt[12]{2} \approx 1.05946$ .

Note	Frequency (Hz)
$A$	440.00
$A\sharp$ / $B\flat$	466.16
B	493.88
C	523.25
$C\sharp$ / $D\flat$	554.37
D	587.33
$D\sharp$ / $E\flat$	622.25
E	659.26
F	698.46
$F\sharp$ / $G\flat$	739.99
G	783.99
$G\sharp$ / $A\flat$	830.61

the next frequency $880.00$ corresponds to the note $A$ in the next octave.