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* src/en/sections/music-and-technology-synthesis-octave-system.tex: Translate
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artyom-poptsov committed Jan 2, 2025
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Expand Up @@ -86,4 +86,59 @@ \section{Octave system}
Where ``f'' is the frequency of a note from the zero octave, and ``n'' is the
number of octave, starting from zero.

To test our formula let's use the octave number zero and the octave number four
-- the frequencies of notes are shown in the table \ref{table:fourth-octave}
(full list of octaves can be found in \nameref{section:appendixA}.)

\begin{tabular}{p{2cm}|p{3cm}|p{2cm}|p{3cm}}
Octave & Syllable notation & Scientific notation & Frequency (Hz) \\
\hline \hline

\multirow{7}{*}{0}
\musicnote{0}{C}{16.352}
\cline{2-4}
\musicnote{0}{D}{18.354}
\cline{2-4}
\musicnote{0}{E}{20.602}
\cline{2-4}
\musicnote{0}{F}{21.827}
\cline{2-4}
\musicnote{0}{G}{24.500}
\cline{2-4}
\musicnote{0}{A}{27.500}
\cline{2-4}
\musicnote{0}{B}{30.868}
\hline

\multirow{7}{*}{4}
\musicnote{4}{C}{261.630}
\cline{2-4}
\musicnote{4}{D}{293.660}
\cline{2-4}
\musicnote{4}{E}{329.630}
\cline{2-4}
\musicnote{4}{F}{349.230}
\cline{2-4}
\musicnote{4}{G}{392.000}
\cline{2-4}
\musicnote{4}{A}{440.000}
\cline{2-4}
\musicnote{4}{B}{493.880}
\hline
\label{table:fourth-octave}
\end{tabular}

As can be seen in the table, ``C0'' has the frequency 16.352 Hz. If we
substitute this value along with the fourth octave number to the formula
\ref{equation:music-note-frequency-equation} we will get the frequency of ``C4''
as is shown in \ref{equation:music-note-frequency-equation-example}.

\begin{equation}
\mbox{C4} = f * 2^n = \mbox{C0} * 2^4 = 16.352\mbox{Hz} * 2^4 = 261.632\mbox{Hz}
\label{equation:music-note-frequency-equation-example}
\end{equation}

With the new knowledge we can program a simple melody -- and that's what we'll be
doing in the next section.

\end{document}

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