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07-04-ACA-Tonal-TuningFreq.tex
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07-04-ACA-Tonal-TuningFreq.tex
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% move all configuration stuff into includes file so we can focus on the content
\input{include}
\subtitle{module 7.4: tuning frequency estimation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
% generate title page
\input{include/titlepage}
\section[overview]{lecture overview}
\begin{frame}{introduction}{overview}
\begin{block}{corresponding textbook section}
%\href{http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6331119&}{Chapter 2~---~Fundamentals}: pp.~14--18\\
%\href{http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6331114}{Appendix A~---~Convolution Properties}: pp.~181--183
section~7.4
\end{block}
\begin{itemize}
\item \textbf{lecture content}
\begin{itemize}
\item definition of the tuning frequency
\item approaches to tuning frequency estimation
\end{itemize}
\bigskip
\item<2-> \textbf{learning objectives}
\begin{itemize}
\item explain the term tuning frequency
\item discuss the necessity of automatic tuning frequency estimation
\item compare different approaches to tuning frequency estimation
\end{itemize}
\end{itemize}
\inserticon{directions}
\end{frame}
\section[intro]{intro}
\begin{frame}{tuning frequency}{introduction}
\begin{block}{tuning frequency}
frequency of the concert pitch A4
\end{block}
\bigskip
\begin{itemize}
\item used to tune groups of instruments
\item standardized as \unit[440]{Hz}\footfullcite{16:1975_acoustics_1975}
\end{itemize}
\end{frame}
\begin{frame}{tuning frequency}{distribution}
\vspace{-5mm}
\begin{columns}
\column{.4\linewidth}
\vspace{4mm}
\begin{itemize}
\item historic tuning frequencies
\bigskip
\bigskip
\bigskip
\bigskip
\item<2-> tuning frequencies today
\begin{itemize}
\item electronic music: often exactly \unit[440]{Hz}
\item 'classical' music:
\begin{itemize}
\item CSO, NYP: \unit[442]{Hz}
\item BPO, VPO: \unit[443]{Hz}
\end{itemize}
\end{itemize}
\end{itemize}
\column{.6\linewidth}
\begin{footnotesize}
\begin{table}
\begin{tabular}{lcc} %{c|p{12mm}p{12mm}p{12mm}p{12mm}p{12mm}p{12mm}p{12mm}}
\\ \hline
\bf{\emph{Year}} & \bf{\emph{Lower Deviation}} & \bf{\emph{Upper Deviation}}\\
\hline
\bf{1750} & $-\unit[50]{Hz}$ & $+\unit[30]{Hz}$\\
\bf{1850} & $-\unit[20]{Hz}$ & $+\unit[20]{Hz}$\\
\bf{1950} & $-\unit[5]{Hz}$ & $+\unit[10]{Hz}$\\
\end{tabular}
\end{table}
\end{footnotesize}
\only<2->{
\figwithmatlab{TuningFreqs}
}
\end{columns}
\phantom{\footfullcite{lerch_requirement_2006}}
\end{frame}
\begin{frame}{tuning frequency estimation}{quick example --- noticeable difference?}
\includeaudio{sine443}
\includeaudio{sine440}
\bigskip
\bigskip
\question{which one is higher?}
\begin{itemize}
\item example 1: \unit[443]{Hz}
\item example 2: \unit[440]{Hz}
\end{itemize}
\end{frame}
\section{task}
\begin{frame}{tuning frequency estimation}{requirement}
\begin{itemize}
\item any pitch-based analysis system relies on tuning frequency (pre-defined or adaptive), recall \[ \mathfrak{p}(f)= 69 + 12\cdot\log_2\left(\frac{f}{\textcolor{highlight}{f_{A4}}}\right)\]
\item tuning frequency can be far from \unit[440]{Hz}
\bigskip
\item<2->[$\Rightarrow$] wrong tuning frequency assumption can significantly impact pitch detection reliability
\end{itemize}
\end{frame}
\begin{frame}{tuning frequency estimation}{assumptions and limits}
\begin{enumerate}
\item \textbf{key is unknown}, i.e., deviation $>\unit[50]{Cent}$ will be mapped back to semitone range
\smallskip
\item<2-> \textbf{temperament/intonation is unknown}, i.e., equally tempered tuning has to be assumed
\smallskip
\item<3-> piece may be \textbf{polyphonic}
\smallskip
\item<4-> piece may \textbf{not contain pitch A4}
\smallskip
\item<5-> \textbf{tuning frequency does not change} or changes slowly over time
\end{enumerate}
\end{frame}
\begin{frame}{tuning frequency estimation}{typical processing steps}
\begin{enumerate}
\item \textbf{estimate fundamental frequencies} or frequencies of tonal components
\smallskip
\item<2-> \textbf{calculate deviation} $\Delta C$ from the nearest equally tempered pitch frequency
\smallskip
\item<3-> \textbf{average all deviations}: $\mu_{\Delta C}$ (or look at histogram)
\smallskip
\item<4-> \textbf{estimate the tuning frequency} from the average deviation:
\[ \hat{f}_\mathrm{A4} = \unit[440]{Hz}\cdot 2^\frac{\mu_{\Delta C}}{1200}\]
\end{enumerate}
\end{frame}
\begin{frame}{tuning frequency estimation}{adaption example}
\vspace{-3mm}
\only<1>{\figwithmatlab{FA4Rprop}}
\only<2>{\includeanimation{FA4FilterBank}{01}{75}{10}}
\end{frame}
\section{summary}
\begin{frame}{summary}{lecture content}
\begin{itemize}
\item \textbf{tuning frequency}
\begin{itemize}
\item important reference for all pitch-based algorithms
\item usually around \unit[440]{Hz}
\end{itemize}
\bigskip
\item \textbf{tuning frequency estimation}
\begin{itemize}
\item assume equally tempered recording without intonation changes
\item map deviations to new estimate
\end{itemize}
\bigskip
\item \textbf{potential issues}
\begin{itemize}
\item frequencies of harmonics distort estimate
\item temperament and tuning break assumptions
\item insufficient reliable real-world ground truth data
\end{itemize}
\end{itemize}
\inserticon{summary}
\end{frame}
\end{document}