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07-01-ACA-Tonal-Perception.tex
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% move all configuration stuff into includes file so we can focus on the content
\input{include}
\subtitle{module 7.1: human perception of pitch}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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?arnumber=6331122}{Chapter 5~---~Tonal Analysis}: pp.~79--82
section~7.1
\end{block}
\begin{itemize}
\item \textbf{lecture content}
\begin{itemize}
\item pitch as perceptual phenomenon
\item non-linear relation of frequency and pitch
\item frequency content of a simple pitched sound
\item dimensions of pitch perception
\end{itemize}
\bigskip
\item<2-> \textbf{learning objectives}
\begin{itemize}
\item describe basic properties of models for pitch
\item explain the two dimensions of pitch perception
\end{itemize}
\end{itemize}
\inserticon{directions}
\end{frame}
\section[intro]{introduction}
\begin{frame}{tonal analysis}{introduction}
\begin{itemize}
\item \textbf{pitch \& pitch-based properties} belong to the most important parameters describing music
\begin{itemize}
\item melody
\item harmony
\item tonality
\item tuning \& intonation
\end{itemize}
\bigskip
\item<2-> \textbf{related ACA tasks}
\begin{itemize}
\item fundamental frequency detection
\item key detection
\item chord detection
\item tuning frequency \& temperament estimation
\end{itemize}
\end{itemize}
\end{frame}
\section[perception]{pitch perception}
\begin{frame}{pitch perception}{pitch definition}
\begin{block}{\textbf{definition (American Standards Association)}}
pitch is that attribute of auditory sensation in terms of which sounds may be ordered on a musical scale\footfullcite{asa_acoustical_1960}
\end{block}
\bigskip
\begin{itemize}
\item<2-> temporal variations in pitch give rise to a sense of melody
\item<2-> closely related to frequency, but \textbf{subjective}
\bigskip
\item<3->[$\Rightarrow$] assigning a pitch value to a sound means \textbf{specifying the frequency of a pure tone having the same subjective pitch} as the sound
\end{itemize}
\end{frame}
\begin{frame}{pitch perception}{fundamental frequency}
\vspace{-2mm}
\figwithmatlab{Harmonics}
\begin{itemize}
\item \textit{fundamental} frequency is relevant for pitch perception ($f_0,2f_0,3f_0,\ldots$)
%\vspace{-3mm}
\item higher fundamental frequency $\Rightarrow$ higher pitch (mono-dimensional)
\end{itemize}
\end{frame}
\begin{frame}{pitch perception}{missing fundamental }
\vspace{-5mm}
\begin{figure}
\includegraphics[scale=.3]{graph/virtualpitchillustration}
\end{figure}
\begin{itemize}
\item basilar membrane location \textbf{does not explain} the pitch perception of complex tones
\bigskip
\item<2->[$\Rightarrow$] \textbf{virtual pitch}, \textbf{residue pitch}
\bigskip
\item<3-> \textbf{example 1}: missing fundamental \only<3->{\includeaudio{zwicker-track-17}}
\begin{itemize}
\item $f_0 = \unit[120]{Hz}$, 33 harmonics, with(out) bandpass \unit[300-2400]{Hz}
\end{itemize}
\item<3-> \textbf{example 2}: missing fundamental \only<3->{\includeaudio{zwicker-track-18}}
\begin{itemize}
\item speech $f_0 \approx \unit[100]{Hz}$, with(out) bandpass \unit[300-4000]{Hz}
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}{pitch perception}{frequency \& pitch}
\figwithmatlab{MelBark}
\only<1>{
\textbf{non-linear} pitch frequency relation:
\begin{itemize}
\item perceptual pitch distance $\neq$ frequency distance
\item[$\Rightarrow$] \textit{models} for psycho-acoustic/physiological data
\begin{itemize}
\item \textit{Mel} scale (equal pitch distance)
\item \textit{Bark} scale (critical band width)
\item physiological frequency location (basilar membrane)
\end{itemize}
\end{itemize}
}
\only<2-3>{
\begin{eqnarray*}
\text{\textbf{Fant}:} & \mathfrak{m}_\mathrm{F}(f) = 1000\cdot \log_{2}\left(1 + \frac{f}{\unit[1000]{Hz}} \right)\\
\text{\textbf{O'Shaughnessy}:} & \mathfrak{m}_\mathrm{S}(f) = 2595\cdot \log_{10}\left(1 + \frac{f}{\unit[700]{Hz}} \right)\\
\pause
& \mathfrak{m}_\mathrm{S}(f) = 1127\cdot \log\left(1 + \frac{f}{\unit[700]{Hz}} \right)
\end{eqnarray*}
}
\only<4>{
\begin{eqnarray*}
\text{\textbf{Schr\"oder}:} & \mathfrak{z}_\mathrm{S}(f) = 7\cdot\arcsinh\left( \frac{f}{\unit[650]{Hz}} \right) \\
\text{\textbf{Terhardt}:} & \mathfrak{z}_\mathrm{T}(f) = 13.3\cdot\arctan\left( 0.75\cdot\frac{f}{\unit[1000]{Hz}} \right) \\
\text{\textbf{Zwicker}:} & \mathfrak{z}_Z(f) = 13\cdot\atan\left( 0.76\cdot\frac{f}{\unit[1000]{Hz}} \right) + 3.5\cdot \atan\left( \frac{f}{\unit[7500]{Hz}} \right)
\end{eqnarray*}
}
\only<5>{
\begin{eqnarray*}
\text{\textbf{ERB}:} & \mathfrak{e}(f) = 9.26 \log \left( 1 + \frac{f}{228.7} \right) \\
\text{\textbf{Cochlear Map}:} & \mathfrak{x}(f) = \frac{1}{2.1} \log_{10}\left( \frac{f}{165.4} + 1 \right)
\end{eqnarray*}
}
\vspace{80mm}
\end{frame}
\begin{frame}{pitch perception}{pitch dimensions}
\textbf{2 dimensions of musical pitch}
\begin{itemize}
\item \textbf{tone height}: monotonic relationship to frequency (increasing frequency $\Rightarrow$ increasing pitch)
\item<2-> \textbf{tone chroma}: two tones separated by octave sound similar (same \textit{pitch class})
\only<2>{\figwithmatlab{PitchHelix}}
\end{itemize}
\end{frame}
\section{summary}
\begin{frame}{summary}{lecture content}
\begin{itemize}
\item \textbf{pitch}
\begin{itemize}
\item \textbf{subjective} phenomenon
\smallskip
\item \textbf{non-linear} monotonic relationship to frequency (tone height increases with fundamental frequency)
\smallskip
\item pitch grouping based on powers of two: tone \textbf{chroma perception}
\end{itemize}
\end{itemize}
\inserticon{summary}
\end{frame}
\end{document}