231 lines
8.5 KiB
HTML
231 lines
8.5 KiB
HTML
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
|
||
|
|
|
||
|
|
<!--Converted with LaTeX2HTML 2002-2-1 (1.71)
|
||
|
|
original version by: Nikos Drakos, CBLU, University of Leeds
|
||
|
|
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
|
||
|
|
* with significant contributions from:
|
||
|
|
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
|
||
|
|
<HTML>
|
||
|
|
<HEAD>
|
||
|
|
<TITLE>Designer spectra</TITLE>
|
||
|
|
<META NAME="description" CONTENT="Designer spectra">
|
||
|
|
<META NAME="keywords" CONTENT="book">
|
||
|
|
<META NAME="resource-type" CONTENT="document">
|
||
|
|
<META NAME="distribution" CONTENT="global">
|
||
|
|
|
||
|
|
<META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1">
|
||
|
|
<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
|
||
|
|
|
||
|
|
<LINK REL="STYLESHEET" HREF="book.css">
|
||
|
|
|
||
|
|
<LINK REL="next" HREF="node104.html">
|
||
|
|
<LINK REL="previous" HREF="node75.html">
|
||
|
|
<LINK REL="up" HREF="book.html">
|
||
|
|
<LINK REL="next" HREF="node90.html">
|
||
|
|
</HEAD>
|
||
|
|
|
||
|
|
<BODY >
|
||
|
|
<!--Navigation Panel-->
|
||
|
|
<A NAME="tex2html1868"
|
||
|
|
HREF="node90.html">
|
||
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/next.png"></A>
|
||
|
|
<A NAME="tex2html1862"
|
||
|
|
HREF="book.html">
|
||
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/up.png"></A>
|
||
|
|
<A NAME="tex2html1856"
|
||
|
|
HREF="node88.html">
|
||
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/prev.png"></A>
|
||
|
|
<A NAME="tex2html1864"
|
||
|
|
HREF="node4.html">
|
||
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/contents.png"></A>
|
||
|
|
<A NAME="tex2html1866"
|
||
|
|
HREF="node201.html">
|
||
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/index.png"></A>
|
||
|
|
<BR>
|
||
|
|
<B> Next:</B> <A NAME="tex2html1869"
|
||
|
|
HREF="node90.html">Carrier/modulator model</A>
|
||
|
|
<B> Up:</B> <A NAME="tex2html1863"
|
||
|
|
HREF="book.html">book</A>
|
||
|
|
<B> Previous:</B> <A NAME="tex2html1857"
|
||
|
|
HREF="node88.html">Exercises</A>
|
||
|
|
<B> <A NAME="tex2html1865"
|
||
|
|
HREF="node4.html">Contents</A></B>
|
||
|
|
<B> <A NAME="tex2html1867"
|
||
|
|
HREF="node201.html">Index</A></B>
|
||
|
|
<BR>
|
||
|
|
<BR>
|
||
|
|
<!--End of Navigation Panel-->
|
||
|
|
|
||
|
|
<H1><A NAME="SECTION001000000000000000000"></A>
|
||
|
|
<A NAME="chapter-paf"></A>
|
||
|
|
<BR>
|
||
|
|
Designer spectra
|
||
|
|
</H1>
|
||
|
|
|
||
|
|
<P>
|
||
|
|
As suggested at the beginning of the previous chapter, a powerful way to
|
||
|
|
synthesize musical sounds is to specify--and then realize--specific
|
||
|
|
trajectories of pitch (or more generally, frequencies of partials), along
|
||
|
|
with trajectories of
|
||
|
|
spectral envelope [<A
|
||
|
|
HREF="node202.html#r-puckette01a">Puc01</A>].
|
||
|
|
The
|
||
|
|
spectral envelope is used to determine the amplitude of the individual
|
||
|
|
partials, as a function of their frequencies, and is thought of as controlling
|
||
|
|
the sound's (possibly time-varying) timbre.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
A simple example of this would be to imitate a plucked
|
||
|
|
string by constructing a sound with harmonically spaced partials in which the spectral
|
||
|
|
envelope starts out rich but then dies away exponentially with higher
|
||
|
|
frequencies decaying faster than lower ones, so that the timbre mellows over
|
||
|
|
time. Spectral-evolution
|
||
|
|
models for various acoustic instruments have been proposed
|
||
|
|
[<A
|
||
|
|
HREF="node202.html#r-grey77">GM77</A>] [<A
|
||
|
|
HREF="node202.html#r-risset69">RM69</A>]
|
||
|
|
. A more complicated example is the
|
||
|
|
spoken or sung voice, in which vowels appear as spectral envelopes, dipthongs
|
||
|
|
and many consonants appear as time variations in the spectral envelopes, and
|
||
|
|
other consonants appear as spectrally shaped noise.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
Spectral envelopes may be obtained from analysis of recorded sounds (developed
|
||
|
|
in Chapter <A HREF="node163.html#chapter-fourier">9</A>) or from purely synthetic criteria.
|
||
|
|
To specify a spectral envelope from scratch for every possible frequency
|
||
|
|
would be tedious, and in most cases you would want to describe them in
|
||
|
|
terms of their salient features. The most popular way of doing this is
|
||
|
|
to specify the size and shape of the spectral envelope's peaks, which are
|
||
|
|
called
|
||
|
|
<A NAME="6795"></A><I>formants</I>. Figure <A HREF="#fig06.01">6.1</A> shows a spectral envelope with two
|
||
|
|
formants. Although the shapes of the two peaks in the spectral envelope
|
||
|
|
are different, they can both be roughly described by giving the coordinates
|
||
|
|
of each apex (which give the formant's
|
||
|
|
<A NAME="6798"></A><I>center frequency</I>
|
||
|
|
and amplitude) and each formant's
|
||
|
|
<A NAME="6800"></A><I>bandwidth</I>. A typical measure of bandwidth would be the width of the
|
||
|
|
peak at a level 3 decibels below its apex.
|
||
|
|
Note that if the peak is at (or near) the <IMG
|
||
|
|
WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
||
|
|
SRC="img11.png"
|
||
|
|
ALT="$f=0$"> axis, we pretend it falls
|
||
|
|
off to the left at the same rate as (in reality) it falls off to the right.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
|
||
|
|
<DIV ALIGN="CENTER"><A NAME="fig06.01"></A><A NAME="6804"></A>
|
||
|
|
<TABLE>
|
||
|
|
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 6.1:</STRONG>
|
||
|
|
A spectral envelope showing the frequencies, amplitudes, and
|
||
|
|
bandwidths of two formants.</CAPTION>
|
||
|
|
<TR><TD><IMG
|
||
|
|
WIDTH="467" HEIGHT="261" BORDER="0"
|
||
|
|
SRC="img551.png"
|
||
|
|
ALT="\begin{figure}\psfig{file=figs/fig06.01.ps}\end{figure}"></TD></TR>
|
||
|
|
</TABLE>
|
||
|
|
</DIV>
|
||
|
|
|
||
|
|
<P>
|
||
|
|
Suppose we wish to generate a harmonic sound with a specified collection of
|
||
|
|
formants. Independently of the fundamental frequency desired, we wish the
|
||
|
|
spectrum to have peaks with prescribed center frequencies, amplitudes, and
|
||
|
|
bandwidths. Returning to the phase modulation spectra shown in Figure
|
||
|
|
<A HREF="node87.html#fig05.16">5.16</A>, we see that, at small indices of modulation at least, the
|
||
|
|
result has a single, well-defined spectral peak. We can imagine adding several
|
||
|
|
of these, all sharing a fundamental (modulating) frequency but with carriers
|
||
|
|
tuned to different harmonics to select the various desired center frequencies,
|
||
|
|
and with indices of modulation chosen to give the desired bandwidths. This was
|
||
|
|
first explored by Chowning [<A
|
||
|
|
HREF="node202.html#r-chowning89">Cho89</A>] who arranged formants generated
|
||
|
|
by phase modulation to synthesize singing voices.
|
||
|
|
In this chapter we'll establish a general framework for building
|
||
|
|
harmonic spectra with desired, possibly time-varying, formants.
|
||
|
|
|
||
|
|
<P>
|
||
|
|
<BR><HR>
|
||
|
|
<!--Table of Child-Links-->
|
||
|
|
<A NAME="CHILD_LINKS"><STRONG>Subsections</STRONG></A>
|
||
|
|
|
||
|
|
<UL>
|
||
|
|
<LI><A NAME="tex2html1870"
|
||
|
|
HREF="node90.html">Carrier/modulator model</A>
|
||
|
|
<LI><A NAME="tex2html1871"
|
||
|
|
HREF="node91.html">Pulse trains</A>
|
||
|
|
<UL>
|
||
|
|
<LI><A NAME="tex2html1872"
|
||
|
|
HREF="node92.html">Pulse trains via waveshaping</A>
|
||
|
|
<LI><A NAME="tex2html1873"
|
||
|
|
HREF="node93.html">Pulse trains via wavetable stretching</A>
|
||
|
|
<LI><A NAME="tex2html1874"
|
||
|
|
HREF="node94.html">Resulting spectra</A>
|
||
|
|
</UL>
|
||
|
|
<BR>
|
||
|
|
<LI><A NAME="tex2html1875"
|
||
|
|
HREF="node95.html">Movable ring modulation</A>
|
||
|
|
<LI><A NAME="tex2html1876"
|
||
|
|
HREF="node96.html">Phase-aligned formant (PAF) generator</A>
|
||
|
|
<LI><A NAME="tex2html1877"
|
||
|
|
HREF="node97.html">Examples</A>
|
||
|
|
<UL>
|
||
|
|
<LI><A NAME="tex2html1878"
|
||
|
|
HREF="node98.html">Wavetable pulse train</A>
|
||
|
|
<LI><A NAME="tex2html1879"
|
||
|
|
HREF="node99.html">Simple formant generator</A>
|
||
|
|
<LI><A NAME="tex2html1880"
|
||
|
|
HREF="node100.html">Two-cosine carrier signal</A>
|
||
|
|
<LI><A NAME="tex2html1881"
|
||
|
|
HREF="node101.html">The PAF generator</A>
|
||
|
|
<LI><A NAME="tex2html1882"
|
||
|
|
HREF="node102.html">Stretched wavetables</A>
|
||
|
|
</UL>
|
||
|
|
<BR>
|
||
|
|
<LI><A NAME="tex2html1883"
|
||
|
|
HREF="node103.html">Exercises</A>
|
||
|
|
</UL>
|
||
|
|
<!--End of Table of Child-Links-->
|
||
|
|
<HR>
|
||
|
|
<!--Navigation Panel-->
|
||
|
|
<A NAME="tex2html1868"
|
||
|
|
HREF="node90.html">
|
||
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/next.png"></A>
|
||
|
|
<A NAME="tex2html1862"
|
||
|
|
HREF="book.html">
|
||
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/up.png"></A>
|
||
|
|
<A NAME="tex2html1856"
|
||
|
|
HREF="node88.html">
|
||
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/prev.png"></A>
|
||
|
|
<A NAME="tex2html1864"
|
||
|
|
HREF="node4.html">
|
||
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/contents.png"></A>
|
||
|
|
<A NAME="tex2html1866"
|
||
|
|
HREF="node201.html">
|
||
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
||
|
|
SRC="file:/usr/local/share/lib/latex2html/icons/index.png"></A>
|
||
|
|
<BR>
|
||
|
|
<B> Next:</B> <A NAME="tex2html1869"
|
||
|
|
HREF="node90.html">Carrier/modulator model</A>
|
||
|
|
<B> Up:</B> <A NAME="tex2html1863"
|
||
|
|
HREF="book.html">book</A>
|
||
|
|
<B> Previous:</B> <A NAME="tex2html1857"
|
||
|
|
HREF="node88.html">Exercises</A>
|
||
|
|
<B> <A NAME="tex2html1865"
|
||
|
|
HREF="node4.html">Contents</A></B>
|
||
|
|
<B> <A NAME="tex2html1867"
|
||
|
|
HREF="node201.html">Index</A></B>
|
||
|
|
<!--End of Navigation Panel-->
|
||
|
|
<ADDRESS>
|
||
|
|
Miller Puckette
|
||
|
|
2006-12-30
|
||
|
|
</ADDRESS>
|
||
|
|
</BODY>
|
||
|
|
</HTML>
|