2022-04-12 22:02:59 -03:00
|
|
|
<!DOCTYPE html>
|
2022-04-12 21:54:18 -03:00
|
|
|
|
|
|
|
|
<!--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>
|
2022-04-12 22:02:59 -03:00
|
|
|
|
|
|
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0">
|
|
|
|
|
|
|
|
|
|
|
2022-04-12 21:54:18 -03:00
|
|
|
<TITLE>Automatic read point precession</TITLE>
|
|
|
|
|
<META NAME="description" CONTENT="Automatic read point precession">
|
|
|
|
|
<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="previous" HREF="node37.html">
|
|
|
|
|
<LINK REL="up" HREF="node32.html">
|
|
|
|
|
<LINK REL="next" HREF="node39.html">
|
|
|
|
|
</HEAD>
|
|
|
|
|
|
|
|
|
|
<BODY >
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html1104"
|
|
|
|
|
HREF="node39.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html1098"
|
|
|
|
|
HREF="node32.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html1094"
|
|
|
|
|
HREF="node37.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html1100"
|
|
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html1102"
|
|
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html1105"
|
|
|
|
|
HREF="node39.html">Exercises</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html1099"
|
|
|
|
|
HREF="node32.html">Examples</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html1095"
|
|
|
|
|
HREF="node37.html">Overlapping sample looper</A>
|
|
|
|
|
<B> <A NAME="tex2html1101"
|
|
|
|
|
HREF="node4.html">Contents</A></B>
|
|
|
|
|
<B> <A NAME="tex2html1103"
|
|
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<BR>
|
|
|
|
|
<BR>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
|
|
|
|
|
<H2><A NAME="SECTION00666000000000000000">
|
|
|
|
|
Automatic read point precession</A>
|
|
|
|
|
</H2>
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
Example B11.sampler.rockafella.pd, shown in part (b) of Figure <A HREF="node37.html#fig02.16">2.16</A>, adapts the ideas
|
|
|
|
|
shown above to a situation where the read point is computed automatically.
|
|
|
|
|
Here we precess the read-point through the sample in a loop, permitting us
|
|
|
|
|
to speed up or slow down the playback independently of the transposition.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
This example addresses a weakness of the preceding one, which is that, if the
|
|
|
|
|
relative precession speed is anywhere near one (i.e., the natural speed of
|
|
|
|
|
listening to the recorded wavetable), and if there is not much transposition
|
|
|
|
|
either, it becomes preferable to use larger grains and lower the frequency of
|
|
|
|
|
repetition accordingly (keeping the product constant to achieve the desired
|
|
|
|
|
transposition.) However, if the grain size is allowed to get large, it is no
|
|
|
|
|
longer convenient to quantize control changes at phase wrappings, because
|
|
|
|
|
they might be too far apart to allow for a reasonable response time to control
|
|
|
|
|
changes.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
In this patch we remove the <TT>samphold~</TT> object that had controlled
|
|
|
|
|
the read point (but we leave in the one for chunk size which is much harder
|
|
|
|
|
to change in mid-loop). Instead, we use the (known) rate of precession of the
|
|
|
|
|
read point to correct the sawtooth frequency, so that we maintain the desired
|
|
|
|
|
transposition. It turns out that, when transposition factor and precession
|
|
|
|
|
are close to each other (so that we are nearly doing the same thing as simple
|
|
|
|
|
speed change) the frequency will drop to a value close to zero, so we will
|
|
|
|
|
have increased the naturalness of the result at the same time.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
In this patch we switch from managing read points, chunk sizes, etc., in
|
|
|
|
|
samples and use seconds instead, converting to samples (and shifting by
|
|
|
|
|
one) only just before the <TT>tabread4~</TT> object.
|
|
|
|
|
The wavetable holds one second of sound, and we'll assume here that the
|
|
|
|
|
nominal chunk size will not exceed 0.1 second, so that we can safely let
|
2022-04-12 23:17:03 -03:00
|
|
|
the read point range from 0 to 0.9; the "real" chunk size will vary, and
|
2022-04-12 21:54:18 -03:00
|
|
|
can become quite large, because of the moving read pointer.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
The precession
|
|
|
|
|
control sets the frequency of a phasor of amplitude 0.9, and therefore the
|
|
|
|
|
precession must be multiplied by 0.9 to set the frequency of the phasor (so
|
|
|
|
|
that, for a precession of one for instance, the amplitude and frequency of
|
|
|
|
|
the read point are both 0.9, so that the slope, equal to amplitude over
|
2022-04-12 23:17:03 -03:00
|
|
|
frequency, is one). The output of this is named "read-pt" as before, and
|
2022-04-12 21:54:18 -03:00
|
|
|
is used by both copies of the wavetable reader.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
The precession <IMG
|
|
|
|
|
WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
|
|
|
|
|
SRC="img57.png"
|
|
|
|
|
ALT="$p$"> and the chunk size <IMG
|
|
|
|
|
WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
|
|
|
|
|
SRC="img293.png"
|
|
|
|
|
ALT="$c$"> being known, and if we denote
|
|
|
|
|
the frequency of the upper (original) <TT>phasor~</TT> by <IMG
|
|
|
|
|
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
|
|
|
SRC="img112.png"
|
|
|
|
|
ALT="$f$">, the transposition factor is given by:
|
|
|
|
|
<BR><P></P>
|
|
|
|
|
<DIV ALIGN="CENTER">
|
|
|
|
|
<!-- MATH
|
|
|
|
|
\begin{displaymath}
|
|
|
|
|
t = p + cf
|
|
|
|
|
\end{displaymath}
|
|
|
|
|
-->
|
|
|
|
|
|
|
|
|
|
<IMG
|
|
|
|
|
WIDTH="71" HEIGHT="27" BORDER="0"
|
|
|
|
|
SRC="img294.png"
|
|
|
|
|
ALT="\begin{displaymath}
|
|
|
|
|
t = p + cf
|
|
|
|
|
\end{displaymath}">
|
|
|
|
|
</DIV>
|
|
|
|
|
<BR CLEAR="ALL">
|
|
|
|
|
<P></P>
|
|
|
|
|
and solving for <IMG
|
|
|
|
|
WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
|
|
|
|
|
SRC="img112.png"
|
|
|
|
|
ALT="$f$"> gives:
|
|
|
|
|
<BR><P></P>
|
|
|
|
|
<DIV ALIGN="CENTER">
|
|
|
|
|
<!-- MATH
|
|
|
|
|
\begin{displaymath}
|
|
|
|
|
f = {{t - p} \over c} = {{{{2 ^ {h/12}}} - p} \over c}
|
|
|
|
|
\end{displaymath}
|
|
|
|
|
-->
|
|
|
|
|
|
|
|
|
|
<IMG
|
|
|
|
|
WIDTH="153" HEIGHT="42" BORDER="0"
|
|
|
|
|
SRC="img295.png"
|
|
|
|
|
ALT="\begin{displaymath}
|
|
|
|
|
f = {{t - p} \over c} = {{{{2 ^ {h/12}}} - p} \over c}
|
|
|
|
|
\end{displaymath}">
|
|
|
|
|
</DIV>
|
|
|
|
|
<BR CLEAR="ALL">
|
|
|
|
|
<P></P>
|
|
|
|
|
where <IMG
|
|
|
|
|
WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
|
|
|
|
|
SRC="img194.png"
|
|
|
|
|
ALT="$h$"> is the desired transposition in half-steps. This is the formula
|
|
|
|
|
used in the <TT>expr</TT> object.
|
|
|
|
|
|
|
|
|
|
<P>
|
|
|
|
|
<HR>
|
|
|
|
|
<!--Navigation Panel-->
|
|
|
|
|
<A NAME="tex2html1104"
|
|
|
|
|
HREF="node39.html">
|
|
|
|
|
<IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="next.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html1098"
|
|
|
|
|
HREF="node32.html">
|
|
|
|
|
<IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="up.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html1094"
|
|
|
|
|
HREF="node37.html">
|
|
|
|
|
<IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="prev.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html1100"
|
|
|
|
|
HREF="node4.html">
|
|
|
|
|
<IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="contents.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<A NAME="tex2html1102"
|
|
|
|
|
HREF="node201.html">
|
|
|
|
|
<IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index"
|
2022-04-12 22:02:59 -03:00
|
|
|
SRC="index.png"></A>
|
2022-04-12 21:54:18 -03:00
|
|
|
<BR>
|
|
|
|
|
<B> Next:</B> <A NAME="tex2html1105"
|
|
|
|
|
HREF="node39.html">Exercises</A>
|
|
|
|
|
<B> Up:</B> <A NAME="tex2html1099"
|
|
|
|
|
HREF="node32.html">Examples</A>
|
|
|
|
|
<B> Previous:</B> <A NAME="tex2html1095"
|
|
|
|
|
HREF="node37.html">Overlapping sample looper</A>
|
|
|
|
|
<B> <A NAME="tex2html1101"
|
|
|
|
|
HREF="node4.html">Contents</A></B>
|
|
|
|
|
<B> <A NAME="tex2html1103"
|
|
|
|
|
HREF="node201.html">Index</A></B>
|
|
|
|
|
<!--End of Navigation Panel-->
|
|
|
|
|
<ADDRESS>
|
|
|
|
|
Miller Puckette
|
|
|
|
|
2006-12-30
|
|
|
|
|
</ADDRESS>
|
|
|
|
|
</BODY>
|
|
|
|
|
</HTML>
|
