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<H2><A NAME="SECTION00595000000000000000">
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Conversion between frequency and pitch</A>
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</H2>
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<P>
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Example A06.frequency.pd (Figure <A HREF="#fig01.13">1.13</A>) shows Pd's object for converting
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pitch to frequency units (<TT>mtof</TT>, meaning "MIDI to frequency") and its
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inverse <TT>ftom</TT>. We also introduce two other object classes,
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<TT>send</TT> and <TT>receive</TT>.
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<P>
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<DIV ALIGN="CENTER"><A NAME="fig01.13"></A><A NAME="1296"></A>
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<TABLE>
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<CAPTION ALIGN="BOTTOM"><STRONG>Figure 1.13:</STRONG>
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Conversion between pitch and frequency in A06.frequency.pd.</CAPTION>
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<TR><TD><IMG
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WIDTH="566" HEIGHT="180" BORDER="0"
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SRC="img153.png"
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ALT="\begin{figure}\psfig{file=figs/fig01.13.ps}\end{figure}"></TD></TR>
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</TABLE>
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</DIV>
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<P>
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<BR><!-- MATH
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$\fbox{ $ \mathrm{mtof} $}$
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-->
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<IMG
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WIDTH="52" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
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SRC="img154.png"
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ALT="\fbox{ $ \mathrm{mtof} $}">, <!-- MATH
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$\fbox{ $ \mathrm{ftom} $}$
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-->
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<IMG
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WIDTH="51" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
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SRC="img155.png"
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ALT="\fbox{ $ \mathrm{ftom} $}">:
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<A NAME="1405"></A><A NAME="1406"></A>convert MIDI pitch to frequency units according to the
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Pitch/Frequency Conversion Formulas (Page <A HREF="node11.html#eq-pitchmidi"><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
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SRC="crossref.png"></A>). Inputs
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and outputs are messages ("tilde" equivalents of the two also exist,
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although like <TT>dbtorms~</TT> they're expensive in CPU time).
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The <TT>ftom</TT> object's output is -1500
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if the input is zero or negative; and likewise, if you give <TT>mtof</TT> -1500 or lower it outputs zero.
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<P>
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<BR><!-- MATH
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$\fbox{ $ \mathrm{receive} $}$
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-->
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<IMG
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WIDTH="66" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
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SRC="img156.png"
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ALT="\fbox{ $ \mathrm{receive} $}">, <!-- MATH
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$\fbox{ $ \mathrm{r} $}$
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-->
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<IMG
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WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
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SRC="img157.png"
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ALT="\fbox{ $ \mathrm{r} $}">:
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<A NAME="1407"></A><A NAME="1408"></A>Receive messages non-locally.
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The <TT>receive</TT> object, which may be abbreviated as "<TT>r</TT>",
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waits for non-local messages to be sent by a <TT>send</TT> object (described below)
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or
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by a message box using redirection (the ";" feature discussed in the
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earlier example, A01.sinewave.pd). The argument (such as "frequency" and "pitch"
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in this example) is the name to which messages are sent. Multiple
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<TT>receive</TT> objects may share the same name, in which case any message
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sent to that name will go to all of them.
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<P>
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<BR><!-- MATH
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$\fbox{ $\mathrm{send}$}$
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-->
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<IMG
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WIDTH="50" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
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SRC="img158.png"
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ALT="\fbox{ $\mathrm{send}$}">, <!-- MATH
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$\fbox{ $\mathrm{s}$\ }$
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-->
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<IMG
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WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
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SRC="img159.png"
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ALT="\fbox{ $\mathrm{s}$\ }">:
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<A NAME="1409"></A><A NAME="1410"></A>The <TT>send</TT> object, which may be abbreviated as "<TT>s</TT>", directs
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messages to <TT>receive</TT> objects.
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<P>
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Two new properties of number boxes are used here. Earlier we've used them
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as controls or as displays; here, the two number boxes each function as both.
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If a number box gets a number in its inlet, it not only displays the number
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but also repeats the number to its output. However, a number box may also be sent
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a "set" message, such as "set 55" for example. This would set the value
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of the number box to 55 (and display it) but not cause the output that would
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result from the simple "55" message. In this case, numbers coming from the
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two <TT>receive</TT> objects are formatted (using message boxes) to read "set 55" instead
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of just "55", and so on. (The special word "$1" is replaced by the
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incoming number.) This is done because otherwise we would have an infinite
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loop: frequency would change pitch which would change frequency and so on
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forever, or at least until something broke.
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