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I keep looking for documentation that explains the usual mappings between beamer element categories (e.g. "structure") and elements in common themes. I haven't found what I'm looking for in any beamer documentation with the distribution, Googling, etc. (I'm not saying the information isn't there--but I haven't found it yet.)

I know that I can globally change the foreground and background colors, and fonts, of various elements of a beamer theme. However, I have been unable to discover what category names typically change what beamer elements except by trial and error using the few examples that I encounter, and the mappings don't seem to be the same in every theme.

For example, I have figured out that I can set the foreground and background color of the title box and upper bar in the Pittsburgh theme using

\setbeamercolor*{structure}{bg=...,fg=...}

but I would not assume, based on past experience, that the same or corresponding elements in other themes would be affected by the same command. More importantly, there are elements which I do not know how to change (the main background, for example).

Is there any way to learn these mappings except by thoroughly digesting the beamer style files?

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perhaps i'm not understanding your question, but i'm surprised that you cannot find what you're looking for in any documentation - the beamer manual is pretty good. here is structure
in the 3.07 manual, for example. so this page says you can use {structure} with \setbeamercolor or \setbeamerfont, or {local structure} with \setbeamercolor et cetera.

then again, if you're looking for documentation from the people that put the themes together, and want to know what they used, i do believe you are out of luck. but since i recently went down this path, i'll share some things i learned.

not all themes were made the same way - they have various authors who tried to do different things, and altered different basic elements. the higher level theme files aren't that scary though, and for your Pittsburgh theme, (which, on a *nix system, you might find in /usr/share/texmf/tex/latex/beamer/themes/theme/ or something like that) it really doesn't change that much. in beamerthemePittsburgh.sty, you can ignore the \ProvidesPackageRCS command (or see this question about it). it only changes two things, and only for the four presentation modes. first, it moves all frame titles to the right. then, it changes the inner theme to circles. you can read beamerinnerthemecircles.sty in the same way, which only changes two templates. as you can see, this is a really simple theme.

if you don't like any of the combinations in the beamer theme matrix enough to make a simple change or two, you might just end up making your own theme like i did. if one of them is close, asking a much more specific question here will go a long way. here are some elements i just learned about and stuck in my theme:

a background image for my title slide

{
\usebackgroundtemplate{
    \includegraphics[width=\paperwidth, height=\paperheight]{titleSlideImage.png} }
    \begin{frame}[plain]
        \titlepage
    \end{frame} }

because of the background image, i want to move all the title slide info down

\addtobeamertemplate{title page}{\vspace{3\baselineskip}}{}

i also wanted the default enumeration numbers

\setbeamertemplate{enumerate items}[default]

all titles to be white

\setbeamercolor{titlelike}{fg=white}

and i also changed my table of contents as i posted here and used \setbeamercolor on item projected and local structure, to change the color of and bullets the default enumeration, respectively. i won't bore you with all my changes, but i'll likely post my code in a question when i finish it later today.

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