Tag 3
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Josia Pietsch
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abc/README
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abc/README
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The abc package lets you include lines of music written in the ABC Plus
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language (http://abcplus.sourceforge.net).
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This is version 2.0b of the package (a maintenance release)
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Copyright 2005-2016 Enrico Gregorio
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This program is provided under the terms of the
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LaTeX Project Public License distributed from CTAN
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archives in directory macros/latex/base/lppl.txt.
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Author: Enrico Gregorio
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Enrico dot Gregorio at univr dot it
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This work has the LPPL maintenance status "author-maintained".
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This work consists of the following files:
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README (this file)
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abc.dtx
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abc.ins
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abc.pdf
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and of the derived files
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abc.sty
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mup.sty
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example.tex
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poll.abc
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mupexa.tex
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simple.mup
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To install the distribution:
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o run "latex abc.ins"
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o run "latex -shell-escape example.tex" for a test
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o move "abc.sty" and "mup.sty" to locations where LaTeX will
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find it (the FAQ on CTAN in /help/uktug-FAQ gives more
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information about this magic place)
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Please note that you need, on your system, the
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utilities "abcm2ps" (http://abcplus.sourceforge.net),
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either "ps2eps" (which comes with TeX Live) or "ps2epsi"
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(which comes with Ghostscript), and epstopdf (which
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comes with TeX Live) if you use pdflatex.
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If you want to compile the Mup examples, you need the
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utility "mup" (http://www.arkkra.com), along with the
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Postscript utilities mentioned above.
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Note also that you must enable "shell escape" on your
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TeX system via the command line switch (at least); see
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your distribution's documentation. However, this is not
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strictly necessary in order to use the package, see the
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documentation.
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2016/05/15
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Enrico Gregorio
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824
abc/abc.dtx
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824
abc/abc.dtx
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% \iffalse meta-comment
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%
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% Copyright (C) 2005-2015 by Enrico Gregorio
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% <Enrico dot Gregorio at univr dot it>
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% -------------------------------------------------------
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%
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% This file may be distributed and/or modified under the conditions of
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% the LaTeX Project Public License, either version 1.2 of this license
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% or (at your option) any later version. The latest version of this
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% license is in:
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%
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% http://www.latex-project.org/lppl.txt
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%
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% and version 1.2 or later is part of all distributions of LaTeX
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% version 1999/12/01 or later.
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%
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% \fi
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%
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% \iffalse
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%<*driver>
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\ProvidesFile{abc.dtx}
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%</driver>
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%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01]
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%<package>\ProvidesPackage{abc}
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%<*package>
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[2016/05/15 v2.0b Enrico Gregorio]
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%</package>
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%<*driver>
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\documentclass{ltxdoc}
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\usepackage{verbatim}
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\newenvironment{smallverb}{\footnotesize\verbatim}{\endverbatim}
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\EnableCrossrefs
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\CodelineIndex
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\RecordChanges
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\begin{document}
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\DocInput{abc.dtx}
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\end{document}
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%</driver>
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% \fi
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%
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% \CheckSum{416}
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%
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% \CharacterTable
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% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
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% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
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% Digits \0\1\2\3\4\5\6\7\8\9
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% Exclamation \! Double quote \" Hash (number) \#
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% Dollar \$ Percent \% Ampersand \&
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% Acute accent \' Left paren \( Right paren \)
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% Asterisk \* Plus \+ Comma \,
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% Minus \- Point \. Solidus \/
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% Colon \: Semicolon \; Less than \<
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% Equals \= Greater than \> Question mark \?
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% Commercial at \@ Left bracket \[ Backslash \\
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% Right bracket \] Circumflex \^ Underscore \_
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% Grave accent \` Left brace \{ Vertical bar \|
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% Right brace \} Tilde \~}
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%
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% \changes{v2.0b}{2016/05/15}{Use shellesc}
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%
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% \changes{v2.0a}{2015/09/09}{Fixed gobbling of leading lines that
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% start with \%}
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%
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% \changes{v2.0}{2008/03/03}{Many changes, in order to allow for Mup
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% support; added saveall and nosaveall options}
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%
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% \changes{v1.1}{2007/03/27}{Added \cs{endgroup} when the warning for
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% a non existent file is issued}
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%
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% \changes{v1.0}{2006/03/22}{After long delay decided to publish it}
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%
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% \changes{v0.7}{2005/11/21}{Corrected some errors from previous
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% version; changed `abcinput' to support keyword-value pairs like
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% the environment; added the production of a batch file when the
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% `noshellescape' option is active; improved the documentation}
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%
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% \changes{v0.7beta}{2005/11/19}{Added the `postoptions' and `width'
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% keywords}
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%
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% \changes{v0.6}{2005/11/18}{Changed options: erased `nix' and
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% `dos', added `ps2epsidos' to correct a mistake}
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%
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% \changes{v0.5}{2005/11/13}{Added the interface to keyval}
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%
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% \changes{v0.4}{2005/11/10}{Initial version; too many things changed}
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%
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% \changes{v.0.1-0.3}{2005/11/01}{Very preliminar versions}
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%
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% \GetFileInfo{abc.dtx}
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%
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% \DoNotIndex{\newcommand,\newenvironment,\def,\ifpdf,\begin}
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% \DoNotIndex{\DeclareOption,\ExecuteOptions,\RequirePackage}
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% \DoNotIndex{\renewcommand,\else,\fi,\relax,\@bsphack,\@esphack}
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% \DoNotIndex{\active,\AtEndOfPackage,\catcode,\centering}
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% \DoNotIndex{\closeout,\comment,\do,\dospecials,\end,\endcomment}
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% \DoNotIndex{\fbox,\gdef,\immediate,\includegraphics,\let}
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% \DoNotIndex{\linewidth,\message,\newif,\newwrite,\openout}
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% \DoNotIndex{\PackageWarning,\space,\the,\verbatim@line}
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% \DoNotIndex{\verbatim@processline,\verbatim@start,\write}
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% \DoNotIndex{\@makeother,\IfFileExists,\ProcessOptions}
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% \DoNotIndex{\@ifnextchar,\define@key,\MessageBreak,\setkeys}
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% \DoNotIndex{\stepcounter,\newcounter,\trivlist,\AtEndDocument}
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% \DoNotIndex{\@empty,\edef,\csname,\endcsname,\edef,\begingroup}
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% \DoNotIndex{\endgroup,\endtrivlist,\global,\if,\ifx,\item}
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% \DoNotIndex{\PackageWarningNoLine,\PassOptionsToPackage}
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% \DoNotIndex{\ProvidesPackage,\@arabic}
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%
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% \title{The \textsf{abc} package\thanks{This document corresponds to
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% \textsf{abc}~\fileversion, dated \filedate.}}
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%
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% \author{Enrico Gregorio \\ \texttt{Enrico dot Gregorio at univr dot it}}
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%
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% \date{\filedate}
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%
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% \maketitle
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%
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% \section{Introduction}
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% There are several ways to set music using \TeX{}, notably
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% Musix\TeX{} and Lilypond. Both are very powerful and,
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% consequently, a bit difficult to learn and to use.
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%
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% From the point of view of notation, the ABC
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% system\footnote{\texttt{http://staffweb.cms.gre.ac.uk/\char`\~c.walshaw/abc/}}
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% is much simpler. A recent extension of this language, called
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% ABC~Plus\footnote{\texttt{http://abcplus.sourceforge.net}}, allows
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% for setting multiple staves and polyphony. One of the best programs
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% for converting these notations into sheet music is
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% \texttt{abcm2ps}, which can take an ABC or ABC~Plus file and
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% transform it into a PostScript\texttrademark{} file.
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%
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% The purpose of this package is to allow \LaTeX{} users to include in
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% their documents small excerpts of music written directly in
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% ABC (Plus). It exploits the \verb|\write18| technique available with
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% the Web2C implementation of the \TeX{} system and free utilities
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% like \texttt{ps2eps}, \texttt{ps2epsi} and \texttt{epstopdf}. From
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% version 2.0b we check the existence of the \textsf{shellesc} package
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% in order to be compatible with Lua\TeX.
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%
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% This package can be used both with \LaTeX{} and
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% \textsc{pdf}\LaTeX{}, without any change in the user's source file.
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% It employs also the package \textsf{keyval} by David Carlisle and
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% ideas from the \textsf{verbatim} package in the \LaTeX{} tools.
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%
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% Martin Tarenskeen wrote me about possible support of Mup--Music
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% Publisher\footnote{\texttt{http://www.arkkra.com}} and actually it
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% was easy to add it along with some improvements partly suggested by
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% him. Therefore the package now comes along with a new \textsf{mup}
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% package; see section~\ref{mup}. I owe many thanks to Martin for
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% testing the new version.
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%
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% We are studying whether it is feasible to extend support also to
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% other music printing programs like Lilypond.
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%
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% \section{Usage}
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% \DescribeEnv{abc}
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% The only environment provided by this package is \verb|abc| with
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% the following syntax:
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% \begin{quote}
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% \verb|\begin{abc}[|\meta{keyword}$=$\meta{value}\verb|...]|\\
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% \meta{ABC Plus material}\\
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% \verb|\end{abc}|
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% \end{quote}
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% The environment should be used only in LR-mode. Its output is set
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% in a `center' environment. We give a list of the available
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% keywords.
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% \begin{description}
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%
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% \item[\normalfont\texttt{name=}\meta{name}:] \meta{name} is a name
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% for the temporary file which will be output and massaged by
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% \texttt{abcm2ps}. \emph{Warning}: the extension \texttt{.abc} is
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% automatically added to the file name; esistent files with the same
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% name will be silently erased. If the keyword is specified without a
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% value, then the output file receives a unique name.
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%
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% \item[\normalfont\texttt{options=}\meta{options}:] \meta{options}
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% are command line parameters to the \texttt{abcm2ps} utility; the
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% default are `\texttt{-O= -c}'.
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%
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% \item[\normalfont\texttt{postoptions=}\meta{postoptions}:]
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% \meta{postoptions} are possible command line options which, in
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% \texttt{abcm2ps} syntax, go after the file name.
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%
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% \item[\normalfont\texttt{program=}\meta{program}:] \meta{program} is
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% used to specify an alternative program to \texttt{abc2mps} (if
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% existent). In this case users must specify completely the command
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% line options, directly in \meta{program} or with \meta{options} and
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% \meta{postoptions}. For example
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% \begin{quote}
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% \verb|\begin[name=song,program=abctoeps,options={-a -b}]|\\
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% \verb|\begin[name=song,program={abc3ps -a -b}]|
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% \end{quote}
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% (assuming there is an \texttt{abc3ps} program).
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%
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% \item[\normalfont\texttt{width=}\meta{width}:] \meta{width} should
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% be a dimension; it is best to express it as a fraction of
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% \verb|\abcwidth|.
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%
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% \item[\normalfont\texttt{center}:] This is a boolean, either true
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% or false; the default is true, if left flush alignment is preferred,
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% specify \texttt{center=false}.
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%
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% \item[\normalfont\texttt{extension}:] This keyword seems practically
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% useless, but is needed if one needs to input both ABC and Mup files
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% in one and the same document. See later on.
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% \end{description}
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%
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% \DescribeMacro{\abcinput}
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% It is also possible to input an available ABC file. The syntax is
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% \begin{quote}
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% \verb|\abcinput|\oarg{options}\marg{name}
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% \end{quote}
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% where \meta{name} is the name of the file, without the extension
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% which should be \texttt{.abc}. In the optional argument users can
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% put keyword-value pairs as for the environment. Of course the
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% keyword \texttt{name} is ignored here.
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%
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% \DescribeMacro{\abcwidth}
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% Users have a minimum control (at least in this version) on how to
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% include some lines of music. The only parameter they can modify is
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% \verb|\abcwidth| with \verb|\renewcommand|. Its normal value is
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% \verb|\linewidth|. The best thing to do is
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% \begin{quote}
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% \verb|\renewcommand{\abcwidth}{|\meta{fraction}\verb|\linewidth}|
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% \end{quote}
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% where \meta{fraction} is some number between $0$ and~$1$. Changing
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% this parameter affects every subsequent music inclusion, obeying to
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% the usual scoping rules. The width can be changed locally for the
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% environment or the command with the method explained before.
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%
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% \DescribeMacro{\normalabcoutputfile}
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% The name for the generic output files is ``\texttt{out-abc}''. In
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% the (improbable) case that some file \texttt{out-abc.}\meta{ext} is
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% present in the directory, users can redefine
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% \verb|\normalabcoutputfile| as they like.
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%
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% \section{Package options}
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% There are some package options, to control what is to be passed for
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% subsequent processing.
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%
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% \subsection{\texttt{shellescape} and \texttt{noshellescape}}
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% The option \texttt{shellescape} (default) means that some external
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% programs will be called by \LaTeX{} to get the inclusion of the
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% music lines. If you don't trust the automatic generation, or your
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% \TeX{} implementation does not allow the trick with \verb|\write18|,
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% then use \texttt{noshellescape}. In this case, a name should be
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% specified for every `abc' environment, because otherwise ABC output
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% files will be overwritten, since they receive the same generic name,
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% by default. A file named \texttt{out-abc.sh} is produced,
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% containing the commands to give for elaborating the music files.
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%
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% \subsection{\texttt{generate} and \texttt{nogenerate}}
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% With the \texttt{generate} option (default) the ABC lines will be
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% processed by the external programs. The \texttt{nogenerate} option
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% can be used when the ABC sources have not changed, in order to
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% increase speed. Also in this case, however, a name should be
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% specified for all output ABC files.
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%
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% \subsection{\texttt{ps2epsi}, \texttt{ps2epsidos} and
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% \texttt{ps2eps}}
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% The option \texttt{ps2eps} (default) means that the \texttt{ps2eps}
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% Perl script will be used for generating the EPS file for graphic
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% inclusion. Specify the \texttt{ps2epsi} option if you prefer the
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% \texttt{ps2epsi} program; specify \texttt{ps2epsidos} if you are on
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% a system where the utility \texttt{ps2epsi} generates a file with
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% three letter extension \texttt{.epi}.
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%
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% \subsection{\texttt{nosaveall} and \texttt{saveall}}
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% The first is the default, but the second is called implicitly when
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% the \texttt{noshellescape} is given. When the \texttt{saveall}
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% option is active, every `abc' environment produces a unique output
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% file; in other words, the \texttt{name} keyword, without value, is
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% given for every environment. So the \texttt{noshellescape} option
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% along with \texttt{generate} will not overwrite the output from
|
||||||
|
% unnamed environment. It is possible that, during the document's
|
||||||
|
% preparation, the numbers added to the default file name are out of
|
||||||
|
% synch, the process should converge. Note that with Lua\TeX{} the
|
||||||
|
% \texttt{nosaveall} option can produce errors, so \texttt{saveall} is
|
||||||
|
% enabled by default, with this engine.
|
||||||
|
%
|
||||||
|
%
|
||||||
|
% \section{Compiling documents}
|
||||||
|
% Users must give the option \texttt{-shell-escape} when compiling
|
||||||
|
% their documents, unless they chose the \texttt{nogenerate} package
|
||||||
|
% option or the \texttt{noshellescape}. Thus one of
|
||||||
|
% \begin{quote}
|
||||||
|
% \texttt{latex -shell-escape} \meta{\TeX{} file name}\\
|
||||||
|
% \texttt{pdflatex -shell-escape} \meta{\TeX{} file name}\\
|
||||||
|
% \texttt{simpdftex latex --extratexopts "-shell-escape"}
|
||||||
|
% \end{quote}
|
||||||
|
% should be used from the command line (or equivalent way, depending
|
||||||
|
% on operating system and distribution).
|
||||||
|
%
|
||||||
|
% \section{An example file}
|
||||||
|
% \iffalse
|
||||||
|
%<*example>
|
||||||
|
% \fi
|
||||||
|
% \begin{smallverb}
|
||||||
|
\documentclass[a4paper,12pt]{article}
|
||||||
|
\usepackage[generate,ps2eps]{abc}
|
||||||
|
\usepackage{mathptmx}
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
|
||||||
|
\title{Example of ABC Plus in \LaTeX{}}
|
||||||
|
\author{Guido Gonzato}
|
||||||
|
\date{}
|
||||||
|
\maketitle
|
||||||
|
|
||||||
|
This is a short piece.
|
||||||
|
|
||||||
|
\medskip
|
||||||
|
|
||||||
|
\begin{abc}
|
||||||
|
X:4
|
||||||
|
T:Cronin's Hornpipe
|
||||||
|
R:hornpipe
|
||||||
|
S:Keenan and Glackin
|
||||||
|
E:7
|
||||||
|
M:C|
|
||||||
|
L:1/8
|
||||||
|
K:G
|
||||||
|
BA|GABc dBde|gage dega|bage dBGB|cABG A2BA|!
|
||||||
|
GABc dBde|gage dega|bage dBAB|G2G2 G2:|!
|
||||||
|
fg|afd^c d2ga|bged e2ga|(3bag (3agf gedB|(3cBA AG AcBA|!
|
||||||
|
GABc dBde|~g3e dega|bage dBAB|G2G2 G2:|!
|
||||||
|
\end{abc}
|
||||||
|
|
||||||
|
\medskip
|
||||||
|
|
||||||
|
This is another short piece, but we would like to keep the
|
||||||
|
ABC source in our directory.
|
||||||
|
|
||||||
|
\begin{abc}[name=jacky]
|
||||||
|
X:9
|
||||||
|
T:Jacky Tar
|
||||||
|
R:hornpipe
|
||||||
|
M:4/4
|
||||||
|
L:1/8
|
||||||
|
K:Edor
|
||||||
|
(Bd) | "Em" e2 ed efge | "G" d2 B2 B2 (dB) | "D" ABde faef | d2 A2 A2 (Bd) |
|
||||||
|
"Em" e2 ef g2 fe | "G" dB GB d2 (cB) | "D" AGFE DEFA | "Em" G2 E2 E2 :|
|
||||||
|
(GA) | "Em" BGEG BGEG | BAGF E2 (FG) | "D" BGEG BGEG | AGFE D2 (EF) |
|
||||||
|
"G" GFGB g2 (fe) | dBGB d2 (cB) | "D" AGFE DEFA | "Em" G2 E2 E2 :|
|
||||||
|
\end{abc}
|
||||||
|
|
||||||
|
\clearpage
|
||||||
|
|
||||||
|
And, finally, we want to set also the last piece; its ABC code
|
||||||
|
is already in our directory.
|
||||||
|
|
||||||
|
\medskip
|
||||||
|
|
||||||
|
\abcinput{poll}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
|
% \end{smallverb}
|
||||||
|
% \iffalse
|
||||||
|
%</example>
|
||||||
|
% \fi
|
||||||
|
%
|
||||||
|
% This file is accompanied by a file \texttt{poll.abc}
|
||||||
|
% \iffalse
|
||||||
|
%<*abc>
|
||||||
|
% \fi
|
||||||
|
% \begin{smallverb}
|
||||||
|
X:12
|
||||||
|
T:Poll Ha'penny
|
||||||
|
T:Garra\'i na bhF\'eile\'og
|
||||||
|
R:hornpipe
|
||||||
|
H:The Irish title means "The Garden of Honeysuckles"
|
||||||
|
D:Mary Bergin: Feadoga Stain
|
||||||
|
D:Noel Hill agus Tony McMahon: I gCnoc na Grai
|
||||||
|
Z:id:hn-hornpipe-26
|
||||||
|
M:C|
|
||||||
|
L:1/8
|
||||||
|
K:Amix
|
||||||
|
(3GAB | =cAAG A2 (3AB=c | (3d=cB (3AGF G2 (3B^cd | ed^cA d^cAG | ~A3 G A2 de |
|
||||||
|
~f3 d ~e3 c | d2 (3Bcd efge | aged (3=cBA GB | ~A3 G A2:|
|
||||||
|
|: ef | ~g3 f gfef | g2 ga gedg | eaag a3 g | eaag a2 ag |
|
||||||
|
~f3 d ~e3 c | d2 (3Bcd efge | aged (3=cBA GB | ~A3 G A2 :|
|
||||||
|
% \end{smallverb}
|
||||||
|
% \iffalse
|
||||||
|
%</abc>
|
||||||
|
% \fi
|
||||||
|
%
|
||||||
|
% \section{Mup support}\label{mup}
|
||||||
|
% Everything we have said about ABC translates verbatim for Mup.
|
||||||
|
% Simply call the package with
|
||||||
|
% \iffalse
|
||||||
|
%<*verb>
|
||||||
|
% \fi
|
||||||
|
\begin{verbatim}
|
||||||
|
\usepackage{mup}
|
||||||
|
\end{verbatim}
|
||||||
|
% \iffalse
|
||||||
|
%</verb>
|
||||||
|
% \fi
|
||||||
|
|
||||||
|
% with options just like before, and substitute the string `mup' to
|
||||||
|
% every occurrence of `abc' in the preceding sections. The only
|
||||||
|
% differences are in the default command line options when calling the
|
||||||
|
% external program (they are \texttt{-F} for `mup').
|
||||||
|
%
|
||||||
|
% It is even possible to use both external programs in the same
|
||||||
|
% document. If this is desired, call the \textsf{abc} package and
|
||||||
|
% define a new environment for Mup inclusion as follows
|
||||||
|
% \iffalse
|
||||||
|
%<*verb>
|
||||||
|
% \fi
|
||||||
|
\begin{verbatim}
|
||||||
|
\newenvironment{mup}[1][]
|
||||||
|
{\renewcommand{\normalabcoutputfile}{out-mup}%
|
||||||
|
\abc[program=mup,options={-F},extension=mup,#1]}
|
||||||
|
{\endabc}
|
||||||
|
\newcommand{\mupinput}[2][]{%
|
||||||
|
\abcinput[program=mup,options={-F},extension=mup,#1]{#2}}
|
||||||
|
\end{verbatim}
|
||||||
|
% \iffalse
|
||||||
|
%</verb>
|
||||||
|
% \fi
|
||||||
|
%
|
||||||
|
% Here is an example with Mup.
|
||||||
|
%
|
||||||
|
% \iffalse
|
||||||
|
%<*example-mup>
|
||||||
|
% \fi
|
||||||
|
% \begin{smallverb}
|
||||||
|
\documentclass[a4paper,12pt]{article}
|
||||||
|
\usepackage[generate,ps2eps]{mup}
|
||||||
|
\usepackage{mathptmx}
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
|
||||||
|
\title{Example of MUP in \LaTeX{}}
|
||||||
|
\author{Martin Tarenskeen}
|
||||||
|
\date{}
|
||||||
|
\maketitle
|
||||||
|
|
||||||
|
This is a short piece.
|
||||||
|
|
||||||
|
\medskip
|
||||||
|
|
||||||
|
\begin{mup}
|
||||||
|
1: a-;b-;c;d;
|
||||||
|
bar
|
||||||
|
1: e;f;g;a;
|
||||||
|
endbar
|
||||||
|
\end{mup}
|
||||||
|
|
||||||
|
\medskip
|
||||||
|
|
||||||
|
This is another short piece, but we would like to keep the
|
||||||
|
MUP source in our directory.
|
||||||
|
|
||||||
|
\begin{mup}[name=mymup]
|
||||||
|
score
|
||||||
|
staffs=2
|
||||||
|
time=6/8
|
||||||
|
beamstyle=4.,4.
|
||||||
|
|
||||||
|
staff 2
|
||||||
|
clef=bass
|
||||||
|
|
||||||
|
music
|
||||||
|
1: 8c;d;e;f;g;a;
|
||||||
|
2: 4.ceg;cfa;
|
||||||
|
repeatend
|
||||||
|
|
||||||
|
\end{mup}
|
||||||
|
|
||||||
|
\clearpage
|
||||||
|
|
||||||
|
And finally, we want to set also the last piece; its MUP code
|
||||||
|
is already in our directory.
|
||||||
|
|
||||||
|
\medskip
|
||||||
|
|
||||||
|
\mupinput{simple}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
|
% \end{smallverb}
|
||||||
|
% \iffalse
|
||||||
|
%</example-mup>
|
||||||
|
% \fi
|
||||||
|
% This file is accompanied by a file \texttt{simple.mup}
|
||||||
|
% \iffalse
|
||||||
|
%<*mup>
|
||||||
|
% \fi
|
||||||
|
% \begin{smallverb}
|
||||||
|
score
|
||||||
|
staffs=2
|
||||||
|
time=6/8
|
||||||
|
beamstyle=4.,4.
|
||||||
|
|
||||||
|
staff 2
|
||||||
|
clef=bass
|
||||||
|
|
||||||
|
music
|
||||||
|
1: 8c;d;e;f;g;a;
|
||||||
|
2: 4.ceg;cfa;
|
||||||
|
repeatend
|
||||||
|
% \end{smallverb}
|
||||||
|
% \iffalse
|
||||||
|
%</mup>
|
||||||
|
% \fi
|
||||||
|
%
|
||||||
|
% \StopEventually{\PrintChanges\PrintIndex}
|
||||||
|
%
|
||||||
|
% \section{The implementation}
|
||||||
|
% After the usual stuff of package presentation, here are the actual
|
||||||
|
% macros. To begin with the option declarations and the defaults.
|
||||||
|
% The first options are boolean.
|
||||||
|
% \begin{macrocode}
|
||||||
|
%<*package>
|
||||||
|
\RequirePackage{ifluatex}
|
||||||
|
\newif\ifabc@shellescape
|
||||||
|
\newif\ifabc@generate
|
||||||
|
\newif\ifabc@warning
|
||||||
|
\newif\ifabc@saveall
|
||||||
|
\newif\ifabc@mup
|
||||||
|
\DeclareOption{mup}{\abc@muptrue}
|
||||||
|
\DeclareOption{noshellescape}{\abc@shellescapefalse\abc@warningtrue
|
||||||
|
\abc@savealltrue}
|
||||||
|
\DeclareOption{shellescape}{\abc@shellescapetrue}
|
||||||
|
\DeclareOption{nogenerate}{\abc@generatefalse}
|
||||||
|
\DeclareOption{generate}{\abc@generatetrue}
|
||||||
|
\DeclareOption{nosaveall}{\abc@saveallfalse}
|
||||||
|
\DeclareOption{saveall}{\abc@savealltrue}
|
||||||
|
% \end{macrocode}
|
||||||
|
% The following options control the external programs to use.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\def\abc@epsext{eps}
|
||||||
|
\DeclareOption{ps2eps}{\def\abc@pscmd{ps2eps -f}}
|
||||||
|
\DeclareOption{ps2epsi}{\def\abc@pscmd{ps2epsi}\def\abc@epsext{epsi}}
|
||||||
|
\DeclareOption{ps2epsidos}{\def\abc@pscmd{ps2epsi}\def\abc@epsext{epi}}
|
||||||
|
% \end{macrocode}
|
||||||
|
% Now we declare the default options and call the user specified
|
||||||
|
% ones. Since Lua\TeX{} doesn't accept loading different PDF files
|
||||||
|
% with the same name, when this engine is used, the \texttt{saveall}
|
||||||
|
% option is enabled by default.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\ExecuteOptions{generate,shellescape,nosaveall,ps2eps}
|
||||||
|
\ifluatex
|
||||||
|
\ExecuteOptions{saveall}
|
||||||
|
\fi
|
||||||
|
\ProcessOptions\relax
|
||||||
|
% \end{macrocode}
|
||||||
|
%
|
||||||
|
% Then we have to load some packages we need. The first one is to do
|
||||||
|
% verbatim output to a file without reinventing the wheel. Then the
|
||||||
|
% package for implementing keyword-value options; we have to take care
|
||||||
|
% of graphics inclusion, and to control whether we are using \LaTeX{}
|
||||||
|
% with DVI or PDF output.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\RequirePackage{verbatim}
|
||||||
|
\RequirePackage{keyval}
|
||||||
|
\RequirePackage{graphicx}
|
||||||
|
\RequirePackage{ifpdf}
|
||||||
|
% \end{macrocode}
|
||||||
|
% Next we define some internal commands. First of all a boolean for
|
||||||
|
% issuing messages if necessary and a counter to assign unique names
|
||||||
|
% to output files
|
||||||
|
% \begin{macrocode}
|
||||||
|
\newif\ifabc@unprocessedfiles
|
||||||
|
\newcounter{abc@count}
|
||||||
|
% \end{macrocode}
|
||||||
|
% We choose to give explicitly the extensions to the graphics files,
|
||||||
|
% since some user could prefer \texttt{ps2epsi}. Everything is
|
||||||
|
% doubled for Mup support.
|
||||||
|
% \begin{environment}{mup}
|
||||||
|
% \begin{macro}{\mupinput}
|
||||||
|
% \begin{macrocode}
|
||||||
|
\ifabc@mup
|
||||||
|
\newcommand{\abc@cmd}{mup} % virtually no choice
|
||||||
|
\newcommand{\abc@parm}{-F} % -F MUST stay
|
||||||
|
\newcommand{\abc@epstopdfcmd}{epstopdf}
|
||||||
|
\newcommand{\abc@pdfext}{pdf}
|
||||||
|
\def\normalabcoutputfile{out-mup}
|
||||||
|
\def\normalmupoutputfile{\normalabcoutputfile}
|
||||||
|
\def\mup{\abc}
|
||||||
|
\def\endmup{\endabc}
|
||||||
|
\def\mupinput{\abcinput}
|
||||||
|
\def\abc@ext{.mup}
|
||||||
|
\def\abc@packagename{mup}
|
||||||
|
\else
|
||||||
|
\newcommand{\abc@cmd}{abcm2ps} % virtually no choice
|
||||||
|
\newcommand{\abc@parm}{-O= -c} % -O= MUST stay
|
||||||
|
\newcommand{\abc@epstopdfcmd}{epstopdf}
|
||||||
|
\newcommand{\abc@pdfext}{pdf}
|
||||||
|
\def\normalabcoutputfile{out-abc}
|
||||||
|
\def\abc@ext{.abc}
|
||||||
|
\def\abc@packagename{abc}
|
||||||
|
\fi
|
||||||
|
\def\abc@tempfile{\normalabcoutputfile}
|
||||||
|
\def\abc@opt{}
|
||||||
|
\let\abc@postopt\@empty
|
||||||
|
\ifpdf
|
||||||
|
\let\abc@finalext\abc@pdfext
|
||||||
|
\else
|
||||||
|
\let\abc@finalext\abc@epsext
|
||||||
|
\fi
|
||||||
|
\newif\ifabc@center
|
||||||
|
\abc@centertrue
|
||||||
|
% \end{macrocode}
|
||||||
|
% \end{macro}
|
||||||
|
% \end{environment}
|
||||||
|
% The following is the only parameter the user is authorized to
|
||||||
|
% tamper with; it has an alias for Mup.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\newcommand{\abcwidth}{\linewidth} % only fractions of \linewidth
|
||||||
|
\let\mupwidth\abcwidth
|
||||||
|
% \end{macrocode}
|
||||||
|
% \begin{macro}{\abc@startgen}
|
||||||
|
% \begin{macro}{\abc@finishgen}
|
||||||
|
% Now something directly borrowed from the package \textsf{verbatim}.
|
||||||
|
% We declare an output stream and define two macros which will be
|
||||||
|
% called by the \texttt{abc} environment or by the \verb|\abcinput|
|
||||||
|
% command in case we are generating the graphics files. The macro
|
||||||
|
% \verb|\abc@startgen| then passes the control to \verb|\abc@process|
|
||||||
|
% which is different, according to the options given to the package.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\newwrite\abc@out
|
||||||
|
\def\abc@startgen{%
|
||||||
|
\@bsphack
|
||||||
|
\immediate\openout\abc@out\abc@tempfile\abc@ext
|
||||||
|
\let\do\@makeother\dospecials
|
||||||
|
\catcode`\^^M\active \catcode`\^^I=12
|
||||||
|
\def\verbatim@processline{%
|
||||||
|
\immediate\write\abc@out
|
||||||
|
{\the\verbatim@line}}%
|
||||||
|
\verbatim@start}
|
||||||
|
\def\abc@finishgen{%
|
||||||
|
\immediate\closeout\abc@out
|
||||||
|
\@esphack
|
||||||
|
\abc@process
|
||||||
|
}
|
||||||
|
% \end{macrocode}
|
||||||
|
% \end{macro}
|
||||||
|
% \end{macro}
|
||||||
|
% \begin{macro}{\abc@doshellcommand}
|
||||||
|
% \begin{macro}{\abc@nodoshellcommand}
|
||||||
|
% We define a macro for the external massaging of the ABC files and
|
||||||
|
% another one for the case the user doesn't trust or have available
|
||||||
|
% the \verb|\write18| trick; the second one spits out a very simple
|
||||||
|
% shell script which can be used to take care of the compilation; this
|
||||||
|
% file is probably compatible with all systems having a command line
|
||||||
|
% interface. Then we check the options again and define the commands
|
||||||
|
% that really do the job.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\ifluatex
|
||||||
|
\IfFileExists{shellesc.sty}
|
||||||
|
{\RequirePackage{shellesc}\let\abc@shell\ShellEscape}
|
||||||
|
{\def\abc@shell{\immediate\write18}}
|
||||||
|
\else
|
||||||
|
\def\abc@shell{\immediate\write18}
|
||||||
|
\fi
|
||||||
|
\def\abc@doshellcommand{%
|
||||||
|
\abc@shell{%
|
||||||
|
\ifabc@mup
|
||||||
|
\abc@cmd\space
|
||||||
|
\abc@opt\space
|
||||||
|
\abc@parm\space
|
||||||
|
\abc@tempfile\abc@ext\space
|
||||||
|
\else
|
||||||
|
\abc@cmd\space
|
||||||
|
\abc@parm\space
|
||||||
|
\abc@opt\space
|
||||||
|
\abc@tempfile\abc@ext\space
|
||||||
|
\fi
|
||||||
|
\ifx\abc@postopt\@empty
|
||||||
|
\else\space\abc@postopt\fi
|
||||||
|
}%
|
||||||
|
\abc@shell{%
|
||||||
|
\abc@pscmd\space\abc@tempfile.ps
|
||||||
|
}%
|
||||||
|
\ifpdf
|
||||||
|
\abc@shell{%
|
||||||
|
\abc@epstopdfcmd\space\abc@tempfile.\abc@epsext
|
||||||
|
}%
|
||||||
|
\fi
|
||||||
|
}
|
||||||
|
\def\abc@nodoshellcommand{%
|
||||||
|
\immediate\write\abc@outsh{%
|
||||||
|
\abc@cmd\space
|
||||||
|
\abc@parm\space
|
||||||
|
\abc@opt\space
|
||||||
|
\abc@tempfile\abc@ext\space
|
||||||
|
\ifx\abc@postopt\@empty
|
||||||
|
\else\space\abc@postopt\fi}%
|
||||||
|
\immediate\write\abc@outsh{%
|
||||||
|
\abc@pscmd\space\abc@tempfile.ps}%
|
||||||
|
\ifpdf
|
||||||
|
\immediate\write\abc@outsh{%
|
||||||
|
\abc@epstopdfcmd\space\abc@tempfile.\abc@epsext}%
|
||||||
|
\fi
|
||||||
|
}
|
||||||
|
% \end{macrocode}
|
||||||
|
% We use a conditional to emit a message at the end of the
|
||||||
|
% compilation if some file has not been found and the
|
||||||
|
% \texttt{nogenerate} option was chosen.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\AtEndDocument{%
|
||||||
|
\ifabc@warning\ifabc@unprocessedfiles
|
||||||
|
\PackageWarningNoLine{\abc@packagename}{%
|
||||||
|
\ifabc@shellescape
|
||||||
|
You have set the `shellescape' option, but you ran%
|
||||||
|
\MessageBreak
|
||||||
|
(pdf)latex without the `-shell-escape' command line%
|
||||||
|
\MessageBreak
|
||||||
|
option. Fix it either with the `noshellescape' option%
|
||||||
|
\MessageBreak
|
||||||
|
in your document or the correct call of (pdf)latex%
|
||||||
|
\else
|
||||||
|
Remember to generate the [eps,pdf] files before compiling%
|
||||||
|
\MessageBreak
|
||||||
|
again. Use the file \abc@tempfile.sh for a list or as a script%
|
||||||
|
\fi}%
|
||||||
|
\fi\fi}
|
||||||
|
% \end{macrocode}
|
||||||
|
% \end{macro}
|
||||||
|
% \end{macro}
|
||||||
|
% Now we define the macro responsible for the massaging of the ABC
|
||||||
|
% files. This is a good moment for inizializing the writing of the
|
||||||
|
% shell script, when needed.
|
||||||
|
% \begin{macro}{\abc@process}
|
||||||
|
% \begin{macrocode}
|
||||||
|
\ifabc@shellescape
|
||||||
|
\let\abc@process\abc@doshellcommand
|
||||||
|
\else
|
||||||
|
\newwrite\abc@outsh
|
||||||
|
\immediate\openout\abc@outsh\abc@tempfile.sh
|
||||||
|
\AtEndDocument{\closeout\abc@outsh}
|
||||||
|
\let\abc@process\abc@nodoshellcommand
|
||||||
|
\fi
|
||||||
|
% \end{macrocode}
|
||||||
|
% \end{macro}
|
||||||
|
% \begin{macro}{\abc@start}
|
||||||
|
% \begin{macro}{\abc@finish}
|
||||||
|
% We now define how to start and finish; if no generation is required,
|
||||||
|
% the ABC lines are skipped like a comment (thanks again to the
|
||||||
|
% \textsf{verbatim} package).
|
||||||
|
% \begin{macrocode}
|
||||||
|
\ifabc@generate
|
||||||
|
\let\abc@start\abc@startgen
|
||||||
|
\let\abc@finish\abc@finishgen
|
||||||
|
\else
|
||||||
|
\let\abc@start\comment
|
||||||
|
\let\abc@finish\endcomment
|
||||||
|
\fi
|
||||||
|
% \end{macrocode}
|
||||||
|
% \end{macro}
|
||||||
|
% \end{macro}
|
||||||
|
% \begin{environment}{abc}
|
||||||
|
% \begin{macro}{\abcinput}
|
||||||
|
% Finally, we define the environment and the command. Some commands
|
||||||
|
% are initialized here; the name of the temporary file is, by default,
|
||||||
|
% ``out-abc'' which should not clobber any existing file.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\def\abc{\@makeother\%\@ifnextchar[\abc@grab{\abc@grab[]}}
|
||||||
|
\define@key{abc}{name}[]{%
|
||||||
|
\if!#1!\stepcounter{abc@count}%
|
||||||
|
\edef\abc@tempfile{\normalabcoutputfile-\@arabic\c@abc@count}%
|
||||||
|
\else
|
||||||
|
\def\abc@tempfile{#1}%
|
||||||
|
\fi
|
||||||
|
}
|
||||||
|
\define@key{abc}{options}{\def\abc@opt{#1}}
|
||||||
|
\define@key{abc}{postoptions}{\def\abc@postopt{#1}}
|
||||||
|
\define@key{abc}{program}{\def\abc@cmd{#1}\let\abc@parm\@empty}
|
||||||
|
\define@key{abc}{width}{\def\abc@width{#1}}
|
||||||
|
\define@key{abc}{center}[true]{\csname abc@center#1\endcsname}
|
||||||
|
\define@key{abc}{extension}{\def\abc@ext{.#1}}
|
||||||
|
\def\abc@grab[#1]{\let\abc@width=\abcwidth
|
||||||
|
\ifabc@saveall
|
||||||
|
\setkeys{abc}{name,#1}%
|
||||||
|
\else
|
||||||
|
\setkeys{abc}{#1}%
|
||||||
|
\fi\abc@start}
|
||||||
|
% \end{macrocode}
|
||||||
|
% The final part of the environment; we do the processing, if
|
||||||
|
% required and then include the graphics file. If none is found, the
|
||||||
|
% simple name is used, to recall that some processing is to be done.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\def\endabc{%
|
||||||
|
\abc@finish
|
||||||
|
\trivlist\item[]\ifabc@center\centering\fi
|
||||||
|
\IfFileExists{\abc@tempfile.\abc@finalext}
|
||||||
|
{\includegraphics[width=\abc@width]{\abc@tempfile.\abc@finalext}}%
|
||||||
|
{\global\abc@warningtrue\fbox{\abc@tempfile}%
|
||||||
|
\global\abc@unprocessedfilestrue}%
|
||||||
|
\endtrivlist
|
||||||
|
}
|
||||||
|
% \end{macrocode}
|
||||||
|
% The command version is similar. The only difference is that we
|
||||||
|
% issue a warning if the named file does not exist.
|
||||||
|
% \begin{macrocode}
|
||||||
|
\def\abcinput{\@ifnextchar[\abc@grabinput{\abc@grabinput[]}}
|
||||||
|
\def\abc@grabinput[#1]#2{\let\abc@width=\abcwidth\setkeys{abc}{#1}%
|
||||||
|
\begingroup\def\abc@tempfile{#2}%
|
||||||
|
\IfFileExists{\abc@tempfile\abc@ext}
|
||||||
|
{%
|
||||||
|
\abc@process
|
||||||
|
\begin{center}
|
||||||
|
\IfFileExists{\abc@tempfile.\abc@finalext}
|
||||||
|
{\includegraphics[width=\abc@width]{\abc@tempfile.\abc@finalext}}%
|
||||||
|
{\fbox{\abc@tempfile}}%
|
||||||
|
\end{center}%
|
||||||
|
\endgroup
|
||||||
|
}
|
||||||
|
{\PackageWarning{\abc@packagename}{No file \abc@tempfile\abc@ext\space found}}%
|
||||||
|
}
|
||||||
|
%</package>
|
||||||
|
% \end{macrocode}
|
||||||
|
% \end{macro}
|
||||||
|
% \end{environment}
|
||||||
|
% \begin{macrocode}
|
||||||
|
%<*package-mup>
|
||||||
|
\ProvidesPackage{mup}
|
||||||
|
\DeclareOption*{\PassOptionsToPackage{\CurrentOption}{abc}}
|
||||||
|
\ProcessOptions\relax
|
||||||
|
\RequirePackage[mup]{abc}
|
||||||
|
%</package-mup>
|
||||||
|
% \end{macrocode}
|
||||||
|
% \Finale
|
||||||
63
abc/abc.ins
Normal file
63
abc/abc.ins
Normal file
|
|
@ -0,0 +1,63 @@
|
||||||
|
%%
|
||||||
|
%% abc.ins
|
||||||
|
%% Copyright 2006-2016 Enrico Gregorio
|
||||||
|
%%
|
||||||
|
%% This program is provided under the terms of the
|
||||||
|
%% LaTeX Project Public License distributed from CTAN
|
||||||
|
%% archives in directory macros/latex/base/lppl.txt.
|
||||||
|
%%
|
||||||
|
%% Author: Enrico Gregorio
|
||||||
|
%% Enrico dot Gregorio at univr dot it
|
||||||
|
%%
|
||||||
|
%% This work has the LPPL maintenance status "author-maintained".
|
||||||
|
%%
|
||||||
|
%% This file will generate fast loadable files and documentation
|
||||||
|
%% driver files from the doc files in this package when run through
|
||||||
|
%% LaTeX or TeX.
|
||||||
|
%%
|
||||||
|
%% --------------- start of docstrip commands ------------------
|
||||||
|
%%
|
||||||
|
\input docstrip
|
||||||
|
\preamble
|
||||||
|
|
||||||
|
Copyright 2006-2016 Enrico Gregorio
|
||||||
|
|
||||||
|
This program is provided under the terms of the
|
||||||
|
LaTeX Project Public License distributed from CTAN
|
||||||
|
archives in directory macros/latex/base/lppl.txt.
|
||||||
|
|
||||||
|
Author: Enrico Gregorio
|
||||||
|
Enrico dot Gregorio at univr dot it
|
||||||
|
|
||||||
|
This work has the LPPL maintenance status "author-maintained".
|
||||||
|
|
||||||
|
\endpreamble
|
||||||
|
|
||||||
|
\keepsilent
|
||||||
|
\askforoverwritefalse
|
||||||
|
|
||||||
|
\Msg{*** Generating the package files ***}
|
||||||
|
\generate{\file{abc.sty}{\from{abc.dtx}{package}}%
|
||||||
|
\file{example.tex}{\from{abc.dtx}{example}}%
|
||||||
|
\file{mup.sty}{\from{abc.dtx}{package-mup}}%
|
||||||
|
\file{mupexa.tex}{\from{abc.dtx}{example-mup}}%
|
||||||
|
\nopreamble\nopostamble
|
||||||
|
\file{poll.abc}{\from{abc.dtx}{abc}}%
|
||||||
|
\file{simple.mup}{\from{abc.dtx}{mup}}%
|
||||||
|
}
|
||||||
|
|
||||||
|
\Msg{***********************************************************}
|
||||||
|
\Msg{*}
|
||||||
|
\Msg{* To finish the installation you have to move the following}
|
||||||
|
\Msg{* files into a directory searched by TeX:}
|
||||||
|
\Msg{*}
|
||||||
|
\Msg{* \space\space abc.sty}
|
||||||
|
\Msg{*}
|
||||||
|
\Msg{*}
|
||||||
|
\Msg{* To produce the documentation on abc's code run the}
|
||||||
|
\Msg{* file ending with `.dtx' through (pdf)LaTeX.}
|
||||||
|
\Msg{*}
|
||||||
|
\Msg{* Happy TeXing}
|
||||||
|
\Msg{***********************************************************}
|
||||||
|
|
||||||
|
\endbatchfile
|
||||||
BIN
abc/abc.pdf
Normal file
BIN
abc/abc.pdf
Normal file
Binary file not shown.
234
inputs/intervalle.tex
Normal file
234
inputs/intervalle.tex
Normal file
|
|
@ -0,0 +1,234 @@
|
||||||
|
\section{Intervalle}
|
||||||
|
|
||||||
|
\begin{definition}[Schall]
|
||||||
|
\vocab{Schall} ist eine Funktion $f: \text{Zeit} \to \text{Druck}$ bzw. $f: \text{Zeit} \to \text{Luftbewegung}$
|
||||||
|
\end{definition}
|
||||||
|
|
||||||
|
\begin{definition}[Ton]
|
||||||
|
Ein \vocab{Ton} entspricht einer Schwingungsfrequenz.
|
||||||
|
\end{definition}
|
||||||
|
|
||||||
|
\begin{observe}
|
||||||
|
Die Funktion $\sin(2\pi \cdot f \cdot t)$ ist periodisch mit $T_0$ genau dann, wenn $f = k \cdot \frac{1}{T_0}$ für ein $k \in \Z$.
|
||||||
|
\end{observe}
|
||||||
|
|
||||||
|
\begin{definition}[Lineares Modell der MTT]
|
||||||
|
Jede Funktion mit Periode $T_0$ kann als Summe von Funktionen der Form $a \cdot \sin(2\pi \cdot f \cdot t), a\cdot \cos(2\pi\cdot f\cdot t)$, $f = k \cdot \frac{1}{T_0}, a \in \R, k \in \Z$ dargestellt werden.
|
||||||
|
|
||||||
|
Für $k=1$ ergibt sich die \vocab{Grundfrequenz} $\frac{2\pi}{T}$, für $k \ge 2$ reden wir von \vocab[Oberton]{Obertönen}.
|
||||||
|
\end{definition}
|
||||||
|
|
||||||
|
|
||||||
|
\todo{Obertöne Saiteninstrument (Alle Obertöne), Flöte, Querflöte (Obertöne nur für $k \in 2\N + 1$)}
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\begin{table}[htpb]
|
||||||
|
\centering
|
||||||
|
\caption{Obertöne}
|
||||||
|
\label{tab:obertoene}
|
||||||
|
\begin{tabular}{clcccc}
|
||||||
|
$k$ & Ton & Frequenz-& Halb- & EDO12 & Reine Intervalle\\
|
||||||
|
& & verhältnis & töne& &(Cent) \\
|
||||||
|
\hline
|
||||||
|
$1$ & C \\
|
||||||
|
& $\shortdownarrow$ Oktave & $2$ & $10$ & $2,000$ & $1200$\\
|
||||||
|
$2$ & C \\
|
||||||
|
& $\shortdownarrow$ Quinte & $\frac{3}{2}$ & $7$ & $1,4989$ & $702$\\
|
||||||
|
$3$ & G \\
|
||||||
|
&$\shortdownarrow$ Quarte & $\frac{4}{3}$ & $5$ & $1,3348$ & $498$\\
|
||||||
|
$4$ & C\\
|
||||||
|
&$\shortdownarrow$ gr. Terz & $\frac{5}{4}$ & $4$ & $1,2599$ & $386$\\
|
||||||
|
$5$ & E \\
|
||||||
|
&$\shortdownarrow$ kl. Terz & $\frac{6}{5}$ & $3$ & $1,1892$ & $316$\\
|
||||||
|
$6$ & G\\
|
||||||
|
&$\shortdownarrow$ & $\frac{7}{6}$ & $3$? & & $267$\\
|
||||||
|
$7$ & B ? \\
|
||||||
|
&$\shortdownarrow$ & $\frac{8}{7}$ & $2$? & & $231$\\
|
||||||
|
$8$ & C\\
|
||||||
|
&$\shortdownarrow$ gr. Sekunde & $\frac{9}{8}$ & $2$ & $1,1225$ & $204$\\
|
||||||
|
$9$ & D \\
|
||||||
|
&$\shortdownarrow$ gr. Sekunde & $\frac{10}{9}$ & 2 & $1,1225$& $182$\\
|
||||||
|
$10$ & E \\
|
||||||
|
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
\begin{observe}
|
||||||
|
$\frac{9}{8} = \frac{10}{9}$ ???
|
||||||
|
\end{observe}
|
||||||
|
|
||||||
|
Es ergeben sich außerdem
|
||||||
|
\begin{table}[htpb]
|
||||||
|
\centering
|
||||||
|
\caption{Intervalle}
|
||||||
|
\label{tab:intervale}
|
||||||
|
\begin{tabular}{lll}
|
||||||
|
Intervall & Verhältnis & Reines Intervall (Cent)\\
|
||||||
|
gr. Sexte & $\frac{5}{3}$ &$884$\\
|
||||||
|
kl. Sexte & $\frac{8}{5}$ &$814$\\
|
||||||
|
kl. Septime & $\frac{9}{5} \approx \frac{7}{4}$ & $1018 \approx 969$\\
|
||||||
|
Tritonus & $\sqrt{2}$
|
||||||
|
\end{tabular}
|
||||||
|
\end{table}
|
||||||
|
|
||||||
|
|
||||||
|
\begin{remark}
|
||||||
|
Es ergibt sich als Frequenzverhältnis (in Bezug auf C)
|
||||||
|
für gis (über E) $25:16$
|
||||||
|
und für as $8:5$. Diese Töne sind hier also tatsächlich verschieden.
|
||||||
|
\end{remark}
|
||||||
|
\begin{remark}
|
||||||
|
Auf der Violine spielt man häufig trotzdem das gis höher als das as.
|
||||||
|
\end{remark}
|
||||||
|
|
||||||
|
\todo{Skizze: Versuch der Konstruktion eines Tonvorrates mit sauberen Intervallen}
|
||||||
|
|
||||||
|
Buchempfehlung: R. Duffin - ``How equal temperament ruined harmony - and why you should care''.
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
\todo{Bild Flageoletttöne}
|
||||||
|
|
||||||
|
|
||||||
|
Da das leider nicht genau aufgeht definieren wir als atomares Intervall:
|
||||||
|
|
||||||
|
\begin{definition}[Halbton]
|
||||||
|
\vocab{Halbton} $\coloneqq 2^{\frac{1}{12}}$.
|
||||||
|
Dieses Stimmungssystem nennt sich \vocab{EDO12} oder auch \vocab{12-TET}.
|
||||||
|
\end{definition}
|
||||||
|
|
||||||
|
Dementsprechend ist ein Intervall mit $n$ Halbtonschritten definiert als $2^{\frac{n}{12}}$.
|
||||||
|
|
||||||
|
Um kleinere Tonabstände beschreiben zu können definieren wir ferner:
|
||||||
|
\begin{definition}[Cent]
|
||||||
|
\vocab{Cent} $\coloneqq 2^{\frac{1}{1200}}$
|
||||||
|
\end{definition}
|
||||||
|
|
||||||
|
\begin{remark}
|
||||||
|
Ein Unterschied von $10ct.$ ist hörbar, im direkten Vergelcih konnten wir im Kurs auch Unterschiede von $3ct.$ hören. \todo{Recherchieren}
|
||||||
|
|
||||||
|
\url{https://sevish.com/scaleworkshop/}
|
||||||
|
\end{remark}
|
||||||
|
|
||||||
|
|
||||||
|
% Tag 3
|
||||||
|
|
||||||
|
|
||||||
|
\begin{definition}[Dur]
|
||||||
|
\vocab{Dur} bezeichnet sowohl eine Tonart, als auch den Akkord, der sich aus den Tönen der 1., 3. und 5. Stufe dieser Tonart ergibt.
|
||||||
|
%\begin{abc}[name=c-dur]
|
||||||
|
% X: 1 % start of header
|
||||||
|
% K: C % scale: C major
|
||||||
|
% "Text"c2 G4 | (3FED c4 G2 |
|
||||||
|
%\end{abc}
|
||||||
|
|
||||||
|
\todo{C-Dur-Tonleiter}
|
||||||
|
Ein Dur-Akkord besteht aus einer großen und einer kleinen Terz, d.h. die Töne haben Frequenzverhältnisse von $1, \frac{5}{4}, \frac{5}{4} \cdot \frac{6}{5} = \frac{6}{4}$.
|
||||||
|
\end{definition}
|
||||||
|
\begin{definition}[Moll]
|
||||||
|
|
||||||
|
\todo{C-Moll-Tonleiter}
|
||||||
|
|
||||||
|
Ein Moll-Akkord besteht aus einer kleinen und einer großen Terz, d.h. die Töne haben Frequenzverhältnisse von $1, \frac{6}{5}, \frac{3}{2}$.
|
||||||
|
\end{definition}
|
||||||
|
|
||||||
|
\begin{definition}[Septakkord]
|
||||||
|
Ein \vocab{Septakkord} fügt zusätzlich noch eine kleine Terz hinzu.
|
||||||
|
Als Septime ergibt sich ein Frequenzverhältnis von $\frac{9}{5}$, $\frac{7}{4}$ oder $\frac{16}{9}$, je nachdem von wo aus der siebte Ton gesucht wird. Für Dur wirkt dabei $\frac{7}{4}$ (Septime zum Grundton) sinnvoller (?)\footnote{Unter der Annahme, dass der Dur-Dreiklang durch die Obertonreihe motiviert ist.}, für Moll $\frac{9}{5}$.
|
||||||
|
|
||||||
|
\end{definition}
|
||||||
|
|
||||||
|
\begin{problem}
|
||||||
|
Wir suchen ein \vocab{equal temperament} / eine \vocab{gleichstufige Stimmung}, die die wichtigsten Intervalle möglichst gut approximiert.
|
||||||
|
\end{problem}
|
||||||
|
|
||||||
|
Die ``Wichtigkeit'' eines Intervalls definieren wir dabei über die Größe des Nenners, d.h. die Intervalle sind in absteigender Wichtigkeit: Oktave, Quinte, Quarte, gr. Terz, \dots
|
||||||
|
|
||||||
|
Falls sowohl Oktaven als auch Quinten übereinstimmen sollen, bräuchten wir $a,b \in \N_{>0}$, so dass $2^a = \left( \frac{3}{2} \right)^b$. Solche existieren offenbar nicht.
|
||||||
|
|
||||||
|
Reelle Lösungen existieren, mit $\frac{b}{a} = \frac{\log 2}{\log \frac{3}{2}}$. Mit Hilfe von \vocab[Kettenbruch]{Kettenbrüchen} finden wir möglichst gute Näherungen.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{notation}[Kettenbruchzerlegung]
|
||||||
|
Wir schreiben $[a;b,c,d,\ldots]$, $a \in \Z, b,c,d, \ldots \in \N_{+}$ für
|
||||||
|
\[
|
||||||
|
a + \frac{1}{b + \frac{1}{c + \frac{1}{d + \ldots}}}
|
||||||
|
\]
|
||||||
|
|
||||||
|
\end{notation}
|
||||||
|
Eine Näherung ist besser, je größer die erste weggelassene Zahl ist. Näherungen sich abwechselnd obere und untere Schranken.
|
||||||
|
\begin{example}
|
||||||
|
\[
|
||||||
|
\sqrt{2} = [1; \overline{2}] = 1 + \frac{1}{2 + \frac{1}{2 + \frac{1}{2 + \frac{1}{2 + \ldots}}}}
|
||||||
|
\]
|
||||||
|
da $\sqrt{2} -1 = \frac{1}{\sqrt{2} +1} = \frac{1}{2 + (\sqrt{2} -1)}$.
|
||||||
|
|
||||||
|
Als Näherung ergibt sich beispielsweise
|
||||||
|
\[
|
||||||
|
[1;2,2,2] = 1+ \frac{1}{2+ \frac{1}{2 + \frac{1}{2}}} = \frac{17}{12} = 1,41\overline{6}
|
||||||
|
\]
|
||||||
|
\end{example}
|
||||||
|
|
||||||
|
Die Kettenbruchentwicklung von $\frac{\log 2}{ \log \frac{3}{2}}$ ist $[1; 1,2,2,3,1,5,2,23, \ldots]$.
|
||||||
|
Näherungen sind:
|
||||||
|
\begin{itemize}
|
||||||
|
|
||||||
|
|
||||||
|
\item $[1;1] = 2$
|
||||||
|
|
||||||
|
Für die Quinte ergibt sich $2^{\frac{1}{2}} \approx 1,4142\ldots$
|
||||||
|
\item $[1;1,2] = \frac{5}{3}$ (ein Halbtonschritt Abweichung, Pentatonik)
|
||||||
|
|
||||||
|
|
||||||
|
Quinte: $2^{\frac{5}{3}} \approx 1,5157\ldots$
|
||||||
|
|
||||||
|
Die große Terz wird durch eine Quarte approximiert, $2^{\frac{2}{5}} = 1,319\ldots$
|
||||||
|
|
||||||
|
\item $[1;1,2,2] = \frac{12}{7}$ (EDO12),
|
||||||
|
|
||||||
|
Quinte: $2^{\frac{7}{12}} \approx 1,49840\ldots$
|
||||||
|
|
||||||
|
Gr. Terz: $2^{\frac{4}{12}} \approx 1,2599\ldots$
|
||||||
|
|
||||||
|
Kl. Septime: $2^{\frac{10}{12}} \approx 1,781\ldots$
|
||||||
|
|
||||||
|
|
||||||
|
\item $[1;1,2,2,3] = \frac{41}{24}$
|
||||||
|
|
||||||
|
Quinte: $2^{\frac{24}{41}} \approx 1,50042\ldots$
|
||||||
|
|
||||||
|
Gr. Terz: $2^{\frac{13}{41}} \approx 1,2458\ldots$
|
||||||
|
|
||||||
|
|
||||||
|
\item $[1;1,2,2,3,1] = \frac{53}{31}$
|
||||||
|
Quinte: $2^{\frac{31}{53}} \approx 1,49994\ldots$
|
||||||
|
|
||||||
|
Gr. Terz: $2^{\frac{17}{53}} \approx 1,24898\ldots$
|
||||||
|
|
||||||
|
Kl. Septime: $2^{\frac{43}{53}} \approx 1,7548\ldots$
|
||||||
|
|
||||||
|
|
||||||
|
\item $[1;1,2,2,3,1,5] = \frac{306}{179}$
|
||||||
|
|
||||||
|
Quinte: $2^{\frac{197}{306}} \approx 1,5000050\ldots$
|
||||||
|
|
||||||
|
\item $[1;1,2,2,3,1,5,2] = \frac{665}{389}$
|
||||||
|
|
||||||
|
\end{itemize}
|
||||||
|
|
||||||
|
Das optimiert zunächst nur Oktaven und Quinten. Da Quarten der Rest einer Quinte zur Oktave sind, werden diese ebenfalls gut approximiert.
|
||||||
|
|
||||||
|
Videos zu EDO53: \url{https://www.youtube.com/watch?v=ILcgB_kOWzM}, \url{https://www.youtube.com/watch?v=T5OvAjzWF2Y}, \url{https://www.youtube.com/watch?v=xVZy9GUeMqY}
|
||||||
|
|
||||||
|
Eine große Terz lässt sich durch Quinten erreichen, indem man 4 quinten nach oben und 2 Oktaven nach unten geht. Als Frequenzverhältnis ergibt sich dann $\left( \frac{3}{2} \right)^4 \cdot \frac{1}{2^2} = \frac{81}{64}$. Die Abweichung $\frac{81}{80}$ zum Frequenzverhältnis $\frac{5}{4}$ wird als \vocab{syntonisches Komma} bezeichnet ($21,5ct.$).
|
||||||
|
In EDO53 entspricht ein Tonschritt ($22,6ct.$ ) in etwa dem syntonischen Komma.
|
||||||
|
|
||||||
|
\begin{remark}[Bohlen-Pierce-Skala]
|
||||||
|
$3^{\frac{k}{13}}, k \in \Z$. Ein einzelner Schritt liegt zwischen einem Halbton und einem Ganzton. Faktor $3$ und Faktor $5$ werden gut approximiert, aber es gibt keine sinnvolle Oktaven.
|
||||||
|
|
||||||
|
``Ich will das jetzt nicht werten, aber ich würde es als experimentell bezeichnen.''
|
||||||
|
\end{remark}
|
||||||
|
\begin{remark}
|
||||||
|
In der Musik aller Kulturen findet sich das Konzept einer Oktave.
|
||||||
|
\end{remark}
|
||||||
|
|
@ -18,15 +18,15 @@
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
\begin{figure}
|
%\begin{figure}
|
||||||
\centering
|
% \centering
|
||||||
\begin{tikzcd}
|
\begin{tikzcd}
|
||||||
\text{Noten} \arrow{r}{}& \text{Instrumente}\arrow{d}{}\\
|
\text{Noten} \arrow{r}{}& \text{Instrumente}\arrow{d}{}\\
|
||||||
& \text{Schall}\arrow{d}{} \\
|
& \text{Schall}\arrow{d}{} \\
|
||||||
\text{Empfindung} \arrow{uu}{\text{komponieren}} & \text{Ohr}\arrow{l}{}
|
\text{Empfindung} \arrow{uu}{\text{komponieren}} & \text{Ohr}\arrow{l}{}
|
||||||
\end{tikzcd}
|
\end{tikzcd}
|
||||||
\label{musikkomdiag}
|
\label{musikkomdiag}
|
||||||
\end{figure}
|
%\end{figure}
|
||||||
|
|
||||||
|
|
||||||
\paragraph{Theorie}
|
\paragraph{Theorie}
|
||||||
|
|
@ -135,110 +135,3 @@ Einige Aspekte werden in klassischer Musiktheorie nicht behandelt:
|
||||||
|
|
||||||
Wir wollen im Folgenden Musiktheorie aus Mathematik und möglichst einfachen Axiomen aufzubauen.
|
Wir wollen im Folgenden Musiktheorie aus Mathematik und möglichst einfachen Axiomen aufzubauen.
|
||||||
|
|
||||||
\subsection{Intervalle}
|
|
||||||
|
|
||||||
\begin{definition}[Schall]
|
|
||||||
\vocab{Schall} ist eine Funktion $f: \text{Zeit} \to \text{Druck}$ bzw. $f: \text{Zeit} \to \text{Luftbewegung}$
|
|
||||||
\end{definition}
|
|
||||||
|
|
||||||
\begin{definition}[Ton]
|
|
||||||
Ein \vocab{Ton} entspricht einer Schwingungsfrequenz.
|
|
||||||
\end{definition}
|
|
||||||
|
|
||||||
\begin{observe}
|
|
||||||
Die Funktion $\sin(2\pi \cdot f \cdot t)$ ist periodisch mit $T_0$ genau dann, wenn $f = k \cdot \frac{1}{T_0}$ für ein $k \in \Z$.
|
|
||||||
\end{observe}
|
|
||||||
|
|
||||||
\begin{definition}[Lineares Modell der MTT]
|
|
||||||
Jede Funktion mit Periode $T_0$ kann als Summe von Funktionen der Form $a \cdot \sin(2\pi \cdot f \cdot t), a\cdot \cos(2\pi\cdot f\cdot t)$, $f = k \cdot \frac{1}{T_0}, a \in \R, k \in \Z$ dargestellt werden.
|
|
||||||
|
|
||||||
Für $k=1$ ergibt sich die \vocab{Grundfrequenz} $\frac{2\pi}{T}$, für $k \ge 2$ reden wir von \vocab[Oberton]{Obertönen}.
|
|
||||||
\end{definition}
|
|
||||||
|
|
||||||
|
|
||||||
\todo{Obertöne Saiteninstrument (Alle Obertöne), Flöte, Querflöte (Obertöne nur für $k \in 2\N + 1$)}
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
\begin{table}[htpb]
|
|
||||||
\centering
|
|
||||||
\caption{Obertöne}
|
|
||||||
\label{tab:obertoene}
|
|
||||||
\begin{tabular}{clcccc}
|
|
||||||
$k$ & Ton & Frequenz-& Halb- & EDO12 & Reine Intervalle\\
|
|
||||||
& & verhältnis & töne& &(Cent) \\
|
|
||||||
\hline
|
|
||||||
$1$ & C \\
|
|
||||||
& $\shortdownarrow$ Oktave & $2$ & $10$ & $2,000$ & $1200$\\
|
|
||||||
$2$ & C \\
|
|
||||||
& $\shortdownarrow$ Quinte & $\frac{3}{2}$ & $7$ & $1,4989$ & $702$\\
|
|
||||||
$3$ & G \\
|
|
||||||
&$\shortdownarrow$ Quarte & $\frac{4}{3}$ & $5$ & $1,3348$ & $498$\\
|
|
||||||
$4$ & C\\
|
|
||||||
&$\shortdownarrow$ gr. Terz & $\frac{5}{4}$ & $4$ & $1,2599$ & $386$\\
|
|
||||||
$5$ & E \\
|
|
||||||
&$\shortdownarrow$ kl. Terz & $\frac{6}{5}$ & $3$ & $1,1892$ & $316$\\
|
|
||||||
$6$ & G\\
|
|
||||||
&$\shortdownarrow$ & $\frac{7}{6}$ & $3$? & & $267$\\
|
|
||||||
$7$ & B ? \\
|
|
||||||
&$\shortdownarrow$ & $\frac{8}{7}$ & $2$? & & $231$\\
|
|
||||||
$8$ & C\\
|
|
||||||
&$\shortdownarrow$ gr. Sekunde & $\frac{9}{8}$ & $2$ & $1,1225$ & $204$\\
|
|
||||||
$9$ & D \\
|
|
||||||
&$\shortdownarrow$ gr. Sekunde & $\frac{10}{9}$ & 2 & $1,1225$& $182$\\
|
|
||||||
$10$ & E \\
|
|
||||||
|
|
||||||
\end{tabular}
|
|
||||||
\end{table}
|
|
||||||
|
|
||||||
\begin{observe}
|
|
||||||
$\frac{9}{8} = \frac{10}{9}$ ???
|
|
||||||
\end{observe}
|
|
||||||
|
|
||||||
Es ergeben sich außerdem
|
|
||||||
\begin{table}[htpb]
|
|
||||||
\centering
|
|
||||||
\caption{Intervalle}
|
|
||||||
\label{tab:intervale}
|
|
||||||
\begin{tabular}{lll}
|
|
||||||
Intervall & Verhältnis & Reines Intervall (Cent)\\
|
|
||||||
gr. Sexte & $\frac{5}{3}$ &$884$\\
|
|
||||||
kl. Sexte & $\frac{8}{5}$ &$814$\\
|
|
||||||
kl. Septime & $\frac{9}{5} \approx \frac{7}{4}$ & $1018 \approx 969$\\
|
|
||||||
Tritonus & $\sqrt{2}$
|
|
||||||
\end{tabular}
|
|
||||||
\end{table}
|
|
||||||
|
|
||||||
|
|
||||||
\begin{remark}
|
|
||||||
Es ergibt sich als Frequenzverhältnis (in Bezug auf C)
|
|
||||||
für gis (über E) $25:16$
|
|
||||||
und für as $8:5$. Diese Töne sind hier also tatsächlich verschieden.
|
|
||||||
\end{remark}
|
|
||||||
|
|
||||||
\todo{Skizze: Versuch der Konstruktion eines Tonvorrates mit sauberen Intervallen}
|
|
||||||
|
|
||||||
Buchempfehlung: R. Duffin - ``How equal temperament ruined harmony - and why you should care''.
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
\todo{Bild Flageoletttöne}
|
|
||||||
|
|
||||||
|
|
||||||
Da das leider nicht genau aufgeht definieren wir als atomares Intervall:
|
|
||||||
|
|
||||||
\begin{definition}[Halbton]
|
|
||||||
\vocab{Halbton} $\coloneqq 2^{\frac{1}{12}}$.
|
|
||||||
Dieses Stimmungssystem nennt sich \vocab{EDO12} oder auch \vocab{12-TET}.
|
|
||||||
\end{definition}
|
|
||||||
|
|
||||||
Dementsprechend ist ein Intervall mit $n$ Halbtonschritten definiert als $2^{\frac{n}{12}}$.
|
|
||||||
|
|
||||||
Um kleinere Tonabstände beschreiben zu können definieren wir ferner:
|
|
||||||
\begin{definition}[Cent]
|
|
||||||
\vocab{Cent} $\coloneqq 2^{\frac{1}{1200}}$
|
|
||||||
\end{definition}
|
|
||||||
|
|
||||||
\begin{remark}
|
|
||||||
Die Wahrnehmungsschwelle liegt bei \todo{Recherchieren}
|
|
||||||
\end{remark}
|
|
||||||
|
|
|
||||||
|
|
@ -5,6 +5,7 @@
|
||||||
\author{}
|
\author{}
|
||||||
|
|
||||||
\usepackage{musiktheorie}
|
\usepackage{musiktheorie}
|
||||||
|
%\usepackage{abc/abc}
|
||||||
|
|
||||||
\begin{document}
|
\begin{document}
|
||||||
|
|
||||||
|
|
@ -17,6 +18,7 @@
|
||||||
\cleardoublepage
|
\cleardoublepage
|
||||||
|
|
||||||
\input{inputs/uebersicht.tex}
|
\input{inputs/uebersicht.tex}
|
||||||
|
\input{inputs/intervalle.tex}
|
||||||
|
|
||||||
|
|
||||||
\end{document}
|
\end{document}
|
||||||
|
|
|
||||||
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skizzen.xopp
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skizzen.xopp
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Reference in a new issue