diff --git a/.skizzen.autosave.xopp b/.skizzen.autosave.xopp
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diff --git a/abc/README b/abc/README
new file mode 100644
index 0000000..d2847d7
--- /dev/null
+++ b/abc/README
@@ -0,0 +1,58 @@
+The abc package lets you include lines of music written in the ABC Plus
+language (http://abcplus.sourceforge.net).
+
+This is version 2.0b of the package (a maintenance release)
+
+ Copyright 2005-2016 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 work consists of the following files:
+
+README (this file)
+abc.dtx
+abc.ins
+abc.pdf
+
+ and of the derived files
+
+abc.sty
+mup.sty
+example.tex
+poll.abc
+mupexa.tex
+simple.mup
+
+To install the distribution:
+
+o run "latex abc.ins"
+o run "latex -shell-escape example.tex" for a test
+o move "abc.sty" and "mup.sty" to locations where LaTeX will
+  find it (the FAQ on CTAN in /help/uktug-FAQ gives more
+  information about this magic place)
+
+Please note that you need, on your system, the
+utilities "abcm2ps" (http://abcplus.sourceforge.net),
+either "ps2eps" (which comes with TeX Live) or "ps2epsi"
+(which comes with Ghostscript), and epstopdf (which
+comes with TeX Live) if you use pdflatex.
+
+If you want to compile the Mup examples, you need the
+utility "mup" (http://www.arkkra.com), along with the
+Postscript utilities mentioned above.
+
+Note also that you must enable "shell escape" on your
+TeX system via the command line switch (at least); see
+your distribution's documentation. However, this is not
+strictly necessary in order to use the package, see the
+documentation.
+
+2016/05/15
+Enrico Gregorio
diff --git a/abc/abc.dtx b/abc/abc.dtx
new file mode 100644
index 0000000..25fb129
--- /dev/null
+++ b/abc/abc.dtx
@@ -0,0 +1,824 @@
+% \iffalse meta-comment
+%
+% Copyright (C) 2005-2015 by Enrico Gregorio 
+% <Enrico dot Gregorio at univr dot it>
+% -------------------------------------------------------
+% 
+% This file may be distributed and/or modified under the conditions of
+% the LaTeX Project Public License, either version 1.2 of this license
+% or (at your option) any later version.  The latest version of this
+% license is in:
+%
+%    http://www.latex-project.org/lppl.txt
+%
+% and version 1.2 or later is part of all distributions of LaTeX
+% version 1999/12/01 or later.
+%
+% \fi
+%
+% \iffalse
+%<*driver>
+\ProvidesFile{abc.dtx}
+%</driver>
+%<package>\NeedsTeXFormat{LaTeX2e}[1999/12/01]
+%<package>\ProvidesPackage{abc}
+%<*package>
+  [2016/05/15 v2.0b Enrico Gregorio]
+%</package>
+%<*driver>
+\documentclass{ltxdoc}
+\usepackage{verbatim}
+\newenvironment{smallverb}{\footnotesize\verbatim}{\endverbatim}
+\EnableCrossrefs         
+\CodelineIndex
+\RecordChanges
+\begin{document}
+  \DocInput{abc.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \CheckSum{416}
+%
+% \CharacterTable
+%  {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
+%   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
+%   Digits        \0\1\2\3\4\5\6\7\8\9
+%   Exclamation   \!     Double quote  \"     Hash (number) \#
+%   Dollar        \$     Percent       \%     Ampersand     \&
+%   Acute accent  \'     Left paren    \(     Right paren   \)
+%   Asterisk      \*     Plus          \+     Comma         \,
+%   Minus         \-     Point         \.     Solidus       \/
+%   Colon         \:     Semicolon     \;     Less than     \<
+%   Equals        \=     Greater than  \>     Question mark \?
+%   Commercial at \@     Left bracket  \[     Backslash     \\
+%   Right bracket \]     Circumflex    \^     Underscore    \_
+%   Grave accent  \`     Left brace    \{     Vertical bar  \|
+%   Right brace   \}     Tilde         \~}
+%
+% \changes{v2.0b}{2016/05/15}{Use shellesc}
+%
+% \changes{v2.0a}{2015/09/09}{Fixed gobbling of leading lines that
+% start with \%}
+%
+% \changes{v2.0}{2008/03/03}{Many changes, in order to allow for Mup 
+% support; added saveall and nosaveall options}
+%
+% \changes{v1.1}{2007/03/27}{Added \cs{endgroup} when the warning for 
+% a non existent file is issued}
+% 
+% \changes{v1.0}{2006/03/22}{After long delay decided to publish it}
+%
+% \changes{v0.7}{2005/11/21}{Corrected some errors from previous 
+% version; changed `abcinput' to support keyword-value pairs like 
+% the environment; added the production of a batch file when the 
+% `noshellescape' option is active; improved the documentation}
+% 
+% \changes{v0.7beta}{2005/11/19}{Added the `postoptions' and `width' 
+% keywords}
+% 
+% \changes{v0.6}{2005/11/18}{Changed options: erased `nix' and
+% `dos', added `ps2epsidos' to correct a mistake}
+% 
+% \changes{v0.5}{2005/11/13}{Added the interface to keyval}
+% 
+% \changes{v0.4}{2005/11/10}{Initial version; too many things changed}
+% 
+% \changes{v.0.1-0.3}{2005/11/01}{Very preliminar versions}
+%
+% \GetFileInfo{abc.dtx}
+%
+% \DoNotIndex{\newcommand,\newenvironment,\def,\ifpdf,\begin}
+% \DoNotIndex{\DeclareOption,\ExecuteOptions,\RequirePackage}
+% \DoNotIndex{\renewcommand,\else,\fi,\relax,\@bsphack,\@esphack}
+% \DoNotIndex{\active,\AtEndOfPackage,\catcode,\centering}
+% \DoNotIndex{\closeout,\comment,\do,\dospecials,\end,\endcomment}
+% \DoNotIndex{\fbox,\gdef,\immediate,\includegraphics,\let}
+% \DoNotIndex{\linewidth,\message,\newif,\newwrite,\openout}
+% \DoNotIndex{\PackageWarning,\space,\the,\verbatim@line}
+% \DoNotIndex{\verbatim@processline,\verbatim@start,\write}
+% \DoNotIndex{\@makeother,\IfFileExists,\ProcessOptions}
+% \DoNotIndex{\@ifnextchar,\define@key,\MessageBreak,\setkeys}
+% \DoNotIndex{\stepcounter,\newcounter,\trivlist,\AtEndDocument}
+% \DoNotIndex{\@empty,\edef,\csname,\endcsname,\edef,\begingroup}
+% \DoNotIndex{\endgroup,\endtrivlist,\global,\if,\ifx,\item}
+% \DoNotIndex{\PackageWarningNoLine,\PassOptionsToPackage}
+% \DoNotIndex{\ProvidesPackage,\@arabic}
+%
+% \title{The \textsf{abc} package\thanks{This document corresponds to
+% \textsf{abc}~\fileversion, dated \filedate.}}
+%   
+% \author{Enrico Gregorio \\ \texttt{Enrico dot Gregorio at univr dot it}}
+% 
+% \date{\filedate}
+%
+% \maketitle
+%
+% \section{Introduction}
+% There are several ways to set music using \TeX{}, notably
+% Musix\TeX{} and Lilypond.  Both are very powerful and, 
+% consequently, a bit difficult to learn and to use.
+% 
+% From the point of view of notation, the ABC
+% system\footnote{\texttt{http://staffweb.cms.gre.ac.uk/\char`\~c.walshaw/abc/}}
+% is much simpler.  A recent extension of this language, called
+% ABC~Plus\footnote{\texttt{http://abcplus.sourceforge.net}}, allows
+% for setting multiple staves and polyphony.  One of the best programs
+% for converting these notations into sheet music is
+% \texttt{abcm2ps}, which can take an ABC or ABC~Plus file and
+% transform it into a PostScript\texttrademark{} file.
+% 
+% The purpose of this package is to allow \LaTeX{} users to include in
+% their documents small excerpts of music written directly in
+% ABC (Plus).  It exploits the \verb|\write18| technique available with
+% the Web2C implementation of the \TeX{} system and free utilities 
+% like \texttt{ps2eps}, \texttt{ps2epsi} and \texttt{epstopdf}. From
+% version 2.0b we check the existence of the \textsf{shellesc} package
+% in order to be compatible with Lua\TeX.
+% 
+% This package can be used both with \LaTeX{} and
+% \textsc{pdf}\LaTeX{}, without any change in the user's source file.
+% It employs also the package \textsf{keyval} by David Carlisle and
+% ideas from the \textsf{verbatim} package in the \LaTeX{} tools.
+% 
+% Martin Tarenskeen wrote me about possible support of Mup--Music
+% Publisher\footnote{\texttt{http://www.arkkra.com}} and actually it
+% was easy to add it along with some improvements partly suggested by
+% him.  Therefore the package now comes along with a new \textsf{mup}
+% package; see section~\ref{mup}.  I owe many thanks to Martin for
+% testing the new version.
+% 
+% We are studying whether it is feasible to extend support also to
+% other music printing programs like Lilypond.
+%
+% \section{Usage}
+% \DescribeEnv{abc}
+% The only environment provided by this package is \verb|abc| with 
+% the following syntax:
+% \begin{quote}
+% \verb|\begin{abc}[|\meta{keyword}$=$\meta{value}\verb|...]|\\
+% \meta{ABC Plus material}\\
+% \verb|\end{abc}|
+% \end{quote}
+% The environment should be used only in LR-mode.  Its output is set
+% in a `center' environment.  We give a list of the available
+% keywords.
+% \begin{description}
+%
+% \item[\normalfont\texttt{name=}\meta{name}:] \meta{name} is a name
+% for the temporary file which will be output and massaged by
+% \texttt{abcm2ps}. \emph{Warning}: the extension \texttt{.abc} is 
+% automatically added to the file name; esistent files with the same 
+% name will be silently erased. If the keyword is specified without a 
+% value, then the output file receives a unique name.
+%
+% \item[\normalfont\texttt{options=}\meta{options}:] \meta{options}
+% are command line parameters to the \texttt{abcm2ps} utility; the
+% default are `\texttt{-O= -c}'.
+%
+% \item[\normalfont\texttt{postoptions=}\meta{postoptions}:]
+% \meta{postoptions} are possible command line options which, in
+% \texttt{abcm2ps} syntax, go after the file name.
+% 
+% \item[\normalfont\texttt{program=}\meta{program}:] \meta{program} is
+% used to specify an alternative program to \texttt{abc2mps} (if
+% existent).  In this case users must specify completely the command
+% line options, directly in \meta{program} or with \meta{options} and
+% \meta{postoptions}.  For example
+% \begin{quote}
+% \verb|\begin[name=song,program=abctoeps,options={-a -b}]|\\
+% \verb|\begin[name=song,program={abc3ps -a -b}]|
+% \end{quote}
+% (assuming there is an \texttt{abc3ps} program).
+% 
+% \item[\normalfont\texttt{width=}\meta{width}:] \meta{width} should 
+% be a dimension; it is best to express it as a fraction of 
+% \verb|\abcwidth|.
+% 
+% \item[\normalfont\texttt{center}:] This is a boolean, either true 
+% or false; the default is true, if left flush alignment is preferred,
+% specify \texttt{center=false}.
+% 
+% \item[\normalfont\texttt{extension}:] This keyword seems practically 
+% useless, but is needed if one needs to input both ABC and Mup files 
+% in one and the same document. See later on.
+% \end{description}
+% 
+% \DescribeMacro{\abcinput}
+% It is also possible to input an available ABC file. The syntax is
+% \begin{quote}
+% \verb|\abcinput|\oarg{options}\marg{name}
+% \end{quote}
+% where \meta{name} is the name of the file, without the extension 
+% which should be \texttt{.abc}. In the optional argument users can 
+% put keyword-value pairs as for the environment. Of course the 
+% keyword \texttt{name} is ignored here.
+% 
+% \DescribeMacro{\abcwidth}
+% Users have a minimum control (at least in this version) on how to
+% include some lines of music. The only parameter they can modify is 
+% \verb|\abcwidth| with \verb|\renewcommand|. Its normal value is 
+% \verb|\linewidth|. The best thing to do is
+% \begin{quote}
+% \verb|\renewcommand{\abcwidth}{|\meta{fraction}\verb|\linewidth}|
+% \end{quote}
+% where \meta{fraction} is some number between $0$ and~$1$.  Changing
+% this parameter affects every subsequent music inclusion, obeying to
+% the usual scoping rules. The width can be changed locally for the 
+% environment or the command with the method explained before.
+% 
+% \DescribeMacro{\normalabcoutputfile}
+% The name for the generic output files is ``\texttt{out-abc}''.  In
+% the (improbable) case that some file \texttt{out-abc.}\meta{ext} is
+% present in the directory, users can redefine
+% \verb|\normalabcoutputfile| as they like.
+% 
+% \section{Package options}
+% There are some package options, to control what is to be passed for 
+% subsequent processing.
+% 
+% \subsection{\texttt{shellescape} and \texttt{noshellescape}}
+% The option \texttt{shellescape} (default) means that some external
+% programs will be called by \LaTeX{} to get the inclusion of the
+% music lines.  If you don't trust the automatic generation, or your
+% \TeX{} implementation does not allow the trick with \verb|\write18|,
+% then use \texttt{noshellescape}.  In this case, a name should be
+% specified for every `abc' environment, because otherwise ABC output
+% files will be overwritten, since they receive the same generic name,
+% by default. A file named \texttt{out-abc.sh} is produced, 
+% containing the commands to give for elaborating the music files.
+% 
+% \subsection{\texttt{generate} and \texttt{nogenerate}}
+% With the \texttt{generate} option (default) the ABC lines will be
+% processed by the external programs.  The \texttt{nogenerate} option
+% can be used when the ABC sources have not changed, in order to
+% increase speed.  Also in this case, however, a name should be
+% specified for all output ABC files.
+% 
+% \subsection{\texttt{ps2epsi}, \texttt{ps2epsidos} and
+% \texttt{ps2eps}}
+% The option \texttt{ps2eps} (default) means that the \texttt{ps2eps}
+% Perl script will be used for generating the EPS file for graphic
+% inclusion.  Specify the \texttt{ps2epsi} option if you prefer the
+% \texttt{ps2epsi} program; specify \texttt{ps2epsidos} if you are on
+% a system where the utility \texttt{ps2epsi} generates a file with
+% three letter extension \texttt{.epi}.
+% 
+% \subsection{\texttt{nosaveall} and \texttt{saveall}}
+% The first is the default, but the second is called implicitly when
+% the \texttt{noshellescape} is given.  When the \texttt{saveall}
+% option is active, every `abc' environment produces a unique output
+% file; in other words, the \texttt{name} keyword, without value, is
+% given for every environment.  So the \texttt{noshellescape} option
+% 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
diff --git a/abc/abc.ins b/abc/abc.ins
new file mode 100644
index 0000000..085dc59
--- /dev/null
+++ b/abc/abc.ins
@@ -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
diff --git a/abc/abc.pdf b/abc/abc.pdf
new file mode 100644
index 0000000..a24052d
Binary files /dev/null and b/abc/abc.pdf differ
diff --git a/inputs/intervalle.tex b/inputs/intervalle.tex
new file mode 100644
index 0000000..56250fd
--- /dev/null
+++ b/inputs/intervalle.tex
@@ -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}
diff --git a/inputs/uebersicht.tex b/inputs/uebersicht.tex
index 47b4630..486271d 100644
--- a/inputs/uebersicht.tex
+++ b/inputs/uebersicht.tex
@@ -18,15 +18,15 @@
 
 
 
-\begin{figure}
-    \centering
+%\begin{figure}
+%    \centering
     \begin{tikzcd}
         \text{Noten} \arrow{r}{}& \text{Instrumente}\arrow{d}{}\\	
                          & \text{Schall}\arrow{d}{} \\
         \text{Empfindung} \arrow{uu}{\text{komponieren}}       & \text{Ohr}\arrow{l}{}
     \end{tikzcd}
     \label{musikkomdiag}
-\end{figure}
+%\end{figure}
 
 
 \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.
 
-\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}
diff --git a/musiktheorie.tex b/musiktheorie.tex
index b9f9b17..87d43a5 100644
--- a/musiktheorie.tex
+++ b/musiktheorie.tex
@@ -5,6 +5,7 @@
 \author{}
 
 \usepackage{musiktheorie}
+%\usepackage{abc/abc}
 
 \begin{document}
 
@@ -17,6 +18,7 @@
 \cleardoublepage
 
 \input{inputs/uebersicht.tex}
+\input{inputs/intervalle.tex}
 
 
 \end{document}
diff --git a/skizzen.xopp b/skizzen.xopp
index 2cbc8d1..64e79a4 100644
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