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support; added saveall and nosaveall options}{1} +\glossaryentry{v1.1> =General:>Added \cs {endgroup} when the warning for a non existent file is issued}{1} +\glossaryentry{v1.0> =General:>After long delay decided to publish it}{1} +\glossaryentry{v0.7> =General:>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}{1} +\glossaryentry{v0.7beta> =General:>Added the `postoptions' and `width' keywords}{1} +\glossaryentry{v0.6> =General:>Changed options: erased `nix' and `dos', added `ps2epsidos' to correct a mistake}{1} +\glossaryentry{v0.5> =General:>Added the interface to keyval}{1} +\glossaryentry{v0.4> =General:>Initial version; too many things changed}{1} +\glossaryentry{v.0.1-0.3> =General:>Very preliminar versions}{1} diff --git a/abc/abc.pdf b/abc/abc.pdf index 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zevbJOn^9MxQ(J>FK|6Hzn`+sEYTAgZR87sF&0VZ26L)>IA;?g4EWl(}RAty6r@V3_ zpLhjRx0XMWGqg*y;WH9TrDGM8OUZ0AWJ@>FrVO@EECY#c*Vjy2$&u&i9}KwW#R^tj zGB2wsyKO51Jmj+9%@I~U_a!zz%HbeZdQYLTU;QU~8A`%VAtNaR0`T&xA=Cl?20C6K A?*IS* diff --git a/inputs/akkorde.tex b/inputs/akkorde.tex new file mode 100644 index 0000000..6a507a1 --- /dev/null +++ b/inputs/akkorde.tex @@ -0,0 +1,142 @@ +\section{Akkorde} + +\begin{definition}[Akkord] + Ein \vocab{Akkord} ist eine Menge von mindestens $3$ Tönen. +\end{definition} + +\begin{notation} + Für Töne mit Frequenzen $n \cdot \alpha, m \cdot \alpha,\ldots$ notieren wir im Folgenden $n:m:\ldots$. +\end{notation} + +\begin{example} + Der Akkord $2:3:4$ wird als \vocab{Powerchord} bezeichnet. + + \begin{itemize} + \item linear: $2,3,4$ + \item quadratisch: $1,2,4,5,6,6,7,1,8$ + \end{itemize} + + Verglichen mit der Quinte (\autoref{quinte}) kommen einige Kombinationstöne mehrfach, d.h.~lauter, vor. + + TODO: Noten cgc +\end{example} + +\begin{example}[Dur-Akkord] + Wir betrachten den Akkord $3:4:5$. + + + \begin{itemize} + \item linear: $3,4,5$ + \item quadratisch: ... + \end{itemize} + + Die Kombinationstöne ergeben ein Obertonspektrum des mittleren Tones. + TODO: Noten cfa +\end{example} + + +\begin{example} + Wir betrachten den Akkord $3:4:6$. + + TODO: Noten cfc +\end{example} + +\begin{example} + $3:5:6$ + + TODO: Noten cac + + Als Grundton ergibt sich ein f, welches allerdings im Akkord nicht vorkommt. +\end{example} + +\begin{example}[Dur-Akkord, Grundstellung] + $4:5:6$ + + TODO: Noten fac + + Als Grundton ergibt sich ein $f$. +\end{example} + +\begin{example} + $4:5:7$ + + TODO: Noten f a es? + +\end{example} + +\begin{example} + $4:6:7$ + + TODO: Noten f c es? + + + $F_{3\!\!\!/}^7$ +\end{example} + +\begin{example} + $4:5:6:7$ + + Dur-Septakkord $F^7$ + TODO: Noten f a c es? + +% Dieser Akkord mit reiner Septime entspricht nicht dem normalerweise verwendeten Dur-Septakkord. +\end{example} + +\begin{example} + Der Akkord $5:6:7$ wird als \vocab{verminderter Akkord} bezeichnet. + + TODO: Noten a c es? + $F\!\!\!\!/^7$ + +\end{example} + +\begin{example} + $5:6:8$ + + TODO: Noten acf + +\end{example} + +\begin{example}[Moll-Akkord] + + Der Akkord $10:12:15$ wird als \vocab{Moll-Akkord} bezeichnet. + + TODO: Noten f as c + + Als Grundton der Kombinationstöne ergibt sich ein des, der \vocab{Gegenklang} zu f. +\end{example} + +\begin{example}[Großer Dur-Septakkord] + + $8:10:12:15$ + + TODO: Noten des f as c + + $D\flat^{\text{maj}7}$ + +\end{example} + +\begin{example}[Moll-Septakkord] + $10 : 12 : 15 : 18$ + + TODO: Noten f as c es + + Als Grundton der Kombinationstöne ergibt sich ein des. + Allerdings ist auch das as relativ stark vorhanden. + + +\end{example} + +\begin{example}[Neopolitaner, Sixte ajout\'ee] + + $4:5:6:7:9$ + + TODO: Noten f a c es? g + + $F^{7,9}$ +\end{example} + +\begin{quote} + ``Wenn wir Jazz machen, packen wir einfach noch ein paar Terzen drauf.'' + +\end{quote} diff --git a/inputs/intervalle.tex b/inputs/intervalle.tex index d77d798..98865a1 100644 --- a/inputs/intervalle.tex +++ b/inputs/intervalle.tex @@ -350,6 +350,7 @@ Siehe auch \url{https://en.wikipedia.org/wiki/Beat_(acoustics)#Binaural_beats}. Für das selbe Signal mit verschiedener Lautstärke, $b(t) \coloneqq \lambda a(t), \lambda < 1$, ändert sich dieser Effekt, bei größerer Lautstärke wird der Kombinationston relativ lauter. \begin{example}[Quinte] + \label{quinte} Wir betrachten das Intervall aus Tönen mit Frequenz $2\alpha$ und $3\alpha$. Als Kombinationstöne ergeben sich: \begin{itemize} diff --git a/musiktheorie.tex b/musiktheorie.tex index 87d43a5..70ddafd 100644 --- a/musiktheorie.tex +++ b/musiktheorie.tex @@ -1,7 +1,7 @@ \documentclass[10pt,ngerman,a4paper, fancyfoot, git]{mkessler-script} \course{Musiktheorietheorie} -\lecturer{} +\lecturer{Georg Schröter} \author{} \usepackage{musiktheorie} @@ -19,6 +19,6 @@ \input{inputs/uebersicht.tex} \input{inputs/intervalle.tex} - +\input{inputs/akkorde.tex} \end{document}