en: music-and-technology-synthesis-staff: New file

* src/en/sections/music-and-technology-synthesis-staff.tex: New file.
* src/en/sparc.tex: Use it.
* Makefile.am (SECTIONS_EN): Register it.

Makefile.am

@@ -190,7 +190,8 @@ SECTIONS_EN = \
 	src/en/sections/music-and-technology-synthesis-octave-system.tex \
 	src/en/sections/music-and-technology-synthesis-simple-melodies.tex \
 	src/en/sections/music-and-technology-synthesis-arrays.tex \
-  src/en/sections/music-and-technology-synthesis-two-dimensional-arrays.tex
+  src/en/sections/music-and-technology-synthesis-two-dimensional-arrays.tex \
+	src/en/sections/music-and-technology-synthesis-staff.tex
 
 SECTIONS_OUT_EN = \
 	$(foreach section, $(SECTIONS_EN), out/$(section))

src/en/sections/music-and-technology-synthesis-staff.tex

@@ -0,0 +1,160 @@
+\documentclass[../sparc.tex]{subfiles}
+\graphicspath{{\subfix{../images/}}}
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newpage
+\section{Musical staff}
+\index{Music!Musical staff}
+
+We can program simple melodies without knowing the musical notation.  For
+example, we can use complete examples from the internet -- and for the most of
+the popular melodies we can find notes written in the scientific notation (or
+even we can find complete programs for Arduino that play music!)  But at some
+point we can find ourselves in the situation where all we have is just a musical
+score and no more.  Because of that, before we go further, we have to get some
+grasp on the \emph{musical staff}.
+
+Let's take another look on the melody ``Twinkle, Twinkle, Little Star''.
+
+\begin{figure}[ht]
+  \centering
+  \begin{lilypond}
+    \relative c' {
+      \numericTimeSignature
+      \time 4/4
+      c4 c g' g
+      a a g2
+      f4 f e e
+      d d c2
+      g'4 g f f
+      e e d2
+      g4 g f f
+      e e d2
+      c4 c g' g
+      a a g2
+      f4 f e e
+      d d c2
+    }
+    \layout {
+      indent = 0\mm
+      line-width = 100\mm
+      ragged-last = ##t
+    }
+  \end{lilypond}
+  \label{fig:sound-fig-4}
+  \caption{``Twinkle, Twinkle, Little Star''}
+\end{figure}
+
+Before we ignored the position of notes on the ``Y'' axis and used only the
+``already decoded'' notes, written in the scientific notation.  Now it's the
+time to look closely on those groups of five lines and the symbols on them.
+
+Let's start from the lines -- they are called the \emph{musical staff}.
+
+\index{Music!Treble clef} The notes and other symbols are written on top of the
+staff.  At the beginning of a musical composition a special big ``squiggle'' is
+written, which is called \emph{clef}.  The clef allows us to read the notes on
+the staff and their octaves.  In the ``Twinkle, Twinkle, Little Star'' melody
+(\ref{fig:sound-fig-4}) only on type of clef is used which is called
+\emph{treble clef}.  This clef circles the second line from the bottom on the
+staff and that means that the line represents ``G4'' note (as is shown on fig.
+\ref{fig:lilypond-clef-example}.)
+
+\begin{figure}[ht]
+  \centering
+  \begin{lilypond}
+    \relative c' {
+      \numericTimeSignature
+      \time 4/4
+      g'1
+    }
+  \end{lilypond}
+  \label{fig:lilypond-clef-example}
+  \caption{Treble clef and the ``G4'' note.}
+\end{figure}
+
+As we can see on the figure above, the second line from the bottom holds the
+``G4'' note, as the line is circled by the treble clef.  That means that all
+notes written on this line are ``G4'' (the ``G'' note from the fourth octave.)
+
+But notes can be written not only on the lines, but in the middle between lines.
+
+Schematically it can be described as the graph, which is shown on the
+fig. \ref{fig:lilypond-music-graph-1}.
+
+\begin{figure}[ht]
+  \centering
+  \begin{tikzpicture}
+    \node (image) at (2, 0) { \resizebox{1.0\textwidth}{!}{
+        \begin{lilypond}
+          \relative c' {
+            \numericTimeSignature
+            \time 4/4
+            c8 d8 e8 f8 g8 a8 b4
+          }
+        \end{lilypond}
+      }
+    };
+    \foreach \n [count=\i, evaluate=\i as \y using real(\i / 2.6)] in {
+      C4, E4, G4, B4, D5, F5
+    } {
+      \node at (-3.3, \y - 1.6) {\tiny \n};
+    };
+    \foreach \n [count=\i, evaluate=\i as \y using real(\i / 2.6)] in {
+      D4, F4, A4, C5, E5, G5
+    } {
+      \node at (-3.0, \y - 1.4) {\tiny \n};
+    };
+    \draw[thick, ->] (-4.0, -2.0) -- (8.0, -2.0) node[anchor=north east] {x};
+    \draw[thick, ->] (-4.0, -2.0) -- (-4.0, 1.5) node[anchor=north east] {y};
+  \end{tikzpicture}
+  \label{fig:lilypond-music-graph-1}
+  \caption{A musical ``graph''.  ``x'' axis represents time, and ``y'' axis
+    represents the sound frequency.}
+\end{figure}
+
+On this musical graph we can see the notes are arranged in order: ``C'', ``D'',
+``E'', ``F'', ``G'', ``A'' and ``B''.  When we move on the ``y'' axis up, the
+frequency of sounds getting higher, when we move down, the frequencies getting
+lower with each step.
+
+That meas if we go up on this ``musical ladder'' starting from ``G4'', the next
+note will be ``A4'' (as it is placed between the second and the third line.)
+The middle line represents ``B4'' -- and it is the end of the fourth octave.
+After that, if we go even higher, we will get ``C5'' -- the first note from the
+fifth octave.  After ``F5'' there are no more lines, but that does not mean we
+cannot go even higher as additional lines can be written above.
+
+If we go down the ``musical ladder'', starting from the ``G4'' we get ``F4'' on
+the first step down, then ``E4'', then ``D4'' and then ``C4'' -- which is written
+on its own line.  As we can see, it is completely normal to add additional short
+lines, if we want to write very high or very low notes.
+
+To help us with remembering the positions of notes on the musical staff we can
+use special mnemonics.  There are many such mnemonics on the internet.  Our
+variant of a mnemonic for the treble clef is shown on
+fig. \ref{fig:lilypond-music-clef-mnemonic}.
+
+\begin{figure}[ht]
+  \begin{tikzpicture}
+    \node (image) at (4, 2) {
+      \includegraphics[width=8cm]{music-clef-mnemonic}
+    };
+    \draw[thick, ->] (0, -1.0) -- (10, -1.0) node[anchor=north east] {x (Time)};
+    \draw[thick, ->] (0, -1.0) -- (0, 4.0) node[anchor=north east] {y (Frequency)};
+  \end{tikzpicture}
+  \label{fig:lilypond-music-clef-mnemonic}
+  \caption{A mnemonic that helps to remember position of notes in the treble
+    clef.}
+\end{figure}
+
+If we read the words from the bottom to the top, we get the humorous phrase
+``\textbf{E}ating \textbf{G}reen \textbf{B}ananas \textbf{D}isgusts
+\textbf{F}riends \textbf{A}nd \textbf{C}oworkers''.  The first letter encodes
+the note in the scientific notation.  On the above we added two additional
+dashed lines (aside from the five main ones).  The mnemonic encodes only the
+notes on the lines, but with that we can figure out what notes are between the
+lines as well.
+
+\end{document}

src/en/sparc.tex

@@ -137,9 +137,9 @@ \chapter{Music and Technology Synthesis}
 \subfile{sections/music-and-technology-synthesis-simple-melodies}
 \subfile{sections/music-and-technology-synthesis-arrays}
 \subfile{sections/music-and-technology-synthesis-two-dimensional-arrays}
+\subfile{sections/music-and-technology-synthesis-staff}
 
 %% TODO:
-%% \subfile{sections/music-and-technology-synthesis-staff}
 %% \subfile{sections/music-and-technology-synthesis-rest}
 %% \subfile{sections/music-and-technology-synthesis-dotted-notes}
 %% \subfile{sections/music-and-technology-synthesis-flats-and-sharps}