en: music-and-technology-synthesis-two-dimensional-arrays: New file

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

Makefile.am

@@ -189,7 +189,8 @@ SECTIONS_EN = \
 	src/en/sections/music-and-technology-synthesis-harmony.tex \
 	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-arrays.tex \
+  src/en/sections/music-and-technology-synthesis-two-dimensional-arrays.tex
 
 SECTIONS_OUT_EN = \
 	$(foreach section, $(SECTIONS_EN), out/$(section))

src/en/sections/music-and-technology-synthesis-two-dimensional-arrays.tex

@@ -0,0 +1,93 @@
+\documentclass[../sparc.tex]{subfiles}
+\graphicspath{{\subfix{../images/}}}
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\newpage
+\subsection{Two-dimensional arrays}
+\index{Programming!Array!Two-dimensional array}
+
+Wouldn't it be cool to store the notes of our composition along with their
+lengths in one array?  Luckily we have an option to do that: using a
+\emph{two-dimensional array}.
+
+Schematic representation of a two-dimensional array is shown as the table
+\ref{table:array-example-2}.
+
+\begin{table}[ht]
+  \centering
+  \begin{tabular}{r|l|l|l}
+    \multicolumn{1}{l}{Row} & \multicolumn{2}{l}{Column}                         &   \\
+    \multicolumn{1}{l}{}         & \multicolumn{1}{l}{0} & \multicolumn{1}{l}{1} &   \\
+    \cline{2-3}
+    0                            & с4                    & 4                     &   \\
+    \cline{2-3}
+    1                            & с4                    & 4                     &   \\
+    \cline{2-3}
+    2                            & g4                    & 4                     &   \\
+    \cline{2-3}
+    3                            & g4                    & 4                     &   \\
+    \cline{2-3}
+    4                            & a4                    & 4                     &   \\
+    \cline{2-3}
+    5                            & a4                    & 4                     &   \\
+    \cline{2-3}
+    6                            & g4                    & 2                     &   \\
+    \cline{2-3}
+  \end{tabular}
+  \label{table:array-example-2}
+\end{table}
+
+Each row of the array stores a description of one note.  The zeroth column holds
+the note frequency and the first column holds its length as the fraction
+denominator, where the numerator is the length of the bar.  For example, the
+zeroth note (``C4'') has the length of $\frac{1}{4}$, so the in the array the
+length is specified as 4.
+
+In the program code we can write down this table as the following array:
+
+\begin{minted}{cpp}
+  float melody[28][2] = {
+    {c4, 4}, {c4, 4}, {g4, 4}, {g4, 4},
+    {a4, 4}, {a4, 4}, {g4, 2},
+    {f4, 4}, {f4, 4}, {e4, 4}, {e4, 4},
+    {d4, 4}, {d4, 4}, {c4, 2},
+    {g4, 4}, {g4, 4}, {f4, 4}, {f4, 4},
+    {e4, 4}, {e4, 4}, {d4, 2},
+    {g4, 4}, {g4, 4}, {f4, 4}, {f4, 4},
+    {e4, 4}, {e4, 4}, {d4, 2},
+  };
+\end{minted}
+
+As can be seen from this example, each element of our array in fact just an
+one-dimensional array, surrounded with curly brackets.  For example, the element
+with the index 0 of our array stores an one-dimensional array \texttt{\{c4,
+ 4\}}, that in turn holds the note (``c4'') and its length (4.)
+
+Now we can adapt the code that plays the melody for using the two-dimensional
+array:
+
+\begin{minted}{cpp}
+  // ...
+
+  void loop() {
+    const long BPM = 120;
+    const long MINUTE = 60000000;
+    const long T = (MINUTE / BPM) * 4;
+
+    for (int note_idx = 0; note_idx < 28; note_idx++) {
+      play_tone(SPEAKER_PIN,
+                melody[note_idx][0],
+                T / melody[note_idx][1]);
+      delay(100);
+    }
+  }
+\end{minted}
+
+Using a two-dimensional array, we can briefly and succinctly describe even more
+complicated melodies than ``Twinkle, Twinkle, Little Star''.
+
+At this stage we have to discuss how the \emph{musical staff}, that holds the
+music notes, works.  We need this to be able to read the notes on our own.
+
+\end{document}

src/en/sparc.tex

@@ -136,9 +136,9 @@ \chapter{Music and Technology Synthesis}
 \subfile{sections/music-and-technology-synthesis-octave-system}
 \subfile{sections/music-and-technology-synthesis-simple-melodies}
 \subfile{sections/music-and-technology-synthesis-arrays}
+\subfile{sections/music-and-technology-synthesis-two-dimensional-arrays}
 
 %% TODO:
-%% \subfile{sections/music-and-technology-synthesis-two-dimensional-arrays}
 %% \subfile{sections/music-and-technology-synthesis-staff}
 %% \subfile{sections/music-and-technology-synthesis-rest}
 %% \subfile{sections/music-and-technology-synthesis-dotted-notes}