Range of a piano : annotate note frequency

Question

I'd like to draw something like this for the piano, but with all notes explicitly draw and labelled with its frequency. I use for the first time the musixtex package so I have no idea how to automate the annotation.

Here is what I've done so far.

\documentclass[preview,border={3cm 2mm 3cm 2mm}]{standalone}% standalone works with adjusting the border.
\usepackage{musixtex}
\begin{document}
\begin{music}
\instrumentnumber{1}
\setstaffs{1}{2}
\setclef{1}{60}
%
\startextract
\notes\qu{`CDEFG 'AB}\enotes
\bar
\notes\qu{CDEFG 'AB}\enotes
\bar
\notes\qu{'CDEFG 'AB}\enotes
\bar
\notes|\qu{cdefg'ab}\enotes
\bar
\notes|\qu{'cdefg 'ab}\enotes
\zendextract
\end{music}
\end{document}

enter image description here

On a different note, do you know lilypond? (http://www.lilypond.org) This is a very sophisticated notation software. — Eekhoorn, Apr 27 '13 at 09:06
@Bugbusters Thanks for editing. The thing with standalone is why is it necessary to adjust the border (maybe I'll ask an other question). — cjorssen, Apr 27 '13 at 09:29
@biologue I'm not stuck with a musixtex answer. If lilypond can do the job, that's ok ;-). — cjorssen, Apr 27 '13 at 09:32
Unrelated: why don't the stems change their orientation at d and b'? — doncherry, Apr 27 '13 at 13:13
@doncherry The \qu in the MWE explicitly draws quarter notes with stem up. There are also \ql for a quarter notes with stem down and \qa for quarter notes with automatic stem direction. — cgnieder, Apr 27 '13 at 15:32

cgnieder · Accepted Answer · 2013-04-29T20:10:14.363

I'm not sure if I understood the question right and this is what you want but here we go: the code uses the fact that a pitch cannot only be specified with a letter but also with a number. The frequencies are calculated with the formula on the linked Wikipedia site. (I don't know why the margins for standalone have to be enlarged manually to see the whole extract...).

% arara: musixtex
\documentclass[preview,border={17cm 2mm 17cm 2mm}]{standalone}
\usepackage[T1]{fontenc}
\usepackage{musixtex}
\usepackage{xcolor}
\usepackage{expl3,xparse}
\ExplSyntaxOn
% define integer variables:
\int_new:N \l__cjorssen_pitch_int
\int_new:N \l__cjorssen_step_int

% define tokenlist variable for the formatted output of the
% frequencies:
\tl_new:N  \l__cjorssen_freq_format_tl
\tl_set:Nn \l__cjorssen_freq_format_tl { \tiny\bfseries }

% macro to write notes and frequencies for one octave
%   #1: the lowest pitch
%   #2: the highest pitch, should not be more than #1+6
%   #3: the difference between pitch number and key number
\cs_new_protected:Npn \cjorssen_write_notes:nnn #1#2#3
  {
    % set the starting pitch:
    \int_set:Nn \l__cjorssen_pitch_int { #1 }
    % set the step to zero:
    \int_zero:N \l__cjorssen_step_int
    % loop until we reach the end pitch:
    \int_do_while:nn { \l__cjorssen_pitch_int <= #2 }
      {
        % \cchar{<pitch>}{<something>} is a musixtex macro that
        % allows setting <something> at the specified <pitch>
        % let's set the frequency below the tone it belongs to:
        \cchar
          { \int_eval:n { \l__cjorssen_pitch_int - 5 } }
          {
            % start a group to keep the format local, just in case
            \group_begin:
              % the format:
              \tl_use:N \l__cjorssen_freq_format_tl
              % let's test at which point of the octave we are
              % and add the needed integer to \l__cjorssen_pitch_int
              % in order to get the right key number with respect to
              % musixtex's pitch number:
              \int_case:nnn { \l__cjorssen_step_int }
                {
                  { 0 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + #3 } }
                  { 1 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 1 + #3 } }
                  { 2 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 2 + #3 } }
                  { 3 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 2 + #3 } }
                  { 4 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 3 + #3 } }
                  { 5 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 4 + #3 } }
                  { 6 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 5 + #3 } }
                }
                {}
              \,Hz
            \group_end:
          }
        % write the note:
        \qu { \int_use:N \l__cjorssen_pitch_int }
        % step the integers for the next round in the loop:
        \int_incr:N \l__cjorssen_step_int
        \int_incr:N \l__cjorssen_pitch_int
      }
  }

% calculate the frequency from the key number
% (using 440Hz for the concert pitch):
\cs_new:Npn \cjorssen_calc_freq:n #1
  { \fp_eval:n { round ( 440 * 2^(((#1)-49)/12) , 2 ) } }

% #1: the lowest pitch
% #2: the highest pitch, should not be more than #1+6
% #3: the difference between pitch number and key number
\NewDocumentCommand \writenotes { mO{#1+6}m }
  { \cjorssen_write_notes:nnn { #1 } { #2 } { #3 } }
\ExplSyntaxOff
\begin{document}
\noindent
\begin{music}
 \instrumentnumber{1}
 \setstaffs{1}{2}
 \setclef{1}{60}
 \setname{1}{}
 \startextract
 \NOTes
  \writenotes{-11}{15}
 \en\bar
 \NOTes
  \writenotes{-4}{20}
 \en\bar
 \NOTes
  \writenotes{3}{25}
 \en\bar
 \NOTEs|
  \writenotes{-2}{42}
 \en\bar
 \NOTEs|
  \writenotes{5}{47}
 \en
 \endextract
\end{music}
\end{document}

enter image description here

Here is the same with the article class:

% arara: musixtex
\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{musixtex}
\usepackage{xcolor}
\usepackage{expl3,xparse}
\ExplSyntaxOn
% define integer variables:
\int_new:N \l__cjorssen_pitch_int
\int_new:N \l__cjorssen_step_int

% define tokenlist variable for the formatted output of the
% frequencies:
\tl_new:N  \l__cjorssen_freq_format_tl
\tl_set:Nn \l__cjorssen_freq_format_tl { \tiny\bfseries }

% macro to write notes and frequencies for one octave
%   #1: the lowest pitch
%   #2: the highest pitch, should not be more than #1+6
%   #3: the difference between pitch number and key number
\cs_new_protected:Npn \cjorssen_write_notes:nnn #1#2#3
  {
    % set the starting pitch:
    \int_set:Nn \l__cjorssen_pitch_int { #1 }
    % set the step to zero:
    \int_zero:N \l__cjorssen_step_int
    % loop until we reach the end pitch:
    \int_do_while:nn { \l__cjorssen_pitch_int <= #2 }
      {
        % \cchar{<pitch>}{<something>} is a musixtex macro that
        % allows setting <something> at the specified <pitch>
        % let's set the frequency below the tone it belongs to:
        \cchar
          { \int_eval:n { \l__cjorssen_pitch_int - 5 } }
          {
            % start a group to keep the format local, just in case
            \group_begin:
              % the format:
              \tl_use:N \l__cjorssen_freq_format_tl
              % let's test at which point of the octave we are
              % and add the needed integer to \l__cjorssen_pitch_int
              % in order to get the right key number with respect to
              % musixtex's pitch number:
              \int_case:nnn { \l__cjorssen_step_int }
                {
                  { 0 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + #3 } }
                  { 1 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 1 + #3 } }
                  { 2 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 2 + #3 } }
                  { 3 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 2 + #3 } }
                  { 4 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 3 + #3 } }
                  { 5 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 4 + #3 } }
                  { 6 } { \cjorssen_calc_freq:n { \l__cjorssen_pitch_int + 5 + #3 } }
                }
                {}
              \,Hz
            \group_end:
          }
        % write the note:
        \qu { \int_use:N \l__cjorssen_pitch_int }
        % step the integers for the next round in the loop:
        \int_incr:N \l__cjorssen_step_int
        \int_incr:N \l__cjorssen_pitch_int
      }
  }

% calculate the frequency from the key number
% (using 440Hz for the concert pitch):
\cs_new:Npn \cjorssen_calc_freq:n #1
  { \fp_eval:n { round ( 440 * 2^(((#1)-49)/12) , 2 ) } }

% #1: the lowest pitch
% #2: the highest pitch, should not be more than #1+6
% #3: the difference between pitch number and key number
\NewDocumentCommand \writenotes { mO{#1+6}m }
  { \cjorssen_write_notes:nnn { #1 } { #2 } { #3 } }
\ExplSyntaxOff
\begin{document}
\noindent
\begin{music}
 \instrumentnumber{1}
 \setstaffs{1}{2}
 \setclef{1}{60}
 \setname{1}{}
 \startpiece
 \NOTes
  \writenotes{-11}{15}
 \en\alaligne
 \NOTes
  \writenotes{-4}{20}
 \en\alaligne
 \NOTes
  \writenotes{3}{25}
 \en\alaligne
 \NOTEs|
  \writenotes{-2}{42}
 \en\alaligne
 \NOTEs|
  \writenotes{5}{47}
 \en
 \endpiece
\end{music}
\end{document}

enter image description here

I don't think your correspondence between the notes and the key numbers used in the formula is correct. The A above middle C should be ~440 Hz. — Alan Munn, Apr 27 '13 at 18:10
Not quite, you're still one octave off. The A440 should be on the first space of the treble clef. — Alan Munn, Apr 27 '13 at 18:55
@AlanMunn Oh &%$?! The last two times the difference between pitch number and key number arguments need to be increased by twelve to 42 and 47, respectively. At least the code seems to work... — cgnieder, Apr 27 '13 at 19:04
@cgnieder Thank you very much for your efforts. That's what I need. Would you mind decyphering some bits of the LaTeX3 code, particularly how the tokens are given back to musictex. — cjorssen, Apr 29 '13 at 19:33

Range of a piano : annotate note frequency

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