217 lines
9.2 KiB
TeX
217 lines
9.2 KiB
TeX
\chapter{Transposition and Octaviation}\label{octaviation}
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Two different subjects are discussed in this section. First, there
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are commands that cause notes to be printed at different pitches than
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entered. We shall refer to this as \ital{logical} transposition.
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Second, there are notations for octaviation that do
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not otherwise alter the appearance of the score, which we'll call
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\ital{octaviation lines}.
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\section{Logical transposition and octaviation}
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Logical transposition is controlled by an integer-valued \TeX\ register
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\keyindex{transpose}. Its default value is $0$. If you enter
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\verb|\transpose=|$n$ outside of notes commands, then all subsequent pitches specified by
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letters will be transposed by $n$ positions. Normally this method would be
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used to transpose an entire piece. Pitches specified with
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numbers will not be affected, so if you think you will ever want to
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transpose a piece, you should enter all note pitches with letters.
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One way to transpose up or down by one octave would be to increase or decrease
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\keyindex{transpose} by $7$.
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A more convenient way to transpose locally up or down by one octave
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makes use respectively of the characters
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\verb|'| (close-quote, interpreted as an \itxem{acute accent}) and \verb|`| (open-quote, interpreted as
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a \itxem{grave accent}),
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placed immediately before the letter specifying the pitch. So
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for example \verb|\qu{'ab}| is equivalent to \verb|\qu{hi}| and
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\verb|\qu{`kl}| is equivalent to \verb|\qu{de}|. These characters have
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cumulative effects; thus,
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for example, \verb|\qu{''A'A}| and \verb|\qu{''A}\qu{'A}| are both equivalent to \verb|\qu{ah}|.
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Alterations to the value of
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\verb|\transpose| in notes commands are \emph{local}: when changing to a different staff or
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instrument or encountering \verb|\en|, \verb|\transpose| will be reset to the
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value it had before the accents were used. (That value is stored in
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another register called \keyindex{normaltranspose}). Another way to localize
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changes to \verb|\transpose| is to create an explicit \TeX\ ''group'' by enclosing commands in \verb|{...}| braces.
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At any point it is possible to reset the \verb|\transpose| register
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explicitly to the \verb|\normaltranspose| value
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by prefacing a pitch indication with
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``\verb|!|''. Thus \verb|\qu{!a'a}| always
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gives the note \verb|a| and its upper octave \verb|h|, shifted by the
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value of {\Bslash normaltranspose},
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regardless of the number of grave and
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acute accents earlier in that group.
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\section{Behavior of accidentals under logical transposition}\label{transposeaccids}
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The above processes indeed change the vertical position of the note heads
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and associated symbols (e.g., stems and beams), but they don't take
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care of the necessary changes of accidentals when transposing. For example,
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suppose an F$\sharp$ occurs in the key of C major. If the piece is
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transposed up three steps to the key of F, the F$\sharp$ should logically
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become a
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B$\natural$. But if all you do is set \verb|\transpose=3|, the note will
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be typeset as a B$\sharp$. In other words, \musixtex\ will interpret the~\verb|\sh|
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or~\verb|^| to mean ``print a $\sharp$''.
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Naturally there is a solution, but it requires the typesetter to plan
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ahead: To force accidentals to behave well under transposition, they
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must be entered according to the \ital{relative
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accidental convention}. To alert \musixtex\ that you are using this
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convention to enter notes, you must issue the command
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\keyindex{relativeaccid}. Once you have done this, the meaning of
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accidental macros and characters (accents) in the input file is changed.
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Under the convention, when for example a
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\verb|\sh| is entered, it indicates a note that is supposed to sound
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\ital{one half step higher than what it would normally be under the
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current key signature}. Flats and naturals on entry similarly indicate
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notes one half step lower or at the same pitch as what the key signature
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dictates. \musixtex\ will take account of the key signature, and print
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the correct symbol according to the modern notational convention,
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provided you have explicitly entered the transposed key signature using
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for example \verb|\generalsignature|.
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Many people have a difficult time understanding how this works, so
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here are two simple examples in great detail. Consider the case already mentioned
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of the F$\sharp$ in the key of C major. With
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\verb|\relativeaccid| in effect, it should still be entered as \verb|\sh f|, and
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with no transposition it will still appear as F$\sharp$. With
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\verb|\transpose=3| and \verb|\generalsignature{-1}| it will appear
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(correctly) as B$\natural$. Conversely, suppose you want to enter a
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B$\natural$ when originally in the key of F. With \verb|\relativeaccid| in effect, it
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should be entered as \verb|\sh i|. (That's the part that people
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have the most trouble with: ``If I want a natural, why do I have to enter a sharp?'' Answer:
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``Go back and re-read the previous paragraph very carefully.'') With no transposition, it will be
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printed as B$\natural$. Now to transpose this to C major, set
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\verb|\transpose=-3| and \verb|\generalsignature0|, and it will appear
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as F$\sharp$.
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If you have invoked \verb|\relativeaccid| and then
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later for some reason wish to revert to the ordinary convention,
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enter \keyindex{absoluteaccid}.
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\section{Octaviation lines}
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The first kind of notation for octave transposition covers a
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horizontal range that must be specified at the outset. The sequence
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\medskip
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\begin{music}\nostartrule
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\startextract
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\NOTEs\octfinup{10}{3.5}\ql{!'a}\ql b\ql c\ql d\en
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\zendextract
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\end{music}
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\noindent can be coded as
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\verb|\NOTEs\octfinup{10}{3.5}\qu a\qu b\qu c\qu d\en|.
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\zkeyindex{octfinup}
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Here, the dashed line is at staff level 10 and extends \verb|3.5\noteskip|.
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Conversely, lower octaviation can be coded. For example
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\begin{music}\nostartrule
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\startextract
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\NOTEs\octfindown{-5}{2.6}\ql j\ql i\ql h\en
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\zendextract
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\end{music}
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\noindent is coded as
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\verb|\NOTEs\octfindown{-5}{2.6}\ql j\ql i\ql h\en|.
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\zkeyindex{octfindown}
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To change the text that is part of these notations, redefine one of
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the macros \keyindex{octnumberup} or \keyindex{octnumberdown}. The reason for
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the distinction between up and down is that, traditionally, upper octaviation
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only uses the figure
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``8'' to denote its beginning, while lower octaviation uses a more
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elaborate indication such as \hbox{\ppffsixteen8$^{va}$\kern 0.2em\eightit bassa}. Thus
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\bigskip
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\begin{music}\nostartrule
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\startextract
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\NOTEs\def\octnumberup{\ppffsixteen8$^{va}$}\octfinup{10}{2.5}\qu c\qu d\qu e\en
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\zendextract
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\end{music}
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\noindent is coded
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\noindent\verb|\NOTEs\def\octnumberup{\ppffsixteen8$^{va}$}\octfinup{10}{2.5}\qu c\qu d\qu e\en|
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\noindent while
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\begin{music}
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\startextract
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\NOTEs\def\octnumberdown{\ppffsixteen8$_{ba}$}\octfindown{-5}{2.5}\ql l\ql
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k\ql j\en
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\endextract
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\end{music}
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\noindent is coded as
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\begin{quote}\begin{verbatim}
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\NOTEs\def\octnumberdown{\ppffsixteen8$_{ba}$}%
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\octfindown{-5}{2.5}\ql l\ql k\ql j\en
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\end{verbatim}\end{quote}
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The foregoing constructions have the drawbacks that (a) the span must be
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indicated ahead of time and (b) they cannot extend across a line break.
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Both restrictions are removed with the use of the alternate macros \keyindex{Ioctfinup},
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\keyindex{Ioctfindown} and
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\keyindex{Toctfin}.
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{\Bslash Ioctfinup}~$np$ indicates an upward octave transposition line with reference number
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$n$ and with dashed line at pitch $p$.
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By default $n$ must be in the range $[0,5]$, but
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you can specify a larger maximum number
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directly with \keyindex{setmaxoctlines}\verb|{|$m$\verb|}|
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where $7<m\leq 100$\footnote{This may require e-\TeX.}; the
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reference number will be in the range between $0$ and $m-1$.
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\label{musixmad_setmaxoctlines}
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Usually $p$ will be numeric and $>9$,
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but it can also be a letter.
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{\Bslash Ioctfindown}~$np$ starts a lower octave transposition line at pitch $p$
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(usually $p<-1$). Both extend until terminated with {\Bslash Toctfin}. The
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difference between {\Bslash Ioctfinup}~$n$ and {\Bslash Ioctfindown}~$n$ is
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the relative position of the figure ``8'' with respect to the dashed line, and
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the sense of the terminating hook As shorthand, \keyindex{ioctfinup} is equivalent to
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\verb|\Ioctfinup 0| and \keyindex{ioctfindown} is equivalent to
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\verb|\Ioctfindown 0|.
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For example,
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\medskip
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\begin{music}\nostartrule
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\instrumentnumber{1}
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\setstaffs12
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\setclef1{6000}
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%
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\startextract
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\notes\wh{CDEFGH}|\wh{cde}\Ioctfinup 1p\wh{fgh}\en
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\bar
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\notes\Ioctfindown 2A\wh{IJKLMN}|\wh{ijklmn}\en
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\bar
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\Notes\wh{NMLKJI}|\wh{nmlkji}\Toctfin1\en
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\bar
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\Notes\wh{HGFED}\Toctfin2\wh C|\wh{hgfedc}\en
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\zendextract
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\end{music}
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\noindent is coded as
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\begin{quote}\begin{verbatim}
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\begin{music}\nostartrule
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\instrumentnumber{1}
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\setstaffs12
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\setclef1{6000}
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%
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\startextract
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\notes\wh{CDEFGH}|\wh{cde}\Ioctfinup 1p\wh{fgh}\en
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\bar
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\notes\Ioctfindown 2A\wh{IJKLMN}|\wh{ijklmn}\en
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\bar
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\Notes\wh{NMLKJI}|\wh{nmlkji}\Toctfin1\en
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\bar
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\Notes\wh{HGFED}\Toctfin2\wh C|\wh{hgfedc}\en
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\zendextract
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\end{music}
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\end{verbatim}\end{quote}
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%\check
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The elevation of octaviation lines may be changed in midstream using
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\keyindex{Liftoctline}~$n$$p$, where $n$ is the reference number of the
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octave line, and $p$ a (possibly negative) number of
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\keyindex{internote}s (staff pitch positions) by which elevation of the dashed line should be changed.
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This may be useful when octaviation lines extend over several systems and the
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elevation needs to be changed in systems after the one where it was initiated.
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