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Re: aiming at 2.2: dodecafonic staves

From: Heikki Johannes Junes
Subject: Re: aiming at 2.2: dodecafonic staves
Date: Sun, 5 Oct 2003 11:23:44 +0300 (EEST)

On Sun, 5 Oct 2003, Juergen Reuter wrote:

> The problem is that there are many different opinions on how a staff for
> contemporary music should look like.  To me, suggestions often give the
> impression of people carrying out a silly contest of who has the fanciest
> idea for a new notation system (see
> for some weired examples).
> I think we should not support a particular one
> of these innummerable systems of equally low(?) quality.  Either there is
> a commonly agreed standard for dodecaphocic music to support (which I do
> not see), or we should look at the underlying common principles and try to
> provide a flexible mechanism such that the user can adopt lily to his or
> her individual notation system.

Actually, I liked all of them. All the samples in that www-site have
three common features:

(a) Staves are logaritmic.
(c) Chromatic marks are not used, instead, note shape is varied so that
    at least dodecafonic scale can be produced.
(b) For a note which is not above, on, or below a solid or a dashed staff line, 
    auxiliary lines may be used in order to guide an eye.

> I agree that a future version of lily should support vertical alignment of
> pitches according to a chromatic scale rather than to a diatonic scale,
> such that the vertical position of a pitch depends linearly on the
> logarithm of its associated frequency (i.e., cisis=d=eses all result in
> the same vertical position, with accidental engraver being turned off).  I
> agree, because this seems to be a common principle among most of the
> suggested notation systems for chromatic scales.  Apart from chromatic
> scales, this principle is also common for frequency-based notation (such
> as in the field of electronic music).  The reason is clear: binding the
> vertical position directly to the frequency is a simple, natural mapping
> in any system with equidistant intervals.
> I disagree with the idea of introducing "chromatic marks".  Accidentals
> are a result of transposing diatonic scales.  In my opinion, they do not
> make any sense in a chromatic scale.  Of course, since lily's input
> language is based on the 7 pitch names of a diatonic scale (letters a..g),
> we currently need alterations "-is" and/or "-es" to express all of the 12
> pitches of a chromatic scale.  But this problem is orthogonal to notation;
> it's just a matter of input language and should be discussed separately.

I agree that `des' and `cis' are the same in equal temperement. Modern
music uses equal temperement, but ancient music used also other
temperements in which `des' and `cis' did not have the same frequency.
In such cases, the diatonic scale does not always sound best with equal

I would put it in such form that even in dodecafonic scale chromatic marks,
i.e. marks for coloring the tone, are needed occasionally. Sometimes one
needs to color the tone by undertuning or overtuning the note, e.g. in the
end of a piece to have something between a major and minor chord. If there
are no chromatic marks, then one has to vary the shape of a note.

One should discuss the common principles how a logarithmic scale is
introduced. They could be

(a) user settable staff lines, either solid or dashed
(b) 3(?), 6, 12 or 24 different notes pitches
(c) in order to represent, e.g., 12 notes in a 6-pitch staff, note shapes
    may also be given by user
(d) an option to have or have not auxiliary lines.

  Heikki Junes

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