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Re: aiming at 2.2: dodecafonic staves

From: Juergen Reuter
Subject: Re: aiming at 2.2: dodecafonic staves
Date: Sun, 5 Oct 2003 04:52:15 +0200 (CEST)

On Sun, 5 Oct 2003, Heikki Johannes Junes wrote:

> ...
> I just figured out that in modern music the diatonic stave (seven pitches
> for chromatic scale in a stave) is not adequate to represent always
> dodecafonic music.

Agreed; the ordinary staff notation as implemented in lily was developed
for notating tunes in diatonic scales (IIRC, it was Guido of Arrezzo who
introduced this scheme, but originally with 4 lines).

> For example, if you want to represent parallel clusters
> (using the current notation), they will be glued together. Instead, a
> chromatic stave (twelve pitches for chromatic scale in a stave) is adequate
> to represent parallel clusters. The most intuive version of such scales is
> the following:
> As a diatonic stave, a cromatic stave would have five lines, starting from
> c'':
> c''   -O-
> b'       O
> ais'  -----O-----------------------------------
> a'           O
> gis'  ---------O-------------------------------
> g                O
> fis'  -------------O---------------------------
> f'                   O
> e'    -----------------O-----------------------
> dis'                     O
> d'    ---------------------O-------------------
> cis'                         O
> c'                            -O-

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.

> It is rather easy to implement, and chromatic marks are optional.  The only
> obscurity here is in the note naming: How should one call the note names so
> that there would not be a conflict between cromatic marks and note names.
> For example, `c + is' is marked with a chromatic mark but `cis' without.
> Apparently, one has to
>    A) invent a set of new note names for such notation, such as:
>       - numbers:    1  2  3  4  5  6  7  8  9 10 11 12
>       - alphabets:  a  b  c  d  e  f  g  h  i  j  k  l
>       - user-given: c  h  r  o  m  a  n  t  i  z  e  d (different letters)
> or B) use current note names and give the chromatic mark as an argument:
>       - the following will result to same notation:   cisis d eses
>       - the following will result to chromatic marks: cis-is d es-es

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.

> Modern music has a lot of new notation, and many of them are good and
> intuitive. For example, accelerando can be marked with increasing number
> of bars (here only two notes are shown).
>    /|
>  -<-|
>  | \|
>  |  |
>  | O
> O
> Here the problem is that what is the mathematical duration of such
> construct. But anyway, the notation exist and is well known.

Can you cite a publisher and/or composer?  The more scores of temporary
music I look at, the more I get the impression, that certain publishers
try to set notational standards solely by their relevance in the market
rather than by carefully designing their notational extensions.  I
think, one should carefully check if pretendedly "well known" notational
standards make sense before implementing them in lily.


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