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Re: \time 2

From: Heikki Johannes Junes
Subject: Re: \time 2
Date: Fri, 13 Dec 2002 16:59:23 +0200 (EET)

On Fri, 13 Dec 2002, Juergen Reuter wrote:

> Mathematically, you are of course right.  But, unfortunately, most
> musicians are no mathematicians.  For example, 3/4 does not equal 6/8: in
> 3/4, 8ths are typically grouped [a8 b8] [c8 d8] [e8 f8], while in 6/8, you
> will typically see [a8 b8 c8] [d8 e8 f8].

That must have been invented by some person who knows maths quite well.
Number 3 is a prime, while 6 = 2*3. So, in 3/4 you can have 3 or 1 beats,
but in 6/8 you can have 6, 3, 2 or 1 beats.

Not all mathematicians are mucisians, either. But Pythagoras (um 570 -
um 509 v. Chr.), the mathematician, invented one of our (at least nearly)
logaritmic tuning systems. Musicians should be grateful for mathematians.

> > That is why 1/4 as a default denominator is simply wrong.
> >From the mensural music point of view, I fully agree.  But most lily
> users probably will not agree from their point of view.  Maybe you want to
> have a look at my proposal for extended time signature syntax a few months
> ago; see:

Syntax 7[2:3:2]/8 works -- even a mathematician can understand it:

    7/8 = 2/8 + 3/8 + 2/8.

If I understood your ideas right 4/4 should be divided somehow, e.g.:

    4/4 = 4 * (1/4) = 2/8 + 2/8 + 2/8 + 3/12,

while still having 4/4 time signature. How to express the above one?
For example, the following notation would contain the needed information

    4[2:2:2:3]/4[8:8:8:12]  % the number of elements inside brackets are same

But, maybe I understood it wrong.

> There, I proposed to introduce a value for transcription shift in duration
> log.  If this value defaults to 2 (i.e. divide duration by 4), then the
> mathmatical denominator would be 1 by default for untranscribed music,
> as you propose, but 4 for transrcibed and/or contemporary music, as most
> users probably will expect.  Moreover, in this system "alla breve" really
> means "beat on brevis", while the transcription shift value moves from
> brevis to half note, which is what most users think of when they are
> referring to "alla breve".  I think this is the only correct overall view
> and could satisfy all of us.
> However, due to the complexity of my suggestion, we could not really agree
> on it.  I am planning to come back to this issue some time later (most
> probably not before lily 1.8).
> Greetings,
> Juergen

I try to express myself clearly. Did you mean in your link also that

  \notes{ \time 4/1         % put between syntax to multiply durations
          a\longa b\breve c1 d2 e4 }

would be transcribed to:

  \notes{ \time 4/4 a1 b2 c4 d8 e16 }

in contemporary music? That I could agree. It would be nice in some
cases, if there were a syntax which would do such a transcription.

For example:

  \time 4/1 * 1/4           % \longa -> 1, \breve -> 2, 1 -> 4, etc.
  \time 4/4 * 4/1           % 1 -> \longa, 2 -> \breve, 4 -> 1, etc.


      Heikki Junes

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