On 3 Jul 2010, at 00:55, Hans Aberg wrote:
On 2 Jul 2010, at 23:11, Carl Sorensen wrote:
In your earlier email (which I didn't understand before, but I
think I
figured it out now), you proposed a working notation with '
indicating "in
one". But then every specific proposal you wrote used ', so I
wasn't able
to understand the difference between "in one" and "not in one".
I did not use that here sorry. Let's try this again.
Start with p/q. If in one, it can be written as (1, p/q); if in p,
it can be written as (p, 1/q). So since I introduced these pairs,
the ' notation is not needed.
I think it is complicated by tuplets. Triplets are by default in 3
(tripartite), and sextuplets in 2 (bipartite) [Hindemith,
"Elementary Training", p. 116].
I have checked Hindemith a bit more carefully, and he notes that
sextuplets are traditionally bipartite and can thus be broken up into
triplets. But he does not indicate that in the beaming; they are
typeset as though in 6.
For triplets, he notes that they are typeset inconsistently: even
though the preferred form would be in three, it is common to do it as
in one. For example, if there are a triplet with 6 1/16 notes, then in
the latter, the double beams are unbroken, but in the former, the
second level beams are broken into 3 groups of 2 1/16 notes.
This might affect the musical interpretation in says MIDI files, if
they should express subaccents, but typesetting alone, one can just
let users choose the pattern they want.
So for the sextuplets, using my pair notation (k, n), they are notated
as (6:4)(6, n). The two types of triplet notation might be (3:2)(3,
1/8) and (3:2)(1, 3/8).
So the notational default seems to be in one for all the tuplets,
except for triplets which are variously typeset as in 3 or in 1. The
sextuplets are bipartite, but typeset in one.
So it might suffice to make default fir all lowest building block to
be in 1, unless called for something else, with some option of the
triplets if they should be in 1 or 3. Some may want to indicate if
sextuplets and other multiples of three, 3*k, should be typeset in 3*k
or k; just a thought.
Hans
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