[David W. Fenton, referring to 2 beats in 6/8 metre:]
>There is not a 2 on top because there's no single digit to represent
>the dotted half not that could be the bottom number.
>
>The whole system of time signatures works right when the subdivision
>of the beat is duple. When it's triple, the system breaks down, as
>there is no way to represent a dotted value in the bottom number of
>the time signature.
There is a system I've heard of somewhere or other, that has been used once
or twice in modern compositions, that does allow you to indicate dotted notes in
the bottom number of a time signature. It would not be mathematically correct,
but it would probably be quite clear (in a funny kind of way).
If 2 on the bottom represents a minim and 4 a crotchet, you use 3 to
represent a dotted crotchet. It's not mathematically correct, because 3 dotted
crotchets don't exactly fill the value of a semibreve. But, looking at it
another way, 3 is half-way between 2 and 4, and a dotted crotchet is half-way
between a minim and a crotchet. It does make a kind of sense; and I have
actually heard of some composer who has done this, but I don't recall where I
heard this, or who it was.
Similarly, use 6 for a dotted quaver, 12 for a dotted semiquaver, and so
on - always choosing a number half-way between two powers of 2.
Of course this system would break down for a dotted minim, because there is
no integer between 1 and 2 - unless you start using fractions, such as 1 1/2.
I'm not advocating it, and would probably be too conservative to do
something odd like this, unless it really was the only solution to an unusual
situation (which it isn't here). But has anyone else seen this system, and is
there something to be said for it? Is there any kind of logic that can actually
justify it, beyond my comment above that it is clear in a funny kind of way?
Regards,
Michael Edwards.
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