To make things clear, a /fraction/ is a mathematical expression which is a /specific
representation/ of a number (or of a formal expression), comprising a numerator, a
denominator, and one kind of division sign (which can be written in different ways, as
there are different ways to write the operator).
A /ratio/ of two numbers is a number resulting from the division of those two. It can
therefore very naturally expressed as a fraction.
So I have no problem considering a musical metric as a fraction!
It is better not to confuse a /fraction/ (as an expression) and it's /value/ (as a
/number/) — a number cannot have a numerator or a denominator!
But whenever we write a fraction in a mathematical expression, it is the /value/ which is
implied, not the fraction itself.
So we do confuse them very commonly, like we commonly confuse a word and it's meaning in
common language (and we survive quite well with this confusion).
In case we need to avoid these confusions, one can use quotation marks... It can be useful
or essential when teaching mathematics or when working in mathematical logic or in
linguistics.
Hope this clarify the matter.
Silvain
Le 18.01.23 à 18:51, Shane Brandes a écrit :
Because terminology amuses me here. Years ago, I learned that time signatures were
decidedly not fractions but ratios from a one Richard Hoffman. But even before that I
learned ratios consisted of antecedents and consequents, which also seems to overlap
musical structural terminology in a weird way making that also fairly useless as a
nomenclature.
Shane
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