Re: irrational meters

[Silvain Dupertuis]

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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