I've always found strange this convention of western-style music notation. Any musician that ever tried to explain it to me always tried to explain it like it is perfectly reasonable, while it has one major inconsistency: there is no unambiguous way to describe the type of subdivision (binary or ternary).
The official explanation is that the first value is the number of pulsation per bar, and the second is the value of this pulsation. Thus, a metric of 3/4 would be 3 𝅘𝅥 (quarternote), a metric of 6/8 would be 6 𝅘𝅥𝅮 (eighthnote). But what isn't immediately obvious for a non-musician, the duration of bars using those two metrics aren't the same: the equivalent metric to 6/8 would be 2/4. Whaaat?
Well, one thing isn't noted at all in this notation: is a 3/4 metric binary or ternary? Meaning, does one quartnote (𝅘𝅥) subdivise into 2 or 3 eighthnotes (𝅘𝅥𝅮)? The names of the subdivisions themselves are confusing by implying binary. Saying that there is 3 eightnotes (𝅘𝅥𝅮) in 1 quarternote (𝅘𝅥) feels wrong at the most fundamental level. Alas, general convention dictates that meters that use quarternotes (𝅘𝅥) are binary and those using eighthnotes (𝅘𝅥𝅮) are ternary.
So, problem solved, isn't it? Not quite. Maybe it's me and the habbits from years of writing code (where ambiguousity isn't accepted by the compiler), but I find this solution absolutely not satisfying: a piece of music that would not use bars would still need to have a subdivision value. Do I have something better (or just something) to suggest? Maybe.
There is another place for this that is better adapted: the tempo. The tempo is described as a note value (generally a quarternote 𝅘𝅥) and the number of those in a minute, for example: 𝅘𝅥=100 is equivalent to say "there is 100 quarternotes in a minute". This tempo notation is the best place to clearly describe how to subdivise notes. Say, writing 𝅘𝅥=100/3 would be clear about the fact that the music on the sheet is ternary, allowing the usage of whatever meter you want without constraint.
Maybe that would make a few sheets easier to read, and the whole mess simpler to explain.