"Irrational" Time Signatures
"Irrational time signatures" is a popular (and inaccurate) name for non-dyadic time signatures amongst Classical and J*zz musicians. Irrational numbers (ex. √2, π) are numbers that can't be expressed as a ratio of two integers. In other words, they're numbers that you can't write as a fraction. At least that's what it used to mean before Classical musicians took that meaning and threw it out the window when they redefined them as “Numbers that describe rhythms that make me feel uncomfortable”.
Non-dyadic time signatures are time signatures with a bottom number that isn’t a power of 2, which means that non-dyadic tuplets (broken tuplets) are a necessary component of them. Wherever there's a non-dyadic time signature, you'll also find a non-dyadic tuplet (and vice versa). Some have speculated that the scary nickname Classical musicians gave to “irrational” time signatures reflects their inability to play tuplets correctly. What’s the point of calling it something more accurate if it’s going to sound like sh*t regardless?
Regular time signatures allow you to write bars whose length is any combination of whole-notes, half-notes, quarter-notes, etc., but non-dyadic time signatures allow you to write bars whose length is any fraction of a whole note. Fractions… weren't we talking about those things earlier? Oh right.
Disclaimer: It's appropriate to call a non-dyadic time signature "irrational" if there's an actual irrational number in it.