Question: I was just reading an e-book and saw this sentence which really confused me:

[![enter image description here](https://i.stack.imgur.com/CuYCV.png)](https://i.stack.imgur.com/CuYCV.png)

"Played twice as fast as written" - This isn't what cut time actually means right, or are there situations where cut time means exactly that?

I thought cut time is basically just 2/2 time signature, but the speed would still depend on the bpm and the note durations...

Answer: 
That sentence "Played twice as fast as written" indicates that someone must have a misunderstanding. Someone who probably thinks that quarter notes are supposed to be played at a certain speed. That person would need more knowledge and experience with both tempo markings and different kinds of time signatures.

I suppose you could say that in the beginning when you learn your first note values and make your first exercises with the values you do get used to think of quarter notes as indicating some basic speed. You need to crawl before you can walk so to speak. But you certainly better learn to walk before you write a work book on the matter.
In a simple sense, it is correct. "Whatever tempo you have in mind, this is twice as fast as that". This works on the assumption that most people are used to the quarter note being the beat, which happens to be true.

But it basically means that the pulse of the song will be on the half-notes. If someone was standing there waving a baton in front of you, they would be counting the half-notes, and counting two beats per measure (2/2 time as you said).

If it says "moderato" on top of the page it would refer to the speed of the half-notes and if there is a bpm marking it would also refer to the half-notes, although it's common to make this explicit by writing "half-note = tempo" (see top two examples here <http://www.janvanbiezen.nl/bachfig01.gif>).

This is common in marching band music where writing in 2/4 would look awkward (I guess?).