Explanation of 2/2 time signature
In the article time signature, this is explained that:
- the top number indicates the number of time units in a measure (bar
- the bottom number determines the unit of time.
We can visually translate
That is to say that there are 2 half notes (minims
1 half note
2 quarter notes
4 eighth notes
and so on...
Examples found in famous works
Johannes Brahms, Symphony No.4
The first movement Allegro non troppo from Symphony No.4 in E minor op. 98 by Johannes Brahms begins with a cut time signature (

This sound sample is not of very high quality, but I think it has historical interest, because it was recorded in 1938 by the London Symphony Orchestra conducted by Felix Weingartner (source, Attribution-Noncommercial-Share Alike 3.0 license).
In this musical sample in E minor, you will notice the use of arpeggios and of an anacrusis.