Well, by definition, 2/4 time has two beats per measure. My personal understanding is that you could rewrite any piece of 2/2 music in either 2/4 or 4/4 time but halving the duration of all notes/rests. However, if 2/2 (cut time) is used, it is because the composer made a decision that the music has a fast enough tempo (or perhaps some other reason as well), that putting the entire score in 2/2 would simplify the counting of the beats by the musicians, and the directing by the director.
Why not use 2/2 in preference to 2/4, when both have the same structure?
There’s always been a far greater flexibility in how pieces are written than a beginner’s guide to music theory might indicate. Never, at any point in history, has the crotchet/quarter note been this dominant ‘normal’ beat. Palestrina didn’t see it this way, nor did Bach, nor did Beethoven or Schoenberg.
What there has been, however, is a gradual reduction in the typical use of note durations as various metrical structures have evolved, from the longa and brevis, through to the semibrevis (semibreve/whole note), minima (minimum?!), and so on. There’s composers now who will happily use a 16th- or even 32nd-note pulse, and the performers working with this music are unfazed by it.
One good reason is that the conductor doesn’t die when conducting in cut.
Since 100 in cut time (2/2) is 200 in common time (4/4)*, you only have to conduct 2 beats at half the speed instead of 4 beats at a more tiring speed, if you’re marching this is even better (reduces chances of tripping, easier to move shorter distances etc).
Cut time also can make it look friendlier by messing with it accordingly, not that most people are fazed by insanely fast runs or weird offbeats nowadays.
Also, it may just be me, but some songs just FEEL right in cut, the way they’re divided by beat and such, you CAN write them either way, and they sound the same, but some have very definite two pulses.
Gradual reduction, eh? My next piece shall be “Song in 7/256 and C phrygian” to keep with tradition!
*Well, 100 half note beats per minute and 200 quarter notes per a minute, it works either way, but you’re usually not going to be writing the former on a 4/4 piece
Nothing has ‘typically’ been used, especially from the baroque period onwards. There’s nothing unusual in finding a frantic duple-time final movement scored in 2/2, a Beethoven scherzo only conductable one-in-a-bar in 3/4, or a slow 6/8 where quavers are the principle beat.
Indeed, this flexibility lends itself to a very important versatility, in that there can be a duality between faster and slower senses of pulse which can coexist and can at various times come to the fore. The introduction to Zadok the Priest is an example, where a faster pulse created by the instrumental writing runs parallel to the slower processional movement from one chord to the next.
This is very true, especially in a lot of musical theater. I’ve done shows (playing double bass) that were almost entirely in cut time. Not to hijack, but if you want a time change workout (and key change, too), play in the pit of a Broadway-type play. That stuff will keep you on your toes!