In music notation, I've always been looking for a simple explanation of those numbers that appear on the far left of musical piece, such as 3 over 4 or 4 over 4.
I have a hunch they affect the tempo, but I'm not sure if they affect the way the piece would sound.
Would the piece sound differently if I change the numbers? Or is that not applicable?
These numbers are time signatures. In brief, they tell you how many beats are in a measure. (This answer might not work as well for people not familiar with music that doesn't have a strong rhythmic component.)
To start this off, think of a waltz. You might count it out like this: One two three one two three (and so on). That's 3/4 time; each measure is three quarter-notes long (or the equivalent number of notes of other lengths).
Most music is in 4/4, also known as common time, where measures are four quarter-notes long. One two three four one two three four (and so on), or perhaps : One two three four (etc), or any other such variation; which beats are stressed doesn't change the time signature, but how many notes you can fit into a measure will.
Tempo is the speed of a piece, and is independent of the time signature. (Think of the movie "That Thing You Do", where the drummer made the band's piece a hit by simply speeding it up. It was still mostly the same song, but had more energy at a faster tempo.)
There are other time signatures, such as 2/4 (think of polkas) and less-common meters like 5/4 and 7/4. You'll also see meters like 7/8, where there are seven eighth notes in a measure. Time signature can change within a piece, although this isn't too common.
Related: Is there any real-world difference between time signatures such as 4/4 and 8/8?
The best way to learn time signatures is to actually read good documentation on them. MusicTheory.net has some great lessons and visual examples to show you how notes are divided in measures.
Link: http://www.musictheory.net/lessons
More specifically, you should look at lesson 12, 15 and 16 that talk about Simple, Compound and Odd meters:
General Time Signature: http://www.musictheory.net/lessons/12
Simple and Compound Meter: http://www.musictheory.net/lessons/15
Odd Meter Lesson: http://www.musictheory.net/lessons/16
Since your question is a pretty basic one, you should look around that website on note values as they are helpful in reading measures.
3/4 means there are three/quarter notes to a measure.
The tempo mark will usually say how many quarter notes to a second since you are saying how many quarter notes to a measure in the time signature.
If you changed the time signature to 4/8 time (four/eighth notes to a measure), it is typical then to say how many eighth notes to a second in the tempo mark.
So, no, it will not change your tempo going from 3/4 to 4/4, however, 3/4 to 3/8 would change things.
But, what 3/4 and 4/4 will change is the beat. 3/4 you would count 1,2,3,1,2,3 (with an accent on the 1 in most cases). But in 4/4, the way the beats are counted changes to 1,2,3,4,1,2,3,4 because now you have 4 beats to a measure. edit: Also, the measure bar lines should always be right before the 1, so if you change from 4/4 to 3/4 then you would have more bar lines and they would mostly all have to move.
I have a hunch they affect the tempo, but I'm not sure if they affect the way the piece would sound.
In music notation, I've always been looking for a simple explanation of those numbers that appear on the far left of musical piece, such as 3 over 4 or 4 over 4.
Erroneous. The tempo is the metronomic pulse of music. The tempo by the "clacking" of the drummers sticks together as he emphatically shouts "1! 2!34!!!"
This is the best explanation I can find. http://www.dolmetsch.com/musictheory4.htm#common
3/4 = 3 beats of 4 quarters where 4*1/4=1 Of course you're aware that 4 quarters make 1 whole, so naturally 4/4 time means four beats of four quarter notes (= 1 measure). Therefore, similarly, you know that three beats of four quarters then, should equal 1 whole.
Manifested in notation you'll find nothing more than the time/space musical sub divisions allow.
The first measure is "Common Time" which is what 4/4 is referred to in our modern era. This is also what the big ol C stands for.
Cut time is second, also called double time, also called half time, rather confusingly. Thus, the C is cut vertically to represent such.
And finally here you can see the juxtaposition of a handful of common measures interrelating to one another intimately so as to demonstrate their nature, and to illustrate how they can maintain confluence while being seemingly inherently contradictory.
