All beginning students of all instruments learn about "time signatures" in the very earliest lessons. But I find that virtually all the early piano books, and many teachers, don't really explain all the information, beyond the mechanics, that time signatures are meant to convey. You might think it's simple enough.... but I have seen so much confusion around this subject, I feel compelled to explain.
The time signature appears at the very beginning of every piece. It's essential that you know it before starting to learn to play the piece. If you are somewhat experienced, you'd figure it out by just seeing the music, even if the time signature were missing, but nevertheless the composer would not omit such an important piece of information.
When you are a beginner, most of your pieces are in 4 - 4 time. (The numbers are actually written vertically. It is important to note here that my use of the dash is not actually the correct notation. Limitations of this software don't allow me to show the time signature with the numbers stacked vertically, with no line between them, which would be the correct way. See below). You learn that the top "4" means 4 beats per measure and the bottom "4" indicates that the quarter note is the unit of the beat. In a piece with this time signature, you will likely encounter one or more whole notes, which get 4 beats each. Later on, you may have a piece in 3 - 4 time; now there are only 3 beats per measure. The quarter note is still the unit of the beat, but you won't be seeing any whole notes, since those have 4 beats.
This might seem a little confusing to the beginner. Why would you have three quarters in a measure, when 3 quarters don't add up to a whole?
The answer is because our musical notation for rhythm was based on the idea of 4. If you go back to my early posts on rhythm, you will see that I use the analogy of a log, which you are chopping in 4 equal pieces. These pieces can be further "chopped" to give eighth notes, sixteenth notes, etc. This is a good representation of the 4 - 4 time signature. Our notation didn't evolve with the idea of three beats. It is, however, very adaptable and can be used to show 3 - 4, 2 - 4 and others.
When I explain time signatures to my students, I prefer to say that they are telling you the "rhythmic organization" of the piece of music. It may be "organized" around a "log" cut in 4 pieces, or in 3, etc.
Eventually the student will see a piece in so-called "cut time," which is 2 - 2 (again, the dash is not correct). The bottom number 2 indicates that the half-note is the unit of the beat. But when the student looks at the music, it looks identical to 4 - 4. There are still 4 quarters in a measure. Why did the composer choose to write it in 2 - 2 rather than 4 - 4? The composer is telling you to "feel" it in two beats. In other words, there are fewer emphasis points in 2 - 2 than there would be in 4 - 4. Imagine you are marching to music for a marching band; you want to hear 4 strong beats, each syncing with a step. But if the piece had more of a graceful, flowing nature, you'd want fewer strong emphases. The "math" may be the same as 4 - 4, but the musical interpretation of the piece is different. This is an example of why it is important that the teacher explain the intent behind the time signatures, not just the math.
A real source of confusion comes when you get 6 - 8. The 6 - 8 time signature arose because the composer wanted the beat (quarter note) to divide in 3. The normal division is in 2, since, again, the notation evolved around the divisions of even numbers, 2 and 4. When the beat divides in 3, it is shown as a triplet. The triplet has to be marked as such, because the division in 2 would otherwise be assumed. If the composer wants triplets for the whole piece, it is cumbersome to have to indicate it everywhere, so the idea of 6 - 8 arose. It would seem to tell you there are 6 beats in the measure and the eighth note gets the beat. However, we would never feel it as 6 beats. We would feel it as two main beats (like 2 - 4), but the beat divides in 3 rather than the normal two. The two main beats is the important point to stress. In 3 - 4 you feel 3 main beats; in 6 - 8 you feel two. A waltz would have to be in 3 - 4 time, but a jig (or gigue) must be in 6 - 8. If the teacher does not explain this, the student would have no way to understand it. Sadly, I have actually seen incorrect information in books. I once saw, in print, the explanation that "6 - 8 was the same as 3 - 4 but faster." Not true in the slightest since the time signature tells you nothing about the actual tempo (speed) of the piece (see below).
There are also time signatures such as 9 - 8 and 12 - 8, which have the beats divide in three just as with 6 - 8.
As you can see, I've gone to some pains to write the time signatures without the slash which you often see when they are written about, but not in the actual score itself. They are not fractions and have nothing to do with fractions. In the score the numbers are written vertically, but there is no line between them, as there would be if they were representing fractions. If time signatures were fractions, then 4 - 4 would equal 1 and 3-2- would equal 1.5 and those number have nothing to do with what is represented in those time signatures. And 3 - 4 and 6 - 8 would be the same, whereas, as we have seen, they are completely different. Again, I recently read a book about music and the brain. The author is a pianist and clearly quite knowledgeable about music, but even she made the mistake of referring to time signatures as fractions.
Which brings me to another misconception about time signatures by beginning students. The time signature does NOT tell you the tempo, or speed, of the piece. A piece in a given time signature can be a fast piece or a slow piece. An indication of the tempo is given at the top of the score with terms such as Allegro or Andante or Largo. (There is no exact speed for these either, which is where the musician has an opportunity for her/his own interpretation.)
Again, if you think of the time signature as the rhythmic organization, you won't be confused. If your teacher cannot explain time signatures to you, or calls them fractions, you will know that the teacher doesn't actually understand them.
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