Time signature
The time signature is the pair of numbers at the start of a piece, right after the clef. The top number tells how many beats are in each measure; the bottom number tells which note gets one beat.
A four on the bottom means the quarter note. So 4/4 means four quarter-note beats in every measure, 3/4 three, 2/4 two. Four-four is so common that it is sometimes written as a large C, called common time.
A time signature is not a fraction and has no line between the numbers — they simply stand one above the other. It is written once, at the beginning, and holds for the whole piece unless a new one appears.
The bottom number can also be 8: in 6/8 time we count eighth notes, six to a measure, grouped in threes. Three-four has the sway of a waltz (one, two, three); two-four sounds like a march (left, right).
What it sounds like
A time signature makes no sound of its own, but you hear it as a way of counting: in fours like walking, in threes like a waltz, in twos like a march.
Where it is taught: the studio’s interactive textbook, chapter 3, “Measures and time signatures” and chapter 14, “6/8 and the waltz pulse”.