Each type of note can also be represented by a fraction with the denominator of four. A whole note would be 4/4 implying that it equals one whole measure. A half note would equal 2/4, a quarter note 1/4. Any note smaller than this uses a multiple of four as the denominator. An eighth note equals 1/8 of the total measure. A sixteenth note is 1/16 and a thirty second note is 1/32. Another way to look at these notes is to use add consecutive powers to the integer two. Two to the zero power would equal a whole note, two to the first power would equal a half note, two to the second power would equal a quarter note and so on using consecutive, positive integers.
             (Math and Music Harmonious Connections by Truth Hammel Garland and Charity Vaughn Kahn, pg. 8)
             Adding a dot after any note increases that note's length by one half. For example, if a dot is added to a quarter note (equals one beat) you get a dotted quarter note which is held for one and one half beats. The mathematical equation equivalent to this would be, 1/4 (quarter note. 1 beat out of four) + 1/2 of 1/4 (the dot) = 1/4 + 1/8 (1 quarter note plus one-eighth note). This can be summed up by saying, if you put a dot after a note it becomes one and one half times itself. All of the these notes can be put together in various ways to create different rhythms as long as the total number of beats in each measure equal 4/4 when they are added up. However, there are other time signatures such as 2/4, 3/4, 6/8 and 3/2 in which these note values do not apply. The notes retain the same name for the sake of consistency but in other time signatures, they do not equal what they say. These other time signatures can be calculated using the same rule, the numerator equals the number of beats in a measure and the denominator indicates which note value gets the beat. So in 3/4 time, there are only three beats in a measure but the quarter note is equal to one beat. So a quarte...