Counting Method / June 6, 2018 / Norah Myles
Like the natural numbers, Z is closed under the operations of addition and multiplication, that is, the sum and product of any two integers is an integer. However, with the inclusion of the negative natural numbers, and, importantly, 0, Z (unlike the natural numbers) is also closed under subtraction. The integers form a unital ring which is the most basic one, in the following sense: for any unital ring, there is a unique ring homomorphism from the integers into this ring. This universal property, namely to be an initial object in the category of rings, characterizes the ring Z.
In music, counting is a system of regularly occurring sounds that serve to assist with the performance or audition of music by allowing the easy identification of the beat. Commonly, this involves verbally counting the beats in each measure as they occur. In addition to helping to normalize the time taken up by each beat, counting allows easier identification of the beats that are stressed. Counting is most commonly used with rhythm and form and often involves subdivision.