Music, as we all know, consists of sound. As an instance of sound, it consists of:
1) Pitch - the subjective perception of 'highness' or 'lowness.' This is measured scientifically in terms of 'frequency.' In the West, it was for this element of music that notation was first developed. This happened around thte 10th century(Blatter, p. 2). They are represented with the first 7 letters of the Roman alphabet (A-G) (Blatter, p. 2).
Essential to the concept of pitch is the concept of octave. This word comes from the Greek "okta," or the Latin "octo," meaning "eight." This is because a note that is 8 pitches from another note has the same pitch. Keep in mind that we represent musical notation with the first seven letters of the Roman alphabet. If we progress beyond G or before A, the alphabet starts all over. Therefore, if we count 8 steps beyond A, we go beyond G and reach A again. It is because of this phenomenon that the octave gets its name (Blatter, pp. 2-3).
Although two sounded notes may be of the same pitch, they may be of a different octave because the two sounds differ by vibrations per second. Two or more notes of equivalent pitch are of different octaves if one has twice as many vibrations per second as the other.
Of course, in modern music, we have 12 pitches, counting sharps and flats. Nevertheless, the concept of octave is still common currency in music theory.
2) Duration - length of sound. This is measured scientifically in terms of 'seconds' (as well as longer units of measurement with which we are all familiar). In the West, musical notation for this concept developed around the 13th century(Blatter, p. 2).
3) Loudness - strength of sound. This concept is measured scientifically by watts or joules per second. In the West, musical notation for loudness was not developed until the 17th century. Tone color came shortly thereafter, in around the 18th century(Blatter, p. 2).
These components are organized in time.
Blatter, Alfred (2007). Revisiting Musical Theory. Routledge, Taylor and Francis Group, NY.