Music is defined as an “art of sound in time that expresses ideas and emotions in significant forms through the elements of rhythm, melody, harmony, and color”.

All the elements mentioned: “rhythm, melody, harmony, and color” have almost infinite variations.  Listing all the known forms of music, from primitive native chants to sophisticated orchestral forms would take a lifetime, and would never be completed. New forms of music appear in every generation.

The broadest category we use to identify music is that of “Contemporary” or “Classical” music; but what do those terms really mean?  Contemporary means existing, occurring, or living at the same time, so contemporary music is any music created and performed that reflects current musical styles and preferences. 

Classical music is even more broadly defined. Some definitions say “Classical music” is music created create between 1750 an 1820. An even more limited definition is “music that includes primarily the works of Haydn, Mozart and Beethoven”; but since we now commonly refer to “Classic Rock” as rock music that is not “contemporary” (that is,  “current”) but still performed and enjoyed by succeeding generations, just as we still listen to “classical” music of the 18^th and 19^th century today.

Thus, modern forms of music become “classics”, just as “classical” music is still popular and “contemporary” as well,. In fact they can be both. Contemporary becomes Classical automatically if it continues to be played and heard over time; and “Classical” music is still “contemporary” by the very fact that is is played and enjoyed by new generations of listeners.

The difference is really about styles. Music, like literature or clothing, becomes “contemporary” when a  society or culture adopts it as a standard, That “style” then becomes “classical” when the style is identified with that specific time frame,  but is still being used and enjoyed; long after the era and culture that created it has passed on.