What are the Theories of music?

It is basically the "math" of music. It explains why certain note sounds as they do Generally speaking, "theory," whether it be science or the arts, is the study of that discipline's principles as...

Music theory was never "discovered". It has been developed over time from the roots and beginnings hundreds of years ago.

Cut time in reference to the time signature is when there are two beats per measure (or bar). Cut time is half of common time (common time "cut" in half).

Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques, across or within genres, styles,...

It means the dominant seventh chord. In C major this would comprise of the notes G B D and the seventh F