A degree is 1/360 of the circumference of a circle. The number 360 may come from older notions about the year being 360 days in length.
in music, any of the tones or notes in a scale or tuning system. European music of the 17th through the 19th century was based on a system of 12 degrees, in which major and minor diatonic scales predominated; chromatic scales, however, were also used. The 12 degrees were divided into two groups: seven degrees corresponding in C major to the white keys on the piano and five degrees corresponding to the black keys. In 20th-century music all 12 degrees are frequently used without such division, yielding a chromatic scale. Other systems include the pentatonic scale, with five degrees, and microtonal scales with 24 or 36 degrees.