Korean music is distinct from that of China or Japan. Although the instruments are similar, the forms are original and the modes are more elaborate. Apparently, this development owes something to the medieval interchange with India, centering on Buddhism. The most elaborate and serious form is the "sanjo" which is essentially a suite of variations. The most highly regarded instrument is the 13-string zither with movable bridge, the kayagum. The style/instrument is superficially similar to Japanese koto music.
The following recording is the most impressive example of this combination:
The performers were both legendary in Korea (now deceased). This is a very illuminating disc, with music which is rather challenging due to its "dissonant" themes.
There are recordings of Korean classical ensemble music which are worth hearing, but the style will not be discussed here. There is also a recording of Sanjo performed by an ensemble on the Ocora label.