It is written that Moshiach will play music on a harp of eight strings. What is the significance of this fact?

Our sages say as follows: "The harp in the Holy Temple had seven strings, as is written (Psalms 16:11), 'You shall let me know the way of life, the fullness (sova) of joys in Your presence.' Do not read sova, but sheva (seven). In the days of Moshiach, the harp will have eight strings, as is written (Psalms 12:1), 'For the conductor on the sheminith,' -- a harp with eight strings.."

The Maharsha, Rabbi Shmuel Eidels, explains that the natural order of creation, as well as many time related mitzvot, consists of a cycle of seven: Seven days of the week. Seven years in the shmitta cycle. Seven shmitta years before yovel (jubilee). The number seven, thus, represents the structure within G-d created the natural world.

In the days of Moshiach, a level of divine radiance will be revealed that is above the order of nature. This is represented by the number eight. 

This change in the G-dly radiance that will shine on the world is represented by a harp, since this musical instrument serves as a vessel to draw down the Divine light into the human soul. This is alluded to in the Hebrew word for harp, kinor, the letters of which can be divided into two: Chof-vov (numerical value of 26), and ner (candle). The number 26 is also the numerical value of the four letter name of G-d, Havaya. A candle symbolizes the soul of man. Thus, a kinor is the link between Havaya and the soul of man.

When our souls were limited and could only contain the Divine light as it was constrained within nature, the harp had seven strings--to represent this level of light. However, in the days of Moshiach, when we will be able to contain the light that is above nature, the harp will have eight strings.