This is an evolution of the musical motif used for Princess Luna throughout the series.

Note: This isn't comprehensive. I missed "For Whom the Sweetie Belle Toils", "Bloom and Gloom", and "To Where and Back Again" (cause its been awhile since I've fully watched the series.

Episodes:
S1 E1, S1 E2 - These were the first snippets of her motif, though only barely in the chord progression
S3 E6 - This was the first usage of her refined and official motif. I did not include the Nightmare Night episode because there was no designated motif for her there.

S5 E13 - The most usage of Lunas Motif, with many tiny variations all over, ending in an elongated, sorrowful, and dramatic version as the Tantabus begins to break out into the real world. The episode finishes _lacking_ Lunas motif, because I personally believe this motif signified her deeper sorrows and regrets, as well as her longing to be accepted. This arc finished, so the motif was not played at the end.

S7 E10 - Luna's Motif is brought back but in a much happier form.

While it is common knowledge that this music was written by William Anderson, certain parts of it in the later seasons, especially in S5 E13, were written by various background musicians.