Compliment or complement

Last night I attended a concert given by the Emily Carr String Quartet. It was a splendid performance, and I will not miss their next one.

In the interval at concerts, I always look for something to read. At Christ Church Cathedral or St. John the Divine, I always pick up the KJB or the BCP or an unbowdlerized hymn book from the back of the pew in front of me, but this was an Evangelical Lutheran church. Nothing for me to read there. Great acoustics though! So I read the program notes. And I noticed this passage about previous concerts by the quartet:

The concerts featured readings from Emily Carr's journals that complimented the music that was being performed.

I remembered a recent exchange with my accountant. He had sent me a letter explaining that his firm was combining with another firm because their services had always been complimentary. I replied saying, no, his services had never been complimentary, I had paid him a lot of money over the years. He took this in good humour and admitted that, yes, the services of the two firms had been complementary. But then he fell into further error by complementing me on my astute eye.

Compliment and complimentary with the "i" have to do with expressing praise or paying a courtesy. You compliment someone on her performance, you pay her a compliment, you write her a complimentary note. And as a courtesy, she may give you a complimentary ticket to her next show.

Complement and complementary with the "e" have to do with completing the whole. Complementary angles together make up 90 degrees. The sauce complements the vegetables.

And,

The concerts featured readings from Emily Carr's journals that complemented the music that was being performed.