Here is a Google image search of rooms using yellow, turquoise, and black. I think I like it! I especially like the dining room on the right end of the top row.

Here is a link that might be useful: rooms using yellow, turquoise, and black

Here is another site that might give you ideas ...she also "shops" by color.
If you look on the right side of the page, you can link to the page with
products by color. I think it is updated daily.

http://www.houseofturquoise.com/

Here is a link that might be useful: http://www.houseofturquoise.com/

Thank you for the links! I was going to ask if red was an accent color, and both websites show pops of red. Of course, I'd need these shoes.

What immediately came to mind for me was white curtains with black ribbon trim 2 or 3 inches from the leading edge and 10" above the bottom. I love black and white with yellow, and with your turqoise cabinet, a pillow or two in a print on a white or pale yellow ground that uses some turquoise, a wee bit of pink, and a bit of black would be nice.

If you are up for some drama, slipcover your loveseat in a turquoise and white awning stripe. To save the scheme from too much sweetness, you might use a black iron or rustic wooden end table, and a heavy aged brass candlestick lamp.

I wouldn't add red - with the pink in the cabinet, I think that's enough colors.

Thank you for your ideas, bronwynsmom. I agree, I have to be careful that it doesn't end up too sweet. The display shelf, now that it's been rehung on the newly-painted wall, reads more teal than turquiose.

I hadn't thought of using pink, but I like pink. I pulled two pillows off my sofa that have an embroidered floral with shades of rose, red, green and gold on a cream background, and they look nice on the loveseat, which is a neutral sage with wine-colored piping. So I might work around that until we replace the loveseat.