Mixing different wood tones is sometimes hard to do, but I've come across it many times when helping clients pick out new hardwood flooring for their home or wood furniture to go with their existing hardwood flooring. There isn't a magic formula, but as with everything when it comes to decorating...balance is key.
When adding new wood into a space with existing wood furniture or flooring, it's best to try not to match exactly. Wood is so unique that even if you're matching one oak bench with oak flooring, it's never going to look exactly the same. It also looks really strange if there is no contrast. Either go with a darker stain on the same wood, go with a completely different wood, or different stain, different wood. You get the picture...mix it up!
Here are a few examples of rooms with well balanced wood tones.
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More tips on mixing wood
Break things up with an area rug. If you have a wood dining table on hardwood floors, add a contrasting area rug to break up all of the wood.
Add other elements to the room. Metals, glass, fabrics....anything that would contrast with the wood will keep the room from looking too much like a forest.
Balance painted wood and natural wood. Too much of each can seem too matchy.
Be strategic when placing wood items in a room. For example, if you have a wood mirror that looks similar to a wood coffee table, try to put them on different sides of the room or separate them as much as possible.
With dark woods, especially, add in light colors throughout the room. An all dark room can feel very heavy without a lighter contrast.