These "look-alikes" have different origins and meanings. Timber, from Old English, means wood as a building material (lumber) and wooded land: "We collected enough timber to build a small shed." "That is a thriving stand of timber." Timbre, from a Greek word meaning "drum," refers to the quality of a sound that distinguishes it from other sounds of identical pitch and volume: "This singer's voice has unusual range and timbre."
Dictionary of problem words and expressions. Harry Shaw. 1975.