 In the Western world, instruments of fixed pitch, such as pianos, are typically tuned using equal temperament, in which intervals other than octaves consist of irrational-number frequency ratios.While those intervals approximate the overtone intervals, they don't match the frequencies of the overtone series exactly and as such don't resonate sympathetically and have as pure a "ring".Tuning systems that have frequency ratios of powers of 2 include perfect octaves and, potentially, octave transposability.