What are the advantages to using the 12th root of 2 over a simple fraction of 1/12 between keys/semitones when setting pitch frequencies on a piano?
In: 0
When looking at the *logarithm base 2* of the frequency, that’s actually exactly what we are doing: Each semitone increases the logarithm by 1/12, until, after 12 semitones, the logarithm has increased by 1, and the frequency thus doubled.
The reason we’re looking at the logarithm is because our ear doesn’t hear frequency differences, it hears frequency ratios. Going up a certain interval (like a semitone) means *multiplying* the frequency with the ratio of that interval. Mathematical phenomena that feature a lot of multiplications (not only music, but also e.g. exponential growth) are often better understood when looking at their logarithms, where the multiplications become simple additions.
Latest Answers