Music Theory for Musicians and Normal People
Here's my layman explanation:<p>Pick a frequency. Let's say you picked 400 hertz. If you multiply this frequency by a simple fraction (1/2, 1/3, 2/5, etc) you get a new frequency that <i>harmonizes</i> with your original frequency. That means they sound nice when played together. The simpler the fraction, the better the two frequencies will sound (1/2 sounds nicer than 7/13, for example).<p>If you pick several of these fractions between 1 and 2 (such as 3/2, 4/3, 5/4, 2/1, etc) you create what's called a scale. All the frequencies in the scale harmonize with the starting frequency, but they don't necessarily harmonize with each other.<p>Musicians don't always want to play with the same starting frequency so they invented "equal temperament". The idea behind equal temperament is to create a scale using logarithms/exponents instead of fractions. Because it's logarithmic, any frequency in the scale can be used as a starting point and you'll get the same result.