Music Theory for Musicians and Normal People
Here's my layman explanation: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 harmonizes 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).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.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.