Abstract
This article describes the fundamentals of tuning and temperament used in music, explaining Pythagorean intonation, just intonation, mean-tone temperament, well-temperament and equal temperament. It starts with the history of tuning and temperament, and then comparisons among them are attempted from view points of the assignments of different fifths in fixing frequency. With regard to each tuning and temperament, basic concepts of it, how to construct it by numerical calculation, characteristics of tone intervals contained in it, and its advantage and disadvantage in musical expressions are discussed. Terminology needed to learn in this subject --- for example, "cent" and "chromatic semi-tone" --- are also commented when necessary.
