Three-limit Tuning
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all interval (music), intervals are determined by choosing a sequence of Perfect fifths, fifthsBruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: McGraw-Hill). Vol. I: p. 56. which are "Five-limit tuning#The justest ratios, pure" or perfect fifth, perfect, with ratio 3:2. This is chosen because it is the next harmonic of a vibrating string, after the octave (which is the ratio 2:1), and hence is the next most consonance and dissonance, consonant "pure" interval, and the easiest to tune by ear. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the Regular diatonic tuning#Syntonic temperament and timbre, syntonic temperament in which the generator (music), generator is the ratio Perfect fifth, 3:2 (i.e., the untempered perfe ...
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