Integer approximation of musical scale frequencies
Rudolf A. Rasch · Interface · 1986
In theory, most frequency values of musical scales are irrational numbers, because of the temperament involved. In practical situations, as well as in numerical presentation, rounding to a certain number of digits is necessary. This rounding causes some inaccuracy. In this article, a measure for this inaccuracy is developed and applied to find series of numbers that represent relatively good approximations of the equal tempered scale. It turns out that series starting with 116, 508 and 1951 are very good ones, considering the magnitude of the numbers. But if we just round the standardized frequencies for equal temperament to integer frequencies, the result is also rather good.