Digital generation of equal temperament
R. Schaefer · IEEE Transactions on Acoustics Speech and Signal Processing · 1975
The generation of pitches of an equally tempered musical scale through nonbinary frequency division is explored, including an analysis of the resulting frequency errors. Useful approximations to 21/12, in addition to the well known 196/185 ratio, are sought. A criterion for allowable errors is developed and applied to ratios involving integers up to 10 000. Based on an optimum tuning algorithm, it is determined that there are other possible ratios that could be implemented more simply and at a lower cost than the 196/185 ratio.