Resistance-Capacitance Oscillator for Generating the Frequencies of the Equally Tempered Musical Scale

Abstract

The frequencies of the equally tempered chromatic scale and the attenuation ratios of a uniform ladder attenuator are both in geometric progression. By modifying a Wien bridge oscillator so that the shunt resistance arm of the bridge is driven from a ladder attenuator, an oscillator has been devised that will generate the frequencies of the scale without requiring awkward component values. Two feedback amplifiers are used: one of them is frequency sensitive, and the other provides the necessary phase reversal and amplitude control. With simple transistor amplifiers, the frequency of oscillation follows the attenuator setting to within about 5 in 104, but ways are described by which the frequency of any semitone within an octave can be made correct to 1 or 2 in 104, without demanding comparable accuracy in the components. The circuit also allows the ratio between semitones to be progressively changed by the small amount required to accommodate the phenomenon of “octave stretching.” The design of an attenuator, using only preferred resistance values, is given, and the question of temperature coefficient and adjustment to standard frequency, A=440 Hz, is considered.