Tempered Music Scales for Sound Synthesis
M. Yunik, G. W. Swift · Computer Music Journal · 1980
Our purpose here is to determine, as objectively as possible, the most pleasing and useful division of a musical octave into k equally spaced tones, meaning that the ratio of the frequency of any tone in the scale to the one below it is a constant. This implies that the frequency ratio of one tone to the next is the kth root of 2. Such a scale is known as a tempered scale, or tempered intonation. It is possible to specify that a scale consist of only selected tones from the full set of k tones (Chalmers 1979). We assume here that all k tones are used. Since the human listening system is complex and varies from one person to the next, objectivity is difficult. It follows that estimation of reasonable er-