Scalar correspondence with the overtone series
Bennett S. Blum · The Journal of the Acoustical Society of America · 1988
It is frequently stated that the overtone series produces the notes (starting on C) C, G, E, (flat) B♭, D, (flat) F♯, and (flat) A. These notes give (a mode of) the ascending melodic minor scale. Since this scale is widely used in western music, one is led to seek a relationship between the physics of overtones and the scale. Unfortunately, it turns out that the overtone corresponding to A is really closer to A♭. If a scale is constructed with the notes in the tempered scale closest to the tones in the overtone series, the results are C, D, E, F♯, G, A♭, B♭, C. This is not a scale in western music. Furthermore, the overtone associated with F♯ is almost as close to F as it is to F♯, and only tempered C, D, E, G are really close to tones in the overtone series. Thus while the overtone series may be applicable to intervals of second, third, fourth, and fifth, and to the major triad, it cannot be applicable to other intervals, the minor triad, or any scales.