When the resonant network is excited by a high gain amplifier, harmonic modes of electromechanical excitation exist. It is desirable to suppress these harmonic modes because they may not be located at perfect multiples of the fundamental mode, resulting in distortion of clock periods. Also, and perhaps more importantly, when a customer wishes to "pull" a crystal frequency, the existence of a harmonic at a frequency imperfectly aligned with an integer multiple of the fundamental mode will cause a transfer of energy in their pulling curve resulting in a discontinuity of the frequency pulling characteristic, which can make it difficult to perform trimming of a clock frequency. Frequency pulling is simply adding or removing load capacitance to tune out any inaccuracy in fundamental mode frequency.
Harmonic modes are not desirable, but they do exist in unregulated oscillators. Because harmonic modes, particularly the third overtone, do exist, specifications are often required to bound the magnitude of harmonics and the tolerance on their location relative to an ideal harmonic.
The third overtone is 3 times the fundamental frequency. R3 is the equivalent ESR of the third overtone resonant system. 3 times FNOM is the electrical third overtone, and nominally the same as the mechanical third overtone, but they are not necessarily the same frequency, which is a problem which can result in discontinuities in a frequency pulling curve. It is necessary, if electrical and mechanical third overtones are different frequencies so that the separation between the electrical and mechanical third overtones is sufficient to prevent such discontinuities from resulting in a discontinuous frequency pulling curve. Both electrical and mechanical third overtones are undesirable.