A tidal wave with a steep rising tide and a slow falling tide can be represented by a combination of two harmonic waves.
The red curve is the observed tide. The green curve is the same tide as it appears in deep water, ie as a strictly harmonic wave with equal rising and falling tidal cycles. The thin blue line is the difference between the tide in deep water (green) and the steepened tide in shallow water (red).
It is seen that the difference has a period 1/2 of the period of the tide itself, ie it is a higher harmonic of the original tide. This higher harmonic (thin blue curve) is called a shallow water tide.