wrote:
The mutual coupling and effect of additional elements can shift
frequency in any dorection depending on parasitic element tuning. The
effect isn't caused by the capacitance of additional elements, it is
caused by the complex interaction or reradiated power arrivibng with a
time delay back at the original source.

This is why, with various element tuning and spacings, feed impedance
of a Yagi can change all over the map.

Same for dipole height, the reflected wave from the earth will change
feed impedance as well as shift resonant frequency.

Same for dipole length, the reflected wave from the ends of the
dipole will change feed impedance as well as shift resonant
frequency.

The feedpoint impedance of any standing wave antenna is the
superposition of all the E-field voltages divided by the
superposition of all the H-field currents and is the result
of the interference pattern. Doing anything to change any of
the voltage or current components will change the feedpoint
impedance.
--
73, Cecil http://www.qsl.net/w5dxp