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The standard antenna on an AM/FM radio is about 30 inches long because that is an average compromise of the wavelengths of the span of radio frequencies. Various designs can be shorter by coiling the conductor, or by using 1/4 wave or some fraction of the desired wavelength.
Anyhow, your shrouds will need to be tuned to some length which is an average wavelength factor of the FM broadcast frequency range. I'm not sure how you would do that - plus, you would need insulators between the wire and the mast and the toggle and the chainplate. That would be difficult, also.