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In an AC SG Tesla coil circuit can the capacitor be half of what it should be?

AC SG Tesla coils usually have a HV AC transformer leading to a capacitor. The capacitor is usually tuned to the transformer so the spark gap will fire twice a cycle at every polarity change due to the 50-60Hz mains frequency. 

Can you match up the transformer to capacitor so the spark gap will fire four times every cycle instead of two and will this still produce good results compared to the conventional method?