Basic question regarding twin systems

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: "Jon Danniken" <danniken@xxxxxxxxxxx>

Hello,

I've built a few single coils over the years, and am currently building a 
six inch coil.  Because I am
planning the coil after that to be a twin system based upon this and 
another six inch coil, I have a
question I would like to ask before I wind the second coil.

I am familiar with the basic concept in a single coil system whereby the 
primary (tank) frequency matches
the secondary (coil + topload) frequency (IpCp = IsCs).

In a twin system, the Ip is split between two different primary coils (Ip1 
and Ip2), with the fundamental
primary (tank) frequency created by both primaries and the main 
capacitor.  Is this fundamental primary
(tank) frequency the same frequency that would normally drive either of the 
secondary coils individually
[((Ip1 + Ip2)Cp) = Is1Cs1] and [((Ip1 + Ip2)Cp) = Is2Cs2]?

In other words, can I just design for a single coil system, but split the 
primary between two inductors
and add an additional secondary?  Thusly, if the primary (tank) frequency 
is 110 kHz, will each secondary
also be 110 kHz?

Sorry for the simplistic descriptions here, and I do realize that either 
one of the secondaries or one of
the primaries needs to out of phase for the two coils to interact.

Thanks,

Jon