I have heard a little about resonating a tesla coil and wan't to make sure that it is going to before I spend money for my primary (copper is expensive). My secondary has about 1400 turns of wire. I am going to be using a bucket capacitor like The Geek Group on youtube built, and a 60 Hz high voltage transformer. My primary will hopefully be 1/4 inch, and I wan't to know how many turns I need and if I can do a funnel looking shape like this one Tesla Coil. One other thing is that my tesla coil is 30 inches tall, so does my primary need to get closer to the top to work. I think I got all of the primaries and secondaries right, I know which is which, but sometimes I swap the words. It would be a great help if you answered my question.

The resonant frequency will be f_secondary_resonance=1/ (2*pi*sqrt {Lsecondary*[Ctop_load + C_secondary] } )

To determine the oscillating frequency of the primary, you will need to know the capacitance of your capacitor and the inductance of your primary winding.

Technically the primary oscillates at what is called the natural frequency, which is slightly less that the driven resonant frequency. But, they are fairly close if the resistance in the primary circuit is relatively low.

f_primary_oscillation= 1/ (2*pi* sqrt[Cprimary*Lprimary])

The required inductance of the primary to drive the secondary at the right frequency will affect how many turns you need on the primary. Keep in mind that Tesla coils almost always need some final adjustment to tune for best results, and this is most readily done by tapping the primary at a different point. So, construct your primary such that it is easy to change the tap point while still making a good connection.

This web site has a list of formulas useful for Teslas coil design, including the inductance of the inverterted conical shape primary you are describing.

http://teslacoils4christ.org/TCFormulas/TCFormulas.htm

I used these same formulas back when I built a coil, and they gave reasonable results. Some parameters, like the secondary self capacitance, are difficult to calculate precisely.

The closer the top of the primary comes to the top of the secondary, the more likely you will have arcs striking the primary. This is undesireable, and some users build a grounded "strike ring" around the top of their primary so that if it arcs that far, it will be conducted to ground instead.