Can Tesla coils up frequency to visibility? So I recently built myself a small ish tesla coil to make my childhood dreams come true, and to further my small understanding of the electromagnetic force. Some people like the musical tesla coils because they can play music with the AC arcs. Although I do not like the "musical" coils, they do supply me with an interesting question, and bear with me as I am just a high school boy:
Suppose we had a frequency generator that could go to frequencies of around 600THz. Because light is "alternating" electromagnetic(ness) could i theoretically produce a color of visible light with my coil? If its problematic that we are outputting pulse waves we can assume that the output of current at mega high voltages is sinusoidal.
 A: A Tesla coil is, in essence, an electrical resonant transformer and, as such, it generates EM fields around it. But, of course, the sound we hear is not produced by oscillating EM fields, but, rather, by air, which expands and contracts in sync with those oscillations due to the heat associated with arcing. The nature of this sound is the similar to the nature of thunder produced by lighting.
We can also note that a typical operating frequency of Tesla coils is in hundreds of kilohertz, well beyond our hearing range (about $20$Hz to $20$KHz), so the sound of music in Tesla coils is created by modulating the amplitude of the electrical oscillations by  an audio signal. 
Going back to your question, we can say that the primary reason Tesla coils are used to make music is due their ability to generate arcs, which convert electric energy to acoustic energy.
Since, as you've mentioned, light is an EM wave, no conversion to other forms of energy is required and, therefore, Tesla coils do not give you advantage over safe, low power high, frequency oscillators.   
The issue here is that the required frequency is too high. 
For really high frequency oscillators, their physical size becomes a limiting factor. Generally, the higher the frequency, the smaller the components of an oscillator have to be, roughly, of the same order of magnitude as the wavelength of the corresponding EM wave. For instance, to generate $600$THz oscillations, the size of the oscillator would have to be on the order of $0.5\mu m$. This calls for a microstructure well below the size of any practical coil. 
