> this is quite frankly very surprising to me.
If we let t be time in seconds, and f be frequency in Hz, the sine wave formula is y = sin(2pitf). The 2pi is the periodicity of the sine function. If f is 1, we sweep through 2pi once per second. If we let f be 2, then it sweeps through two times per second, and so on.
So, you can think of the lookup index as being the tf part, but with t counting in integer fractions of a second, with the caveat that you'll want to perform some interpolation between values.
If the waveform were more complex than a sine wave, then in the general case this "skipping agead" could cause distortion. A sine wave is one of a couple special cases (square wave being another, and arguably it's "cheating") where you're not skipping "too far" to cause distortion. (That relates to the Nyquist sampling theorem and low-pass filtering, as kens mentions)
If we let t be time in seconds, and f be frequency in Hz, the sine wave formula is y = sin(2pitf). The 2pi is the periodicity of the sine function. If f is 1, we sweep through 2pi once per second. If we let f be 2, then it sweeps through two times per second, and so on.
So, you can think of the lookup index as being the tf part, but with t counting in integer fractions of a second, with the caveat that you'll want to perform some interpolation between values.
If the waveform were more complex than a sine wave, then in the general case this "skipping agead" could cause distortion. A sine wave is one of a couple special cases (square wave being another, and arguably it's "cheating") where you're not skipping "too far" to cause distortion. (That relates to the Nyquist sampling theorem and low-pass filtering, as kens mentions)