# Why are C, G and C all played open on the trumpet?

Why are C, G and C all played open on the trumpet? I would expect C, F# and C to be produced by adjusting embouchure as they're evenly each a half octave apart. What am I missing?

To get the F#, a flat 5th, is mathematically difficult. In the modern equal temperament, that interval is exactly $$\sqrt2$$ times the fundamental, and since $$\sqrt2$$ is irrational, you cannot achieve it exactly with any ratio of integers, although of course you can approximate it as closely as you want, if you use large enough integers, eg 17/12. But I doubt you'd have much luck trying to blow that on a trumpet without using valves. ;)