In article , RST Engineering \(jw\) wrote:
Sorry, dude, 50 years of designing with crystals, right from when I ground
my first surplus WWII rock on a piece of glass with toothpaste as the
abrasive says that what the original poster asked is correct.

Will the harmonic be precise? No. Will it be "close", which is what the
original poster asked? You bet. Depending on the oscillator circuit, can
it be "pulled" on frequency? Perhaps.

But to say that the crystal doesn't resonate anywhere near the harmonic is,
as I said, bullpuckey.

This reminds me of a colleague who can easily tell everyone
qualitatively that a situation deviates from theoretical ideals and as a
result (using my words and not his) "$#!+ (poop) will splatter!" But he
at least often in my experience have trouble saying this quantatively!

For one project, I decide to try something, and tell my boss what I am
trying. This colleague of mine says (using words of mine and not his),
"slop will spatter"! (As in light for adding optics to a light source for
a specific application. This application has multiple LEDs shining onto
an optical device with multiple elements.)
Boss tells me that what I delivered to him and he found working should
not have worked according to this colleague of mine, due to stray beams
forming. So what do I do - I send photos to the boss of the beam pattern
including the stray beams predicted by my colleague. I even named these
stray beams after my colleague. But they were minor due to most light
produced by the light source being on paths that resulted in adding to the
desired beam combination as opposed to the undesired stray beams.
Furthermore, my boss's industrial designer designed a baffling system
that blocked the small amount of light from the multi-element light source
that was on paths towards the stray beams as opposed to the desired rays
that were "on course" to be utilized by the multi-elemt optical assembly
as planned.

So beware that the situation may not be much worse than ideal when
someone can tell you how you are deviating from ideal!