Depends on which stops are pulled on the organ. If it's just octaves (8', 4', 2', 16'...), then it will be quite pure, depending on what kind of stops are playi

Depends on which stops are pulled on the organ. If it's just octaves (8', 4', 2', 16'...), then it will be quite pure, depending on what kind of stops are playing (flutes and principals are purer than reeds, for instance). If you add a mutation (2-2/3', 1-3/5', a mixture of multiple mutations...), then you'll have both the impurity of the mutations themselves, as well as their own overtones. Or, you could have a string stop pulled, which is purposefully slightly out-of-tune to produce a "string" sound when paired with an in-tune stop. A typical "pipe organ" sound on a digital keyboard will often have mixtures and other mutations. I've found that settings with names like "church organ" tend to be purer, perhaps only some flutes and principals.