Why does the natural horn have a purer major triad than the valve horn?

Hello!

I know that this forum is about woodwind instruments, but maybe one of you also plays brass instruments or knows more about it than I do.

In the preface of the horn concertos by Mozart in the New Mozart Edition the following is said:

"Fortunately, efforts are again underway today to help the natural horn to a new flowering. Reproductions of instruments and teaching facilities allow the advantages of the valveless instrument for 18th century music to become evident in practice. First and foremost is probably the effect of the inimitable horn sound in the corresponding key in which the instrument is built and which is required by the respective piece of music. Horn voices blown on a natural instrument, for example, give a symphony a much purer and deeper sense of tonality, a much more characteristic key colour than with a valve instrument."


And Nikolaus Harnoncourt also writes that the natural horn has the following advantage over the valve horn:

“absolute purity of the major triads”

I would be interested to know why a horn built in the respective key has purer major triads than a valve horn in F which plays these notes.
 
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