The valves were invented to replace the most commonly used crooks for
Eb, E & D. It is right, that just the full step valve would be the most
practical, as a full chromatic scale with nearly no loss in quality was
made possible, just involving the right (muting) hand a bit. Further,
the valves were invented, to enable the player to perform an instant
switch between the tonalities AND the chromatic scale. 
 
The second valve brought an additional first fine tuning for the half
steps. As players found out, that the combination of the two valves were
insufficient as being too sharp in the combination, the third valve was
added.

Simon, there are some examples of single or two-valved horns preserved.
But just a few, as few have been built before the three-valved-horn came
into existence.

The third slide, by the way, touches the bell only on poorly designed
horns. As a designer, one has to care not only for the right function,
but for the esthetics also. You do not see single horns with a design,
where the third slide hits the bell, no single F, no single Bb. But you
see a lot of imbalanced design with double horns.

If your friends in Japan would think more "natural-horn-wise", they
would understand. But they are not alone. They are in the same community
of "fingering-thinking-only" players.


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