At the risk of winning another scathing rebuke from Hans, I thought I'd
weigh in on the tuning issue.  

Hans states: " If the horn is tuned using our written "e2"
(= first space from top) the horn will result quite sharp, relatively, as
you tuned it
with a relatively flat natural pitch."

http://en.wikipedia.org/wiki/Harmonic_series_(music)

The link is to information about the harmonic series - that function of
nature upon which we triumph or fail - and how each point on that harmonic
series varies from the equal tempered A-440 to which we tune.  

Knowing well that the whole equal vs. just intonation topic is often a total
minefield for wind players, I will none the less say an "e2" (First space
from top) is an 8th partial - a VERY stable and in-tune partial relative to
A-440.  If one carefully tunes their instrument to 8th partial notes on both
the Bb (first...) and F sides (2nd) - one has the opportunity to play freely
down the 'center' of the pitch.  

Of course, numerous notes must be played on less 'in-tune' partials (5th
partials, 6th partials...as well as the ever popular 9th and 10th
partials...).  As the diagram in the center of the linked article indicates,
ONLY partials 1, 2, 4, 8, and 16 are stable and in tune relative to the
A-440 to which we tune (or A-442 in San Francisco...or A-448 in Berlin...or
whatever).  

A short word about just intonation:  A very smart mathematician I know
recently said something to this effect:  "we play pitches and scales in
equal temperament...but we play chords in just intonation".  I believe
players can use the flatness and sharpness of certain partials to their
benefit in placing their pitches in the proper position for the just tuning
of various chords during performance.

Sandra
Toledo Ohio



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