Thus spoke Zarathoustra +

[Horace Greeley]

Bob,

I respectfully disagree.

First, the piano string analogy is flawed.  The pitches
are connected because they are produced by the various
lengths of the vibrating string (to say nothing of other
influences of the structure.)  They are, therefore, not
free to vibrate independently, but are dependent one upon
the other.  (Hmm, if Jefferson were alive today, would he
be writing the Declaration of Co-Dependence?)

As to an organ, I am sure that you are correct, as long
as we assume that you are dealing with a single pipe
played at STP (Standard Temperature & Pressure).  The minute
any variation is made, the speed, if not the volume as well, of 
the air column changes - voila! The upper partials are no longer
locked to the lower ones.  Further, lots of stops, especially lower
(pedal) flutes and bourdons have few, if any fundamentals.  Working
with them is sort of like tuning a bell - from what area do you
add/remove how much to produce what change, under what circumstances.
Actually the bell is a better comparison to an organ than a piano is;
much more complex sound, with much less definable pitch.  I seem
to remember reading somewhere that bell makers look for individual
"signatures" of tone, and that these are (most usually) combinations
of the something like the 4th, 6th, 7th and 9th harmonics, with a dash
of fundamental thrown in for good measure.  Probably the writer had
spent too many years doing change ringing...

Random thoughts.

Best.

Horace



At 07:52 PM 10/15/97 -0400, you wrote:
>Horace wrote:
>
>>I don't think a case can be made for having no inharmonicity in
>>organ pipes - quite the opposite.
>[..snip..]
>>They are simply massively responsive
>>to minute variations in temperature, humidity, draft, dust,
>>perhaps, even, lumpy gravy.  Minute variations in voicing can
>>be induces simply by the position of the tuner's body relative to a given
>>distance from a "tuned" pipe.
>
>  Although organ pipes are very sensitive to minute variations,
>that does not mean they have inharmonicity.  In a piano string,
>the partials have the freedom to ring at their own independent
>pitches because after the initial impulse from the hammer,
>they have no connection with each other.  No so with an organ
>pipe.  In place of an initial impulse you have a continuing
>series of impluses formed by the oscillations at the fundamental frequency.
>This forces the harmonics to remain locked to the
>fundamental, hence no inharmonicity.
>
>Bob Scott
>Ann Arbor, Michigan
>
>
>
Horace Greeley

Systems Analyst/Engineer
Controller's Office
Stanford University

email: hgreeley@leland.stanford.edu
voice mail: 650.725.906
fax: 650.725.8014