Re: technical \'Q\'uestion
Glad you got some sleep.OK!!! it is cheating & it is the most,but least effective way of producing this 32 ft pitch.
Let's try this one:
When pure tones (sine waves) are sounded together, they combine to produce two additional tones whose frequencies are the sum and difference of the two original tones. For example, if the original frequencies are 32hz and 48hz, the resultant frequencies will be 80hz and 16 hz. While this effect occurs at all frequencies, it is most effective to the human ear at low frequencies. (This same acoustical principle is used by celestes to produce a different effect.)
These stops use this acoustical effect to produce tones in the 32' and 64' octaves, using smaller (and thus less costly) pipes than would normally be necessary. One of these stops, labeled as 32' or 64' pitch, is comprised of two ranks which sound an octave and a twelfth above the desired pitch (that is, at the 1st & 2nd harmonics). For a 32' stop, the two ranks are 16' and 10-2/3'; for a 64' stop, the two ranks are 32' and 21-1/3'.
In many cases both pitches are taken from the same rank of pipes, a fifth apart, as a further cost-saving measure. Because 5ths in the equal-tempered scale are not perfect fifths, the resultant tones will not be quite in tune, but it works because the human ear does not hear such low tones with enough accuracy to tell the difference.
The name Gravissima is typically only used for a 64' stop.
N.B. There are exactly two true 64' stops in existence. One is the Diaphone Profundo at Atlantic City; the other is a Contra Trombone at the Sydney Town Hall.
Tonal Attributes
In order to be effective, the pipes should be large scale flues, either open or stopped. Bourdons and Diapasons are most often used; reeds are almost never used.
Usage
This stop is a replacement for a true 32' or 64' stop. It is not as effective as a true stop, but is often the only economical way to obtain 32' tone in a modest instrument. It is almost invariably found in the pedal.
Variants
A single 5th sounding stop at 10-2/3' or 21-1/3' pitch is often provided to achieve the same effect. This has the advantage that it can be combined with a variety of octave sounding stops. See Grossquintenbass.
Examples
32' examples are fairly common. 64' examples are rare, Julian Rhodes keeps a compilation by David Willey that lists about 40 examples (see Bibliography below). A few examples are listed here.
Gravissima 64'; Woolsey Hall, Yale University, New Haven CT; Hutchings-Votey Organ Company.
Gravissima 64'; Worcester Cathedral, Worcester, England; Hope-Jones.
Gravissima 64'; Liverpool Cathedral, Liverpool England; Willis.
Gravissima 64'; Bremen Cathedral, Bremen, Germany (destroyed?); J. F. Schulze.
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Now corno,at this hour in the morning I had to resort to going to The Bible for Organ Builders & Organists. lol.
http://www.organstops.org/ Click Middle link on page & all
sorts of things appear about pipes and also somewhere in there is all about this 'Q' factor (I think).
hehe
I forgot I was talking to a Horn Guy,and you would have been aware of all this double-tone & harmonic minus's and plus's etc.I do understand this '(inside the horn)'.Us keyboard players and other intrumentalists have all the Keys in front of us.But you Horn Players (and Strings) have a lot more to do to produce sounds.I admire all the hard work required and
for more use of the Brass Section in new works.etc.
So I have to fully agree with Pythagoras (let's not disturb him now) and also in answer to your question,NO.!!!! there is no real way that you can produce an 'audible' & 'true' sound BELOW its fundamental.(without cheating).Also,your 'bottleneck' comparison is a very spot on way of understanding the upper harmonics. etc.
Many have tried. Haskell was one who tried in the early 1900's of taking a pipe and inserting another pipe to try and lower pitch,without lengthening the pipe (was also tried in the early 17th cent in spanish organs)."Haskelling" a pipe is sometimes still used now,but not very good results.
I am sure Haskell and other methods are in The Bible at above link.The mutation section is interesting,in relation to the higher notes.....this is where,I think, the 'Q' factor is explained better.
Time for a coffee break. Jamie