From: florianp@cs.rpi.edu (Peter Floriani)
Subject: Re: Speaking of Pipes (LONG)
Summary: Overview of pipe organ info (LONG)
Organization: Rensselaer Polytechnic Institute Computer Science, Troy NY
Date: Tue, 14 Apr 1992 17:57:13 GMT

This is an overview of some (pipe) organ terminology.
  
Keyboards:

An organ may have one or more manual keyboards
(manual=with the hand) and a pedal keyboard
(pedal=with the feet).  The American Guild of
organists (AGO) standards specify 61 keys 
(5 octaves plus a note) for the manuals, and
32 keys (2 octaves and a fifth) for the pedal.
Organ consoles with two, three, or four
manual keyboards are common, and the manuals
have (relatively) standard names:

from Lower -> Upper
  2  Great Swell
  3  Choir Great Swell
  4  Choir Great Swell Solo

On the Wanamaker organ in their department store
in Philadelphia, PA, there are SIX manuals:
   Choir, Great, Swell, Solo, Ethereal, Stentor
The organ in the Convention Hall in Atlantic City
New Jersey has (I think) seven.

Stops:

A stop is the set of pipes (typically 61 or 32)
which is controllable by a keyboard. On most
organs, a stop is assigned to a particular keyboard
also called a "division" or organ, named after
the keyboard controlling it.  The stop
has three parameters: 
   1. Its name, which specifies its timbre
      or its pipe form
   2. Its foot marking, which specifies where
      its longest pipe fits onto the musical
      pitches
   3. The division to which it belongs; that
      is, on which keyboard it can be played.

1. The names of stops are so diverse there is an
entire book on them ("Dictionary of Pipe Organ
Stops")  Some are unique to the pipe organ, 
others are imitative of orchestral instruments,
and some merely describe the form of the pipe.
Two categories must be mentioned, however.
In pipe organs, a pipe is either a "flue" or
a "reed".  Flues produce the "organ" sound
which comes from pipes called "diapasons"
for which "principal" is more-or-less synonymous.
Flute and string sounds are imitated by flues.
Brass (trumpets, etc) and other woodwinds
(clarinet, oboe, etc) are imitated by reeds.

2. The octave or foot marking specifies
the effective size of the longest pipe in the stop.
The word "effective" is used since some reeds and
aall closed ("stopped") pipes do not measure this
length.  Generally, 8' is at the same octave as
pianos and other instruments, 4'is an octave up,
16' is an octave down.  

Here is a table giving the relation of length and
pitch.
 
Note that the frequencies are APPROXIMATE and not
on the A440 system.

   32'    16 Hz  third C below bass clef
   16'    32 Hz  second C below bass clef
    8'    64 Hz  first C below bass clef
    4'   128 Hz  C in bass clef
    2'   256 Hz  middle C
    1'   512 Hz  C in treble clef
   1/2' 1024 Hz  C above treble clef

There is a convenient equation to compute the
relation between size and approximate frequency:
   log(size) + log(frequency) = 9

where the logs are to the BASE 2.  So, to determine
the frequency of a 64' pipe, we figure:
   "64 is 2*2*2 * 2*2*2 or two to the sixth.
    So log(64) is 6.  Take 6 from 9 and get 3.
    Multiplying two by itself three times gives 8.
    So a 64 foot pipe speaks at about 8 Hz."
Incidentally, the above book mentions that
only two organs in the world were known to
have 64' (pitch) pipes: The Atlantic City
Convention Hall organ and the one in
the Sydney, Australia Opera House; but both
are fractional length reeds.

There are also fractional numbers used as 
a foot marking.  These pipes speak notes in the harmonic
series of another pipe.  For example:
  We have a 8' diapason (61 pipes).  Its octave is a 4'
  diapason (another 61 pipes).   Those pipes sound
  a pitch TWICE the frequency of the fundamental of the 
  8' pipes from a pipe HALF the size.  To add the FIFTH 
  above this octave, we must have a note THREE times the 
  fundamental pitch of the 8' pipe.  This comes from
  a pipe one third the size of the 8', or 2+2/3'
So using the harmonic series, we can figure out the
sizes of common pitches.

 Fund. 1st 2nd    3rd  4th     5th     6th   7th harmonic 
  16'  8'  5+1/3'  4'  3+1/5'  2+2/3'  2+2/7' 2'
   8'  4'  2+2/3'  2'  1+3/5'  1+1/3'  1+1/7' 1'
   c   c'  g'      c'' e''     g''     bf-''  c'''
(The "bf-" is the "blues seventh" b-flat)

When two or more of these "mutation stops" are combined,
this is called a "mixture" and is notated with a ROMAN
numeral indicating the number of pipes sounding
simultaneously from one key.


3. A pipe's division tells which keyboard
plays that pipe (when the stop is selected).
Except in some larger instruments, this cannot
be altered.  Those larger organs may have "floating
divisions" of pipess, which can be assigned to any
of the physical keyboards.  The String and
Orchestral Divisions of the Wanamaker Organ are
of this kind.


There are numerous other controls on organs.  
One of the other important ones relevant to this
discussion is couplers.  A coupler provides an
automatic way of having one keyboard control
another division.  A coupler is specified
by three parameters: the division to be played,
the keyboard which will play it, and a foot marking.
So a Swell-to-Great 8' plays the Swell division stops
currently selected by means of the Great keyboard
and at unison pitch.  A Swell-to-Choir 4' plays
the Swell division on the Choir keyboard up one octave.
(That is middle C key on the Choir plays Swell pipes
which sound the C in the treble clef.)

The "unison off" are an inverse X-to-X 8' coupler.
They disable the normal binding between division and
keyboard.

One other note :-)  Much technological work early this
century on the electric action of pipe organs was done
by Robert Hope-Jones, who "worked for the telephone
company" (?).  If there is interest, I will do some
more research.

Peter J. Floriani


Other refs:
"The Art of Organ Building"
"The Contemporary American Organ"