Math on the mighty Aeolian

Today I had a two-hour lesson with David A., organist extraordinaire, on the Aeolian organ in Duke Chapel. The electro-pneumatic organ was built in 1932, the last major instrument made by Aeolian before the company merged with Skinner. Duke refurbished the organ last year. With approximately 6,600 pipes, 120 stops, and 30 couplers, with four manuals plus pedals and three expression boxes, and with a digital sequencer that allows pre-programming hundreds of settings, the sleek Aeolian is capable of a range of sounds not possible on the Flentrop at the other end of the Chapel. Thus, as wonderful as the Flentrop is, and as befuddling as I find electro-pneumatic action, the Aeolian is my instrument of choice for Franck's Grande Piece Symphonique. Hence, multiple lessons with David to figure out how to register the piece.

I've been giving myself a hard time, wondering why I'm so incompetent at choosing stops without help. Franck himself offered suggestions in his score, and I know more than the basics about combining assorted sounds. Admittedly, I came to the organ relatively late in life, but after several years of playing, I really ought to be getting the hang of this. Happily, after this morning's lesson, I finally figured out why this is such a challenge.

Here is a photograph of the Aeolian console. There are approximately 120 of those white knobs. There are so many knobs, in fact, that I couldn't get all of them to fit into the photograph. They're new and pretty, and they glide out and in smoothly, quietly, satisfyingly. They're lovely.

The knobs are divided into different sections, corresponding to the four different manuals and the pedal board. Pulling out a knob sends a signal to the organ's innards, allowing air to flow through a subset of pipes that produce a characteristic sound--a reed, say, or a flute, or a diapason, or whatever timbre is indicated on the knob.

Above the uppermost manual is a row of about 30 coupler tabs. Couplers allow you to take sounds from one manual and add them to another manual or pedals. They also allow you to take the stops you've chosen for one manual, knock the frequency up or down an octave, and fold them back into the same manual, either with or without the original octave.

Now let's do some math. If you have 120 knobs to pull, how many different combinations of pulled knobs are within your grasp? Why, 2ⁿ-1, that's how many! When n=120, there's not much point in subtracting 1, since 2⁽¹²⁰⁾ is about 1.3 x 10⁽³⁶⁾. That's a lot, and that's not even counting the couplers.

Of course, you wouldn't ever dream of actually using all of those combinations. You're not going to accompany a nearly inaudible four-foot flute in the swell with a bombastic 32-foot diapason in the pedals, or combine a tuba mirabilis with a gamba. So let's say you'll never use 99.99% of the available possibilities. That leaves 1.3 x 10⁽³²⁾ options, still a ridiculously large number. Let's chuck a few more. Say I can ignore a whopping 10⁽³³⁾ of the combinations--99.9999999999999999999999999999999%, poof, gone.

Lucky me, I have only 1300 combinations of stops to learn. Now all I have to do is remember which 1300 of the original 1.3 x 10⁽³⁶⁾ they are.