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Category: Organ playing

  1. The Science of Registration

    Posted on

    While organ registration is first and foremost an art, to be practised (hopefully) with musical sensitivity and good taste, there is an interesting mathematical side to it too. Now, if the mere mention of maths is enough to bring you out in a cold sweat, please don't panic just yet. There is no calculus or quadratic equations in what follows - just basic primary school arithmetic.

    The relevant branch of mathematics is known as "permutations and combinations" or "perms and coms" as we used to call it when I was at school. To take permutations first, these are concerned with arranging things. If you haven't come across them before, a simple example will give you the idea. Suppose you have a small bookshelf which holds 6 books. How many different ways are there of arranging the books on the shelf?

    The answer isn't hard to find if the problem is broken down into stages. Starting with an empty bookshelf, how many ways are there of choosing a book to go in the first position? Six, of course! What about the second position? One book is now used, so there are only five books left to choose from. Each of the six first choices gives a different five second choices, so the total number of ways of choosing books for both the first and second positions is
     
    6 x 5 = 30


    If we go one stage farther, the number of different ways of arranging books in the first three positions is

    6 x 5 x 4 = 120

    We can now see that the number of ways of arranging all six books is

    6 x 5 x 4 x 3 x 2 x 1 = 720

    That's a surprisingly large number of permutations, considering we are only dealing with six books, but if we increase the number of books, the number of permutations rises very dramatically:

    7 books      5,040
    8 books     40,320
    9 books    362,880
    10 books 3,628,800

    So much for permutations. Combinations are the number of ways of selecting things. Again, a simple example will make the idea clear. Suppose, from our set of six books mentioned earlier, we wish to choose three to take on holiday. How many different ways are there of doing this? Following a similar line of reasoning we can say that there are six ways of choosing the first book, five of choosing the second, and four of choosing the third. This gives us

    6 x 5 x 4 = 120.

    However, this is not the whole story. With permutations,the order of the books is important, with combinations it isn't. Choosing books A,D and E to take on holiday is just the same as choosing books D,E and A, so we must adjust our answer (making it smaller)  to allow for this. To do this we have to think of the number of permutations of 3 books, which we now know is

    3 x 2 x 1 = 6

    To get the answer we divide our first number by our second number:

    120 / 6 = 20

    So there are 20 ways of choosing 3 items from 6 when the order isn't important, or 20 "combinations". Again if we were to increase the total number of books we would see the  number of combinations rising dramatically.

    Strangely enough, the words permutation and combination are often used incorrectly in everyday speech. Take the case of the so-called combination lock. The order of the digits is important, so it should really be called a permutation lock, while the so-called permutations of the football pools are actually combinations. I'm pleased to say organists are a lot more logical in their thinking, and the combinations we refer to in connection with organ registration (yes, I'm getting to the point at last!) are true combinations in the mathematical sense.

    Using the simple tools above, we now have a means of working out the total number of possible combinations for any organ. If, for example, we have a small  instrument with 6 speaking stops, we already know (from the holiday books example above) that there are twenty possible combinations involving 3 stops. To get the total number of combinations, using any number of stops, we need to repeat the calculation for 1,2,4,5 and 6 stops drawn, and then add all the answers together:


    One stop combinations:  (6)/(1) = 6
    Two stop combinations:  (6 X 5)/(2 x 1) = 15
    Three stop combinations: (6 x 5 x 4)/(3 x 2 x 1) = 20
    Four stop combinations:  (6 x 5 x 4 x 3)/(4 x 3 x 2 x 1) = 15
    Five stop combinations:  (6 x 5 x 4 x 3 x 2)/(5 x 4 x 3 x 2 x 1) = 6
    Six stop combinations:  (6 x 5 x 4 x 3 x 2 x 1)/(6 x 5 x 4 x 3 x 2 x 1) = 1
    TOTAL    63

    As you can see, the numbers fall into a symmetrical pattern, and this agrees with common sense, because choosing four stops to draw is equivalent to choosing two stops not to draw.

    If we are interested only in the total number of combinations, there is a quicker way to get at the answer. We consider each stop control in turn and remember it can be either ON or OFF. If we just look at one, there are two possible states. If we look at two together, the number of possible states is

    2 x 2 = 4

    Finally, if we consider all six stops, the total number is

    2 x 2 x 2 x 2 x 2 x 2 = 64.

    At first sight, our two answers don't quite agree, but this is because the second method of calculation includes the case of zero stops drawn. If we agree not to include this as a combination, the answer is 63 in both cases. Yes, an organ with only 6 speaking stops gives you a total of 63 possible combinations! (Not all may be musically pleasing, of course). But if this number surprises you, see what happens when the number of speaking stops increases:

    10 stops         1,023 combinations
    20 stops         1,048,575 combinations
    30 stops         1,073,741,823 combinations
    40 stops         1,099,511,627,780 combinations (approximately)

    (Don't try this sum for the Wanamaker organ or your calculator may explode!)

    It's mind boggling stuff, and one of the reasons playing the pipe organ is so fascinating. Even if your instrument isn't a particularly large one, and even if you've been playing it for years, there are sure to be plenty of combinations which you haven't even heard yet! Perhaps you are inhibited from experimenting due to preconceived notions of what is "allowed"? Why not let an inquisitive child loose on your instrument? Let them pull stops at random and see what they come up with.

     

  2. Using the swell pedal

    Posted on

    At first glance there isn't a great deal which can be said about using the swell pedal. Isn't it the most obvious, the most straightforward, and the most instinctive part of playing the organ?  Surely it requires no more skill than, say, using the accelerator of a car? Well no, that isn't quite true, especially if one aspires to perform pieces from the classical repertoire where a degree of ambipodiousness is called for.

    It's different for those who have home electronic instruments with just the one octave of pedals. In that situation, there's a clear division of labour between the feet - the left plays the bass notes and the right operates the expression pedal, and for either to encroach on the other's territory would be unthinkable.  The same is true to some extent when playing in a popular style with a full  pedalboard, as in the theatre organ tradition. Maybe the right foot helps out a little, but it's usually the left which does the lion's share of the note playing, leaving the right free for expression pedal duty.

    In the classical tradition of organ playing, the pedal part is likely to be more complex, more melodic and more legato - something which can only be realised by both feet working together in close co-operation. In this situation, the swell pedal needs to be operated by whichever foot can best be spared at the time. This means that a competent classical organist will be as happy using the left foot as the right, and able to swap them frequently when required. I must admit I don't find this at all easy. Somehow, it seems far more natural to have my right foot on the swell pedal. I have to concentrate quite hard to use the left one, otherwise my brain seems to lose track of which foot is which, with disastrous consequences!

    This ambipodious quality I've described is greatly assisted by good console design.  An obvious requirement is that expression pedal(s) should be mounted centrally. This can be taken for granted with modern consoles, but was not always the case. The Victorian pipe organ I learned on had the swell pedal tucked away in the RH corner making use of the left foot physically impossible. It should also be easy to find the swell pedal and to slide the foot on and off it. The common practice of putting the swell pedal in a little pocket surrounded by speaker grille is not good from this point of view. Many VPO setups are superior because they have the swell pedal bolted on top of a free-standing pedalboard with plenty of space all around it. One final ergonomic consideration is that there should be sufficient vertical space above the pedal. The knee is sure to rise higher when using the swell pedal than when playing notes on the pedalboard, so this should be the deciding factor when positioning the lowest manual. It should not be necessary to twist the leg sideways when the foot is on the pedal. Again, those of us who assemble our own VPO console have the advantage of being able to adjust this dimension to suit our leg length, unlike those buying an  organ "off-the-shelf".

    When it comes to the artistic aspects of swell pedal use, the best advice is probably to use the damn thing sparingly - incessant pumping is downright irritating! To create a truly impressive crescendo the opening of the swell box can be combined with the addition of stops. In this situation, I always think it's best to add stops to the swell department first, then open the swell box, as the effect is all the more dramatic with more stops drawn. The famous toccata from Boellman's' Gothic Suite is a good example of simple but effective swell pedal use. For a large part of the piece the swell box is firmly closed, then it is opened over the space of a few bars and remains open to the end. It couldn't possibly be simpler, but it makes a big impression, like lifting the lid off strongly felt emotions.

    An organist also needs to develop a sixth sense to know where in its travel the swell pedal is currently located. There's nothing more annoying than peaking too soon!  Theatre organs often provided a visual indicator of the current state of the expression pedals (a feature duplicated in Miditzer) and such an indicator would be a valuable addition to a classical organ's console, but I don't ever remember coming across one.