In my last post I mentioned Taffanel and Gaubert’s daily exercises. One of the most popular of these has been nicknamed the Scale Game. It might be more accurately named the Pentachord Game as it only covers 5 notes of the scale at a time.

Here is a sample of the scale game applied to the major scale starting in C Major:

As you see the first four measures just consist of the first five notes of the major scale: 2212. In measure 5 the bottom note switches from being the first note (tonic) of C to being the seventh note (leading note) 0f Db. So the next three measures play on 1221, that is the seventh and then the first four notes of Db Major.

Finally in measure 8 there is a little turnaround to reestablish the 2212 pentachord in the new scale (Db).  You can see that in measure 9, the beginning of the same 8-measure unit transposed up by a halfstep (+1).

The whole game takes 96 measures to cover all twelve keys and is followed on the next page by the same exercise again using a minor pentachord (2122).

In MOVES the idea can be rather clumsily coded thus:

{+1 +2 +2 +1 +2 -2 -1 -2 {{-2 +2 +2 +1 +2 -2 -1 -2}}
-2 +1 +2 +2 +1 -1 -2 -2 {-1 +1 +2 +2 +1 -1 -2 -2} -1 +1 +2 +2 +1 -3 -2 -1}

…which, if I’ve got it right, should add up to +1, meaning it rises by a semitone/halfstep at each cycle. (The +1 move at the beginning is the chaining move.)

Some years back, during one of my bouts of aiming at total world saxophone domination, I was interested in playing this game with other exotic or non-diatonic scales or ragas.  The only qualifying condition was that the scale should contain a leading note a halfstep below the tonic, so that the pattern would cover all keys in rising halfsteps.

But since then, I have realized you don’t need to depend on a given scale structure to limit its possibilities.

Imagine any series of five notes separated by the intervals w, x, y, z  or in MOVES parlance, the array (w x y z). If we give these values an upper limit of 4, you can immediately see that the possibilities are mind boggling: 256 of them to be precise. The leading note is fixed at one halfstep below the bottom note, and this gives us:

{+1 +w +x +y +z -z -y -x {{-w +w +x +y +z -z -y -x}}
-w +1 +w +x +y -y -x -w {-1 +1 +w +x +y -y -x -w} -1 +1 +w +x +y -(x+y) -w -1}

When you have exhausted all those possibilities, there is one more ridge to cross, and like Xenophon and the Ten Thousand or Vasco Nuñez de Balboa, you stumble upon another equally vast ocean and shout thalassa! thalassa! or ¡Coño! ¡el mar! respectively. For as with all MOVES exercises, you can simply swap the plus and minus signs and get another play!

Even if it doesn’t win you the Saxophone World Cup, the exploration is its own reward, and the mental exercise gets you away from mindless dot-reading. For the more advanced, a greater range of values for w, x, y, and z can be envisaged, including negative values, which make the melodic possibilities much more interesting.

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