In the beginning, there was improvisation. Music wouldn't be written down for thousands of years. Composition as we know it today didn't exist. All that existed was the voice and some rudimentary instruments. The only music that could exist was that which could be held in the mind and expressed from within. The only way to pass that music on was from voice to voice. When music started being written down about a thousand years ago, things rapidly changed and music became capable of being preserved forever, and also grew to where it could do things beyond the capabilities of a single human mind.
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Perhaps the most important thing you can do with improvisation is to try to define just what it is. It's a problematic endeavor because the concept changes depending who you ask, and that goes for professionals, amateurs, and lay people equally.
The most concise definition I can think of is: Improvisation is composition at the keyboard (or fret-board, or whatever instrument or voice is used). It seems that improvisation for most everyone implies a certain degree of 'unpreparedness', or conversely, spontaneity. Music is spontaneously created, not from memory, nor from an existing page. What differs in the definition is the degree of 'unpreparedness' or just how much preparation is really involved.
Dupre would take musical themes submitted from the audience and spontaneously create organ symphonies based on them, after a few short seconds of pondering the theme. He improvised hundreds of symphonies over his long touring career, and most of them were almost totally spur-of-the-moment creations. The long preparation of these improvisations were not notes jotted on paper, but years of practice in improvising. Like the oft used image of the iceberg, the shining point visible above the murky waters is dwarfed by the massive bulk submerged below the surface. It remains hidden from view, but it is the foundation of all that we see.
When he came across the idea of improvised musical commentary on Le Chemin de la Croix (The Way of the Cross) by Paul Claudel, he actually spent some time considering the 14 stations of the cross. Then he carefully selected his themes that would symbolize everything from weariness and compassion, to the ropes that lowered Jesus' body from the cross. He knew the plan of what he would play before the occasion, just not all of the notes. As he said on later occasions, improvisation is like driving home. You know the general route you are going to take before you start and have no problems changing your plan to avoid other cars, accidents, or detours. He prepared not just generally by practicing improvisation, but specifically for this piece.
Improvisation is on the same plane as composition. It is the meeting point between composition and performance. One must be proficient enough in their playing as well as their theory to present a cohesive improvisation.
While in Rochester, I was surprised by how much the organ students would practice one improvisation for a week, or even several weeks. This seemed like an oxymoron to me, practicing a spontaneous piece over and over again. After enough practice, some of them would play the same notes every time, having effectively composed a piece at the keyboard, which is technically speaking not an improvisation; these same students would have difficulty if asked to change a passage or try a different technique. Other students remained flexible keeping the 'improvisatory spirit'. Here students learned to give their improvisations form and found they could fit that form with any theme, supplied or created.
Making the connection between composition and improvisation was quite a cathartic moment for me, and I've been dealing the the ramifications ever since then.
Improvisation is by its nature a creative act, one that can permit differing degrees of preparation. Just as importantly, it is a living act, not one set down on paper over time. It lives on the keyboard and only exists during its performance. Each one is unique, never heard before, never to be heard again. From this perspective, even a bad improvisation is something of a privilege. A great improvisation, on the other hand, can really be a miracle.
When Bach was getting on in years, he was becoming, according to contemporary composers, increasingly out-of-date and old-fashioned; boring, you might say. He had occasion to visit Frederick the Second at his residence in Potsdam, as Bach's son C.P.E. Bach was employed there. The king showed Old Bach his collection of fortepianos, a newly invented instrument and had him improvise on them. Then the king asked that Bach improvise a 3 voice fugue on a given subject, a particularly difficult one:
Old Bach did so. Then the king asked him to improvise a fugue with 6 voices. Bach answered he would have to write it in score and send it to him. Two months later he published what we know today as The Musical Offering, a set of two fugues, a trio sonata, and riddle canons all based on the Royal Theme. Included was the 6 voice Ricercare fugue that the king requested, and also was included the 3 voice fugue that Bach had improvised, remembered, and written down. It might have sounded something like this:


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