This is a question that's come up for me any time I'm choosing a name for my piece. I tend to oscillate between wanting to give away too much and too little when it comes to the name or any extra-musical description of my pieces.
It's an interesting question - in so many cases, composers have initially presented their works with elaborate descriptions of what the music is meant to 'mean', only to later retract everything and end up with a nondescript title such as 'Symphony no. 1', as Mahler did with his first symphony. With the rise of program music in the 19th century, propelled forward by Liszt's invention of the 'Symphonic Poem', came more frequent extra-musical associations with new pieces of music. This trend culminated perhaps in Richard Strauss, with his vast catalogue of elaborate symphonic poems and his boasting that he could depict a teaspoon in musical terms.
However, a natural rebuttal to this trend is that 'good music' should be able to hold our attention and arouse our interest without the need for an extra-musical description. Beethoven said of his 'Pastoral Symphony' that the "whole work can be perceived without description – it is more an expression of feelings rather than tone-painting", despite including a movement that is an almost sonic soundscape of a storm, along with various bird-calls and other sonic depictions of natural scenery. Furthermore, even if a piece of music is composed with a specific 'meaning' in mind, due to music's inherently abstract nature, one can always find a meaning different to the intended one which fits the music just as well. Leonard Bernstein, in one of his concerts for children, did just that, when he made up an alternative story to a section of Strauss's tone poem Don Quixote which fit the music completely convincingly, only to reveal at the end that the original story was completely different.
Why, then, do I, or does any composer, ever choose to include descriptive titles or addendums to their music? And if they do, why do they sometimes retract them? I think the answer offers an interest insight into the nature of our experience of music.
When composing a piece with a specific program, story or image in mind, that program may dominate the composer's mind and may inform every single decision they make about how their music should go. So strong is this image, that when they first complete the piece, they feel an overwhelming desire to share it with their audience, so that they may be understood, which, in some sense, is what many composers strive for above all else. However, once a piece is written, there is no longer a constant engagement with the story that brought it about. A composer, upon repeated internal or external hearings, comes to hear their piece in purely musical terms - because that is the only form in which it actually exists (outside of the composer's mind, of course). The story was only ever an idea, impossible to concretely express in sounds that aren't language, despite what Strauss may have thought about teaspoons.
When that shift happens in the composer's mind, they no longer feel the need for a program - indeed, they may become frustrated or bored by their original imagery, or sick of people constantly referring to it, rather than to the qualities of the music itself. So, they retract it, claiming that their music needs no explanation.
Where do I stand in all this? I do think that my music can be enjoyed with no description whatsoever. Yet, most of my pieces have descriptive titles. The primary reason for this is that I want to offer people a way in to the music - kind of like a hook. If I call my new composition simply 'Sonata', or 'Piece no. 5', then I feel that there is nothing to distinguish it from the plethora of other sonatas or pieces that have been written throughout the ages. But a descriptive title serves to single out the piece as something uniquely mine.
Sometimes such tactics are extremely effective. Penderecki's famous piece Threnody for the Victims of Hiroshima originally had the horrendously boring title 8'37". Penderecki said, when he first heard the work, "I was struck by the emotional charge of the work ... I searched for associations and, in the end, I decided to dedicate it to the Hiroshima victims". We can only guess whether it would have won the Tribune Internationale des Compositeurs UNESCO prize in 1961 had it retained its original title.
Similarly, 20th Century American composer Aaron Copland's now famous Appalachian Spring suite was first titled Ballet for Martha - it was Martha's idea (Martha Graham, a choreographer and dancer) that the piece be renamed Appalachian Spring, after a phrase in a poem she was fond of. This new name was suggested just a few days before the premiere, well after the piece had been composed - so Copland was quite amused when people told him he had captured the beauty of the Appalachians in the music.
All this goes to show that music can 'mean' many different things, just as Bernstein asserted; and thus, it really means nothing, but what the perceiver makes of it. However, it cannot be denied that a descriptive name can help fire up the audience's imagination; especially an audience which is not accustomed to listening to 'absolute music' (and I'm quite confident that most untrained musicians would fall into that category these days).
When it comes to my own names, I can at least assure you that to date, all my descriptive titles have come about either before or during the process of writing, so that they are all 'honest' windows into my compositional process - not clever afterthoughts!
If you are a composer reading this, what are your preferences? Do you feel compelled to give your music extra-musical titles or description, or do you find such things superfluous? Are you led by extra-musical imagery while you compose, or is your inspiration of a purely musical nature?