# A Question about Variations



## Kieran (Aug 24, 2010)

Hi friends, :tiphat:

A set of variations is begun by a theme, and then the breaking up and changing around of that theme into variations of the same theme. Is this correct?

At what point does a variation depart so far from the home-theme as to become something that's no longer a variation of that theme, but actually has become a variation _of a variation_ of the theme? It's so distant a relative of the original theme as to be from a different country and actually unrelated at all.

If this happens, has the chain been broken and the movement is no longer a set of variations on a theme?

Or is this the purpose of variations: to explore the sub-atomic structure of a theme, in all its generations?

I was thinking of how Dali explodes things into dots and yet from a distance we still see the whole. I was also thinking of some variations by Mozart and Beethoven, and how they break music down in a welter of rhythms and music, and yet apparently they're still operating from homebase.

Are their limitations to where variations can go, before they break the link with their origins? I hope I expressed this clearly enough! :devil:

Cheers!


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## Weston (Jul 11, 2008)

Interesting question. I'm curious to know opinions on this too, so I am bumping to keep the thread on the front page.


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## Mahlerian (Nov 27, 2012)

There are different types of variations. Variations may change the harmony of the theme while keeping the melody, or they may keep the harmony and change the melodic line. They can be based on a single idea that may never be explicitly stated, or the statement may appear right at the outset. They can go through different keys, or they can stay mostly (or entirely!) in the same key. The challenge facing any composer who attempts to write a variation movement or work is to avoid monotony, usually by making the fullest use of many or all of the above techniques. Great composers can write variations on trivial or simple themes (Beethoven's Diabellis) or potentially counter-intuitive ones (Bach's Musical Offering).


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## KenOC (Mar 7, 2011)

Kieran said:


> Are their limitations to where variations can go, before they break the link with their origins?


I don't think there are any rules or defined penalties for going too far! Certainly Beethoven gets pretty far afield in his Diabellis, though the connection back to the theme seems somehow magically always to be there. And some people consider the fugal finale to the Hammerklavier to be a set of variations, culminating in a totally wild passage that is nothing but a variation on the trill in the fuge's subject!

Paganini, in his Rhapsody on a Theme of Paganini (really a set of variations) bases his famous 18th variation on the theme in inversion -- because of that and the total change in style, any apparrent connection with the theme is totally lost, but somehow it still works.

So in short, I don't know the answer!


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## BurningDesire (Jul 15, 2012)

Check out Frederic Rzewski's The People United Will Never Be Defeated which takes its tune through many incredibly diverse variations. There's really almost limitless possibilities for variations


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## Novelette (Dec 12, 2012)

Exactly like Mahlerian said, variations could simply be a serial melodic embellishment over the same fundamental harmony, you could easily see this in Brahms' B Flat Sextet in B Flat: the chords are generally the same for each variation. This can still be the case even if the music has shifted from a minor to a major, or a major to a minor, mode--the intervallic functions remain the same. You can also see this in Beethoven's 32 C Minor Variations.

Other variations are more harmonically derived. Variations could be based upon particular phrases in a theme, emphasizing trills, or auxiliary notes. Bach's Goldberg Variations are almost entirely based upon the intervallic relations of the thematic aria, deploying the same essential functions but in entirely new contexts, complicated by diminution or augmentation, etc.

Beethoven's Diabelli Variations are astounding in how they begin as very simple elaborations of the melody, with little harmonic change. But each variation seems to become more distant from the original theme until one could hardly recognize that they are variations of previous variations, _a fortiori_ not variations of the primary theme.

Key changes are common, but not necessary. Brahms' Handel Variations really only modulate to the parallel minor, but they usually stay in B Flat.

There's no generic formula for the composition of variations, just like KenOC said. Listen to various sets of variations, and you could do no better than to listen to those of the most highly acclaimed masters of the variation form: Bach, Beethoven, Schubert, and Brahms. Schumann has a few excellent sets of variations, as well. Haydn and Mozart were likewise masters of the form.


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## KenOC (Mar 7, 2011)

BTW, re Beethoven: The conclusion of a 1799 review of his WoO 73 piano variations: "It is true that Mr. B. might be able to improvise, but he can't write variations very well." :lol:


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## Novelette (Dec 12, 2012)

KenOC said:


> BTW, re Beethoven: The conclusion of a 1799 review of his WoO 73 piano variations: "It is true that Mr. B. might be able to improvise, but he can't write variations very well." :lol:


LOL! You know, many of Beethoven's early works just don't resonate with me. They're so sterile sometimes, like most of his violin sonatas and cello sonatas. Only my opinion, of course. But many of his early works might deceive us, they give little indication of the monumental genius that truly laid behind them. Notable exceptions, of course, though!


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## Kieran (Aug 24, 2010)

Thanks for the replies.! :tiphat:

I think it must be part of a composers training, to take a tune and rip it up, then piece it together again in a new way. I suppose a distant question to the one I asked would be, has there ever been an incident of 'variation fraud,' where a musician embarks on a set of variations but runs out of options and pretends to be working off the same piece, but in such an obscure way as to conceal what they're actually doing?

I found it interesting to read that the variations need not necessarily be of the whole theme, but of parts of it, and then the famous soaring strings of Rachmaninov's Rhapsody on a Theme are based on an inversion of the theme, which is excellent! Just looked up about that, and I see that Rachmaninov was so pleased with this that he said, 'this one is for my agent!'

He knew it would sell more than seats in a hall...


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## Novelette (Dec 12, 2012)

It reminds me of canons, a little bit.

We know of Pachelbel's Canon: ostinato chords, never changing, only the melody progressing in regular patterns, etc.

But there are canons that employ methods that don't, at first glance, seem canonic, especially in relation to Pachelbel's Canon and similar canons. Ockeghem's Prolation Mass in one massive canon after another, but it doesn't always sound like it, as it is a canon of augmentation and diminution on different intervals.

And then there's Bach! Canon by inverted retrograde diminution?  Sometimes, if I didn't see the title or see the score, I would never have known that it was a canon at all!

Kieran, it's an interesting and amusing question about whether a composer has ever been caught faking the variations. Sometimes I wonder how the composer cooked up this or that variation from the theme too.


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