But some of the most powerful musical ideas are remarkably brief and I want to look at four of them. Coincidentally, each of these ideas consists of only four notes. They might sometimes appear as a whole phrase, especially if in longer note-values, but they usually function as what we might call a musical "cell". I'm not saying these are the only four-note cells in music history, but these are the only ones that come to mind.
The first is one that has a non-musical reference. This is the four-note cell that spells out the name of "Bach" and that J. S. Bach used as a third subject in the last fugue of his Art of Fugue, giving a musical "signature" to the work:
This works because of the way the notes are pronounced in German. In German-speaking countries the first note, B flat, is pronounced "B". The A is A, the C is C, but the B natural is pronounced "H" so the four notes can form a musical cryptogram spelling out "BACH". Other composers have either used this cell as a structural element, as Webern did in his String Quartet, op. 28, or quoted it. There is a list in the Wikipedia article I linked to above.
Here is the last fugue of the Art of Fugue, Contrapunctus XIV:
Another famous four-note cell is a very old one that has been traced back as far as a mass by Josquin. It was also used in the later 18th century by Joseph Haydn in the finale of his Symphony No. 13. But the most famous use was as one of the five themes of the fugal finale of Mozart's Symphony No. 41:
I talked about this movement in some detail in this post. And here is a performance of the finale:
As you can hear, that four-note cell permeates the music from the first bar.
My next example is the four-note cell that permeates the late-Beethoven String Quartet in A minor, op 132. In the first movement it is used in a fugal stretto:
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Shostakovich used this in a number of places in his music, most notably in his Quartet No. 8, a work permeated with quotations from his other compositions. The cell is heard in various rhythmic configurations throughout the quartet. Sometimes a quick version is used to accompany a version in longer note values. Here is a clip of the quartet. As you can see, the cello begins with the cell:
Each of these four cells has a kind of distilled intensity that the composers make full use of. I wonder if there are any other similar examples? I can't think of any at the moment, so feel free to suggest others in the comments.