I introduced Mozart in my Intro to Classical Music. Mozart made frequent use of the sonata form, one of classical music’s most important legacies. In his short life, he composed 18 piano sonatas, 36 violin sonatas, and several more for other instruments. Today we consider the third movement of his 11th Piano Sonata, Rondo alla Turca. This allows us to learn about the rondo form and observe the mathematical symmetry that is common to Classical-era pieces.

Mozart was born in Austria and spent most of his life there. Austria’s great military foe in those days was the Ottoman Empire, known to the people simply as “the Turks.” Mozart, like all great composers, was eager to learn about the musical cultures of other parts of the world. One of the only cultural exposures the Austrians had to the Ottoman Empire came from their military bands, which featured high-speed percussion ensembles accompanied by a few brass and winds. This fast-paced movement with staccato left-hand rhythms and dramatic pianistic flourishes represents one of Mozart’s attempts to mimic the Turkish musical style. Hence, Rondo alla Turca.

Our performer today is Daniel Barenboim (b. 1942), a world-renowned pianist and conductor. He pays meticulous attention to every written note when interpreting a piece of music. In this rondo, his attention to detail is evident. He brings the different sections of the piece to life by giving each its own unique, spirited character.

The rondo is a common musical form with a simple concept: introduce an A theme, then a B theme, then go back to the A theme, then maybe do this a few more times and conclude the piece. ABA is the simplest rondo form. ABACA is also very common. Mozart here writes ABCDECABC with an elaborate Coda at the end. (Coda is the musical term for “ending”, from the Italian word for “tail”.)

As you listen to the rondo, you can use the following guide to help you identify each section. Every section repeats itself until the Coda. Note also how section C at the end, though essentially unchanged, breaks up its right-hand octaves into individual notes. This lets us know that the piece is nearing its climax, and lets the performer show off his virtuosity.

A – 0:00

B – 0:14

C – 0:43

D – 0:57

E – 1:11

C – 1:39

A – 1:53

B – 2:08

C* – 2:38

Coda – 2:51

To observe the symmetry of classical forms, here are some details about the rondo sections:

Section A is 8 measures long in A minor.

Section B is 16 ms. long. It starts in C major for 8 ms, then reprises Section A for 8 ms.

Section C is 8 ms. long in A major.

Section D is 8 ms. long in F# minor.

Section E is 16 ms. long. It starts in A major for 8 ms., then reprises Section D for 8 ms.

The Coda (the musical term for “ending”) is 31 ms. long in A major.

Do you see how every single section (apart from the Coda) is built around segments of 8 measures each? Even the sections of 16 ms. break down evenly into 8 and 8. (The reprises of A and D are not their own sections because there is some variation.) Would it surprise you to learn that each of these 8 ms. sections can be broken down further into binary pairs of 4 and 4? This is the beautiful symmetry of the classical sonata form. The four-measure pattern holds throughout until the Coda, where Mozart uses a technique called contraction to bring about musical resolutions more quickly and drive the piece to its conclusion.

A minor and C major have zero sharps or flats. C major is therefore the relative major of A minor. Likewise, A major and F# minor have three sharps, so F# minor is the relative minor of A major. When this rondo changes keys, it either travels between A minor and A major, or between one relative key and another. View the symmetry of the keys Mozart uses: (Minor keys are indicated with a lower-case “m.” Major keys include no addendum.)

Section     A        B                  C      D        E                 C        A       B                   C*  Coda

Key       { (Am – C – Am) – (A – F#m – A – F#m – A) – (Am – C – Am) } – A – A.

Lastly, it is most common for pieces to begin and end in the same key. Here, Mozart starts in A minor and ends in A major. But it would be shortsighted to accuse him of changing keys. This piano sonata started its first movement with a beautiful, slow theme and variations in A major. In the third movement, we see a perfect symmetry of thematic material and keys until the ending, when Mozart transitions from A minor to A major permanently in section C*. This calls to mind an even greater symmetry with its return to the opening key of the first movement, providing bookends to the entire sonata.

The first movement is also very recognizable. Listen to it here.