The “Aria mit verschiedenen Veränderungen” (“Aria with diverse variations”), most commonly known as the “Goldberg Variations”, BWV 988, constitutes the fourth and last part of Bach’s “Clavier-Übung”, one of the few works that were published during Bach’s lifetime. The Clavier-Übung, or “Keyboard Exercise”, is comprised of the following parts:

• Part I: Six keyboard partitas, published separately and later grouped in one volume in 1731
• Part II: Italian Concerto and French Overture (1735)
• Part III: The so-called German Organ Mass (1739)
• Part IV: Aria with Diverse Variations, aka the Goldberg Variations (1741)

Johann Nikolaus Forkel, Bach’s first biographer, popularized the story of a commission by the insomniac Count Hermann Carl von Keyserlinck, of Dresden, who wanted keyboard music “of a soft a lively character” for his house harpsichordist to play during the Count’s sleepless nights. The harpsichordist was Johann Gottlieb Goldberg, a former pupil of Bach’s – and thus the “Goldberg Variations” moniker was born, even though the tale is now regarded as false due to lack of any supporting evidence.

The Aria and its 30 variations are based on an ostinato bass line, derived from a chaconne with variations by Handel, composed in the early 1700’s and which Bach probably came across via a printed edition released in the 1730’s. Handel’s bass line is shorter – just 8 bars – and one of the variations in the set is a canon at the octave, which is quite unsophisticated by Bach’s counterpoint standards. (In later years, Bach also composed a set of 14 canons on Handel’s original bass line, catalogued as BWV 1087.)

The Goldberg Variations are the only part of the Clavier-Übung meant to be performed as one unit. As such, Bach took care to structure the work in a way that would avoid monotony and spark interest, while still adhering to a well thought out plan.

The first step was to expand Handel’s original ground bass from 8 to 32 bars. He kept the original 8 bars and added 8 more to conform the first section, and then added a whole second section of 16 bars. The resulting harmonic pattern is kept constant throughout the Aria and all the variations (the first cadence is G major, then it goes to D major, then to E minor, and back to G major), but the bass line itself is different for each variation.

The roadmap for the variations includes a strict 2-part canon as every third variation, starting at the unison and growing the interval progressively in each canon (at the second, third, fourth, etc., all the way to the ninth). Between the canons, he inserted variations that don’t conform to a given pattern, instead presenting a wide array of styles, tempos and meters. Some notable structural elements for the work as a whole are an inflexion point in the middle with the first minor-mode variation (#15), and then opening the second half of the work with a mini-French overture (#16). Instead of a final canon, variation 30 is a “quodlibet” – a combination of two popular melodies on top of the ground bass. The piece concludes with a second performance of the Aria.

The Aria is a slow, delicate and heavily ornamented signing line in 3/4 meter, on top of the ground bass, resembling a sarabande. Between the tune and the bass line, there is a middle voice supporting the harmony and moving motivically as well on occasion.

In contrast, variation 1 is agile, in two parts, with a jumpy bass line and rapid scales and arpeggios on both lines, still in ternary rhythm. Variation 2 goes back to three parts, switching the meter to binary, with the two upper voices moving imitatively over a walking bass line mostly in eighths. Variation 3 is the first canon, at the unison, with the second voice coming in one full bar after the first one. The meter is 12/8, creating the feeling of a dance, with a busy bass line moving in triplets and sixteenths.