In three independent variation sets, Joachim pursued three distinct endeavours: the Variations on an Original Theme Op. 10 treated the Gis-ELa cipher, the Elfenlied cycle explored and reconsidered variation form, and the last work, Variations for Violin with Orchestral Accompaniment, offered a synthesis. Joachim's choice of themes revealed his continued weakness for ciphers (Op. 10) and his continuing infatuation with Gisela (Gis-E-La). The Irish national folk style, explored twice in Joachim's output (in the Goldschmidt–Joachim Fantasy of 1859 and in the here discussed piano variations), became the centre of the Elfenlied Variations and perhaps left a trace in the theme of the Variations for Violin. Only the Elfenlied Variations used a pre-existing theme.

Joachim's life-long fascination with virtuosity – ranging from the early hyper-virtuosity to the later ‘tamed’ type – is again evident in the E minor Variations for Violin with Orchestral Accompaniment, which balance lyricism and effect-laden applications of virtuosity, as was fitting for the dedicatee, Pablo de Sarasate (1844–1908), then one of Europe's most eminent virtuosi.

The composer's changing personal situations in 1854, 1856, and 1878–79 differed as much as the three variations. In 1854 Joachim entered his second year in Hanover, but frequently visited Berlin, which in the summer of 1854 replaced Göttingen as his chosen place to spend the summer months. The blissful period in Berlin indeed provided frequent opportunities for Hausmusik of the sorts depicted in Carl Arnold's watercolour Quartettabend bei Bettine. And some time between early June and late August Joachim’s cipher FAE – which previously stood for his bachelorhood – changed its meaning to ‘Für alle Ewigkeit’ – as the composer wrote to Gisela one day that summer. On 30 August 1854, Gisela's birthday, Joachim began his variations by writing down a theme that included her cipher and a note announcing his intention to compose a variation work on Gis-E-La.

Rather different was the background to the Elfenlied Variations. In 1856 Joachim was beginning to feel the tensions of his triangular relationship with Herman and Gisela but nevertheless went on a trip to Venice with Herman, returning to Heidelberg for the summer. He composed one large work, the Kleist Overture, which was premiered on 14 March 1857, and several smaller works, including Versuch eines Tanzes – an attempt at a melodrama for Gisela with no afterlife– and the Elfenlied set, as well as many compositional exercises.