In an arpeggio the notes of a chord are rendered sequentially, from lowest to highest, rather than simultaneously. This is one of the most difficult kinds of vocal embellishment, requiring a perfectly even delivery from the first pitch to the last.

[…]

Among the examples here is the so-called “Rossini arpeggio” as it appeared in a singing method published by the famous soprano Gemma Bellincioni (Berlin, 1912). Bellincioni was the original Santuzza in Mascagni’s Cavalleria rusticana (Rome, 1890) and a memorable Salome for the Italian premiere of the eponymous opera by Richard Strauss (Turin, 1906, with the composer conducting), not to mention an “incomparable” Violetta, according to Verdi himself. in La traviata. This particular arpeggio, first attributed to Rossini by Heinrich Panofka in his L’Art de chanter (1853), is perhaps the most familiar exercise in all of vocal pedagogy. The great contralto and didact Pauline Viardot-Garcia (1821-1910), Maria Malibran’s sister, identified its original inspiration in a passage for violin from Beethoven’s Septet in E-flat Major, Op. 20.

Battaglia, Elio. L’arte del vocalizzo, Antologia critico-tecnica per gli studenti di canto. Ricordi, 2011.