Dancing Wavelets by Alfred Frederic Mullen is a standard salon-style piece popular in the early 20th century. Its distinctive feature is the fluid, rolling accompaniment pattern that mimics the motion of water.
At Henle 2 this is a beginner-level piece, where steady coordination between the hands is the main hurdle. The main demands: a waltz lilt that needs charm and a flexible left hand; a true singing tone, with the melody floating above the accompaniment; and sweeping arpeggio figures that must stay smooth across positions.
Maintain a supple wrist to achieve the rolling, fluid motion required in the left-hand arpeggiated figures.
Comparable difficulty and character — good candidates for what to learn next.
A level or two down with the same spirit — ideal if this piece is still out of reach.
Where this piece's skills lead: slightly harder works making similar technical demands.
Dancing Wavelets is rated Henle level 2 of 9 — beginner repertoire, roughly ABRSM grades 2–3. In the RCM system it corresponds to about level 3.
You should be comfortable at Henle level 2 — meaning you can already play level 1–2 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Dancing Wavelets lasts about 2.5 minutes.
Dancing Wavelets is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Danish Suite by Alfred Frederic Mullen, Brises d'été by Alfred Frederic Mullen, At Twilight by Rudolf Friml — see the full similar-pieces list on this page.