The cheap music stands sold by Lidl have an extension to support wide sheet music parts. Unfortunately that extension bar tends to sag, thus not continuing to offer support. This T-shaped piece holds the extension bar in the correct (horizontal position).
The stl file is for the right-hand side. You need to print one mirrored along the X axis to generate the left-hand side. Use black abs to match the black color of the music stand.
Update: fixed a detail in the center, and added the Google Sketchup file.