The muted background is shaded from light to dark (Steps 3 and 4). It was painted with a mix of Shadow Green, Winsor Violet, and French Ultramarine. The darker background area on the right (Step 3) was done with two applications of wash, wet-on-dry.
The predominant color in this darker section of wash is Winsor Violet.
Steps 4 shows the left background, done with a single wash. I used more blue and green in this wash, to keep it greyed down and neutral. A final glaze of a thin wash evens out the texture. See the finished painting, "Blossom Dearie," here. It sold almost immediately, so it no longer available... but I'll be completing another, similar painting soon.