I decided to revisit this after reading a comment by Michael Freeman in "The Photographer's Eye." He says:
"Violet ...is easily confused with purple."
I think my beetroot image is definitely purple. So 2 days ago I went in search of violet, and took this shot through the window of a shoe shop in Central London. There was also a pair of purple trainers in the same display, so I could immediately appreciate the difference in tones.
I cropped it in Photoshop to achieve the required ratio.
I consider myself very fortunate to have found a violet shoe with a yellow lining, although in Summer fashion styles it seems to be a popular combination.