The image above shows the usual garden form of Paeonia officinalis known as 'Rubra Plena'. I purchased the pot-grown plant about two weeks ago; the flower is a bit smaller and less full than those seen on well grown large plants.
Until the end of the eighteenth century, this was the common garden peony in European and American gardens. The introduction of Paeonia lactiflora to Europe at the end of the eighteenth century, and the rapid development of seed grown cultivars of that species, soon displaced Paeonia officinalis, and today Paeonia officinalis is no longer the common garden peony.
American books sometimes call it the Memorial Day peony, but here in zone 7 Maryland it blooms long before that. In most areas it is said to bloom about two weeks before the start of the Paeonia lactiflora season. The scent of peonies of the lactiflora group varies, but many have very agreeable scents, some of them distinctly rose-like. The scent of Paeonia officinalis on the other hand is usually described disparagingly as soap-like.