Why does Frenhofer burn all of his paintings before dying in the short-story, The Unknown Masterpiece?

Frenhofer has a deep love for love, life, beauty, and art, and how all are one in the same to him. Frenhofer considers such things pure, and considers the love of his life to be his masterpiece, something he will not show the rest of the world exposed and unfinished.

However, Frenhofer is floored by the appearance of beauty in his life once more by the way of Gillette, for whom he surrenders a glimpse of his masterpiece to Nicolas and Porbus. Having experienced such beauty as can never be conveyed in paint, Frenhofer burns all of his paintings and dies.