The tumbler is part of the Copenhagen-Clear range which comprised shotglasses, huge tall tumblers, and all shades of sizes betwixt. And I think there were some bowls too. I think it is by Lutken, but can't be 100%.
Oh, and the 'Holmegaards Glas' and separate 'Made In Denmark' labels are the ones used on pieces exported to America, as far as I've made out. I might be wrong, but whenever I've bought glass with these labels, it's always been from America (one instance was from an old jewellers' who had a lot of old-new stock they were selling, which makes the US export label theory more likely).