I suppose that it is good that I really didn't know what cows ate (at least cows raised in commercial dairies). It wouldn't have contributed to my abilities to read music. There is no "H" note. The "H" refers to haylige. What, you may ask, is haylige? Well, it is silage made of hay instead of corn. Around here (the Pacific NW) this is what is most commonly fed to dairy cows, as well as grain and straight hay.
Yes, there are a few lucky herds who get to occasionally graze. But this is not the norm.
When we got Rustina she was living in a dairy barn and had not been outdoors for all of her milking life. After she came to live on Haldan Farm we kept her, at first, in a coral and a small barn-like shelter. She could go outdoors, but the coral had no grass though she got very good at sticking her head through the fence to graze around the edges of the coral. We fed her hay and supplemented with some alfalfa and a small amount of grain at milking time. We didn't know her and were not ready to allow her to go out to pasture for fear that we wouldn't be able to get her back in!
This spring we've been able to have her on pasture. It has been an enlightening experience. If All Cows Eat Grass was true the world would be a different place. Milk from a cow on pasture is completely different from anything any of us have ever tried. The cream is yellow from the grass. The butter is so yellow that I said the other day that if I bought butter this yellow I'd return it and accuse the company which made it of using too much anatto coloring. The yogurt is so good it is hard to stop eating.