There are no guarantees on hymn tune names. There can be many names for the same tune (Avon, Martyrdom, Sacred Throne) and the same name used for completley different tunes. From literary mentions, it's a best guess, unless you know a specific tune was really popular & likely to be the one mentioned. My supposition is that a Scottish tune from 1615 was more likely to be the tune mentioned in Scotland in 1679, as opposed to one published over 100 years later. It seems like a tune could easily pick up an "Old" modifier between 1679 & 2000.

I found 'Old Martyrs' when I was scanning the CM (Common Meter) tunes in Cyberhymnal's Meter index. I thought the other link was better because it gives the background info. "Old Martyr" is the last thing listed next to the picture on the page.

Mantius, I've never seen Amazing Grace in other than 3/4 time. Did the 4/4 setting shorten the 1st note of the measure? It not being traditional as a pipe tune, one can only wonder why they would want to change it. I think I have seen Martyrdom in 4/4 & I think it's first publication was also.