The Watchmaker, the Precentor, and the Problem of Tuning a Guitar

I've been enjoying the miniseries Longitude, the story of a man who worked for decades to solve the problems of longitudinal navigation at sea. It's a good story, well-told, and it talks about both creative insight and bureaucracy in an effective way.

I thought I'd google the hero of the story, John Harrison, and I was very interested to see that he worked not only in making maritime timepieces, but also in solving the problems of musical tuning. Now in a way this is not too far-fetched: both clock making and music are very mathematical. On the other hand, solving the problems of the ticking of a clock seem more like solving problems of rhythm, but Harrison's concern was in the perennial musical question of the musical intervals.

Apparently there have been recent manuscript discoveries that reveal in Harrison's writings a new way of tuning, which one man, Charles Lucy, has applied to guitars. Here is an introductory essay to what is called "Lucy Tuning" after its pioneering enthusiast and promotor.

The precis of Harrison's manuscript:

Wherein is shown the Absurdity of such imaginary stuff as was first crowded into the Scale of Musick by the Ancients, and has still been retained therein by our more modern Writers, in order to make the matter seem more Reasonable or Philosophical, whenas in reality it is even as hence, or would be as thence, bereaved of all such Ornament, and as, when at the same time, its Foundation or basis as in another Sense tho' secret, is most strictly true or perfect in itself; and therefore, as being otherwise therefrom not only to a much higher degree than what we should think. or have thought to have been Mathematically Beautiful, or even as otherwise so Perfection itself, consequently, it can have nothing to do with any such Arbitrary Conjectures:
And herein are also, very necessary Observations exhibited and as with Instructions about the highest, the most Important, or the most Undeniable life of the Subject.