# Lucy tuning

$\def\val#1{\left\langle\begin{matrix}#1\end{matrix}\right]}$ Lucy tuning is the meantone tuning advocated by Charles Lucy, with a fifth of precisely 600 + 300/π = 695.493 cents. This is close to the 88edo fifth of 695.455 cents, and shares its general characteristics such as being a good tuning for mothra and eupterpe temperaments, providing a mothra generator, an approximate 8/7, of 200+100/π cents, which extends 5-limit meantone Lucy tuning to a version with a mothra (1/3 meantone fifth) generator. As a tuning for 5-limit meantone, it has the softer quality characteristic of the flatter fifth meantones between 50edo and 19edo. It has a major third of 1200/π cents, or 1/π of an octave, 381.972 cents, 4.342 cents flat of 5/4, but 2.827 cents sharp of 1/3-comma meantone's major third.
$\val{1200 & 1800 + \frac{300}{π} & 2400 + \frac{1200}{π} & 3400 - \frac{100}{π} & 4400 - \frac{800}{π}}$
$\val{1200 & 1800 + \frac{300}{π} & 2400 + \frac{1200}{π} & 2400 + \frac{3000}{π} & 5400 - \frac{3900}{π}}$