  This study considers rational approximations of musical constant
$\beta=\log_2(3/2)$, which defines perfect fifth. This constant has been the
subject of the numerous studies, and this paper determines quality of rational
approximations in regards to absolute error. We analysed convergents and
secondary convergents (some of these are the best Huygens approximations).
Especially, we determined quality of the secondary convergents which are not
the best Huygens approximations - in this paper we called them non-convergents
approximations. Some of the microtonal scales have been positioned and
determined by using non-convergents approximation of music constant which
defines perfect fifth.
