  The purpose of this paper is to give a systematic study of two new classes of
commutative nonassociative algebras, the so-called isospectral and medial
algebras. An isospectral algebra $\mathbb{A}$ is a generic commutative
nonassociative algebra whose idempotents have the same Peirce spectrum. A
medial algebra is algebra with identity $(xy)(zw)=(xz)(yw)$. We show that these
two classes are essentially coincide. We also prove that any medial spectral
algebra is isomorphic to a certain isotopic deformation of the commutative
associative quotient algebra $\mathbf{K}[z]/(z^n-1)$.
