Abstract: If P is some real polynomial and L is some unimodular lattice, what is the infimum that the absolute value of P achieves on the non-trivial vectors of L? The set of these infima, when L ranges over all unimodular lattices, is called the bass note spectrum of P. For indefinite binary quadratic forms, this question leads to the classical Markoff spectrum. For binary forms of degree higher than 2, not much was known until recently. In 1940, Mordell conjectured the existence of spectral gaps for the bass note spectra of binary cubic forms, a statement disproved later by Davenport. As for degrees greater than 3, even less was known. In this talk, we discuss how to show that the bass note spectrum of every binary form is an interval. Time permitting, we will discuss bass note spectra of ternary forms and use them to construct infinite families ofSL_2(Z)-inequivalent integer primitive binary cubic forms F, such that the smallest integer that F represents non-trivially is of size |Disc(F)|^{1/4}.