  We report an approach to obtaining complex networks with diverse topology,
here called syntonets, taking into account the consonances and dissonances
between notes as defined by scale temperaments. Though the fundamental
frequency is usually considered, in real-world sounds several additional
frequencies (partials) accompany the respective fundamental, influencing both
timber and consonance between simultaneous notes. We use a method based on
Helmholtz's consonance approach to quantify the consonances and dissonances
between each of the pairs of notes in a given temperament. We adopt two
distinct partials structures: (i) harmonic; and (ii) shifted, obtained by
taking the harmonic components to a given power $\beta$, which is henceforth
called the anharmonicity index. The latter type of sounds is more realistic in
the sense that they reflect non-linearities implied by real-world instruments.
When these consonances/dissonances are estimated along several octaves,
respective syntonets can be obtained, in which nodes and weighted edge
represent notes, and consonance/dissonance, respectively. The obtained results
are organized into two main groups, those related to network science and
musical theory. Regarding the former group, we have that the syntonets can
provide, for varying values of $\beta$, a wide range of topologies spanning the
space comprised between traditional models. Indeed, it is suggested here that
syntony may provide a kind of universal complex network model. The musical
interpretations of the results include the confirmation of the more regular
consonance pattern of the equal temperament, obtained at the expense of a wider
range of consonances such as that in the meantone temperament. We also have
that scales derived for shifted partials tend to have a wider range of
consonances/dissonances, depending on the temperament and anharmonicity
strength.
