  Many music theoretical constructs (such as scale types, modes, cadences, and
chord types) are defined in terms of pitch intervals---relative distances
between pitches. Therefore, when computer models are employed in music tasks,
it can be useful to operate on interval representations rather than on the raw
musical surface. Moreover, interval representations are
transposition-invariant, valuable for tasks like audio alignment, cover song
detection and music structure analysis. We employ a gated autoencoder to learn
fixed-length, invertible and transposition-invariant interval representations
from polyphonic music in the symbolic domain and in audio. An unsupervised
training method is proposed yielding an organization of intervals in the
representation space which is musically plausible. Based on the
representations, a transposition-invariant self-similarity matrix is
constructed and used to determine repeated sections in symbolic music and in
audio, yielding competitive results in the MIREX task "Discovery of Repeated
Themes and Sections".
