  To explain the consonance of octaves, music psychologists represent pitch as
a helix where azimuth and axial coordinate correspond to pitch class and pitch
height respectively. This article addresses the problem of discovering this
helical structure from unlabeled audio data. We measure Pearson correlations in
the constant-Q transform (CQT) domain to build a K-nearest neighbor graph
between frequency subbands. Then, we run the Isomap manifold learning algorithm
to represent this graph in a three-dimensional space in which straight lines
approximate graph geodesics. Experiments on isolated musical notes demonstrate
that the resulting manifold resembles a helix which makes a full turn at every
octave. A circular shape is also found in English speech, but not in urban
noise. We discuss the impact of various design choices on the visualization:
instrumentarium, loudness mapping function, and number of neighbors K.
