The effects of aging and musical experience on the representation of tonal hierarchies

Two experiments explored the representation of the tonal hierarchy in Western music among older (aged 60 to 80) and younger (aged 15 to 22) musicians and nonmusicians. A probe tone technique was used: 4 notes from the major triad were presented, followed by 1 note chosen from the 12 notes of the chromatic scale. Whereas musicians had a better sense of the tonal hierarchy than nonmusicians, older adults were no worse than younger adults in differentiating the notes according to musical principles. However, older adults were more prone than younger adults to classify the notes by frequency proximity (pitch height) when proximity was made more salient, as were nonmusicians compared with musicians. With notes having ambiguous pitch height, pitch height effects disappeared among older adults but not nonmusicians. Older adults seem to have internalized tonal structure, but they sometimes fail to inhibit less musically relevant information.

Equivariant inverse spectral theory and toric orbifolds

Let O-2n be a symplectic toric orbifold with a fixed T-n-action and with a tonic Kahler metric g. In [10] we explored whether, when O is a manifold, the equivariant spectrum of the Laplace Delta(g) operator on C-infinity(O) determines O up to symplectomorphism. In the setting of tonic orbifolds we shmilicantly improve upon our previous results and show that a generic tone orbifold is determined by its equivariant spectrum, up to two possibilities. This involves developing the asymptotic expansion of the heat trace on an orbifold in the presence of an isometry. We also show that the equivariant spectrum determines whether the toric Kahler metric has constant scalar curvature. (C) 2012 Elsevier Inc. All rights reserved.