Resultant Tones and the Harmonic Series

Pitch circularity from tones comprising full harmonic series.

This paper describes an algorithm for producing pitch circularity using tones that each comprise a full harmonic series, and reports an experiment that demonstrates such circularity. Banks of 12 tones (i.e., scales) were created, with F0 varying in semitone steps. For each scale, as F0 descended, the amplitudes of the odd-numbered harmonics were reduced relative to the even-numbered ones by 3.5...

Detection and F0 discrimination of harmonic complex tones in the presence of competing tones or noise.

Normal-hearing listeners' ability to "hear out" the pitch of a target harmonic complex tone (HCT) was tested with simultaneous HCT or noise maskers, all bandpass-filtered into the same spectral region (1200-3600 Hz). Target-to-masker ratios (TMRs) necessary to discriminate fixed fundamental-frequency (F0) differences were measured for target F0s between 100 and 400 Hz. At high F0s (400 Hz), asy...

Distortion products and the perceived pitch of harmonic complex tones

Combination tones (CTs) produced by acoustic stimuli have been studied by many authors as an efficient way to learn about the numerous physiological nonlinearities involved in auditory processing. As far as perception is concerned, CTs have been proposed as a basis for the perception of the pitch of the missing fundamental (Helmholtz, 1877). It has since been shown that the missing fundamental ...

Harmonic theta series and equidistribution

is a holomorphic modular form of weight 4 for the subgroup [1] Γθ, from the fact that there are no weight 4 cuspforms for Γθ, and from explicit computation of the Fourier coefficients of the two types of weight 4 Eisenstein series for Γθ. Toward a less frivolous result, recall that the irreducibility of spaces Hd of homogeneous, degree d harmonic polynomials f on R as O(n)-spaces gives Hecke’s ...

Random Harmonic Series