Smooth pitch spectrum

Creates an object of class smooth_pi_spectrum, describing a smooth pitch spectrum. A smooth pitch spectrum describes perceptual weight along a continuous MIDI pitch scale. The representation incorporates smoothing to account for imprecisions in pitch perception.

smooth_pi_spectrum(x, sigma = 6.83, ...)

# S3 method for default
smooth_pi_spectrum(
  x,
  sigma = 6.83,
  num_harmonics = 11L,
  roll_off = 1,
  coherent = FALSE,
  ...
)

# S3 method for sparse_pi_spectrum
smooth_pi_spectrum(x, sigma = 6.83, coherent = FALSE, ...)

Arguments

x	Object to convert. By default sparse_pi_spectrum is called first to convert the object to a sparse pitch spectrum.
sigma	(Numeric scalar) Standard deviation of the Gaussian distribution used to simulate perceptual blurring. Defaults to 6.83 cents, after Milne and Holland (2016) .
...	Provided for S3 method consistency.
num_harmonics	(Integerish scalar) Number of harmonics (including the fundamental) to which each tone should be expanded.
roll_off	(Numeric scalar) Parametrises the amount of amplitude roll-off in the harmonics, with greater values corresponding to higher roll-off.
coherent	Whether the amplitudes from different spectral components should be combined assuming coherent summation, where the amplitudes simply add together (default is FALSE). Otherwise incoherent summation is used, where the amplitudes are squared, added, then square rooted.

Details

This representation is created by expressing the sonority as a sparse pitch spectrum (see sparse_pi_spectrum) and convolving the result with a Gaussian distribution with standard deviation sigma.

References

Milne AJ, Holland S (2016). “Empirically testing Tonnetz, voice-leading, and spectral models of perceived triadic distance.” Journal of Mathematics and Music, 10(1), 59--85. doi: 10.1080/17459737.2016.1152517 .

See also

This representation was inspired by milne_pc_spectrum, which embodies similar ideas with a slightly different implementation. See smooth_pc_spectrum for an equivalent representation in the pitch-class domain.