This function represents an input object as a 'Milne pitch-class spectrum'. A Milne pitch-class spectrum defines 'perceptual weight' as a continuous function of 'pitch class'.
milne_pc_spectrum(x, ...) # S3 method for pc_set milne_pc_spectrum( x, weights = 1, num_harmonics = 12, rho = 0.75, sigma = 6.83, array_dim = 1200, ... ) # S3 method for default milne_pc_spectrum(x, ...) # S3 method for milne_pc_spectrum milne_pc_spectrum(x, ...)
| x | Input sonority. |
|---|---|
| ... | Provided for S3 method consistency. |
| weights | (Numeric vector) Vector of weights to assign to each pitch class. If a scalar value is provided, this value is assigned to all pitch classes. |
| num_harmonics | (Integerish scalar) Number of harmonics to use when expanding tones into their implied harmonics, and when defining the harmonic template (including the fundamental frequency). Defaults to 12, after Milne and Holland (2016) . |
| rho | (Numeric scalar) Roll-off parameter for harmonic expansion. Defaults to 0.75, after Milne and Holland (2016) . |
| sigma | (Numeric scalar) Standard deviation of the Gaussian smoothing distribution (cents). Defaults to 6.83, after Milne and Holland (2016) . |
| array_dim | (Integerish scalar) Dimensionality of the pitch-class spectrum array. Defaults to 1200, after Milne and Holland (2016) . |
An object of class milne_pc_spectrum.
This spectrum is typically constructed from musical chords by expanding each note into its implied harmonics and applying a Gaussian smoothing to account for perceptual uncertainties. See Milne and Holland (2016) for details.
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 .
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 .