tone {MixSemiRob}

Tone perception data

Description

The data originates from an experiment of Cohen (1980) and has been analyzed in de Veaux (1989) and Viele and Tong (2002). In this experiment, a pure fundamental tone was played to a trained musician. To create different auditory conditions, electronically generated overtones were introduced, which were determined by a stretching ratio. When stretchratio = 2.0, it aligns with the harmonic pattern usually heard in traditional definite pitched instruments. The musician was asked to tune an adjustable tone to the octave above the fundamental tone. The variable tuned gives the ratio of the adjusted tone to the fundamental tone. For example, tuned = 2.0, would be the correct tuning for all stretchratio values. This dataset comprises data collected from 150 trials conducted with the same musician. In the original study, data were gathered from an additional four musicians as well. The dataset and the description have been sourced from the tonedata of the ‘fpc’ package.

Usage

tone

Format

A data frame containing 150 observations and the following 2 variables.

stretchratio:

electronically generated overtones added to a pure fundamental tone.

tuned:

ratio of the adjusted tone to the fundamental tone.

Source

Original source:

Cohen, E. (1980). Inharmonic tone perception. Unpublished Ph. D. Dissertation, Stanford University.

R source:

Hennig C (2023). fpc: Flexible Procedures for Clustering. R package version 2.2-10, https://CRAN.R-project.org/package=fpc

Benaglia, T., Chauveau, D., Hunter, D. R., and Young, D. S. (2010). mixtools: an R package for analyzing mixture models. Journal of statistical software, 32, 1-29.

References

De Veaux, R. D. (1989). Mixtures of linear regressions. Computational Statistics & Data Analysis, 8(3), 227-245.

Viele, K. and Tong, B. (2002). Modeling with mixtures of linear regressions. Statistics and Computing, 12, 315-330.