Normalise f0 by speaker

Adds a within-speaker normalised f0 column to a long-format f0 data frame. Speaker normalisation puts contours from male and female speakers on a comparable scale, and is a near-universal pre-processing step before cross-speaker tone modelling, plotting, or contour summarisation (Rose 1987; Zhu 1999).

Two formulae are available. Semitones above or below the speaker's mean give a perceptually uniform scale. By-speaker z-scores combine centring with unit-variance scaling. Both formulae rely on a per-speaker mean of f0, which can itself be computed in two ways: a simple arithmetic mean of all observations, or a mean of per-tone means so that every tone contributes equally to the speaker's centre.

Usage

normalise_f0(
  data,
  f0 = "f0",
  speaker = "speaker",
  tone = "tone",
  method = c("semitone", "zscore"),
  mean_method = c("weighted", "simple")
)

Arguments

data

A long-format data frame with one row per f0 sample. Must contain at least the f0, speaker, and (for "weighted" means) tone columns named below.

f0

Name of the column with raw f0 values, in Hz. Default "f0".

speaker

Name of the speaker ID column. Default "speaker".

tone

Name of the tone category column. Default "tone". Only read when mean_method = "weighted".

method

Normalisation formula. One of:

• "semitone" (default): ST = 12 * log2(f0 / speaker_mean). Result is 0 at the speaker mean and ±12 at one octave above or below.

• "zscore": Z = (f0 - speaker_mean) / sd(speaker_f0). Result has mean approximately 0 and SD approximately 1 within each speaker.

mean_method

How the per-speaker mean used by method is computed: "weighted" (default; mean of per-tone means) or "simple" (arithmetic mean across all observations).

Value

The input data frame with two added columns:

• speaker_mean: the per-speaker mean used for normalisation.

• f0_st (if method = "semitone") or f0_zscore (if method = "zscore").

Details

What the function does internally

1. Compute a per-speaker mean of f0 using mean_method (see below).

2. Join that mean back to data as a new column called speaker_mean.

3. Apply the selected normalisation formula sample by sample and return the augmented data frame.

Choosing method

• "semitone" is the standard for citation-tone work. The scale is perceptually uniform (one semitone is roughly one just-noticeable pitch step), centred on the speaker's own range, and preserves the logarithmic structure of musical pitch perception.

• "zscore" is useful when both centring and scaling are desired, i.e., when you want to remove each speaker's baseline and equalise their f0 variability. Useful for cross-speaker statistical models where the raw variance differs strongly across speakers.

Choosing mean_method

• "weighted" (default) first computes a mean f0 per (speaker, tone) cell, then averages those per-tone means. Each tone contributes equally to the speaker's centre regardless of how many tokens it has. This is the right default for unbalanced designs in which token counts differ across tones, common in fieldwork and naturalistic corpora.

• "simple" takes the arithmetic mean of every f0 observation for a speaker. Faster, and equivalent to weighted when the design is balanced.

NA handling

All summary statistics use na.rm = TRUE. Sample-level NA f0 values propagate as NA in the normalised column.

References

Rose, P. (1987). Considerations in the normalisation of the fundamental frequency of linguistic tone. Speech Communication, 6(4), 343–352. doi:10.1016/0167-6393(87)90008-1

Zhu, X. (1999). Shanghai Tonetics. LINCOM Europa.

Xu, C., & Zhang, C. (2024). A cross-linguistic review of citation tone production studies: Methodology and recommendations. The Journal of the Acoustical Society of America, 156(4), 2538–2565. doi:10.1121/10.0032356

See also

• fit_polynomial(), fit_gca(), fit_gamm() for downstream contour modelling that typically operates on the normalised column.

• contour_to_chao() for converting mean contours to Chao tone numerals, often called on normalise_f0() output.

Examples

data(sample_f0)

out <- normalise_f0(sample_f0,
                    f0      = "f0_Hz",
                    speaker = "speaker",
                    tone    = "tone",
                    method  = "semitone")
head(out[, c("speaker", "tone", "f0_Hz", "speaker_mean", "f0_st")])
#>   speaker tone    f0_Hz speaker_mean     f0_st
#> 1   dc102    3 245.7078     237.0675 0.6197450
#> 2   dc102    3 246.4516     237.0675 0.6720735
#> 3   dc102    3 247.5111     237.0675 0.7463436
#> 4   dc102    3 248.5496     237.0675 0.8188289
#> 5   dc102    3 249.7015     237.0675 0.8988754
#> 6   dc102    3 251.6647     237.0675 1.0344568

# Same data, z-score instead of semitones:
out_z <- normalise_f0(sample_f0,
                      f0      = "f0_Hz",
                      speaker = "speaker",
                      tone    = "tone",
                      method  = "zscore")
head(out_z[, c("speaker", "f0_Hz", "speaker_mean", "f0_zscore")])
#> # A tibble: 6 × 4
#>   speaker f0_Hz speaker_mean f0_zscore
#>   <chr>   <dbl>        <dbl>     <dbl>
#> 1 dc102    246.         237.     0.194
#> 2 dc102    246.         237.     0.210
#> 3 dc102    248.         237.     0.234
#> 4 dc102    249.         237.     0.257
#> 5 dc102    250.         237.     0.283
#> 6 dc102    252.         237.     0.327