Speech Synthesis with KlattGrid

Introduction

KlattGrid is pladdrr’s implementation of the Klatt cascade/parallel formant synthesizer, for generating synthetic speech from parametric descriptions. Unlike recording or playing back audio, KlattGrid creates speech from parameters by specifying:

Pitch contours (fundamental frequency)
Formant frequencies (F1, F2, F3, …)
Formant bandwidths (spectral width)
Voicing amplitude (phonation intensity)

This approach is used for:

Voice manipulation research
Perceptual experiments with controlled stimuli
Teaching phonetics concepts
Speech resynthesis with modified parameters

library(pladdrr)
library(ggplot2)

Why Speech Synthesis?

Research Applications

KlattGrid enables experiments that natural speech cannot provide:

Independent control - Change F1 independently of F2, not possible in human speech
Parametric variation - Generate continua (e.g., /i/ to /u/ in 10 steps)
Non-natural voices - Male formants + female pitch
Reproducibility - Exact same stimulus across sessions

The Klatt Synthesizer

Dennis Klatt’s 1980 formant synthesizer is a cascade/parallel model of parametric speech synthesis. It models the vocal tract as a cascade of resonant filters (formants) excited by a periodic source (voicing) or noise.

pladdrr provides direct R access to Praat’s KlattGrid implementation.

Basic Usage

Recommended: Pre-configured Vowels

The safest way to create a KlattGrid is with klattgrid_create_from_vowel():

# Synthesize /a/ vowel (low central)
kg <- klattgrid_create_from_vowel(
  duration = 0.5,           # 500 ms
  f0start = 120,            # Pitch: 120 Hz (adult male)
  f1 = 800, b1 = 80,        # First formant + bandwidth
  f2 = 1200, b2 = 120,      # Second formant + bandwidth
  f3 = 2500, b3 = 150       # Third formant + bandwidth
)

# Synthesize to audio
sound <- kg$to_sound()

cat("Created sound:\n")
#> Created sound:
cat("  Duration:", sound$get_duration(), "s\n")
#>   Duration: 0.5 s
cat("  Samples:", sound$get_number_of_samples(), "\n")
#>   Samples: 22050
cat("  Sampling rate:", sound$get_sampling_frequency(), "Hz\n")
#>   Sampling rate: 44100 Hz

Save to File

# Save synthesized audio
sound$save(file.path(tempdir(), "vowel_a.wav"), "WAV")

# Save KlattGrid parameters
kg$save(file.path(tempdir(), "vowel_a.KlattGrid"))

Avoid Empty Grids

Do not use the empty constructor for synthesis:

# THIS WILL ERROR -- the error below is the point of the example.
# Praat's own error text uses typographic quotes, which can break the
# CRAN vignette-rebuild pass under a non-UTF-8 locale, so it's caught and
# re-printed here as plain ASCII rather than let through raw.
kg <- KlattGrid(tmin = 0, tmax = 1, numberOfFormants = 5)
tryCatch(
  kg$to_sound(),
  error = function(
    e) cat("Error: uninitialized tiers (pitch, voicing, formants)\n")
)
#> Error: uninitialized tiers (pitch, voicing, formants)

Why? Empty grids need complete initialization: - Pitch tier (fundamental frequency) - Voicing amplitude tier (phonation) - All formant frequency tiers (F1, F2, F3, …) - All formant bandwidth tiers (B1, B2, B3, …)

Always use klattgrid_create_from_vowel( ) or klattgrid_create_example() instead.

Vowel Synthesis

The Vowel Triangle

The three corner vowels (/i/, /a/, /u/) define the vowel space:

# /i/ - high front vowel (English "beet")
kg_i <- klattgrid_create_from_vowel(
  duration = 0.3, f0start = 200,
  f1 = 280, b1 = 50,
  f2 = 2250, b2 = 100,
  f3 = 2890, b3 = 120
)

# /a/ - low central vowel (English "father")
kg_a <- klattgrid_create_from_vowel(
  duration = 0.3, f0start = 200,
  f1 = 730, b1 = 80,
  f2 = 1090, b2 = 120,
  f3 = 2440, b3 = 140
)

# /u/ - high back vowel (English "boot")
kg_u <- klattgrid_create_from_vowel(
  duration = 0.3, f0start = 200,
  f1 = 310, b1 = 60,
  f2 = 870, b2 = 90,
  f3 = 2250, b3 = 140
)

# Synthesize all three
sound_i <- kg_i$to_sound()
sound_a <- kg_a$to_sound()
sound_u <- kg_u$to_sound()

cat("Vowel triangle synthesized:\n")
#> Vowel triangle synthesized:
cat("  /i/: F1=", 280, " F2=", 2250, " Hz (high front)\n", sep="")
#>   /i/: F1=280 F2=2250 Hz (high front)
cat("  /a/: F1=", 730, " F2=", 1090, " Hz (low central)\n", sep="")
#>   /a/: F1=730 F2=1090 Hz (low central)
cat("  /u/: F1=", 310, " F2=", 870, " Hz (high back)\n", sep="")
#>   /u/: F1=310 F2=870 Hz (high back)

Formant Values for Common Vowels

Adult male (~120 Hz pitch):

Vowel	IPA	F1 (Hz)	F2 (Hz)	F3 (Hz)	Example Word
beet	/i/	280	2250	2890	“beet”
bit	/ih/	400	2000	2550	“bit”
bait	/e/	550	1770	2490	“bait”
bet	/eh/	660	1720	2410	“bet”
bat	/ae/	860	1760	2390	“bat”
father	/a/	730	1090	2440	“father”
bought	/ao/	570	840	2410	“bought”
boat	/o/	500	700	2410	“boat”
book	/uh/	440	1020	2240	“book”
boot	/u/	310	870	2250	“boot”

Voice Types

Different speakers require different formant and pitch values:

# Male voice (low pitch, lower formants)
kg_male <- klattgrid_create_from_vowel(
  duration = 0.5, f0start = 100,
  f1 = 750, b1 = 80,
  f2 = 1100, b2 = 120,
  f3 = 2400, b3 = 150
)

# Female voice (higher pitch, higher formants)
kg_female <- klattgrid_create_from_vowel(
  duration = 0.5, f0start = 220,
  f1 = 850, b1 = 70,
  f2 = 1300, b2 = 110,
  f3 = 2800, b3 = 140
)

# Child voice (very high pitch)
kg_child <- klattgrid_create_from_vowel(
  duration = 0.4, f0start = 300,
  f1 = 900, b1 = 60,
  f2 = 1400, b2 = 100,
  f3 = 3000, b3 = 130
)

cat("Pitch ranges:\n")
#> Pitch ranges:
cat("  Male:   80-180 Hz (typical ~100-120 Hz)\n")
#>   Male:   80-180 Hz (typical ~100-120 Hz)
cat("  Female: 160-250 Hz (typical ~200-220 Hz)\n")
#>   Female: 160-250 Hz (typical ~200-220 Hz)
cat("  Child:  250-400 Hz (typical ~300 Hz)\n")
#>   Child:  250-400 Hz (typical ~300 Hz)

Pitch Contours

Dynamic Intonation

Add pitch points to create dynamic intonation patterns:

# Start with base vowel
kg <- klattgrid_create_from_vowel(
  duration = 0.6, f0start = 120,
  f1 = 500, b1 = 50,
  f2 = 1500, b2 = 100,
  f3 = 2500, b3 = 150
)

# Add rising intonation (question)
kg$add_pitch_point(0.2, 110)  # Slight dip
kg$add_pitch_point(0.4, 105)  # Lower
kg$add_pitch_point(0.6, 150)  # Rise at end

sound <- kg$to_sound()
pitch <- sound$to_pitch()

# Visualize pitch contour
df <- as.data.frame(pitch)
df <- df[!is.na(df$frequency), ]

ggplot(df, aes(time, frequency)) +
  geom_line(color = "#E41A1C", linewidth = 1) +
  geom_point(color = "#E41A1C", size = 2, alpha = 0.5) +
  labs(
    title = "Question Intonation Pattern",
    subtitle = "Rising pitch contour: 120 -> 105 -> 150 Hz",
    x = "Time (s)",
    y = "Frequency (Hz)"
  ) +
  theme_minimal()

Common Pitch Patterns

# Flat pitch (citation form)
kg_flat <- klattgrid_create_from_vowel(
  duration = 0.5, f0start = 120,
  f1 = 500, b1 = 50, f2 = 1500, b2 = 100, f3 = 2500, b3 = 150
)
# No additional points needed

# Falling pitch (statement)
kg_fall <- klattgrid_create_from_vowel(
  duration = 0.5, f0start = 150,
  f1 = 500, b1 = 50, f2 = 1500, b2 = 100, f3 = 2500, b3 = 150
)
kg_fall$add_pitch_point(0.5, 100)  # Fall from 150 to 100 Hz

# Rising pitch (question)
kg_rise <- klattgrid_create_from_vowel(
  duration = 0.5, f0start = 100,
  f1 = 500, b1 = 50, f2 = 1500, b2 = 100, f3 = 2500, b3 = 150
)
kg_rise$add_pitch_point(0.5, 180)  # Rise from 100 to 180 Hz

Formant Transitions

Diphthongs

Create smooth vowel-to-vowel transitions:

# /ai/ diphthong: /a/ -> /i/ (as in "buy")
kg <- klattgrid_create_from_vowel(
  duration = 0.5, f0start = 150,
  f1 = 730, b1 = 80,      # Start: /a/
  f2 = 1090, b2 = 120,
  f3 = 2440, b3 = 140
)

# Transition to /i/ at end (formantType 1 = oral formants)
kg$add_formant_point(1, 1, 0.5, 280)   # F1: 730 -> 280 Hz
kg$add_formant_point(1, 2, 0.5, 2250)  # F2: 1090 -> 2250 Hz
kg$add_formant_point(1, 3, 0.5, 2890)  # F3: 2440 -> 2890 Hz

sound <- kg$to_sound()

# Extract formants to visualize transition
frm_result <- sound$to_formant_burg(max_frequency = 5500)
df <- as.data.frame(frm_result)
df <- df[df$formant %in% 1:3, ]
names(df)[names(df) == "formant"] <- "formant_number"

ggplot(df, aes(time, frequency, color = factor(formant_number))) +
  geom_line(linewidth = 1, alpha = 0.8) +
  scale_color_manual(
    values = c("1" = "#E41A1C", "2" = "#377EB8", "3" = "#4DAF4A"),
    labels = c("F1", "F2", "F3")
  ) +
  labs(
    title = "Diphthong /ai/ Formant Transitions",
    subtitle = "/a/ -> /i/ transition over 500 ms",
    x = "Time (s)",
    y = "Frequency (Hz)",
    color = "Formant"
  ) +
  theme_minimal() +
  theme(legend.position = "top")

Vowel Continuum

Generate perceptual continua for experiments:

# Create /i/ to /u/ continuum (10 steps)
f1_seq <- seq(280, 310, length.out = 10)  # F1: 280 (/i/) -> 310 (/u/)
f2_seq <- seq(2250, 870, length.out = 10)  # F2: 2250 -> 870

vowel_continuum <- lapply(1:10, function(i) {
  kg <- klattgrid_create_from_vowel(
    duration = 0.3, f0start = 200,
    f1 = f1_seq[i], b1 = 50,
    f2 = f2_seq[i], b2 = 100,
    f3 = 2500, b3 = 150
  )
  kg$to_sound()
})

# Save each step
for (i in 1:10) {
  vowel_continuum[[i]]$save(
    file.path(tempdir(), sprintf("continuum_%02d.wav", i)), "WAV")
}

Visualizing Synthesis

Spectrogram of Synthetic Vowel

# Synthesize /a/ vowel
kg <- klattgrid_create_from_vowel(
  duration = 0.5, f0start = 120,
  f1 = 730, b1 = 80,
  f2 = 1090, b2 = 120,
  f3 = 2440, b3 = 140
)

sound <- kg$to_sound()

# Create spectrogram
spec <- sound$to_spectrogram(
  window_length = 0.005,
  max_frequency = 5000
)

# Extract formants for overlay
frm_result <- sound$to_formant_burg(max_frequency = 5500)
formant_df <- as.data.frame(frm_result)
formant_df <- formant_df[formant_df$formant %in% 1:3, ]
formant_df$formant_num <- formant_df$formant

# Plot
autoplot(spec) +
  geom_line(
    data = formant_df,
    aes(time, frequency, color = factor(formant_num)),
    linewidth = 1.5, alpha = 0.8, inherit.aes = FALSE
  ) +
  scale_color_manual(
    values = c("1" = "red", "2" = "yellow", "3" = "white"),
    labels = c("F1", "F2", "F3")
  ) +
  labs(
    title = "Synthetic /a/ Vowel Spectrogram",
    subtitle = "F1=730, F2=1090, F3=2440 Hz (male voice, 120 Hz pitch)",
    color = "Formant"
  ) +
  theme(legend.position = "right")

Comparing Real vs Synthetic

# Load real speech
sound_real <- Sound(system.file("extdata", "test.wav", package = "pladdrr"))

# Extract mean formants from real speech
formant_real <- sound_real$to_formant_burg()
df_real <- as.data.frame(formant_real)

f1_mean <- mean(df_real$frequency[df_real$formant == 1], na.rm = TRUE)
f2_mean <- mean(df_real$frequency[df_real$formant == 2], na.rm = TRUE)
f3_mean <- mean(df_real$frequency[df_real$formant == 3], na.rm = TRUE)

cat("Extracted formants from real speech:\n")
#> Extracted formants from real speech:
cat(sprintf("  F1: %.0f Hz\n", f1_mean))
#>   F1: 421 Hz
cat(sprintf("  F2: %.0f Hz\n", f2_mean))
#>   F2: 465 Hz
cat(sprintf("  F3: %.0f Hz\n", f3_mean))
#>   F3: 3080 Hz

# Resynthesize with extracted formants
kg_synth <- klattgrid_create_from_vowel(
  duration = min(sound_real$get_duration(), 1.0),
  f0start = 120,
  f1 = f1_mean, b1 = 80,
  f2 = f2_mean, b2 = 120,
  f3 = f3_mean, b3 = 150
)

sound_synth <- kg_synth$to_sound()

# Compare spectrograms side-by-side
spec_real <- sound_real$to_spectrogram(max_frequency = 5000)
spec_synth <- sound_synth$to_spectrogram(max_frequency = 5000)

cat("\nSynthetic sound matches real speech formant averages\n")
#> 
#> Synthetic sound matches real speech formant averages

Advanced Features

Voice Quality Control

Manipulate voicing amplitude for breathiness or creaky voice:

kg <- klattgrid_create_from_vowel(
  duration = 0.5, f0start = 120,
  f1 = 800, b1 = 80, f2 = 1200, b2 = 120, f3 = 2500, b3 = 150
)

# Add breathiness (fade voicing)
kg$add_voicing_amplitude_point(0.0, 60)  # Start normal
kg$add_voicing_amplitude_point(0.5, 30)  # End breathy

sound <- kg$to_sound()

Complex Synthesis Example

Use the pre-configured example for complex synthesis:

# Pre-configured grid with multiple tiers
kg_complex <- klattgrid_create_example()

# Synthesize full signal
sound_complex <- kg_complex$to_sound()

cat("Complex KlattGrid example:\n")
#> Complex KlattGrid example:
cat("  Duration:", sound_complex$get_duration(), "s\n")
#>   Duration: 6.88 s
cat("  Uses multiple pitch points, formant tiers, and amplitude control\n")
#>   Uses multiple pitch points, formant tiers, and amplitude control

Analysis -> Synthesis Workflow

Complete Pipeline

# 1. Load real speech
sound_orig <- Sound(system.file("extdata", "test.wav", package = "pladdrr"))

# 2. Extract formants (using FormantPath for robustness)
fp <- sound_orig$to_formant_path(num_steps_up_down = 2L)
frm_result <- fp$extract_formant()

# 3. Get mean formant values
df <- as.data.frame(frm_result)
f1_mean <- mean(df$frequency[df$formant == 1], na.rm = TRUE)
f2_mean <- mean(df$frequency[df$formant == 2], na.rm = TRUE)
f3_mean <- mean(df$frequency[df$formant == 3], na.rm = TRUE)

# 4. Extract pitch
pitch <- sound_orig$to_pitch()
f0_mean <- mean(as.data.frame(pitch)$frequency, na.rm = TRUE)

cat("Extracted parameters:\n")
#> Extracted parameters:
cat(sprintf("  F0: %.0f Hz\n", f0_mean))
#>   F0: 440 Hz
cat(sprintf("  F1: %.0f Hz\n", f1_mean))
#>   F1: 421 Hz
cat(sprintf("  F2: %.0f Hz\n", f2_mean))
#>   F2: 465 Hz
cat(sprintf("  F3: %.0f Hz\n", f3_mean))
#>   F3: 3080 Hz

# 5. Resynthesize
kg_resynth <- klattgrid_create_from_vowel(
  duration = min(sound_orig$get_duration(), 1.0),
  f0start = f0_mean,
  f1 = f1_mean, b1 = 80,
  f2 = f2_mean, b2 = 120,
  f3 = f3_mean, b3 = 150
)

sound_resynth <- kg_resynth$to_sound()

cat("\nResynthesis complete - compare original vs synthetic\n")
#> 
#> Resynthesis complete - compare original vs synthetic

Use Cases

1. Perceptual Experiments

Control stimuli precisely for categorical perception studies:

# Voice onset time (VOT) continuum simulation
# Generate /ba/ to /pa/ continuum by manipulating voice onset

vot_values <- seq(0, 60, by = 10)  # 0-60 ms VOT

stimuli <- lapply(vot_values, function(vot_ms) {
  # Voicing delay = VOT
  kg <- klattgrid_create_from_vowel(
    duration = 0.5, f0start = 120,
    f1 = 730, b1 = 80, f2 = 1090, b2 = 120, f3 = 2440, b3 = 140
  )
  
  # Manipulate voicing onset (simplified)
  if (vot_ms > 0) {
    kg$add_voicing_amplitude_point(0, 0)
    kg$add_voicing_amplitude_point(vot_ms / 1000, 60)
  }
  
  kg$to_sound()
})

2. Voice Morphing

Create intermediate voices between two speakers:

# Male voice parameters
f1_male <- 730
f2_male <- 1090
f0_male <- 100

# Female voice parameters
f1_female <- 850
f2_female <- 1300
f0_female <- 220

# Morph continuum (10 steps)
morph_steps <- seq(0, 1, length.out = 10)

morphed_voices <- lapply(morph_steps, function(alpha) {
  # Linear interpolation
  f1 <- f1_male + alpha * (f1_female - f1_male)
  f2 <- f2_male + alpha * (f2_female - f2_male)
  f0 <- f0_male + alpha * (f0_female - f0_male)
  
  kg <- klattgrid_create_from_vowel(
    duration = 0.5, f0start = f0,
    f1 = f1, b1 = 80, f2 = f2, b2 = 120, f3 = 2500, b3 = 150
  )
  
  kg$to_sound()
})

3. Teaching Phonetics

Demonstrate formant-vowel relationships interactively:

# Function to synthesize any vowel from F1/F2
synthesize_vowel <- function(f1, f2, label = "") {
  kg <- klattgrid_create_from_vowel(
    duration = 0.5, f0start = 120,
    f1 = f1, b1 = 80, f2 = f2, b2 = 120, f3 = 2500, b3 = 150
  )
  
  sound <- kg$to_sound()
  filename <- file.path(tempdir(),
    sprintf("vowel_%s_F1%d_F2%d.wav", label, f1, f2))
  sound$save(filename, "WAV")
  
  cat(sprintf("Created %s: F1=%d, F2=%d Hz\n", label, f1, f2))
}

# Generate examples
synthesize_vowel(280, 2250, "i")
#> Created i: F1=280, F2=2250 Hz
synthesize_vowel(730, 1090, "a")
#> Created a: F1=730, F2=1090 Hz
synthesize_vowel(310, 870, "u")
#> Created u: F1=310, F2=870 Hz

Known Limitations

1. Empty Grid Errors on Synthesis

Issue: Direct synthesis from an empty KlattGrid( ) errors ("Pitch tier should not be empty.")

Workaround: Always use klattgrid_create_from_vowel( ) or klattgrid_create_example()

Example of safe usage:

# safe
kg <- klattgrid_create_from_vowel(
  duration = 0.5, f0start = 120,
  f1 = 800, b1 = 80, f2 = 1200, b2 = 120, f3 = 2500, b3 = 150
)

# safe
kg <- klattgrid_create_example()

# unsafe - errors, uninitialized tiers
kg <- KlattGrid(tmin = 0, tmax = 1, numberOfFormants = 5)
tryCatch(
  kg$to_sound(),
  error = function(
    e) cat("Error: uninitialized tiers (pitch, voicing, formants)\n")
)
#> Error: uninitialized tiers (pitch, voicing, formants)

2. Limited Tier Manipulation

Current limitations: - Cannot query tier contents directly - Cannot remove points after adding - No direct formant amplitude control

Best practice: Create new grid with desired parameters rather than modifying existing grid

3. Formant Constraints

Physical constraints that must be maintained: - F1 < F2 < F3 (formants increase monotonically) - Bandwidths > 0 Hz (zero bandwidth causes artifacts) - Pitch in range 50-400 Hz (outside this sounds unnatural)

Best Practices

Do

Always use klattgrid_create_from_vowel() for vowel synthesis
Start with known formant values from the reference table
Adjust formants gradually (+/-50-100 Hz steps)
Keep bandwidths proportional: B1 < B2 < B3 (typically 50-80-120 Hz)
Match pitch to speaker type: male ~100-120 Hz, female ~200-220 Hz
Test with short durations (0.3-0.5s) before scaling up
Export to WAV for analysis in other tools

Don’t

Don’t use empty KlattGrid() constructor (errors on synthesis)
Don’t violate F1 < F2 < F3 (unnatural synthesis)
Don’t use zero bandwidth (causes artifacts)
Don’t expect consonant synthesis (formants only, no articulation model)
Don’t modify existing grids (create new ones instead)

Troubleshooting

Error on `to_sound()`

Cause: Incomplete grid initialization

Solution: Use klattgrid_create_from_vowel() instead of empty grid

Unnatural sounding synthesis

Cause: Formant values out of range or wrong bandwidths

Solution: - Check F1 < F2 < F3 relationship - Use bandwidth ratio B1:B2:B3 ~ 1:1.5:2 - Verify pitch is in 80-300 Hz range

No sound output

Cause: Voicing amplitude too low or pitch out of range

Solution: Ensure f0start is 80-300 Hz and voicing amplitude > 40 dB

Comparison with Other Tools

pladdrr vs Praat GUI

Feature	pladdrr KlattGrid	Praat GUI
Vowel synthesis	`createFromVowel()`	Manual setup
Pitch contours	`add_pitch_point()`	PitchTier editor
Batch synthesis	R loops	Manual, one at a time
Parametric experiments	Scriptable continua	Repeated manual steps
Visualization	ggplot2	Built-in

vs Parselmouth

Parselmouth does not currently expose KlattGrid - pladdrr is the only R package with direct Klatt synthesis support.

vs Other R Synthesis

Existing R packages (e.g., phonTools) use simpler synthesis methods. pladdrr’s KlattGrid wraps Praat’s own cascade/parallel Klatt synthesizer C++ code directly, rather than reimplementing it.

Summary

KlattGrid is used for: - Perceptual experiments requiring controlled stimuli - Voice manipulation research - Teaching phonetic concepts - Speech resynthesis with modified parameters

Key functions: - klattgrid_create_from_vowel() - Safe vowel synthesis - add_pitch_point() - Dynamic intonation - add_formant_point() - Formant transitions - to_sound() - Generate audio

Typical workflow: 1. Define formant parameters (F1/F2/F3, B1/B2/B3) 2. Set pitch contour (f0start + optional points) 3. Create grid with createFromVowel() 4. Synthesize with to_sound() 5. Analyze or export

Session Info

sessionInfo()
#> R version 4.6.1 (2026-06-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 24.04.5 LTS
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0
#> 
#> locale:
#>  [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
#>  [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
#>  [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
#> [10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   
#> 
#> time zone: UTC
#> tzcode source: system (glibc)
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#> [1] ggplot2_4.0.3 pladdrr_5.0.5
#> 
#> loaded via a namespace (and not attached):
#>  [1] gtable_0.3.6        jsonlite_2.0.0      dplyr_1.2.1        
#>  [4] compiler_4.6.1      tidyselect_1.2.1    Rcpp_1.1.2         
#>  [7] jquerylib_0.1.4     systemfonts_1.3.2   scales_1.4.0       
#> [10] textshaping_1.0.5   yaml_2.3.12         fastmap_1.2.0      
#> [13] R6_2.6.1            labeling_0.4.3      generics_0.1.4     
#> [16] knitr_1.52          tibble_3.3.1        desc_1.4.3         
#> [19] bslib_0.12.0        pillar_1.11.1       RColorBrewer_1.1-3 
#> [22] rlang_1.3.0         cachem_1.1.0        xfun_0.60          
#> [25] fs_2.1.0            sass_0.4.10         S7_0.2.2           
#> [28] otel_0.2.0          cli_3.6.6           pkgdown_2.2.1      
#> [31] withr_3.0.3         magrittr_2.0.5      digest_0.6.39      
#> [34] grid_4.6.1          lifecycle_1.0.5     vctrs_0.7.3        
#> [37] evaluate_1.0.5      glue_1.8.1          data.table_1.18.6.1
#> [40] farver_2.1.2        codetools_0.2-20    ragg_1.5.2         
#> [43] rmarkdown_2.32      tools_4.6.1         pkgconfig_2.0.3    
#> [46] htmltools_0.5.9