paper/main.tex

\documentclass[12pt]{article}
\usepackage[T5,T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[vietnamese,english]{babel}
\usepackage{tipa}
\usepackage[hyphens]{url}
\usepackage{multirow}
\usepackage{adjustbox}
\usepackage{rotating}
\usepackage[table]{xcolor}
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\setcitestyle{authoryear,open={(},close={)}}

% Custom citation command for family name only
\newcommand{\citeF}[1]{\citeauthor{#1} (\citeyear{#1})}

\let\oldfootnote\footnote
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\makeatletter
\renewcommand\@makefnmark{\hbox{\@textsuperscript{\normalfont\textcolor{magenta}{\@thefnmark}}}}
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% Custom command for phonetic labels
\newcommand{\phonlabel}[1]{\scriptsize{#1}}

\title{IPA Guideline in Vietnamese}
\author{
  Trang Phan\\
  {\small Ca' Foscari University of Venice}
  \and
  Vu Anh\\
  {\small Underthesea NLP}
}
\date{}

\begin{document}

\maketitle

\section{Introduction}

Vietnamese is considered the national and official language in Vietnam. Vietnamese ranks at number 10 on the 10 most spoken languages in the world, sorted by number of first language speakers\footnote{\url{https://www.translateday.com/most-spoken-languages-in-the-world/}}, and ranks at number 20 on the 20 most spoken languages in the world, sorted by number of both first language and second language speakers\footnote{\url{https://www.ethnologue.com/guides/ethnologue200}} (both rankings are in 2022).

The demand of learning Vietnamese as a second language in Vietnam and overseas is huge and increasing. Samsung, one of the largest foreign companies in Vietnam, requires their South Korean employees to learn Vietnamese. Vietnamese is the second most popular language to learn in Taiwan\footnote{\href{https://word.tips/multilingual-world/?fbclid=IwAR2c6hS0rjZj7x2pXxLvBMv2JSpMlXBf0ZbcXF6-CVPMpevjeJv5mZVKLEE}{https://word.tips/multilingual-world/}} (the ranking is in 2021). In Italy, by 2025, 3 universities offer Vietnamese courses: Ca' Foscari University of Venice, ``L'Orientale'' University of Naples, and University of Turin.

There is also a growing number of people speaking Vietnamese as a heritage language in the US, Cambodia, France, Australia and other countries. Vietnamese has been officially recognized as a minority language in the Czech Republic since 2013\footnote{\url{https://ec.europa.eu/migrant-integration/news/czech-republic-vietnamese-and-belarusians-recognized-ethnic-minorities_en}}. In Australia, Vietnamese occupies 82.7\% of the main languages spoken at home by Vietnam-born people there, according to the 2016 Census\footnote{\url{https://www.homeaffairs.gov.au/mca/files/2016-cis-vietnam.PDF}}.

Responding to strong demand, numerous instructional textbooks have been published worldwide, including series by \citet{mai2007a}, \citet{vu2011}, \citet{doan2012,doan2014}, \citet{nguyen2019}, and more recently by \citet{phan2024vibes} and \citet{phung2025}. Additionally, there are descriptive guides to the Vietnamese language including \citet{nguyen1997} by John Benjamins\footnote{\url{https://benjamins.com/catalog/loall.9}}, and \cite{ngo2021} by Routledge\footnote{\url{https://www.routledge.com/Vietnamese-An-Essential-Grammar/Ngo/p/book/9781138210707}}.

There is also a great leap in Vietnamese linguistic research over the past decade. There are three edited volumes devoted to Vietnamese: \cite{hole2013}, De Gruyter Mouton\footnote{\url{https://www.degruyter.com/document/doi/10.1515/9783110289411/html?lang=en}}; \cite{duffield2019}, John Benjamins\footnote{\url{https://benjamins.com/catalog/slcs.211}}; and \cite{phan2024springer}, Springer. Vietnamese has also been the focus of several special issues in Journal of East Asian Linguistics (2017)\footnote{\url{https://link.springer.com/journal/10831/volumes-and-issues/26-4}}, Journal of the Southeast Asian Linguistics Society (\cite{phan2022}\footnote{\url{https://evols.library.manoa.hawaii.edu/handle/10524/52500}}), Taiwan Journal of Linguistics (\cite{duffield2024,phan2025tjl}), and Languages (\cite{phan2025lang}).

However, there is little communication and connection between learning and teaching practice and linguistic research. Our book, therefore, aims to bridge this gap. We tackle one of the most fundamental tasks that are encountered by any speaker, learner, teacher, and researcher of Vietnamese: \textbf{pronouncing Vietnamese syllables}. In particular, the objective of this book is to represent how a native speaker of Vietnamese of different dialects pronouns each syllable in isolation.

We bring different perspectives to the task: as a native speaker of Vietnamese, as a teacher of Vietnamese as a second language, as a specialist of Vietnamese natural language processing, and as a researcher in comparative linguistics.

Our transcription is based on a standardized system applicable to all the languages in the world, namely the International Phonetic Alphabet (IPA), with some language-specific and user-friendly modifications. Our main point of reference is Kirby (2008)'s vPhon, a Vietnamese phonetizer whose current version can be retrieved from \url{http://github.com/kirbyj/vPhon/}.

In this study, we have compiled a comprehensive list of Vietnamese syllables by integrating data from two primary sources. The output of our research is a comprehensive list of 6000 syllables, each of which is transcribed in the International Phonetic Alphabet (IPA) according to the two main dialects of Vietnamese, Northern and Southern. For example, the syllable "{\fontencoding{T5}\selectfont kiểm}" is transcribed as /\textipa{ki\textschwa m}\super{312}/ in the Northern dialect and as /\textipa{ki\textlengthmark m}\super{214}/ in the Southern dialect. Our aim is to provide a valuable resource for learners of Vietnamese as a second language, as well as for Vietnamese language teachers, researchers and specialists in various fields of Vietnamese studies.

\section{The Vietnamese syllabic structure and the main dialects}

A Vietnamese syllabe consists of three obligatory elements (an onset, a tone and a nuclear vowel), and two optional elements (a lip-rounding (labialization) medial following the onset, and a final consonant or a coda).

\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
\multicolumn{4}{|c|}{Tone} \\
\hline
\multirow{2}{*}{Onset} & \multicolumn{3}{c|}{Rhyme} \\
\cline{2-4}
 & Medial & Nuclear vowel & (Coda) \\
\hline
\end{tabular}
\end{center}

For instance, the syllable {\fontencoding{T5}\selectfont toán} (`math') is transcribed as /t\super{w}an\super{34}/, with the onset /t/, the labialized \super{/w/}, the nuclear vowel /a/, the coda /n/ and the rising tone \super{/34/}.

\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
\multicolumn{4}{|c|}{Tone} \\
\hline
\multicolumn{4}{|c|}{Rising \super{/34/}} \\
\hline
Onset & Medial & Nuclear vowel & Coda \\
/t/ & \super{/w/} & /a/ & /n/ \\
\hline
\end{tabular}
\end{center}

There are two mutually intelligible main dialects differing in terms of pronunciation and to a certain extent in vocabulary: Northern Vietnamese and Southern Vietnamese. In the following sections, we present the phonemic system including onsets, medial, nuclear vowels, codas and tones for each dialect. We follow \cite{michaud2004}, \cite{pham2006}, \cite{kirby2011}, \cite{brunelle2015}, and \cite{shimizu2022} for the distinction between the phonemic system of Northern Vietnamese and that of Southern Vietnamese.

\section{The phonemic system of Northern Vietnamese}

\begin{center}
\begin{tabular}{|l l|}
\hline
Onsets & 
\textipa{
  /t \textrtailt\textrtails~c k
  \textglotstop\
  t\textsuperscript{h}~b d f v s z
  \textrtails\ 
  \textrtailz\ x
  \textgamma~h m n
  \textltailn\ \ng\ r l/
} \\
Medial & /w/ \\
Vowels &
\textipa{
  /a: a \textschwa: \textschwa\ \textbari:\ \textepsilon:\ e: i: \textopeno:\ o: u: i\textschwa\ u\textschwa\ \textturnm\textschwa/
} \\
Codas & 
\textipa{
  /p t k/k\super p m n \ng/\ng\super m w j/
} \\
Tones &
 1. \makebox[3cm][l]{ngang} 33 \\
 & 2. \makebox[3cm][l]{{\fontencoding{T5}\selectfont huyền}} 21 \\
 & 3. \makebox[3cm][l]{{\fontencoding{T5}\selectfont hỏi}} 312 \\
 & 4. \makebox[3cm][l]{{\fontencoding{T5}\selectfont ngã}} 35g \\
 & 5. \makebox[3cm][l]{{\fontencoding{T5}\selectfont sắc}} 24 \\
 & 6. \makebox[3cm][l]{{\fontencoding{T5}\selectfont sắc nhập}} 45 \\
 & 7. \makebox[3cm][l]{{\fontencoding{T5}\selectfont nặng}} 21 \\
 & 8. \makebox[3cm][l]{{\fontencoding{T5}\selectfont nặng nhập}} 21g \\
\hline
\end{tabular}
\end{center}

(adopted from \cite{shimizu2022} and \cite{kirby2008})

\subsection{The onsets of Northern Vietnamese}

\begin{figure}[h]
\centering
\includegraphics[width=1\textwidth]{images/onsets_northern.pdf}
\end{figure}

\subsection{Medial of Northern Vietnamese}

There is one medial /w/ which serves to labialize/lip-round the syllables.

\subsection{The vowels of Northern Vietnamese}

\begin{center}
\begin{tabular}{|l|l|c|c|c|}
\hline
\multicolumn{2}{|c|}{} & Front & \multicolumn{2}{c|}{Back} \\
\cline{4-5}
\multicolumn{2}{|c|}{} & & Unround & Round \\
\hline
\multirow{3}{*}{Monothong} & Open & {\fontencoding{T3}\selectfont \textepsilon:} & {\fontencoding{T3}\selectfont a:} \hspace{1em} {\fontencoding{T3}\selectfont a} & {\fontencoding{T3}\selectfont \textopeno:} \\
\cline{2-5}
 & Mid & {\fontencoding{T3}\selectfont e:} & {\fontencoding{T3}\selectfont \textschwa:} \hspace{1em} {\fontencoding{T3}\selectfont \textschwa} & {\fontencoding{T3}\selectfont o:} \\
\cline{2-5}
 & Close & {\fontencoding{T3}\selectfont i:} & {\fontencoding{T3}\selectfont \textsubdot{\i}:} & {\fontencoding{T3}\selectfont u:} \\
\hline
\multicolumn{2}{|l|}{Dipthong} & {\fontencoding{T3}\selectfont i\textschwa} & {\fontencoding{T3}\selectfont u\textschwa} & {\fontencoding{T3}\selectfont u\textschwa} \\
\hline
\end{tabular}
\end{center}

\subsection{The codas of Northern Vietnamese}

\begin{center}
\begin{tabular}{|l|c|c|c|}
\hline
 & Labial & Dental & Velar \\
\hline
Plosive & {\fontencoding{T3}\selectfont p} & {\fontencoding{T3}\selectfont t} & {\fontencoding{T3}\selectfont k/k\super p} \\
\hline
Nasal & {\fontencoding{T3}\selectfont m} & {\fontencoding{T3}\selectfont n} & {\fontencoding{T3}\selectfont \ng/\ng\super m} \\
\hline
Approximant & {\fontencoding{T3}\selectfont w} & {\fontencoding{T3}\selectfont j} & \\
\hline
\end{tabular}
\end{center}

Note that velar codas are often pronounced as labio-velar in a lip-rounded context:

\begin{itemize}
\item ung $\rightarrow$ {\fontencoding{T3}\selectfont /u\ng\super m/}
\item uc $\rightarrow$ {\fontencoding{T3}\selectfont /uk\super p/}
\item {\fontencoding{T5}\selectfont ông} $\rightarrow$ {\fontencoding{T3}\selectfont /o\ng\super m/}
\item {\fontencoding{T5}\selectfont ôc} $\rightarrow$ {\fontencoding{T3}\selectfont /ok\super p/}
\item ong $\rightarrow$ {\fontencoding{T3}\selectfont /\textopeno\ng\super m/}
\item oc $\rightarrow$ {\fontencoding{T3}\selectfont /\textopeno k\super p/}
\end{itemize}

\subsection{Tones of Northern Vietnamese}

The tones of Northern Vietnamese transcribed in Chao tone numbers:

\begin{center}
\begin{tabular}{|l|c|c|}
\hline
 & Upper register & Lower register \\
\hline
Level & 33 (ngang) & 21 (huy{\fontencoding{T5}\selectfont ề}n) \\
\hline
Rising & 35g (ng{\fontencoding{T5}\selectfont ã}) & 24 (s{\fontencoding{T5}\selectfont ắ}c) \\
\hline
Falling & 312 (h{\fontencoding{T5}\selectfont ỏ}i) & \\
\hline
\multicolumn{3}{|c|}{Tones in syllables closed by /p, t, k/} \\
\hline
 & 45 (s{\fontencoding{T5}\selectfont ắ}c nh{\fontencoding{T5}\selectfont ậ}p) & 21g (n{\fontencoding{T5}\selectfont ặ}ng nh{\fontencoding{T5}\selectfont ậ}p) \\
\hline
\end{tabular}
\end{center}

(g: glotalized)

(adopted from \cite{shimizu2022} and \cite{kirby2008})

\section{The phonemic system of Southern Vietnamese}

According to the existing literature (\cite{thompson1959}, \cite{doan1977}, \cite{thompson1984}, \cite{nguyentaican1985}, \cite{nguyentaican1995}, \cite{mai1992}, \cite{vuong1994}, \cite{cao1988}, \cite{nguyen1997}, \cite{hoang2004}, \cite{shimizu2022}), the main differences between Northern Vietnamese and Southern Vietnamese are as follows:

\begin{enumerate}
\item[(i)] Initial consonants in Southern Vietnamese are more conservative than in Northern Vietnamese.
\item[(ii)] Southern Vietnamese rhymes lack of the contrast between coronal and velar codas.
\item[(iii)] There is no distiction between between the two tonemes h{\fontencoding{T5}\selectfont ỏ}i and ng{\fontencoding{T5}\selectfont ã} in Southern Vietnamese.
\end{enumerate}

The phonemic system of Southern Vietnamese is as follows:

\begin{center}
\begin{tabular}{|l l|}
\hline
Onsets & {\fontencoding{T3}\selectfont /t \textrtailt\textesh\ c k \textgamma\textesh\ t\super h d \textrtailt\ f s z \textrtails\ \textgamma\ x h m n \textltailn\ \ng\ r l j/} \\
Medial & /w/ \\
Vowels & {\fontencoding{T3}\selectfont /a: a \textopeno\ i: i \textepsilon: e: i: \textopeno: o: u: i\textschwa\ u\textschwa\ i\textschwa/} \\
Finals & {\fontencoding{T3}\selectfont /p t k k\super p m n \ng\ \ng\super m w j/} \\
Tones & 1. ngang \hfill 33 \\
 & 2. huy{\fontencoding{T5}\selectfont ề}n \hfill 21 \\
 & 3. h{\fontencoding{T5}\selectfont ỏ}i-ng{\fontencoding{T5}\selectfont ã} \hfill 214 \\
 & 4. s{\fontencoding{T5}\selectfont ắ}c \hfill 24 \\
 & 5. s{\fontencoding{T5}\selectfont ắ}c nh{\fontencoding{T5}\selectfont ậ}p \hfill 45 \\
 & 6. n{\fontencoding{T5}\selectfont ặ}ng \hfill 21 \\
 & 7. n{\fontencoding{T5}\selectfont ặ}ng nh{\fontencoding{T5}\selectfont ậ}p \hfill 21g \\
\hline
\end{tabular}
\end{center}

(adopted from \cite{shimizu2022} and \cite{kirby2008})

\subsection{The onsets of Southern Vietnamese}

\begin{center}
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline
 & Labial & Labio-Dental & Dental & Alveolar & Palatal & Velar & Glottal \\
\hline
Plosive & {\fontencoding{T3}\selectfont b} & & {\fontencoding{T3}\selectfont t \hspace{1em} t\super h} & {\fontencoding{T3}\selectfont d} & {\fontencoding{T3}\selectfont \textrtailt\textesh \hspace{1em} c} & {\fontencoding{T3}\selectfont k} & {\fontencoding{T3}\selectfont \textglotstop} \\
\hline
Nasal & {\fontencoding{T3}\selectfont m} & & {\fontencoding{T3}\selectfont n} & & {\fontencoding{T3}\selectfont \textltailn} & {\fontencoding{T3}\selectfont \ng} & \\
\hline
Fricative & & {\fontencoding{T3}\selectfont f} & & {\fontencoding{T3}\selectfont s \hspace{1em} z} & {\fontencoding{T3}\selectfont \textrtails} & {\fontencoding{T3}\selectfont x \hspace{1em} \textgamma} & {\fontencoding{T3}\selectfont h} \\
\hline
Approximant & & & & & {\fontencoding{T3}\selectfont j} & & \\
\hline
Lateral approximant & & & {\fontencoding{T3}\selectfont l} & & {\fontencoding{T3}\selectfont r} & & \\
\hline
\end{tabular}
\end{center}

\subsection{Medial of Southern Vietnamese}

There is also one medial /w/ which serves to labialize/lip-round the syllables.

\subsection{The vowels of Southern Vietnamese}

\begin{center}
\begin{tabular}{|l|l|c|c|c|}
\hline
\multicolumn{2}{|c|}{} & Front & \multicolumn{2}{c|}{Back} \\
\cline{4-5}
\multicolumn{2}{|c|}{} & & Unround & Round \\
\hline
\multirow{3}{*}{Monothong} & Open & {\fontencoding{T3}\selectfont \textepsilon:} & {\fontencoding{T3}\selectfont a:} \hspace{1em} {\fontencoding{T3}\selectfont a} & {\fontencoding{T3}\selectfont \textopeno:} \\
\cline{2-5}
 & Mid & {\fontencoding{T3}\selectfont e:} & {\fontencoding{T3}\selectfont \textschwa:} \hspace{1em} {\fontencoding{T3}\selectfont \textschwa} & {\fontencoding{T3}\selectfont o:} \\
\cline{2-5}
 & Close & {\fontencoding{T3}\selectfont i:} & {\fontencoding{T3}\selectfont \textsubdot{\i}:} \hspace{1em} {\fontencoding{T3}\selectfont \i} & {\fontencoding{T3}\selectfont u:} \\
\hline
\multicolumn{2}{|l|}{Dipthong} & {\fontencoding{T3}\selectfont i\textschwa} & {\fontencoding{T3}\selectfont u\textschwa} & {\fontencoding{T3}\selectfont i\textschwa} \\
\hline
\end{tabular}
\end{center}

Examples of the different realizations of diphthongs between Northern Vietnamese and Southern Vietnamese:

\begin{center}
\begin{tabular}{lll}
Orthography & North & South \\
{\fontencoding{T5}\selectfont tìm} & {\fontencoding{T3}\selectfont /ti:\ng/} & {\fontencoding{T3}\selectfont /ti:\ng/} \\
{\fontencoding{T5}\selectfont kiểm} & {\fontencoding{T3}\selectfont /ki\textschwa\ng/} & {\fontencoding{T3}\selectfont /ki:\ng/} \\
{\fontencoding{T5}\selectfont cùm} & {\fontencoding{T3}\selectfont /ku:\ng/} & {\fontencoding{T3}\selectfont /k\i\ng/} \\
{\fontencoding{T5}\selectfont buồm} & {\fontencoding{T3}\selectfont /bu\textschwa\ng/} & {\fontencoding{T3}\selectfont /bu:\ng/} \\
\end{tabular}
\end{center}

(adopted from \cite{shimizu2022})

\subsection{The codas of Southern Vietnamese}

\begin{center}
\begin{tabular}{|l|c|c|c|}
\hline
 & Labial & Dental & Velar \\
\hline
Plosive & {\fontencoding{T3}\selectfont p} & {\fontencoding{T3}\selectfont t} & {\fontencoding{T3}\selectfont k/k\super p} \\
\hline
Nasal & {\fontencoding{T3}\selectfont m} & {\fontencoding{T3}\selectfont n} & {\fontencoding{T3}\selectfont \ng/\ng\super m} \\
\hline
Approximant & {\fontencoding{T3}\selectfont w} & {\fontencoding{T3}\selectfont j} & \\
\hline
\end{tabular}
\end{center}

There is a lack of the contrast between coronal and velar codas in Southern Vietnamese rhymes. For instance, speakers of Northern Vietnamese differentiate distinctively between final [t] and final [k], whereas Southern speakers pronounce both as [k].

Examples of the distribution of coronal and velar codas in two major dialects can be given as follows:

\begin{center}
\begin{tabular}{llll}
Orthography & North & South & Gloss \\
a. {\fontencoding{T5}\selectfont đứt} & {\fontencoding{T3}\selectfont [d\i t]} & {\fontencoding{T3}\selectfont [d\i k]} & `be broken' \\
b. {\fontencoding{T5}\selectfont ớt} & {\fontencoding{T3}\selectfont [?\textopeno:t]} & {\fontencoding{T3}\selectfont [?\textopeno:k]} & `pepper' \\
c. kh\'at & {\fontencoding{T3}\selectfont [xa:t]} & {\fontencoding{T3}\selectfont [xa:k]} & `thirsty' \\
d. {\fontencoding{T5}\selectfont mắt} & {\fontencoding{T3}\selectfont [mat]} & {\fontencoding{T3}\selectfont [mak]]} & `eyes' \\
e. h\'et & {\fontencoding{T3}\selectfont [he:t]} & {\fontencoding{T3}\selectfont [he:k]} & `to scream' \\
f. chu{\fontencoding{T5}\selectfont ột} & {\fontencoding{T3}\selectfont [cu\textschwa t]} & {\fontencoding{T3}\selectfont [cu:k]} & `mouse' \\
g. d\'ich & {\fontencoding{T3}\selectfont [d\i c]} & {\fontencoding{T3}\selectfont [d\i t]} & `target' \\
h. l{\fontencoding{T5}\selectfont ệ}nh & {\fontencoding{T3}\selectfont [l\textepsilon n]} & {\fontencoding{T3}\selectfont [l\textschwa:n]} & `order' \\
i. kh\'ach & {\fontencoding{T3}\selectfont [xa\super jc]} & {\fontencoding{T3}\selectfont [xa\super jt]} & `guest' \\
j. kh\'ac & {\fontencoding{T3}\selectfont [xa:k]} & {\fontencoding{T3}\selectfont [xa:k]} & `different' \\
k. kh{\fontencoding{T5}\selectfont ắ}c & {\fontencoding{T3}\selectfont [xak]} & {\fontencoding{T3}\selectfont [xak]} & `to engrave' \\
\end{tabular}
\end{center}

(adopted from \cite{shimizu2022})

\subsection{Tones of Southern Vietnamese}

The tones of Southern Vietnamese transcribed in Chao tone numbers:

Note that there is no distiction between between the two tonemes h{\fontencoding{T5}\selectfont ỏ}i and ng{\fontencoding{T5}\selectfont ã} in Southern Vietnamese.

\begin{center}
\begin{tabular}{|l|c|c|c|c|}
\hline
\multicolumn{2}{|c|}{} & Level & \multicolumn{2}{c|}{Oblique} \\
\hline
\multicolumn{2}{|c|}{Tonal contour} & & & \\
\hline
\multirow{2}{*}{Tonal register} & High & Ngang /33/ & S{\fontencoding{T5}\selectfont ắ}c \hspace{2em} /24/ & H{\fontencoding{T5}\selectfont ỏ}i-Ng{\fontencoding{T5}\selectfont ã} /214/ \\
 & & & S{\fontencoding{T5}\selectfont ắ}c nh{\fontencoding{T5}\selectfont ậ}p \hspace{1em} /45/ after the codas /p,t,k/ & \\
\cline{2-5}
 & Low & Huy{\fontencoding{T5}\selectfont ề}n /21/ & N{\fontencoding{T5}\selectfont ặ}ng \hspace{2em} /21/ & H{\fontencoding{T5}\selectfont ỏ}i-Ng{\fontencoding{T5}\selectfont ã} /214/ \\
 & & & N{\fontencoding{T5}\selectfont ặ}ng nh{\fontencoding{T5}\selectfont ậ}p /21g/ after the codas /p,t,k/ & \\
\hline
\end{tabular}
\end{center}

(g: glotalized)

(Adopted from Kirby 2008)

\section{Conclusion}

This is a work in progress toward a dialect-sensitive inventory of $\sim$6,000 Vietnamese syllables with IPA (North/South) and example audio. The aim is a modest, reliable reference for teaching, learning, and basic research. We invite testing, critique, and incremental improvement.

\nocite{*}
\bibliographystyle{plainnat-custom}
\bibliography{main}

\end{document}