International Symposium on Tonal
Aspects of Languages:
With Emphasis on Tone Languages
Beijing, China, March 28-31, 2004
ISCA Archive
http://www.isca-speech.org/archive
Occurrence Frequency and Transition Probability
of the Chinese Four Tones
Shizuo Hiki1), Kazuko Sunaoka2), Liming Yang3) and Yasuyo Tokuhiro4)
1)
4)
School of Human Sciences, 2) School of Political Science and Economics,
3)
Institute of Language Teaching, Waseda University, Japan
{hiki; ksunaoka; youl}@waseda.jp
Graduate School of Japanese Applied Linguistics, Waseda University, Japan
[email protected]
Abstract
Occurrence frequency and transition probability of the Chinese
four tones were analyzed statistically. The database used for
the analysis was the Grammatical Knowledge-base of
Contemporary Chinese (S-W. Yu, editor, Tsinghua University
Press, China, 1998). One, two, three and four syllable words,
about 55,000 words in total, were categorized into more than
twenty kinds of parts of speech in this database.
The occurrence frequency of the four tones deviated
from 25%, depending on number of syllables in a word or
position of the syllables in the word. In nouns, Tone-2 was
always around 25% but Tone-3 was 5% to 10% less. In the
1st syllables of the words with any number of syllables, Tone1 were more than 25%, but it became less in the back position
of syllables. Tone-4 was 5% more even in the 1st syllables
and became as large as 40% in the last syllables.
In the total 38,968 syllables of the nouns, occurrence
frequencies of Tone-1, Tone-2, Tone-3 and Tone-4 were 24%,
23%, 18% and 33%, respectively. The deviations were much
larger in the cases of some of the other parts of speech such as
verb, adjective, adverb and onomatopoeia.
The entropy of the four tones, which is 2 bits when the
ratios are equal, decreased by less than 0.05 bit when
averaged over all positions of syllables. This indicates that
the four tones are used fairly effectively in Chinese language.
In the nouns, transition probability between Tone-2 and
Tone-3 were less than average. Transitions beginning at
Tone-1 and ending at Tone-4, or beginning at Tone-4 and
ending at Tone-4 in the two, three and four syllable words
were much more. Some other kind of parts of speech showed
characteristic transition such as repetition of the same tone in
successive syllables.
1. Database used for the statistical analysis
The database used for extracting occurrence frequency and
transition probability of the Chinese four tones was the
Grammatical Knowledge-base of Contemporary Chinese
edited by Shiwen Yu of Institute of Computational Linguistics,
Beijing University, and published by Tsinghua University
Press, China, 1998. The database was converted into Japanese
computer code by Ming Yin and Kazuko Sunaoka, under a
project of the Chinese division, Cross-Cultural Distance
Learning, Waseda University, Japan.
Tone symbols of the four tones of Standard Chinese
were furnished to each of the syllables involved in one, two,
three and four syllable words, about 55,000 words in total.
About 124,000 syllables were involved in those words.
Parts of speech of the words were categorized in this
database into more than twenty kinds, but following nine parts
of speech were used for the present analysis:
Number of words (Items less than 20 are not shown.)
Number of syllables in a word
One
Two
Three
Four
Total
Part of Speech
Noun
325 10,039 5,511
508
16,383
Verb
1,660 12,400
415
14,479
Morpheme
7,129
7,142
Set phrase
5,254
5,252
Idiom
450 2,584
3,045
Adjective
284
2,531
39
2,856
Adverb
183
908
78
1,172
Word of state
341
420
225
986
Onomatopoeia
68
63
145
2. Occurrence frequency of the four tones
In order to make it easier to grasp the ratio among the
occurrence frequency of the four kinds of tones, namely,
Tone-1: high flat, Tone-2: rising, Tone-3: low flat and rising,
and Tone-4: falling, the value of occurrence frequency is
converted into percentage, then, plotted on a two dimensional
plane along the upward, rightward, downward and leftward
axes from the origin, respectively, and connected by solid lines
in this order in Figure 1. As most of the values stayed in the
range from 10% to 40%, 10% is taken as the origin and up to
40% was plotted on each axis, so that their differences are
magnified. The case of all 25% is indicated by gray bold lines
for reference.
2.1. Nouns
The number of nouns was most among the parts of speech, and
they occupied about 30% of the total of words accommodated
in the database. Total of the syllables involved was 38,968
syllables. By taking the noun as a typical example of the part
of speech, firstly, occurrence frequency of the Chinese four
tones was examined for each number of syllables in a word,
and for each position of syllables in the word.
2.1.1.
Position of syllable in the word
Ratio of the occurrence frequency for one, two, three and four
syllable words are shown from the top in the left column of
Figure 1. In each figure, the data is subdivided by their
position of syllables such as the 1st, 2nd, 3rd and 4th syllable,
and the plots are superposed in each figure.
The occurrence frequency of the four tones deviated from
the average of 25%, depending on number of syllables of the
word or position of syllable in the word.
Tone-2 was always around 25% but Tone-3 was 5% to
10% less. In the first syllable of the word with any number of
syllables, Tone-1 were more than 25%, but it became less than
25% in the syllables in the back position in the word. Tone-4
was 5% more even in the first syllables and became as large as
40% in the last syllables, regardless of the number of syllables
in the words.
2.1.2.
Number of syllable in a word
The bottom of the left column in Figure 1 is average of all
positions of syllables for each of the one, two, three and four
syllable words of nouns.
Although the ratios were
characteristic of the position of syllables, the frontal and back
syllables cancelled each other characteristics and the average
became quit similar among the words with different number of
syllables.
2.1.3.
Average occurrence frequency
In the total 38,968 syllables of the nouns, occurrence
frequencies of Tone-1, Tone-2, Tone-3 and Tone-4 were 24%,
23%, 18% and 33%, respectively. These ratios are very close
to the traditionally referred ratios; “3, 3, 2 and 4,” as they
become 2.88, 2.76, 2.16 and 3.96, if 25% is converted to 3.
2.2. Other parts of speech
In other kinds of parts of speech, the characteristic deviations
of occurrence frequency of kind of tones were observed.
1) In the average of all syllable positions of one, two and
three syllable words of verbs, Tone-2 was about half of that of
noun, as shown in the top of the right column of Figure 1.
2) In the adverbs, Tone-1 and Tone-3 were less than that
of the nouns, while Tone-4 was more than twice of any other
tones, as shown in the second from the top.
In the one and two syllable words of adjectives, the rate
of occurrence frequency was similar to that of nouns, but,
Tone-1 was few in any syllable positions of the three syllable
words. In the three syllable word adjectives, Tone-4 was
frequent but Tone-1 was few in any position of syllables.
3) In onomatopoeias, most of the syllables were Tone-1,
as shown in the third from the top.
4) In the four syllable words of idioms and set phrases,
Tone-2 was more than that of the nouns, as shown in the
bottom of the right column.
2.3. Entropy of the four tones
In order to assess the efficiency of use of the four kind of
tones, entropy of the tone in each number of syllables in the
word or each position of syllable in the word was calculated
from their occurrence frequency.
The entropy is derived by summation over the four kind
of tones of - pi log(2) pi, where pi is occurrence probability of
Tone-i in each number of syllable in a word, or each position
of syllable in the word. The value is 2 bits when the
occurrence frequencies are even among the four tones, but,
decreases from 2 bits according to the degree of deviation
from the even.
Amount of the decrease from 2 bits are shown for each
plot in Figure 1. The entropy decreased by more than 0.1 bit
only in the last syllables of some of the words. But, the
decrease was less than 0.05 bit when averaged over all
positions of syllables, and this indicates that the four kind of
tones are used fairly effectively in the Chinese language.
3. Transitions probability of the four tones
As the transitions among the four tones have 16 combinations
(4 kinds in preceding syllable x 4 kinds in following syllable),
5% which corresponds to about their average, is set as base
plane in this figure, and the combination of tones from the
preceding to following syllables are coordinated as array
composed by columns of tones of preceding syllables and
rows of tones of following syllables on this base plane. The
transition probabilitiy above the base plane is shown threedimensionally by the top of upward cones. The vertical axes
are limited up to 10% in order to magnify the difference, as
the value for most combinations stayed within this range.
When the value exceeds 10%, the top of the cone becomes a
flat disk.
3.1. Nouns
In the three syllable words of nouns, as shown in the
upper half of the left column in Figure 2, Tone-1 was frequent
in the first syllables, but, Tone-4 was frequent in the
following syllables. Similar tendency was observed in the
two or four syllable words of nouns.
Transition probability between Tone-2 and Tone-3 were
less than average. Transitions beginning at Tone-1 and
ending at Tone-4, or beginning at Tone-4 and ending at Tone4 in the two, three and four syllable words were much more.
3.2. Other parts of speech
Kind of part of speech also showed characteristic transition of
kind of tone.
1) In the three syllable words of the words of state, as
shown in the lower half of the left column of Figure 2, most of
the 2nd syllables were Tone-1. From 2nd to 3rd syllables,
repeating transitions such as Tone-1+Tone-1, Tone-2+Tone-2,
Ton-3+Tone-3 and Tone-4+Tone-4 were frequent.
These transitions along diagonal line on the base plane
were also observed in the onomatopoeias.
2) In the adjectives, as shown in the right column,
transitions in the two syllable words were similar as those of
the first two syllables in the noun. But, from 1st to 2nd
syllables in the three syllable words, Tone-4+Tone-2, -3 and -4
but not +Tone-1 were frequent. The transitions along the antidiagonal line on the base plane, such as Tone-2+Tone-4 and
Tone-4+Tone-2, from the 2nd to 3rd syllables were noticeable.
Similar tendency was observed in the adjectives.
Tone-5 (light tone or weakened tone) were more than 5%
in the 2nd and 3rd syllables of the three syllable words of
adjectives. Tone-5 was not shown in other figures, because
the percentage was very small.
4. Influence of syllable structure
Preliminary analysis on this database shows that the syllabic
structures and categories of consonants and vowels are
associated with particular kind of tones. This suggests their
relevance to the properties of occurrence frequency and
transition probability of the Chinese four tones obtained in this
statistical analysis.
.
NOUN (16,383 words) TONE-1
40%
1 SYL. WORD
(325 words) 35%
30%
25%
20%
15%
10%
TONE-4
1ST SYL. (325 syls) 2-0.02 bits
25% ALL 2.00 bits
TONE-2
VERB (14,479)
AVERAGE OF
ALL SYL. POSITIONS
(27,714)
TONE-4
TONE-4
30%
25%
20%
15%
10%
1ST SYL.(10,039 syls) 2-0.02 bits
2ND SYL.(10,039 syls) 2-0.06 bits
25% ALL 2.00 bits
ADVERB (1,172)
AVERAGE OF
ALL SYL. POSITIONS
(2,233)
TONE-4
TONE-2
1ST SYL. (5,511 syls) 2-0.03 bits
2ND SYL. (5,511 syls) 2-0.06 bits
3RD SYL. (5,511 syls) 2-0.09 bits
25% ALL 2.00 bits
TONE-4
25%
20%
15%
10%
TONE-3
1 SYL. WORD (183) 2-0.08 bits
2 SYL. WORD (1,816) 2-0.06 bits
3 SYL. WORD (234) 2-0.18 bits
25% ALL 2.00 bits
TONE-2
25%
20%
15%
10%
1 SYL. WORD (68) 2-1.51 bits
2 SYL. WORD (63) 2-1.05 bits
4 SYL. WORD (13) 0.00 bits
25% ALL 2.00 bitss
TONE-2
TONE-3
1ST SYL. (508 syls)
2ND SYL. (508 syls)
3RD SYL. (508 syls)
4TH SYL. (508 syls)
25% ALL 2.00 bits
2-0.06 bits
2-0.01 bits
2-0.02 bits
2-0.13 bits
TONE-2
TONE-3
NOUN (16,383 words) TONE-1
40%
AVERAGE OF
ALL SYL. POSITIONS 35%
(38,968 syllables) 30%
TONE-1
40%
35%
30%
25%
20%
15%
10%
ONOMATOPOEIA (145) TONE-1
40%
AVERAGE OF
ALL SYL. POSITIONS 35%
(249)
30%
TONE-4
TONE-2
TONE-3
NOUN (16,383 words) TONE-1
40%
4 SYL. WORD
(508 words) 35%
30%
25%
20%
15%
TONE-4
10%
TONE-2
TONE-3
TONE-3
NOUN (16,383 words) TONE-1
3 SYL. WORD
40%
(5,511 words) 35%
30%
25%
20%
15%
TONE-4
10%
1 SYL. WORD (1,669) 2-0.06 bits
2 SYL. WORD (24,800) 2-0.07 bits
3 SYL. WORD (1,245) 2-0.15 bits
25% ALL 2.00 bits
TONE-3
TONE-3
NOUN (16,383 words) TONE-1
40%
2 SYL. WORD
(10,039 words) 35%
TONE-1
40%
35%
30%
25%
20%
15%
10%
SET PHRASE (5,262) TONE-1
4 SYL. WORD (5,254) 40%
35%
30%
25%
20%
15%
10%
TONE-4
1ST SYL. (5,254) 2-0.04 bits
2ND SYL. (5,254) 2-0.03 bits
3RD SYL. (5,254) 2-0.05 bits
4TH SYL. (5,254) 2-0.06 bits
25% ALL 2.00 bits
TONE-2
TONE-3
1 SYL. WORD (325 syls)
2 SYL. WORD (20,078 syls)
3 SYL. WORD (16,533 syls)
4 SYL. WORD (2,032 syls)
25% ALL 2.00 bits
TONE-2
2-0.02 bits
2-0.03 bits
2-0.05 bits
2-0.05 bits
Figure 1: Occurrence frequency of the Chinese four tones.
Left, from the top;
noun, one syllable words, two syllable words, three syllable
words and four syllable words for each syllable positions, and
average of all syllable positions.
Right, from the top;
average of all syllable positions for verb, adverb and
onomatopoeias, and four syllable words of set phrase for each
syllable positions.
NOUN (16,383 ws)
3 SYL WORD (5,111 ws)
1ST SYL+2ND SYL
ADJECTIVE (2,856 ws)
2SYL. WORD (2,531 ws)
1ST SYL+2ND SYL
FREQUENCY
FREQUENCY
10%
10%
TONE-4
(1,964 ws)
TONE-3
8%
1+3
2+3
3+3
4+3
(966 ws)
7%
TONE-2
1+2
2+2
3+2
4+2
(1,277 ws)
6%
TONE-1
1+1
2+1
3+1
4+1
(1,198 ws) 2ND SYL.
5%
TONE-1 TONE-2 TONE-3 TONE-4
(1,633 ws) (1,143 ws) (1,068 ws) (1,667 ws)
1ST SYL.
9%
1+4
2+4
3+3
9%
4+4
NOUN (16,383 ws)
3 SYL WORD (5,111 ws)
2ND SYL+3RD SYL
1+4
8%
1+3
2+4
2+3
3+4
3+3
4+3
7%
6%
1+2
2+2
3+2
TONE-4
(1,164 ws)
TONE-3
(401 ws)
4+4
4+2
1+1
2+1
3+1
4+1
TONE-1 TONE-2 TONE-3 TONE-4
(880 ws) . (655 ws) (409 ws) (587 ws)
1ST SYL.
5%
TONE-2
(525 ws)
TONE-1
(281 ws)
2ND SYL.
ADJECTIVE (2,856 ws)
3SYL. WORD (39 ws)
1ST SYL+2ND SYL
FREQUENCY
FREQUENCY
10%
TONE-4
(2,116 ws)
TONE-3
8%
1+3
2+3
3+3
4+3
(934 ws)
7%
TONE-2
1+2
2+2
3+2
4+2
(1,036 ws)
6%
TONE-1
1+1
2+1
3+1
4+1
3RD SYL.
(1,270 ws)
5%
TONE-1 TONE-2 TONE-3 TONE-4
(1,198 ws) (1,277 ws) (966 ws) (1,964 ws)
2ND SYL.
9%
1+4
2+4
3+
4+4
WORD OF STATE (986 ws)
3SYL. WORD (240 ws)
1ST SYL+2ND SYL
1+5
10%
1+4
9%
8%
1+3
TONE-5
(6 ws)
TONE-4
4+4
(12 ws)
TONE-3
4+3
(9 ws)
TONE-2
(7 ws)
2+5
4+5
2+4
2+3
3+3
7%
1+2
6%
2+2
3+2
1+1
2+1
3+1
4+1
5%
TONE-1 TONE-2 TONE-3 TONE-4
(2 ws) .
(5 ws)
(6 ws)
(25 ws)
1ST SYL.
4+2
TONE-1
(4 ws) 2ND SYL.
ADJECTIVE (2,856 ws)
3 SYL WORD (39 ws)
2ND SYL+3RD SYL
FREQUENCY
10%
9%
1+4
2+4
8%
7%
6%
1+2
2+2
3+2
1+1
2+1
3+1
4+1
TONE-1 TONE-2 TONE-3 TONE-4
(119 ws).
(118 ws) (61 ws)
(122 ws)
1ST SYL.
5%
TONE-4
(45 ws)
TONE-3
(25 ws)
4+3
TONE-2
4+2
(39 ws)
TONE-1
(306 ws) 2ND SYL.
3+4
WORD OF STATE (986 ws)
3 SYL WORD (240 ws)
2ND SYL+3RD SYL
FREQUENCY
10%
TONE-4
(46 ws)
TONE-3
8%
1+3
2+3
3+3
4+3
(25 ws)
7%
TONE-2
1+2
2+2
3+2
4+2
(41 ws)
6%
TONE-1
1+1
2+1
3+1
4+1 (305 ws)
5%
3RD SYL.
TONE-1 TONE-2 TONE-3 TONE-4
(306 ws).
(39 ws)
(25 ws)
(45 ws)
2ND SYL.
9%
1+
2+4
3+4
FREQUENCY
4+4
4+4
TONE-5
(10 ws)
TONE-4
9%
1+4
2+4
3+
4+4
5+4
(16 ws)
TONE-3
8%
1+3
2+3
3+3
+3
5+3
(7 ws)
7%
TONE-2
(5 ws)
1+2
2+2
3+2
4+2
5+2
6%
TONE-1
1+1
2+1
3+1
4+1
5+1
5%
(1 ws)
3RD SYL.
TONE-1 TONE-2 TONE-3 TONE-4 TONE-5
(4 ws) .
(7 ws)
(9 ws)
(12 ws) (6 ws)
2ND SYL.
10%
1+5
2+
3+5
4+5
5+5
Figure 2: Transition probability amolng the Chinese four tones.
Left, from the top;
transitions from 1st to 2nd syllables and from 2nd to 3rd
syllables in three syllable words of noun, and the same set of
transitions in three syllable words of word of state.
Right, from the top;
transition from 1st to 2nd syllables in two syllable words, and
transitions from 1st to 2nd and from 2nd to 3rd syllables in
three syllable words of adjective.