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3-1 LA PRIMERA DERIVADA Y LA GRÁFICA DE LA FUNCIÓN

Approximately 50% (Hyman, 2011, p. 198) or as much as 60-70% (Yip, 2002, p. 1) of the world’s spoken languages are tonal, which are largely distributed in Sub-Saharan Africa, south-central Mexico, and East and Southeast Asia (Pike, 1948; Wang, 1967; Yip, 2002; Hyman, 2011), and partly exist in Amazonia and New Guinea (Donohue, 2003; Hyman, 2006; 2011). The definition of what a tonal language is varies among linguists (e.g., Pike, 1948; Gandour, 1978; Yip, 2000; Hyman, 2006, 2011; Maddieson, 2013). For example:

A tone language may be defined as a language having lexically significant, contrastive, but relative pitch on each syllable (Pike, 1948, p. 3).

A tone language is language in which pitch is used to contrast individual lexical items or words (Gandour, 1978, p. 41).

A language is a “tone language” if the pitch of word can change the meaning of the word (Yip, 2000, p. 1).

A language with tone is one in which an indication of pitch enters into the lexical realisation of at least some morphemes (Hyman, 2006, p. 229).

Tone is the term used to describe the use of pitch patterns to distinguish individual words or the grammatical forms of word (Maddieson, 2013).

Similarly, linguists have devoted themselves to addressing the issue of how tones can be represented formally, as shown in Table 1-4; however, consensus has not yet been reached on some essential issues. For example,

● What are the nature of the primitive features of tones?

● What is the tone-bearing unit?

● Are tonal features binary or privative?

● How are different features arranged?

Table 1-4. Comparisons of different models for tonal feature representation

Model Number of feature Number of level Number of

register Register feature Pitch feature Wang, 1967 7 5 1 [high], [central], [mid], [contour], [rising],

[falling], [convert]

Woo, 1969 3 5 1 [high], [low], [modify]

Maran, 1971 2 3 1 [raised F0], [lowered F0] Halle & Stevens, 1971 2 3 1 [stiff], [slack]

Yip, 1980 2 4 2 [upper] [high]

Clements, 1981 2 4 2 [high] [low]

Yip, 1989 2 4 2 [upper] [raised]

Bao, 1990 2 4 2 [stiff] [slack]

Duanmu, 1990 4 9 3 [stiff],[slack] [above],[below] Chang, 1992 3 4/6 2 [stiff] [constricted glottis],

[spread glottis] Hyman, 1993 1/2 9 3 [high], [low] [high], [low]

Fu, 1995 2 5 3 [high], [low] [high], [low]

1.3.1. What are the primitive features of tones?

Many attempts have been made to formulate a set of distinctive features for the underlying tonal representation of Asian tonal languages (e.g., Wang, 1967; Woo, 1969; Yip, 1980, 1989; Bao, 1990; Duanmu, 1990; Chang, 1992; Fu, 1995) and African tonal languages (e.g., Maran, 1971; Halle & Stevens, 1971; Clements, 1981; Hyman, 1993). Nevertheless, the questions remain as to what are the primitive features for tones; how many features are needed for an adequate account, and how many pitch levels and registers can be distinguished? For example, as indicated in Table 1-4, the various models can be essentially classified into one-register (Wang, 1967; Woo, 1969; Halle & Stevens, 1971; Maran, 1971), two-register (Yip, 1980; Clements, 1981; Yip, 1989; Bao, 1990; Chang, 1992), and three-register systems (Duanmu, 1990; Hyman, 1993; Fu, 1995). In the one-register system, tonal features were arranged as part of the feature matrix of vowels while, in the multi-register systems, different features for tones were structured hierarchically, separated from their bearing units on a different tier, and separate feature(s) for register were introduced to encode the articulatory correlation between tonal pitch and segments. Consensus

has not yet been reached on how many contrastive pitch levels are needed (four, five, or nine), and how many registers are distinguished (two or three), although the diversity of tonal systems across linguistic areas may also constrain the development of a unified interpretation.

1.3.2.How are tonal features defined?

The distinctive features have specific phonetic bases for their definitions (Hyman, 1975; Clark & Yallop, 1990); however, different proposals for tonal representations vary in how tonal features can be defined perceptually, acoustically, or by articulation, as discussed below.

1.3.2.1 Perceptual features

Wang (1967), Yip (1980), Duanmu (1990), Hyman (1993), and Fu (1995) adopted the perceptual dimension of pitch to define tonal features in their models; however, their terminologies varied considerably. For example, Yip (1980) used [upper] and [low] while Duanmu (1990) used [above] and [below]. Wang (1967) used [high], [mid], and [central] to account for five pitch levels but used [contour], [falling], [rising], and [convex] to distinguish different shapes of pitch contour. 1.3.2.2 Articulatory features

Articulatory features are used to encode the physiological correlations between tonal and segmental production (Halle & Stevens, 1971; Duanmu, 1990; Bao, 1990; Chang, 1992; Zhu, 2012). For example, Halle and Stevens (1971) used the laryngeal features [stiff] and [slack] to specify three pitch levels associated with three states of vocal cord tension. Nevertheless, no consensus exists on what motivates the physiological correlations between tones and segments. For example, Halle and Stevens (1971) related pitch production with the states of vocal cord tension, and Duanmu (1990) correlated them with the thickness of vocal cord tension. Bao (1990) suggested the muscle activities of vocal cords while Chang (1992) indicated a different status of the glottis. Thus, how tonal features can be defined from the articulatory point of view still remains an open question.

1.3.2.3 Acoustic features

Acoustic features are less frequently used to specify tonal features in the literature, presumably because of the highly variable property of fundamental frequency (F0), the acoustic correlate of pitch. It appears that only Maran (1971, p. 9) adopted [raised F0] and [lowered F0] to account for tones in African languages.

1.3.3.Are tonal features binary or privative?

The distinctive features in phonology are often assigned values to indicate their presence or absence in specific entities. Two different ways have been observed with respect to how tonal features are valued. Most models (e.g., Wang, 1967; Woo, 1969; Yip, 1980, 1989; Clements, 1981; Hyman, 1993; Bao, 1990; Duanmu, 1990; Chang, 1992) considered tonal features as binary, given both values “+” and “-” could be equally active in making tonal contrasts. For example, the

opposition of high and low tones was represented as [+high] or [-high] (Yip, 1980; Hyman, 1993) or [-slack] or [+slack] (Halle & Stevens, 1971; Bao, 1990). Nevertheless, this binary treatment is claimed to be over-generative and inter-determinate (Clements, 1983; Hyman, 1978; Fu, 1995). For example, Duanmu (1995)’s model is regarded able to generate as many as nine contrastive pitch levels, overpredicting the possible maximum of five levels observed cross-linguistically (Wang, 1967).

Alternatively, some other scholars (e.g., Clements, 1985; Hyman, 1978; Fu, 1995) claimed the privative features for a simple and economic explanation, because they considered only the positive value was able to fulfil the linguistic function while the negative value was phonologically inert. For example, Fu (1995) eliminated extraneous negative values in his model. Thus, high tone/register was specified as [high], and low tone/register was specified as [low] in his model while no feature was specified for the neutral tone or register.

The privative approach appears to have an advantage in eliminating redundancy toward an economical representation. Nevertheless, whether features should be doubled-valued or single- valued depends on several factors, for example, whether the tonal system investigated is African or Asian. Further factors include what the inventory of tonal contrasts is and how the feature geometry is constructed.

1.3.4. What is the tone-bearing unit?

The literature has offered different answers to the question of what is the tone-bearing unit (TBU), including the mora (Duanmu, 1990; Hyman, 1993; Chang, 1992; Fu, 1995), the syllabic segment (Woo, 1969; Maran, 1971; Halle & Steven, 1971; Bao, 1990), and the syllable (Wang, 1967; Yip, 1980). The question of what domain a tonal feature is aligned with at the underlying level is not a simple one. It is a problem that may trigger a series of theoretical constraints for an economic and adequate account of tonal representations, in particular,

● How many tones can a TBU take?

● What is the tone-bearing ability of a TBU?

● Why is the existence of contour tones greatly constrained?

● How does a TBU accommodate tonal contour complexity?

● What are the relations among rhyme structure, tonal contour complexity, and the TBU? For example, the moraic theory was proposed to accommodate the relation between rhyme structures and tonal contour complexity (Duanmu, 1990; Hyman, 1993; Chang, 1992; Fu, 1995), which reflected the tone-bearing ability of syllable rhymes, as Duanmu (1990, p.125) asserted,

When the tone-bearing ability is increased, the rime must be lengthened; when the rime is shortened, the tone-bearing ability is reduced.

1.3.5.How are different features arranged?

In the theory of feature geometry, distinctive features are assumed to be structured hierarchically, rather than stored in a simple matrix (McCarthy, 1988; Clements, 1985). In previous tonal models, the features for register and tone are treated in different ways, giving rise to differences in the internal structures of the geometry trees, as shown in Figure 1-1.

Figure 1-1. Comparison of the internal structures of different tonal models.

As indicated in Figure 1-1, the register and tone tend to be formulated either in a parallel or a dominant correlation. Some proposals (Yip, 1980; Bao, 1990; Duanmu, 1990; Fu, 1995) indicated tone and register are parallel, thus the existence of tone is independent of the existence of register. For example, Yip (1980) asserted that register and tone are independent autosegmentally, so the register feature may remain stable while the tone feature changes in a sandhi process of deletion. Alternatively, some proposals (Yip, 1989; Hyman, 1993) treated tone and register as hierarchical, with the register dominating tone. This dominant relation is proposed based on the assumption that register and tone may simultaneously undergo a process, such as spreading. Because multiple instances of spreading are generally prohibited in feature geometry (Clements, 1985), it seems appropriate to require register to dominate tone, and moving a register node means the features for tone have to be moved simultaneously.

As discussed, considerable disagreements can be identified with respect to how tones should be represented. The representability of most existing models may also be challenged by the polydimensional reality of tonal category, as increasingly revealed in cross-linguistic data (see Section 1.4, and this thesis). Thus, conducting a sophisticated phonetic study is imperative for a better understanding of how tones should be better represented abstractly, which is one of the major aims to be achieved in this thesis.