RESEARCH
Headedness in Element Theory: The case for multiple
heads
Phillip Backley
Tohoku Gakuin University, 1-3-1 Tsuchitoi, Aoba-ku, Sendai, 980-8511, JP
backley@mail.tohoku-gakuin.ac.jp
Like distinctive features, elements identify natural classes and model the structure of segments.
But unlike features, they combine asymmetrically in expressions, with head-dependent relations
between elements making a significant contribution to the expressive power of representations.
Most versions of Element Theory follow the general principle that a structural domain—such as
a segmental expression—can have just one head element. In Backley (2011), however, element
structures are permitted to have two heads. Multiple headedness is a consequence of allowing
dual interpretation, where each element has two different phonetic realisations depending on its
head or non-head status. While dual interpretation is better equipped to capture natural classes
and explain phonological processes, its by-product is the need for double-headed expressions,
which present a challenge to element-based theory. It is proposed that the six elements (|I|, |U|,
|A|, |H|, |L|, |ʔ|) naturally form three pairs of opposing (dark vs light) values, each pair being
associated with one of three fundamentals of spoken language: colour, resonance, frequency. It
is then argued that headedness relations refer separately to each fundamental property. So, if
there are three fundamentals in a melodic structure, then there is the potential for up to three
heads in any one expression. The implications of this approach are considered with regard to
segmental markedness and language typology.
Keywords: Element Theory; melodic headedness; marked element combinations; dark versus light
1 Introduction
This paper discusses the nature of headedness in Element Theory (ET; e.g. Harris 1994;
Scheer 1999; Kaye 2000; Backley & Nasukawa 2009a; Cyran 2010), arguing for a view
of headedness which departs from standard assumptions about head-dependent relations
between elements. Element Theory—one of several representational approaches in which
headedness plays a role (van der Hulst & Ritter 1999)—has always distinguished between
head elements and non-head (or dependent) elements, this distinction being just one manifestation
of the asymmetric relations that characterise phonological structure in general
(Anderson & Ewen 1987; van der Hulst 1989).
Elements offer an alternative to distinctive features for describing the internal structure
of segments. Like features, they define natural classes of sounds, which allows them to
express lexical contrasts and to represent the properties that are active in phonological
processes. Unlike features, however, they are associated with acoustic patterns in the
speech signal rather than with properties of articulation. The relevant acoustic patterns
are those that are believed to serve a linguistic function by carrying information about
the identity of morphemes. Most scholars working with elements agree that we need to
recognise six such patterns, and therefore, that there are six elements in the phonological
grammar.1
Some of these elements predate Element Theory itself; for example, the
	1
	For an alternative view of the element set, see Pöchtrager & Kaye (2013).
Glossa general linguistics
a journal of Backley, Phillip. 2017. Headedness in Element Theory: The case
for multiple heads. Glossa: a journal of general linguistics 2(1):
89. 1–17, DOI: https://doi.org/10.5334/gjgl.463
Backley: Headedness in Element TheoryArt. 89, page 2 of 17
elements |A|, |I| and |U| have their origins in early Dependency Phonology (Anderson &
Jones 1974). The remaining elements |H|, |L| and |Ɂ| were first introduced in the early
Government Phonology literature (e.g. Kaye et al. 1985).
Although Element Theory (hereafter ET) has evolved and diversified over time (Backley
2012), current versions of ET agree on at least one point: head-dependency relations
remain integral to element-based representations. In most forms of ET, headedness is a
relational property with scope over a single expression; it identifies one element as the
head of the expression and all other elements as non-heads. The difference between heads
and non-heads is important because it affects the way an expression is phonetically interpreted,
with heads typically making a bigger contribution than non-heads to the overall
phonetic outcome.2
Moreover, the head versus non-head distinction has a linguistic motivation,
in that the two have different functions. Head elements define broad melodic categories;
for example, the class of low vowels is identified by headed |A| (by convention,
head elements are underlined). Meanwhile, dependent elements describe additional properties
that further specify a segment within its broad category; for example, the expression
|A I| represents a low vowel (headed |A|) which is also front (non-headed |I|), i.e. [æ] or
[ɛ]. On this basis, making a distinction in the grammar between headed and non-headed
elements seems to be well motivated.
There are, however, differing views on the nature of this head/non-head asymmetry
and on the way that headedness functions as a structural property. Acknowledging the
diversity that now exists within element-based phonology, this paper focuses on the version
of ET described in Backley (2011). In many respects, this version follows ET conventions:
it uses the standard set of six elements (|I|, |U|, |A|, |H|, |L|, |ʔ|) and it allows each
element to appear in either its headed or non-headed form. Yet in one respect, its use of
headedness departs from the standard view of headedness found in most formulations
of ET. As already noted, headedness is usually seen as a relational property involving all
the elements in an expression: one (head) element dominates the expression while any
number of other (dependent) elements may combine with it. That is, within the domain
of a melodic expression only one element can be a head. In Backley (2011), however,
the distinction between headed and non-headed is treated differently—not as something
which refers to whole expressions but as an inherent property of individual elements. This
allows a compound expression to have more than one head element.
Multiple headedness presents a conceptual challenge not just to the ET model but to any
representational approach that relies on head-dependent asymmetry, since it runs counter
to the tacit assumption that a structural domain (in any part of the grammar) should
have just one head. The aim of this paper is therefore to motivate the need for multiple
headedness in element representations and to show how ET can accommodate this by
rethinking the way elements are organised in relation to one another. The paper is set out
as follows. The next section compares the approach to headedness in Backley (2011) with
the standard view found in most versions of ET. It also introduces typological data which
call for representations containing more than one headed element. Then in Section 3 the
discussion turns to the question of relatedness between elements, focusing on a polar relation
within the element set between dark elements and light elements. Section 4 argues
that multiple headedness may be incorporated into the ET model by assuming the existence
of three fundamental properties which underlie language sound systems and which
determine the size and appearance of the element set. These fundamental properties also
reveal how the element set divides into two natural groupings, light and dark. The discussion
concludes in Section 5 with a summary of the main points.
	2
	See Nasukawa & Backley (2015a) for an alternative view of the roles of heads and dependents in melodic
and prosodic structure.
Backley: Headedness in Element Theory Art. 89, page 3 of 17
2  Two approaches to headedness
Most current versions of ET follow early formulations of the element-based approach (e.g.
Kaye et al. 1985) in assuming that headedness refers to the asymmetry between a head
element and its dependent element(s). This approach sees headedness as a relational concept,
since it captures the relations between elements within the same segmental structure.
It also sees the domain for headedness as being an entire melodic expression. Note
how this view of headedness follows linguistic convention by assuming that each structural
domain has a single head, as in the example structures in (1).
(1) a. [p] |U H ʔ|
[s] |H A|
b. [ɒ] |A U|
[o] |U A|
It has already been pointed out that the headedness properties of an expression can influence
phonetic interpretation. This is because head elements typically show greater acoustic
salience than dependents, so they are relatively prominent when a complex expression
is realised phonetically. Consider, for example, the structures for [p] and [s] in (1a),
which both contain the |H| element. Headed |H| in [s] contributes strong (fortis) frication,
giving [s] a perceptually salient sibilance. By contrast, non-headed |H| in [p] is interpreted
with less phonetic prominence as non-aspirated stop release.
If headedness is related to phonetic interpretation, then it follows that a given element
may have more than one phonetic identity—that is, it has a dual interpretation— depending
on whether it is headed or non-headed. For instance, headed |L| represents voicing
in a voiced obstruent, while non-headed |L| is interpreted as nasal resonance (Nasukawa
2005).3
In the case of the |A| element, headed |A| is associated with the high F1 value that
inheres in low vowels such as [a ɑ æ], whereas non-headed |A| is present in vowels with
a less prominent F1 value such as the mid vowels [e o].
Turning to the version of ET described in Backley (2011), however, we see headedness
taking on a more central role than it does in the standard ET approach just described. Not
only does the idea of dual interpretation apply to all elements, but this is fully exploited
as a means of identifying natural classes and explaining certain phonological patterns. To
illustrate this, Table 1 shows how this alternative form of ET views the main consonantal
characteristics of each element in its headed and non-headed forms.
	3
	Some scholars (e.g. Breit 2013) assert precisely the opposite, i.e. that headed |L| expresses nasality while
non-headed |L| represents obstruent voicing. Whichever way the headedness of |L| is analysed, the fact
remains that this element is thought to have a dual interpretation.
Table 1: Phonological characteristics of headed/non-headed elements in consonants.
phonological category
element acoustic property non-headed headed
|I| high F2 converging with F3 (some) coronals palatals
|U| low frequency energy in F1–F3 velars labials
|A| high F1 converging with F2 (some) coronals uvulars, pharyngeals
|Ɂ| abrupt drop in amplitude stops ejectives, implosives
|H| aperiodic noise obstruents fortis/aspirated obstruents
|L| periodic murmur nasals voiced obstruents
Backley: Headedness in Element TheoryArt. 89, page 4 of 17
In some cases, headed versus non-headed expresses the relation of general category ­versus
specific category. For example, non-headed |Ɂ| identifies the general category of stops while
headed |Ɂ| describes specific kinds of stops, i.e. ejectives and implosives. The same is true
of |H|, where non-headed |H| roughly equates to the general category obstruent while
headed |H| specifies the subset of strong (fortis or aspirated) obstruents. Arguably, |I| also
functions this way if we assume the existence of a general place ­category ­non-peripheral
which includes both coronal and palatal resonance.
On the other hand, headed versus non-headed can also represent two quite distinct
categories that are related primarily by their acoustic attributes. For example, |U| is associated
with a falling formant pattern in which acoustic energy is concentrated at low frequencies.
This pattern is present in labials and in velars, appearing stronger (i.e. showing
a greater modulation of the carrier signal) in headed labials and weaker in non-headed
velars (Backley & Nasukawa 2009b). Acoustic similarity is not the only reason for associating
labials and velars with the same element, however. There is also a phonological
link, in that the two categories are seen to pattern together in some phonological (notably,
diachronic) processes (Backley 2011: 79). In |A| and |L| too, the headed and non-headed
forms of each element represent categories which, at first sight, appear to be unrelated.
For example, there is no obvious link between nasality (non-headed |L|) and obstruent
voicing (headed |L|) in terms of articulation, but there is acoustic and phonological motivation
for representing them using the same element (Nasukawa 2005).
What emerges from this approach to headedness is the idea that category distinctions can
be made by referring to just the head/non-head status of a single element. For instance, a
consonant will be a palatal if it contains headed |I|, no matter which dependent elements
|I| is associated with. Similarly, a vowel will be categorised as low if it contains headed
|A|, regardless of which other elements are present in its structure. This suggests the need
to review our assumptions regarding the domain for headedness—from being a property
of whole expressions to being a property of individual elements. The examples in Table 2
confirm this by showing the representation of glides as simplex melodic expressions. Note
how the phonetic realisation of a lone element changes depending on whether it appears
in its headed or non-headed form.
One consequence of treating headedness as a property of individual elements, rather
than of whole expressions, is that it allows a complex expression to have more than
one head. For example, according to Table 1 labial consonants have headed |U| while
fortis/aspirated obstruents have headed |H|. But there are many languages, including
English, in which these two properties combine to form an aspirated labial stop [pʰ].
The expectation is that, in the model of ET described in Backley (2011), [pʰ] should be
represented by the double-headed expression |U H Ɂ|, where headed |U| contributes
labiality and headed |H| contributes aspiration. And indeed, this is what the model
claims. The problem, however, is that this structure breaks with the conventions of
ET with respect to headedness, since ET has always assumed that a melodic expression
can have only one head element. Note that [pʰ] is not an isolated case; it is easy
to conceive of other segments which require double-headed structures too, including
those in (2).
Table 2: Glides as simplex representations.
|I| |U| |A|
non-headed [ɾ] [ɰ] [ɹ]
headed [j] [w] [r], [ɽ]
Backley: Headedness in Element Theory Art. 89, page 5 of 17
(2) a. [ʃ] |I A H| voiceless palato-alveolar sibilant fricative
(|I A| = palatal resonance; |H| = fortis frication)
b. [b] |Ɂ U L| fully voiced labial stop
(|Ɂ| = occlusion; |U| = labial resonance; |L| = obstruent
voicing)
c. [qʰ] |A U H Ɂ| aspirated uvular stop
(|Ɂ| = occlusion; |A U| = uvular resonance; |H| =
­aspiration)
For this version of ET, then, the challenge is to explain how the use of double-headed
expressions is possible within a framework which otherwise adheres to the general principle
of one head per structural domain. One approach to this question is described in the
following sections, where it is proposed that ET’s six elements be organised into three pairs.
The claim is that each pair is made up of two naturally opposed elements, and that these
opposing properties together form a headedness domain. This allows ­head-dependency
to remain as a strictly binary relation, and it also allows for the possibility of multiple
­headedness in a single melodic expression.
3  Dark versus light elements
In standard versions of ET, the six elements all have autonomous status in the grammar;
this gives each element the freedom to participate in distributional patterns and phonological
processes independently of the others. Having said that, many ET practitioners
also follow the convention of dividing the set of elements into the two groups shown in
Table 3. This division is based on the elements’ phonetic characteristics and phonological
distribution.
This split between vocalic and consonantal elements reflects a difference in the kinds of
acoustic properties associated with each group. The resonance elements |A|, |I| and |U| are
associated with formant structure patterns and represent place properties in both vowels
and consonants. For example, headed |U| is interpreted as rounding in vowels and as
labiality in consonants.4
By contrast, the laryngeal/source elements |H|, |L| and |ʔ| refer to
	4
	The elements are described here in familiar articulatory terms such as labial, round, high and voiceless. It will
be recalled, however, that in the ET tradition elements are associated not with properties of articulation but
with acoustic patterns in the speech signal; for example, |A| is associated with high F1, |I| with high F2, and
|U| with lowered F1 and F2. Strictly speaking, therefore, labels such as labial and round do not describe the
identifying properties of elements; rather, they describe the articulatory gestures that speakers adopt when
trying to reproduce the relevant acoustic pattern for a given element.
Table 3: Vocalic and consonantal elements.
distribution acoustic properties
elements
vocalic resonance |I|, |U|, |A|
consonantal laryngeal/source |H|, |L|, |ʔ|
Table 4: Dark and light elements.
perceptual quality acoustic energy
elements
dark low frequency |A|, |U|, |L|
light high frequency/dispersed |I|, |H|, |ʔ|
Backley: Headedness in Element TheoryArt. 89, page 6 of 17
other aspects of the speech signal such as periodicity. They represent manner and laryngeal
properties, e.g. headed |H| is present in voiceless obstruents and in high tone vowels.
However, there is also another way of dividing the element set along phonetic lines.
This refers to the difference between dark and light elements (Backley 2011: 195), as
shown in Table 4.
The dark elements |A|, |U| and |L| share a tendency for their acoustic energy to be
concentrated at lower frequencies. By contrast, the light elements |I|, |H| and |ʔ| show a
different pattern in which low-frequency energy is either less prominent or absent altogether;
instead, energy may be concentrated at higher frequencies or it may be distributed
more evenly across the spectral range. From a listener’s perspective, the general impression
is of a difference in timbre or sound quality: dark elements sound warm and mellow,
whereas light elements sound bright, thin, and in some cases hissy. The difference can
be illustrated by comparing the dark and clear realisations of l in English. Dark-l gets its
dark character from the presence of |U| in its structure (Backley 2011: 175), where |U|
is ­non-headed and contributes velar resonance and a back quality. In contrast, clear-l has
light features that derive from the presence of |I|, which in some languages represents
coronal resonance resulting from a front, apical articulation.5
The terms dark and light do not refer to formal linguistic categories. Nor do they identify
structural units such as class nodes, which group together elements showing similar
behaviour. Moreover, they have no precise definition—it is difficult to capture their characteristics
other than in relative or impressionistic terms. (In this sense, a suitable parallel
might be the distinction between warm colours and cold colours in the visual dimension.)
Nevertheless, the notion of dark-light can still be useful for describing sound patterns. For
example, Jakobson et al. (1952) refer to dark and light in the description of the acoustic
features [grave] and [acute], stating that “[t]wo phonemes contrasted as grave and acute
(e.g. /u/ vs. /y/, or /ɨ/ vs. /i/, or /f/ vs. /s/) are easily identified as dark and light respectively
by responsive subjects” (Jakobson, Fant & Halle 1952: 32). This suggests that dark
and light may play a role in speech perception, perhaps by helping listeners to make broad
perceptual distinctions before they try to discriminate between specific sound categories.
If the split between dark and light is relevant to speech perception, then we might
expect it to have a bearing on diachronic phonology, given that perceptual factors are
thought to be instrumental in triggering certain sound changes (e.g. Ohala 1981, 1993).
In fact, the historical phonology of the Germanic languages provides illustrations of how
a sound change can be sensitive to the dark-light distinction. The most well-known case
is that of i-mutation (Campbell 1959; Lass 1994) in Germanic and early Old English,
where back vowels were fronted and low vowels were raised before [i]/[j] later in the
word. Both these changes involve a shift from a dark to a lighter vowel, triggered by the
presence of the light element |I| in the following [i]/[j]. The effects of i-mutation are preserved
in modern English dark-light pairs such as full-fill, man-men, tooth-teeth, tale (= OE
[tɑlu])-tell. Another dark-light process is the shift [ɑ]→[æ] in pre-Old English known as
First Fronting or Anglo-Frisian Brightening (Campbell 1959). This change occurred spontaneously,
but was blocked by a following w, a nasal cluster, or a back vowel in the next
syllable. In structural terms these three blocking environments appear to have nothing in
common, and therefore do not make a natural grouping. In perceptual terms, however,
they are brought together by the fact that they all have a dark acoustic quality—dark |U|
in w, dark |L| in nasals, and dark |A| or |U| in back vowels—which evidently prevented
dark [ɑ] from being fronted to light [æ].
	5
	In Backley (2011: 72ff.) it is proposed that coronal consonants are represented by |I| in some languages and
by |A| in other languages, depending on their phonological behaviour (see Table 1).
Backley: Headedness in Element Theory Art. 89, page 7 of 17
Aside from its influence on historical change, the dark-light distinction is relevant to
melodic descriptions because it plays a role in determining how elements combine in
expressions (Backley & Nasukawa forthcoming). It also relates to the present discussion
because it reveals something about the nature of element headedness. In Section 4 it will
be described how the distinction between dark and light can ensure that melodic structure
maintains head-dependent relations that are strictly binary, i.e. a maximum of one
dependent per head.
Before turning to multiple headedness, however, let us consider the motivation for distinguishing
between dark and light elements by focusing on element combinations. In
principle, any element is free to combine with any other element within the same expression.
In practice, however, some combinations are more marked (e.g. cross-linguistically
rarer) than others. The clearest cases of marked combinations are those in (3).
(3) a. |U| + |I| (formant lowering + high F2)
b. |A| + |ʔ| (high F1 + reduction in acoustic energy)
c. |L| + |H| (low fundamental frequency + high fundamental frequency)
Their marked status derives from the fact that they involve opposing or contradictory
acoustic properties, as described on the right-hand side in (3). In (3a) |I| raises the frequency
of F2, while |U| introduces a lowering of all formants including F2. In (3b) |A|
increases overall resonance by raising F1, while |ʔ| produces a rapid drop in acoustic
energy causing a momentary loss of resonance. In (3c) |L| concentrates energy at low
frequencies while |H| does so at higher frequencies. When these conflicting acoustic cues
co-occur in a single segment, it results in an expression that can be difficult for speakers
to produce and for listeners to perceive, since the relevant cues tend to mask one another.
Not surprisingly, then, many languages avoid such combinations in the interests of communicative
efficiency. To reflect their opposing properties, the element combinations in
(3) have been dubbed antagonistic pairs (Backley 2011; van der Hulst 2015).6
Antagonistic pairs influence the shape of sound inventories by identifying certain segmental
categories as being universally disfavoured. Having said that, there is no outright
ban on their appearance in the grammar (Backley 2011: 195). For example, the categories
in Table 5 function contrastively in at least some languages, even though they contain
antagonistic element pairs.
Notice that these categories are all relatively uncommon, their marked status deriving
from the fact that they contain antagonistic element combinations. Compare the front
vowels [y] |I U| and [e] |I A|, for instance. Both have the same number of elements in their
structure, yet [y] is cross-linguistically much rarer than [e]; the difference comes down
to the presence or absence of an antagonistic relation—in this case, between |I| and |U|.
As another example, consider the combination of |L| and |H| in consonants. Individually,
	6
	Expressing melodic properties in terms of opposing pairs is by no means a new idea: acoustic features in the
Jakobsonian tradition show a similar polarity, e.g. [grave] vs. [acute], [compact] vs. [diffuse].
Table 5: Antagonistic element pairs.
antagonistic pair melodic category example
|U| + |I| front rounded vowels [y] |I U|
|A| + |ʔ| uvular stops [q] |U A H ʔ|
|L| + |H| voiced aspirated stops [gʱ] |U L H ʔ|
Backley: Headedness in Element TheoryArt. 89, page 8 of 17
each refers to an unmarked category: non-headed |L| represents nasality and non-headed
|H| represents frication, as shown in (4a). When |L| and |H| combine, however, they create
categories such as those in (4b), which are all marked to varying degrees.7
(4) a. |L U ʔ| [m] nasals
|H U| [f]~[ɸ]8
plain fricatives
b. |L H U| [v]~[ß] voiced fricatives
|L H U ʔ| [bʱ] voiced aspirated (breathy voiced) stops
|L H U ʔ| [m̥ ] voiceless nasals9
It is evident that the relationships between |I| and |U|, between |A| and |ʔ|, and between
|L| and |H| are in some sense special and require explanation. What distinguishes them
from other relations in melodic structure is the fact that they involve elements which are
not merely different from each other (i.e. contrastive), but rather, which express contrasting
values with respect to the same basic property. Following Backley (2011), I refer to
these basic properties or fundamentals using the informal labels colour, resonance and
frequency.10
The claim is that colour, resonance and frequency are three fundamental aspects of spoken
language that contribute to the overall identity of speech sounds. In phonetic terms
these are gradient properties; but in linguistic terms only their polar values are relevant
to sound contrasts. In the case of frequency, for example, the presence of high-frequency
energy and low-frequency energy are both linguistically significant, whereas other values
(e.g. mid-frequency, variable frequency) are not. The grammar must therefore have the
means of referring to low and high frequency as independent melodic properties—which
is the precisely role of the elements |L| and |H|.
The same applies to colour and resonance. In its broadest sense colour refers to the timbre
or quality of a physical sound independently of other acoustic properties such as pitch
and intensity. However, when it comes to characterising language sounds, only two values
for colour are relevant: dark (|U|) and light (|I|). The difference between them forms
the basis for several broad distinctions within melodic systems such as the split between
back (|U|) vowels and front (|I|) vowels and the division between peripheral (|U|) consonants
and coronal (|I|) consonants (Dixon 1980: 139; Backley & Nasukawa 2009b). Again,
|U| and |I| mark the two extreme and opposing values of a single fundamental property.
Finally, resonance is another aspect of spoken language that is relevant to language only
in terms of its polar values. The |A| element is associated with a peak of resonance and is
present in sounds of high sonority such as low vowels, while its opposing value |ʔ| marks
a sudden drop in acoustic energy and a momentary loss of resonance. Speakers create this
break in resonance by interrupting the airflow, which causes vocal fold vibration to cease.
It is therefore associated with the hold phase of stops.
It has already been suggested that the division between dark and light may play a role
in speech perception. And this idea is supported by the fact that it functions as a cue to
the location of prosodic and morphological boundaries (Nasukawa & Backley 2015b). In
general, there is a tendency for light elements to appear at the left boundary of a prosodic
	7
	That is, voiced fricatives are marked relative to voiceless fricatives, voiced aspirated stops are marked relative
to voiced unaspirated stops, and voiceless nasals are marked relative to spontaneously voiced nasals.
	8
	On the distinction between bilabial and labiodental place, see Backley (2011: 98).
	9
	The status and typology of voiceless nasals is discussed in Bhaskararao & Ladefoged (1991).
	10
	Van der Hulst (2015: 155) refers to the same three fundamentals as “phonetic dimensions”, which he labels
place, manner and laryngeal, respectively. These terms align with the articulatory classes of sub-segmental
organisation employed in his Radical CV Phonology model.
Backley: Headedness in Element Theory Art. 89, page 9 of 17
domain; this allows listeners to use them as cues to the onset of a syllable or the beginning
of a word domain. For example, stops (with light |ʔ|) typically occupy onsets rather than
codas, as do palatals such as [ʃ] and [ʤ] (with light |I|). Obstruents (with light |H|) are
also favoured in onsets and at the left edge of a word. By contrast, dark elements naturally
occur non-initially. In many languages such as Japanese, nasals (with dark |L|) function as
the definitive (or the only) coda consonant, while effects such as consonant velarisation
(involving dark |U|) tend to occur domain-finally (e.g. call [kɔːɫ], filled [fɪʊd] in varieties
of British English). And low/non-high vowels (with |A|) are associated exclusively with
the syllable nucleus (cf. high vowels, which frequently have onset (glide) realisations).
Given that dark and light elements have differing patterns of distribution, it is reasonable
to expect listeners to exploit these differences in order to locate syllable domains—and
then, in order to segment the speech stream into word-sized chunks.
The difference between dark and light is also relevant to the description of certain phonological
patterns. In element compounds there is a tendency for dark elements to combine
with other dark elements, while light elements prefer to combine with light. This is
evident from the way languages use melodic enhancement to increase the acoustic prominence
of segments. The purpose of enhancement is to make segments more distinctive or
salient. So, to enhance the salience of a light segment (i.e. a segment consisting mainly
of light elements), a language will typically add another light property. This occurs in
Navajo, where the syllable onset supports a contrast between the dark glide [ɰ] and the
light glide [j]. To increase the perceptibility of this contrast, Navajo speakers have the
option of reinterpreting [j] as a fricative [ʝ] (Hoijer 1945): in element terms, the palatal
glide [j] represented by |I| is enhanced by the addition of another light element |H| to
become a palatal fricative |I H|.11
Further arguments in support of the division between dark and light elements can be
found in Backley (2011) and van der Hulst (2015). What concerns the present discussion
is the way in which the dark-light division can contribute to our understanding of headedness
relations in compound element structures. This is the focus of the next section.
4  Multiple headedness
It has already been suggested that a special relation holds between the elements in an antagonistic
pair because they both refer to the same fundamental property—colour, resonance
or frequency, as shown in Table 6. For example, |U| and |I| express opposing (dark versus
light) values, but the fact that they both refer to the same fundamental means that they are
related to each other in a way that, say, |U| and |A| are not: the relation between |U| and
|I| is contrastive and polar, whereas the relation between |U| and |A| is merely contrastive.
This section shows how this difference is relevant to the issue of headedness, where headedness
encodes the relative prominence of an element when two elements are combined.
	11
	By contrast, we do not expect to find languages enhancing |I| by adding, say, the nasal element |L| ­(resulting
in a palatal nasal [ɲ]). This can be ruled on the grounds that |I| is light whereas |L| is dark.
Table 6: Three fundamentals of spoken language.
dark light
fundamental value element value element
colour dark |U| vs. light |I|
resonance resonant |A| vs. non-resonant |ʔ|
frequency low |L| vs. high |H|
Backley: Headedness in Element TheoryArt. 89, page 10 of 17
(5) expression salient property
a. |U A| [o] colour
|U A| [ɔ]~[ɒ] resonance
b. |U H| [v]~[ß] colour
|U H| [x] frequency
Consider the examples in (5a), both of which combine the colour element |U| with the
resonance element |A|. Following the general assumption that concatenation is always
asymmetric, this combination may take one of two possible forms: either the |U|-headed
expression |U A| or the |A|-headed expression |U A|. In |U A| colour is more salient than
resonance because the head element |U| refers to the colour fundamental, while in |U A|
resonance is stronger than colour because the head element |A| refers to the resonance
fundamental. Similarly, in (5b) there are two options for making a compound of |U| and
|H|: in |U H| colour dominates the entire expression (again, because |U| is a colour element),
while in |U H| frequency is more salient because the head element |H| refers to
the frequency fundamental. In the latter case, headed |H| is associated with voicelessness
(aperiodic energy) in the acoustic signal, giving a voiceless/fortis fricative [x], while
the velar resonance in [x] comes from |U|. Note that velar resonance is represented by
­non-headed |U| whereas labial resonance in [v]~[ß] (see footnote 8) comes from headed
|U| (Backley & Nasukawa 2009b).
As discussed in Section 2, the convention in standard versions of ET is to isolate one
element as the head of an entire expression. Alternatively, however, headedness could be
viewed as the property of a fundamental—colour, resonance, or frequency—and we could
require every fundamental in a representation to have a head. In this way, contrastiveness
would derive from whether each fundamental is dark-headed or light-headed, as illustrated
in (6) and (7). In fact, it will be argued that this is the only head-dependent relation
that is relevant to melodic structure. This approach to headedness means that melodic
structure contains two kinds of information, as shown in (6): it states which elements are
present in an expression, and in addition, it states whether the fundamental associated
with each of those elements is dark-headed or light-headed.
(6) a. [o] b. [ɒ] c. [x]
colour |U|, dark head |U|, light head |U|, light head
resonance |A|, light head |A|, dark head – –
frequency – – – – |H|, light head
structure |U A| |U A| |U H|
The vowel [o] in (6a) is specified as containing |U| and as having dark-headed colour.
Since the dark value for the colour fundamental is |U| (see Table 6), and colour is specified
as being dark-headed in this expression, it follows that [o] must have headed |U| in
its structure. This is realised as acoustic prominence, which comes in the form of stronger,
more salient acoustic cues. [o] is also specified as containing |A| and as having lightheaded
resonance. Given that the light value for the resonance fundamental is |ʔ|, and
that the element |ʔ| is not present in [o], it follows that resonance cannot be interpreted
as a headed property in this expression. The dark resonance element |A| which is present
must therefore be realised in its dependent form and the overall structure has the shape
|U A|. The structures |U A| (for [ɒ]) and |U H| (for [x]) are derived in the same way.
The following paragraphs show how this approach to headedness can help explain why
­languages usually avoid certain element combinations.
Backley: Headedness in Element Theory Art. 89, page 11 of 17
Assigning head or dependent status to a fundamental, rather than to an individual
­element, has two consequences. First, if a complex expression refers to more than one
fundamental in its structure, then it should be possible for it to have more than one head.
Second, if an expression contains both the elements of an antagonistic pair, only one of
those elements can be headed, e.g. |L H| and |L H| are possible but |L H| is not. Each of
these outcomes is now considered in turn. The first says that, in principle, an expression
may have up to three heads. This is because it has a structure which may contain at least
one colour element, at least one resonance element and at least one frequency element,
with each fundamental being independently specified as dark-headed or light-headed.12
An example of a structure with two head elements is given in (7c).
(7) a. [ɒ] b. [x] c. [χ]
colour |U|, light head |U|, light head |U|, light head
resonance |A|, dark head – – |A|, dark head
frequency – – |H|, light head |H|, light head
structure |U A| |U H| |U A H|
(7a) (repeated from (6b)) shows the lexical structure for [ɒ], which has a headed resonance
element |A|. Then (7b) (repeated from (6c)) shows the structure for the fortis velar
fricative [x], which has a headed frequency element |H|. Now consider the uvular fricative
[χ] in (11c).13
As a fortis obstruent, [χ] contains the headed frequency element |H|,
and as a uvular it has the headed place specification |U A| (Backley (2011: 98ff.). The
result is a double-headed structure |U A H|, in which the two head elements are permitted
to coexist because they belong to different fundamentals. Multiple headedness of this kind
is made possible by the fact that each fundamental has autonomous status; that is, each
constitutes an independent structural unit and a separate domain for headedness.
The examples in (8) and (9) further illustrate how contrasts are expressed using the
proposed system of headedness.
(8) a. [u] b. [ʊ] c. [ø]
colour |U|, dark head |U|, light head |I|, |U|, light head
resonance – – – – |A|, light head
frequency – – – – – –
structure |U| |U| |I U A|
The difference between (8a) and (8b) is relevant in languages that have vowel contrasts
based on the difference between tense and lax. In (8a) the only specified element is |U|,
the dark realisation of the colour fundamental; and because (8a) is also specified as having
dark-headed colour, |U| appears in its headed form |U| and is realised as tense [u].
(8b) has the same element |U|, but the colour fundamental is now marked as having a
light head. The structure contains no |I| element (i.e. no light realisation of colour), so
colour cannot be interpreted here as a headed property. The colour element |U| therefore
appears in its dependent form and is realised as lax [ʊ]. In (8c) both colour elements are
present, but because the expression is specified as having light-headed colour it is |I|
which is headed, giving |I U A| for the front vowel [ø].
	12
	While triple-headed structures are grammatically possible, most melodic contrasts are expressed using
structures that are either non-headed, single-headed or double-headed.
	13
	ET has always maintained that any element should be able to appear in both consonant and vowel
­expressions. In (7a) the element combination |U A| is interpreted as the low vowel [ɒ] in a syllable nucleus
and as uvular resonance/place in a syllable onset—see (2).
Backley: Headedness in Element TheoryArt. 89, page 12 of 17
The same principles allow us to derive the non-headed consonant expressions in (9a)
and (9b): |I A| for (clear) [l] and |I L ʔ|14
for [n], respectively.
(9) a. [l] b. [n] c. [d]
colour |I|, dark head |I|, dark head |I|, dark head
resonance |A|, light head |ʔ|, dark head |ʔ|, dark head
frequency – – |L|, light head |L|,|H|, dark head
structure |I A| |I L ʔ| |I L H ʔ|
(9c) shows the representation for [d] in languages such as French, where obstruent
voicing functions as a marked property.15
The expression |I L H ʔ| contains the two frequency
elements |L| and |H|, and because the frequency fundamental is specified here
as ­dark-headed, |L| appears in its headed form |L| and is realised as obstruent voicing
­(Nasukawa 2005) (cf. dependent |L| as nasality in (9b)).
As already mentioned, the second consequence of assigning head or dependent status
to a fundamental is that, in an expression containing antagonistic elements, only one of
those elements can be a head. This is because each fundamental is specified lexically as
being either dark-headed or light-headed—it cannot be both. So, a structure ought to be
ill-formed if it contains the two heads |U| and |I|, or the two heads |A| and |ʔ|, or the
two heads |L| and |H|. To help determine whether this is really the case, (10) lists the
­phonological categories that are usually associated with these headed elements.
(10) a. colour |U| back rounded Vs, labial Cs
|I| front Vs, palatal Cs
b. resonance |A| low Vs, uvular Cs, pharyngeal Cs
|ʔ| ejective Cs, implosive Cs
c. frequency |L| voiced obstruent Cs
|H| voiceless/aspirated obstruent Cs
In general, it seems that languages avoid combining antagonistic elements if the two
elements in question are both heads. The expressions resulting from such combinations
rarely function as contrastive categories, and when they do occur in languages, they are
highly marked. Beginning with |U|+|I|, it is surprising that any language should make
use of a vowel category that combines the back quality of |U| with the front quality of |I|.
In articulatory terms back and front are clearly incompatible; and in acoustic terms too
there is a conflict between the formant lowering associated with |U| and the raising of
F2 associated with |I|. Even the well-known case of high vowel contrasts in Norwegian is
expressible without the need for double-headed representations (Backley 2011: 199), as
shown in (11).
(11) Norwegian (Backley 2011: 199)
do [du] ‘toilet’ |U| back, protruded lips
du [dʉ] ‘you (sg.)’ |U I| fronted, compressed lips
dy [dy] ‘forbear!’ |U I| front, protruded lips
ti [ti] ‘ten’ |I| front, spread lips
	14
	In languages where nasals pattern with obstruent stops, |ʔ| is present in both categories. However, there
are also languages in which nasals behave as continuants, in which case they presumably lack |ʔ|. For
­discussion, see Botma (2004) and Mielke (2005).
	15
	On the issue of laryngeal realism, see Honeybone (2005) and references therein.
Backley: Headedness in Element Theory Art. 89, page 13 of 17
[y] and [ʉ] are both round and front(ed), so each must be represented by a combination
of |U| and |I|. But they differ in the relative prominence of each element. The phonetic
characteristics of [y] suggest that this is, in effect, a front vowel i (headed |I|) with additional
rounding (dependent |U|), resulting in the structure |U I|. By contrast, [ʉ] has a
different lip shape and a weaker palatal quality which identify it as a back rounded vowel
u (headed |U|) with some degree of additional fronting (dependent |I|). For the reasons
already stated, the marked combination of headed |U| and headed |I| is avoided in the
vowel system of Norwegian—and perhaps, universally.
The same applies to consonant systems, where it is rare to find headed |U| (labial resonance)
and headed |I| (palatal) in the same expression. Each may function independently as
a secondary articulation, producing a labialised or palatalised consonant; but significantly,
there is a strong tendency for labialisation and palatalisation to target coronals (e.g. [tʷ nʲ])
and velars (e.g. [gʷ kʲ]) rather than palatals (e.g. [ʧʷ ʒʷ]) or labials (e.g. [bʲ mʲ]). This
bias appears to be based on whether the target segment has a headed or non-headed place
property. Coronals (|I|) and velars (|U|) both have a place element that is non-headed, so
they readily acquire headed |I| or |U| as a secondary place property. By contrast, palatals
(|I|) and labials (|U|) already have a headed colour element, and these do not easily
combine with another headed |I| or |U|. Consequently, labials rarely undergo palatalisation
and palatals rarely undergo labialisation. Note that, although palatalised labials are
reported in a minority of languages (e.g. Scots Gaelic, Russian), their status as singletons
(cf. ­consonant-glide sequences, for instance) is open to question (Gussmann 1992).
Like |U|+|I|, the antagonistic combination |A|+|ʔ| involves a conflict between opposing
physical properties. In the case of |A|+|ʔ|, the relevant property is resonance. While all
sonorant sounds produce resonance—that is, they allow air in the vocal tract to vibrate naturally
at certain frequencies—it is in the low and mid vowels (containing |A|) that vocal tract
resonance is most easily perceived. By contrast, oral stops (with |ʔ|) display very low audible
resonance: they have a hold phase during which airflow is interrupted, causing acoustic
energy to drop sharply and vocal fold vibration to cease. By removing the sound source in
this way, the resonance frequencies of the vocal tract become inaudible. The acoustic cues
for |A| and |ʔ| are therefore in opposition, and this can affect their ability to combine.
If |A| and |ʔ| are both in their weak, non-headed form then they can freely co-occur.
For example, in languages such as English where coronals are represented by |A|,16
the
coronal stop [t] has the representation |A H ʔ|. Once headedness is introduced into the
­structure, however, the outcome is always a more marked expression (Backley 2011: 196):
the categories in (12b), with headed |ʔ|17
or headed |A|, have a much narrower distribution
cross-linguistically than the plain stop in (12a), while those in (12c) are extremely
rare—only a handful of possible examples have been reported.
(12) a. non-headed [t] |A H ʔ| coronal stop
b. single-headed [ʡ] |A H ʔ| pharyngeal stop
[tʼ] |A H ʔ| ejective coronal stop
c. double-headed [ʡ’] |A H ʔ| pharyngeal ejective stop
[ʛ] |A U L ʔ| uvular implosive stop
	16
	There is a typological split between languages in which coronal resonance is represented by |A| (e.g.
­English) and languages where |I| represents coronal resonance (e.g. Japanese). The choice of |A| or |I|
depends more on the phonological behaviour of the consonant in question than on its acoustic properties.
For a discussion of |A| and/or |I| in coronal consonants, see Backley (2011: 72ff.) and footnote 5.
	17
	When an element is headed, its acoustic properties show greater prominence in the overall expression.
Headed |Ɂ| in ejectives and implosives corresponds to the prolonged and more prominent hold phase that
predominates in these sounds.
Backley: Headedness in Element TheoryArt. 89, page 14 of 17
The rarity of the categories in (12c) reflects the anomalous nature of their double-headed
structures. If headedness increases the prominence of a fundamental, then we can express
this prominence in one of two ways, i.e. by strengthening either its dark value or its
light value. There is, however, nothing to be gained from strengthening both values in
the same expression because their respective acoustic cues are in conflict—the increased
prominence of one set of cues will be masked by the increased prominence of the opposing
set of cues. Applying this to the resonance fundamental, it rules out a combination
of headed |A| and headed |ʔ| on perceptual grounds. It is also supports the claim that
melodic ­head-dependency refers to fundamentals (colour, resonance, frequency) and not
to individual elements.
Finally, the antagonistic combination |L|+|H| is analysed in a similar way to |U|+|I|
and |A|+|ʔ|. It has already been shown that |L| and |H| mark the opposing (dark versus
light) values of the frequency fundamental. This suggests that listeners pay attention to
changes in the distribution of acoustic energy when they are decoding running speech,
focusing on points of low frequency (in nasals, voiced stops and low-tone vowels, all
containing |L|) and points of high frequency (in fricatives, voiceless stops, and high-tone
­vowels, all containing |H|). So again, there is a polar relation between the acoustic cues
for |L| and those for |H|, and this affects their ability to combine. This is illustrated in
(13), where all the categories are marked to varying degrees. They owe their marked status
to the co-occurrence of |L| and |H|.
(13) marked (|L|+|H|) example cf. less marked (|L| or |H|)
voiced fricative [ʒ] |A I H L| plain fricative [ʃ] |A I H|
breathy voiced stop [bʱ] |U H L ʔ| voiced stop [b] |U L ʔ|
voiceless nasal [n̥] |A H L ʔ| nasal [n] |A L ʔ|
aspirated nasal [m͈ ] |U H L ʔ| nasal [m] |U L ʔ|
Note that, in the case of |L|+|H|, it is unclear as to whether any languages allow |L| and
|H| to co-exist when both are heads. Should such a combination be found, the ­category
in question would be expected to show the highly unusual behaviour of patterning with
fully voiced obstruents (with |L|) and also with voiceless aspirates (with |H|). In terms
of markedness this would place it alongside other highly marked categories that are
­(tentatively) associated with a double-headed antagonistic structure, e.g. palatalised labials
with |U|+|I| and uvular implosives with |A U|+|ʔ|.
5 Conclusion
This paper contributes to the ongoing debate on the issue of headedness in ET by challenging
the tacit assumption that complex melodic expressions can have just one head
element. In fact, it argues for an approach to segmental representation in which there is a
need to posit element structures containing two heads. The system of element representation
described in Backley (2011) views headedness as a property of fundamentals rather
than of whole melodic expressions. It also sees dual interpretation as the norm—that is,
a single element has two different phonetic interpretations depending on whether it is
headed or non-headed. And with dual interpretation comes multiple headedness: to represent
certain segmental categories—even some unmarked categories which are common
to many of the world’s languages—it is necessary for the grammar to permit element
structures with two headed elements.
Double headedness presents a conceptual challenge to standard theories of segmental
structure, and indeed, to theories of linguistic structure in general. It therefore requires
justification on at least two levels. First, the need for double headedness must be made
Backley: Headedness in Element Theory Art. 89, page 15 of 17
clear, by presenting language data that can best (or can only) be accounted for by
­appealing to double headedness. Second, the way double headedness is implemented in
the grammar must be consistent with existing principles of structural and grammatical
well-formedness. Regarding this second point, it has been argued here that double headedness
is incorporated into the ET grammar by organising the element set into three pairs
of opposing elements, with each pair marking out the polar values of three fundamental
properties of spoken language: colour, resonance, and frequency. Within each pair, one
element displays the characteristics of a light element and the other the characteristics of
a dark element. Moreover, the distinction between light and dark serves as the domain for
headedness; that is, in a given expression each fundamental property is specified as being
either light- or dark-headed.
Because melodic structure recognises three fundamental properties, there is the potential
for up to three heads in one element expression (though in practice, most languages
express all the segmental categories they need by using just non-headed, single-headed
and double-headed structures). This is possible because each fundamental has autonomous
status—it is individually specified as dark-headed or light-headed. While this approach to
headedness allows the two elements in an opposing pair to co-occur in the same expression,
it rules out the possibility of both being heads. That is, the double-headed combinations
|U|+|I|, |A|+|ʔ|, and |L|+|H| are, in principle, disallowed. Whether this is
universally the case or not is an empirical question which can only be answered by analysing
more language data. For now, it seems prudent to settle for the claim that such
combinations may be unattested, but if they are found to exist then they must belong to
expressions that are particularly rare or unusual.
Abbreviations
et = Element Theory, oe = Old English, sg = singular
Acknowledgements
The author wishes to thank Dirk van Gorp (Journal Manager, Glossa) and three anonymous
reviewers for their valuable comments on an earlier draft. The author alone is
responsible for any remaining inadequacies. This work was partially funded by a grant
(15K02611) from the Japanese government: Grant-in-Aid for Scientific Research (C),
­Ministry of Education, Culture, Sports, Science and Technology (MEXT).
Competing Interests
The author has no competing interests to declare.
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How to cite this article: Backley, Phillip. 2017. Headedness in Element Theory: The case for multiple heads. Glossa: a
journal of general linguistics 2(1): 89. 1–17, DOI: https://doi.org/10.5334/gjgl.463
Submitted: 22 Jun 2017 Accepted: 22 Jun 2017 Published: 06 October 2017
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