Tone interval theory
Laura Dilley PhDSpeech Communication Group
Massachusetts Institute of Technology
and
Departments of Psychology and Linguistics
The Ohio State University
Chicago Linguistics Society
Annual Meeting
April 9 2005
Overviewbull Whatrsquos the problem
ndash Failure of descriptive apparatus for some tonal systems
bull Why concepts from music theory can help resolve the problems
bull Introduction to tone interval theory
Prior assumptionsbull Early autosegmental theory made several
strong claims regarding tonesndash Tones segments represented on different
tiers
ndash Tones are exactly like segments
bull The claim that tones are exactly like segments leads to a failure of descriptive adequacy for some tonal systems
x
Exactly like segmentsbull Idea Tones segments are defined without
reference to one another in series
bull No inherent relativity of tones to other tones
bull Relative heights of tones are not part of the phonology
ndash But cf Jakobson Fant and Halle (1952)
Relative height must be part of
phonetics
Strong phonetic view (Pierrehumbert 1980)
bull Extended autosegmental theory to English
bull Treated relative tone height as part of phonetic component of grammarndash Phonological primitives based on H L
tones plus phonetic tone scaling rules
bull Insufficent constraints on relative tone height in phonetic rules lead to problems with descriptive adequacy testability
Defining descriptive adequacybull Q What should a theory of the phonology and
phonetics of tone and intonation do
bull A Define a clear and consistent relation between phonology and aspects of F0 shape
bull A Support descriptive linguistic intuitions ndash Eg LHL should correspond to a rising-falling
pattern
A phonology-phonetics test case
bull Q If we assume that LHL corresponds to then what are the critical restrictions on H L
bull A H must be higher than adjacent L and L must be lower than adjacent Hndash Permits a sequence of H L tones to give rise to a
predictable F0 shape
bull What would happen if these restrictions are not in place
L
H
L
bull If critical restrictions on adjacent H L are not in placendash Cannot predict F0 shape from phonology (overgeneration)ndash Cannot describe an F0 contour in terms of a unique
phonological specification (indeterminacy)ndash Cannot test a theory
Some dire consequences
Phonetic rules (Pierrehumbert 1980)
1 In Hi (+T) (T+)Hj f(Hj) = f(Hi) [p(Hj)p(Hi)]
2 In H+L f(L) = kf(H) 0 lt k lt 1
3 In H (+T) L+ f(L) = nf(H) [p(H)p(L)] 0 lt n lt k
4 In H(+T) L- f(L-) = p0f(H) 0 lt p0 lt k
5 In H+L Hi and H L+Hi f(Hi) = kf(Hi) 0 lt k lt 1
6 In H- T f(T) = f(H-) + f(T)
7 f(L) = 0
8 f(Li+1) = f(Li)[p(Li)p(Li+1)]
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Overviewbull Whatrsquos the problem
ndash Failure of descriptive apparatus for some tonal systems
bull Why concepts from music theory can help resolve the problems
bull Introduction to tone interval theory
Prior assumptionsbull Early autosegmental theory made several
strong claims regarding tonesndash Tones segments represented on different
tiers
ndash Tones are exactly like segments
bull The claim that tones are exactly like segments leads to a failure of descriptive adequacy for some tonal systems
x
Exactly like segmentsbull Idea Tones segments are defined without
reference to one another in series
bull No inherent relativity of tones to other tones
bull Relative heights of tones are not part of the phonology
ndash But cf Jakobson Fant and Halle (1952)
Relative height must be part of
phonetics
Strong phonetic view (Pierrehumbert 1980)
bull Extended autosegmental theory to English
bull Treated relative tone height as part of phonetic component of grammarndash Phonological primitives based on H L
tones plus phonetic tone scaling rules
bull Insufficent constraints on relative tone height in phonetic rules lead to problems with descriptive adequacy testability
Defining descriptive adequacybull Q What should a theory of the phonology and
phonetics of tone and intonation do
bull A Define a clear and consistent relation between phonology and aspects of F0 shape
bull A Support descriptive linguistic intuitions ndash Eg LHL should correspond to a rising-falling
pattern
A phonology-phonetics test case
bull Q If we assume that LHL corresponds to then what are the critical restrictions on H L
bull A H must be higher than adjacent L and L must be lower than adjacent Hndash Permits a sequence of H L tones to give rise to a
predictable F0 shape
bull What would happen if these restrictions are not in place
L
H
L
bull If critical restrictions on adjacent H L are not in placendash Cannot predict F0 shape from phonology (overgeneration)ndash Cannot describe an F0 contour in terms of a unique
phonological specification (indeterminacy)ndash Cannot test a theory
Some dire consequences
Phonetic rules (Pierrehumbert 1980)
1 In Hi (+T) (T+)Hj f(Hj) = f(Hi) [p(Hj)p(Hi)]
2 In H+L f(L) = kf(H) 0 lt k lt 1
3 In H (+T) L+ f(L) = nf(H) [p(H)p(L)] 0 lt n lt k
4 In H(+T) L- f(L-) = p0f(H) 0 lt p0 lt k
5 In H+L Hi and H L+Hi f(Hi) = kf(Hi) 0 lt k lt 1
6 In H- T f(T) = f(H-) + f(T)
7 f(L) = 0
8 f(Li+1) = f(Li)[p(Li)p(Li+1)]
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Prior assumptionsbull Early autosegmental theory made several
strong claims regarding tonesndash Tones segments represented on different
tiers
ndash Tones are exactly like segments
bull The claim that tones are exactly like segments leads to a failure of descriptive adequacy for some tonal systems
x
Exactly like segmentsbull Idea Tones segments are defined without
reference to one another in series
bull No inherent relativity of tones to other tones
bull Relative heights of tones are not part of the phonology
ndash But cf Jakobson Fant and Halle (1952)
Relative height must be part of
phonetics
Strong phonetic view (Pierrehumbert 1980)
bull Extended autosegmental theory to English
bull Treated relative tone height as part of phonetic component of grammarndash Phonological primitives based on H L
tones plus phonetic tone scaling rules
bull Insufficent constraints on relative tone height in phonetic rules lead to problems with descriptive adequacy testability
Defining descriptive adequacybull Q What should a theory of the phonology and
phonetics of tone and intonation do
bull A Define a clear and consistent relation between phonology and aspects of F0 shape
bull A Support descriptive linguistic intuitions ndash Eg LHL should correspond to a rising-falling
pattern
A phonology-phonetics test case
bull Q If we assume that LHL corresponds to then what are the critical restrictions on H L
bull A H must be higher than adjacent L and L must be lower than adjacent Hndash Permits a sequence of H L tones to give rise to a
predictable F0 shape
bull What would happen if these restrictions are not in place
L
H
L
bull If critical restrictions on adjacent H L are not in placendash Cannot predict F0 shape from phonology (overgeneration)ndash Cannot describe an F0 contour in terms of a unique
phonological specification (indeterminacy)ndash Cannot test a theory
Some dire consequences
Phonetic rules (Pierrehumbert 1980)
1 In Hi (+T) (T+)Hj f(Hj) = f(Hi) [p(Hj)p(Hi)]
2 In H+L f(L) = kf(H) 0 lt k lt 1
3 In H (+T) L+ f(L) = nf(H) [p(H)p(L)] 0 lt n lt k
4 In H(+T) L- f(L-) = p0f(H) 0 lt p0 lt k
5 In H+L Hi and H L+Hi f(Hi) = kf(Hi) 0 lt k lt 1
6 In H- T f(T) = f(H-) + f(T)
7 f(L) = 0
8 f(Li+1) = f(Li)[p(Li)p(Li+1)]
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Exactly like segmentsbull Idea Tones segments are defined without
reference to one another in series
bull No inherent relativity of tones to other tones
bull Relative heights of tones are not part of the phonology
ndash But cf Jakobson Fant and Halle (1952)
Relative height must be part of
phonetics
Strong phonetic view (Pierrehumbert 1980)
bull Extended autosegmental theory to English
bull Treated relative tone height as part of phonetic component of grammarndash Phonological primitives based on H L
tones plus phonetic tone scaling rules
bull Insufficent constraints on relative tone height in phonetic rules lead to problems with descriptive adequacy testability
Defining descriptive adequacybull Q What should a theory of the phonology and
phonetics of tone and intonation do
bull A Define a clear and consistent relation between phonology and aspects of F0 shape
bull A Support descriptive linguistic intuitions ndash Eg LHL should correspond to a rising-falling
pattern
A phonology-phonetics test case
bull Q If we assume that LHL corresponds to then what are the critical restrictions on H L
bull A H must be higher than adjacent L and L must be lower than adjacent Hndash Permits a sequence of H L tones to give rise to a
predictable F0 shape
bull What would happen if these restrictions are not in place
L
H
L
bull If critical restrictions on adjacent H L are not in placendash Cannot predict F0 shape from phonology (overgeneration)ndash Cannot describe an F0 contour in terms of a unique
phonological specification (indeterminacy)ndash Cannot test a theory
Some dire consequences
Phonetic rules (Pierrehumbert 1980)
1 In Hi (+T) (T+)Hj f(Hj) = f(Hi) [p(Hj)p(Hi)]
2 In H+L f(L) = kf(H) 0 lt k lt 1
3 In H (+T) L+ f(L) = nf(H) [p(H)p(L)] 0 lt n lt k
4 In H(+T) L- f(L-) = p0f(H) 0 lt p0 lt k
5 In H+L Hi and H L+Hi f(Hi) = kf(Hi) 0 lt k lt 1
6 In H- T f(T) = f(H-) + f(T)
7 f(L) = 0
8 f(Li+1) = f(Li)[p(Li)p(Li+1)]
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Strong phonetic view (Pierrehumbert 1980)
bull Extended autosegmental theory to English
bull Treated relative tone height as part of phonetic component of grammarndash Phonological primitives based on H L
tones plus phonetic tone scaling rules
bull Insufficent constraints on relative tone height in phonetic rules lead to problems with descriptive adequacy testability
Defining descriptive adequacybull Q What should a theory of the phonology and
phonetics of tone and intonation do
bull A Define a clear and consistent relation between phonology and aspects of F0 shape
bull A Support descriptive linguistic intuitions ndash Eg LHL should correspond to a rising-falling
pattern
A phonology-phonetics test case
bull Q If we assume that LHL corresponds to then what are the critical restrictions on H L
bull A H must be higher than adjacent L and L must be lower than adjacent Hndash Permits a sequence of H L tones to give rise to a
predictable F0 shape
bull What would happen if these restrictions are not in place
L
H
L
bull If critical restrictions on adjacent H L are not in placendash Cannot predict F0 shape from phonology (overgeneration)ndash Cannot describe an F0 contour in terms of a unique
phonological specification (indeterminacy)ndash Cannot test a theory
Some dire consequences
Phonetic rules (Pierrehumbert 1980)
1 In Hi (+T) (T+)Hj f(Hj) = f(Hi) [p(Hj)p(Hi)]
2 In H+L f(L) = kf(H) 0 lt k lt 1
3 In H (+T) L+ f(L) = nf(H) [p(H)p(L)] 0 lt n lt k
4 In H(+T) L- f(L-) = p0f(H) 0 lt p0 lt k
5 In H+L Hi and H L+Hi f(Hi) = kf(Hi) 0 lt k lt 1
6 In H- T f(T) = f(H-) + f(T)
7 f(L) = 0
8 f(Li+1) = f(Li)[p(Li)p(Li+1)]
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Defining descriptive adequacybull Q What should a theory of the phonology and
phonetics of tone and intonation do
bull A Define a clear and consistent relation between phonology and aspects of F0 shape
bull A Support descriptive linguistic intuitions ndash Eg LHL should correspond to a rising-falling
pattern
A phonology-phonetics test case
bull Q If we assume that LHL corresponds to then what are the critical restrictions on H L
bull A H must be higher than adjacent L and L must be lower than adjacent Hndash Permits a sequence of H L tones to give rise to a
predictable F0 shape
bull What would happen if these restrictions are not in place
L
H
L
bull If critical restrictions on adjacent H L are not in placendash Cannot predict F0 shape from phonology (overgeneration)ndash Cannot describe an F0 contour in terms of a unique
phonological specification (indeterminacy)ndash Cannot test a theory
Some dire consequences
Phonetic rules (Pierrehumbert 1980)
1 In Hi (+T) (T+)Hj f(Hj) = f(Hi) [p(Hj)p(Hi)]
2 In H+L f(L) = kf(H) 0 lt k lt 1
3 In H (+T) L+ f(L) = nf(H) [p(H)p(L)] 0 lt n lt k
4 In H(+T) L- f(L-) = p0f(H) 0 lt p0 lt k
5 In H+L Hi and H L+Hi f(Hi) = kf(Hi) 0 lt k lt 1
6 In H- T f(T) = f(H-) + f(T)
7 f(L) = 0
8 f(Li+1) = f(Li)[p(Li)p(Li+1)]
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
A phonology-phonetics test case
bull Q If we assume that LHL corresponds to then what are the critical restrictions on H L
bull A H must be higher than adjacent L and L must be lower than adjacent Hndash Permits a sequence of H L tones to give rise to a
predictable F0 shape
bull What would happen if these restrictions are not in place
L
H
L
bull If critical restrictions on adjacent H L are not in placendash Cannot predict F0 shape from phonology (overgeneration)ndash Cannot describe an F0 contour in terms of a unique
phonological specification (indeterminacy)ndash Cannot test a theory
Some dire consequences
Phonetic rules (Pierrehumbert 1980)
1 In Hi (+T) (T+)Hj f(Hj) = f(Hi) [p(Hj)p(Hi)]
2 In H+L f(L) = kf(H) 0 lt k lt 1
3 In H (+T) L+ f(L) = nf(H) [p(H)p(L)] 0 lt n lt k
4 In H(+T) L- f(L-) = p0f(H) 0 lt p0 lt k
5 In H+L Hi and H L+Hi f(Hi) = kf(Hi) 0 lt k lt 1
6 In H- T f(T) = f(H-) + f(T)
7 f(L) = 0
8 f(Li+1) = f(Li)[p(Li)p(Li+1)]
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
bull If critical restrictions on adjacent H L are not in placendash Cannot predict F0 shape from phonology (overgeneration)ndash Cannot describe an F0 contour in terms of a unique
phonological specification (indeterminacy)ndash Cannot test a theory
Some dire consequences
Phonetic rules (Pierrehumbert 1980)
1 In Hi (+T) (T+)Hj f(Hj) = f(Hi) [p(Hj)p(Hi)]
2 In H+L f(L) = kf(H) 0 lt k lt 1
3 In H (+T) L+ f(L) = nf(H) [p(H)p(L)] 0 lt n lt k
4 In H(+T) L- f(L-) = p0f(H) 0 lt p0 lt k
5 In H+L Hi and H L+Hi f(Hi) = kf(Hi) 0 lt k lt 1
6 In H- T f(T) = f(H-) + f(T)
7 f(L) = 0
8 f(Li+1) = f(Li)[p(Li)p(Li+1)]
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Phonetic rules (Pierrehumbert 1980)
1 In Hi (+T) (T+)Hj f(Hj) = f(Hi) [p(Hj)p(Hi)]
2 In H+L f(L) = kf(H) 0 lt k lt 1
3 In H (+T) L+ f(L) = nf(H) [p(H)p(L)] 0 lt n lt k
4 In H(+T) L- f(L-) = p0f(H) 0 lt p0 lt k
5 In H+L Hi and H L+Hi f(Hi) = kf(Hi) 0 lt k lt 1
6 In H- T f(T) = f(H-) + f(T)
7 f(L) = 0
8 f(Li+1) = f(Li)[p(Li)p(Li+1)]
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Pierrehumbert (1980)Example H L+H Rewrite as H1 L H2
f(T) = F0 level of tone Tp(T) = tone scaling value of tone T (ldquoprominencerdquo)
f(L) = n bull f(H1) bull [p(H1)p(L)] for 0 lt n lt 1[f(L)f(H1)] = n bull [p(H1)p(L)]
bull Therefore the F0 of L f(L) is higher than the F0 of H1 f(H1) when [p(H1)p(L)] gt 1n
bull The F0 of L can also be higher than F0 of H2 (Dilley 2005)
bull No restrictions are in place to prevent this
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Pierrehumbert and Beckman (1988)
bull Example H L+H Rewrite as H1 L H2
bull Each tone is independently assigned a value for a parameter p (for prominence) where p determines F0 H1 L2 H3 rarr p(H1) p(L2) p(H3)
bull Critical restrictions are not in place
H1
L2
H3
H1
L2
H3h
l
1
p(H)
0
0
p(L)
1
L1
H2
L3
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Summary and implicationsbull Treating tones as exactly like segments
relegated relative tone height to phoneticsndash Phonetic rules mechanisms were proposed
to control relative tone height
bull In no version of the phonetic theory do the rules specify sufficient constraints
bull This leads to a failure of descriptive adequacy and testability
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
What to doQ Is the problem adequately addressed
simply by adding constraints to phonetic rules
A NoThere is evidence that relative tone height
is part of phonology not the phoneticsThe problems run deeper phonological
categories are not fully supported by data
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Relative height is phonologicalContrastive downstep Igbo (Williamson 1972)
aacutemaacute lsquostreetrsquo
aacutemaacute lsquodistinguishing markrsquo
Contrastive upstep Acatlaacuten Mixtec (Pike and Wistrand 1974)
iacutekuacutemiacutedaacute lsquowe (incl) haversquo
iacutekuacutemiacuted^aacute lsquoyou (pl fam) haversquo = downstep ^ = upstep
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Music as inspirationbull Claim Music theoretic concepts provide
a way of addressing problems in intonational and tonal phonologyndash Describing relative tone height as part of
the phonological representationndash Achieving descriptive adequacy testabilityndash Pitch range normalizationndash Typological differences among tonal
systemsndash Others
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
bull Musical scales and melodies are represented in terms of frequency ratios (Burns 1999)
233 277 311 370 415 466 554 622220 247 262 294 330 349 392 440 494 523 587 659
Frequency (Hz)
A B C D E F G A B C D E
A C D F G A C D
Notes
G392
G392
A440
G392
C523
B494
C262
C262
D294
C262
F349
E330
10112
089133
0951
112089
133095
Frequency Ratios
One semitone = 122 105946Key of C Key of F
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
More on melodic representationbull Nature of frequency ratios differs for distinct
musical culturesndash eg Number and size of scale steps
bull Layers of representation for musical melody (Handel 1989)ndash Up-down pattern Whether successive notes are
eg higher lower than other notes ndash Interval Distance between notes cf a specific
frequency rationdash Scale Relation between a note and a tonic referent
note in a particular key
ALL melodies
SOME melodies
SOME melodies
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Scales and frequency ratiosbull Scales correspond to a set of ratios defined with
respect to a tonic (referent) note
I II III IV V VI VII
C (Key) C D E F G A B262 294 330 349 392 440 494
F (Key) F G A Bb C D E 349 392 440 466 523 598 659
Tonic
Ratio 1 112 126 133 150 168 189
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
G392
G392
A440
G392
C523
B494
10 112 089 133 095
Up-down pattern
Interval
Scale
38
r = 1 r gt 1 r lt 1 r gt 1 r lt 1
V4 V4 VI4 V4 I5 VII4
Layers of representation
bullEach successive layer of representation encodes more information than the previous layer
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Tone interval theorybull Tone intervals I are abstractions of frequency
ratios
bull Tones T are timing markers that are coordinated with segments via metrical structure (cf onsets)
bull Tone intervals relate a tone to one of two kinds of referent1) Referent is another tone (up-down pattern interval)
2) Referent is the tonic (cf scale)
T1 T2 rarr I12 = T2T1
Iμ2 = T2μ
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Tone interval theory contrsquodbull Every pair of adjacent tones in sequence is
joined into a tone interval in ALL languages
bull Each tone interval is then assigned a relational feature (cf up-down pattern)
higher implies that T2 gt T1 or I12 gt 1
lower implies that T2 lt T1 or I12 lt 1
same implies that T2 = T1 or I12 = 1
I12=1 I23gt1 I34lt1 I45gt1 etc
T1 T2 T3 hellip Tn rarr I12 I23 hellip In-1n (I12 = T2T1)
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Tone interval theory contrsquodbull SOME languages further restrict these ratio
values (cf Interval)I12=1 I23=112 I34=089 I45=133 etc
bull SOME languages define tones with respect to a tonic (cf Scale)
bull Tones tone intervals occupy different tiers and are coindexed (cf tonal stability)
x x x x
T1 T2 T3 hellip Tn
I12 I23 hellip In-1n
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Advantages of this approach Defining the phonology in this way
Achieves descriptive adequacy and generates testable predictions
Proposes explicit connection with music Builds on earlier work
T1 T2 T3
I12 gt1 I23lt1
T1
T2
T3
I12 gt1 I23lt1
L
H
L
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Summary and Conclusionsbull Autosegmental theory was based on the strong
claim that tones are exactly like segmentsndash Relative tone height was relegated to phonetics
bull Theories attempting to extend this approach intonation languages have led to problemsndash Eg inability to generate testable predictions
bull Relative tone height is almost certainly part of phonology not phonetics
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Summary contrsquodbull Musical melodies are represented in terms of
ndash Frequency ratios between notes in sequence and between a note and the tonic
ndash Up-down pattern interval and scale
bull Tone interval theoryndash The representation is based on tone intervals
(abstractions of frequency ratios)ndash Notion of up-down pattern permits a clear definition
between phonology phoneticsndash Builds on earlier work
Thank you
Thank you