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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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 theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

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
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27

Thank you

• Tone interval theory
• Overview
• Prior assumptions
• Exactly like segments
• Strong phonetic view (Pierrehumbert 1980)
• Defining descriptive adequacy
• Slide 7
• A phonology-phonetics test case
• Some dire consequences
• Phonetic rules (Pierrehumbert 1980)
• Pierrehumbert (1980)
• Pierrehumbert and Beckman (1988)
• Summary and implications
• What to do
• Relative height is phonological
• Music as inspiration
• Slide 17
• More on melodic representation
• Scales and frequency ratios
• Layers of representation
• Slide 21
• Tone interval theory contrsquod
• Slide 23
• Advantages of this approach
• Summary and Conclusions
• Summary contrsquod
• Slide 27