A presentation given by Kevin McMullin on January 16, 2013 at the CUNY Conference on the Feature in Phonetics and Phonology.

1. Similarity and the perception
of half-rhymes
Kevin McMullin and Molly Babel
Department of Linguistics - University of British Columbia
January 16, 2013
1

2. Overview
• Do we need features to measure similarity?
• Background and context
• Similarity
• Half-rhymes
• Methodology
• Half-rhyme judgment task
• Results
• Mixed-effects logistic regression models show that perceptual
similarity is best for modeling half-rhyme acceptability judgments
• Discussion
2

3. Similarity
• Some sounds of natural language are more alike than others
• This “similarity” has been shown to play a role in many
linguistic phenomena
• Speech errors (Frisch 1996; Rose & King 2007; Stemberger 1991)
• Phoneme confusability in noise (Luce 1986; Woods et al. 2010)
• Short-term memory phoneme confusion (Wicklegren 1966)
• The nature of phonotactic constraints (Frisch et al. 2004)
• Ease of learning phonotactic dependencies (Moreton 2008; 2012)
• Half-rhyme frequencies (Kawahara 2007; Steriade 2003)
• One goal of the literature has been to find a unifying metric of
similarity
3

4. Phonological similarity
• A phonologically informed calculation that determines how
similar two phonemes are
• Sometimes these are based solely on distinctive features
(Bailey & Hahn 2005; Rose & King 2007)
• Another commonly used metric is Frisch’s natural class metric
of similarity (Frisch 1996; Frisch et al. 2004)
• It has been shown to be especially good at modeling English
speech errors (Frisch 1996) as well as a gradient OCP-Place
constraint in Arabic (Frisch et al. 2004)
Phonological Similarity =
Shared Natural Classes
Shared Natural Classes + Unshared Natural Classes
4

5. Other types of similarity
• Perceptual similarity
• Based on how the sounds are perceived by listeners
• Must be obtained indirectly through experimental studies
• Confusion in noise, AXB similarity tasks, similarity ratings
• Acoustic similarity
• Based on a quantitative measure from the acoustic signal
• Formant frequencies, pitch, amplitude, VOT, and so on
• Articulatory similarity
• Based on the articulatory properties of the sounds
• Mielke (2012) develops a measure based on oral airflow, nasal
airflow, vocal fold contact, and larynx height
5

6. Rhymes and half-rhymes
• Rhyming is a tradition in many languages: songs, poems, puns
• The definition of what rhymes can differ by language
• Japanese – The ends of two rhyming lines have all of the same
vowels (Kawahara 2007)
• The syllable onsets need not match (nor any codas)
• English – Two words share a nucleus of primary stress and all
following segments are identical (Rickert 1979)
• {pack, stack}; {surrender, defender}
• Sometimes two words are found as a rhyming pair, but not all of
these conditions are met
• These are called half-rhymes
• “With a knick-knack paddy-whack give a dog a bone / This old man
came rolling home”
• English speakers seem to share an intuition that some half-
rhymes are “better” than others - {time, line} vs. {time, life}
6

7. Previous literature
7
• Half-rhymes have been used before as a tool to investigate
similarity
• Zwicky 1976 – raw counts of half-rhymes with mismatched codas
in English rock song lyrics
• Steriade 2003 – half-rhymes in Romanian poetry and their
relationship to phonological constraints
• Kawahara 2007 – relative frequency of consonant pairs for half-
rhymes in Japanese rap lyrics
• McMullin 2009 – relative frequency of half-rhymes in a corpus of
Red Hot Chili Peppers lyrics

8. The biggest problem
8
• There are some deviations from what phonological similarity
should predict
• In Japanese, some consonant pairs that are phonologically quite
different, such as [tʃ] and [kʲ], are overrepresented in the data
(Kawahara 2007)
• He suggests this may be because of the acoustic/perceptual
similarity of these pairs, but does not test it
• In English, coda consonants sharing the same place of
articulation, such as [t] and [d] or [b] and [m] are
underrepresented in the data
• McMullin (2009) argued that this is because the acoustics of the
preceding vowel often change in such cases (length, nasality)
• Do we need to reference features at all when talking about
similarity?

9. This study
• Investigates whether data from a half-rhyme judgment task show
the same generalizations as half-rhyme corpus frequencies
• To our knowledge, this is the first experimental study of half-rhymes
in any language
• We model the data using two phonological measures of similarity
and one perceptual measure of similarity
• We hypothesized that perceptual similarity would be a better
predictor of the results than phonological similarity
• This is based on the systematic deviations from phonological
similarity that seem to be well explained by perceptual similarity
• {b,d} vs. {b,p}
• The acoustics of the preceding vowel may play a role in half-rhyme
acceptability, but this is outside the scope of phonological similarity
9

10. Methodology
• Subjects
• 10 native English speakers (3 male, 7 female, mean age of 24)
• Stimuli
• 90 CVC English words recorded by a male English speaker
• He was unaware that these would be used as half-rhyme pairs
• Words were presented to him in a random order
• 15 words with each of the following coda consonants
[b,d,m,n,p,t], chosen to give minimal distinctions between
voicing, place, and nasality
• Vowels were [i,ɪ,e,ɛ,æ,ɑ,o,u,ʌ], chosen because they had at least
two words that ended with each of the above consonants
• Onset consonants were not controlled
• 25% most and least frequent words were omitted, based on
SUBTLEXus frequencies (Brysbaert & New 2009) 10

11. Methodology
• Design and procedure
• Words were organized into sets of three in order to have a
comparison of two consonant pairs
• On each trial, subjects were presented with two pairs of words and
were instructed to choose which one was a better rhyme by pressing
a button (time between words within pairs was 100ms, and time
between pairs was 500ms)
• The first word of each pair was always the same for both pairs
• Ex: {robe, code}, {robe, foam} gives the comparison of {b,d} vs. {b,m}
• From here on, we will refer to the above comparison as {bdbm}
• This process gave three comparisons of 60 total pairs, which
counterbalanced for order to give a total of 360 trials per subject
• Trials were randomized for each subject
• Each subject was given a short break half-way through the
experiment 11

12. • These numbers are based on Frisch’s analysis of distinctive
features and natural classes in English
Similarity measures
Consonant d m n p t
b 0.28 0.39 0.12 0.40 0.14
d 0.11 0.38 0.14 0.39
m 0.26 0.19 0.06
n 0.06 0.19
p 0.30
12
Natural class similarity (Frisch 1996:45)

13. Similarity measures
Consonant d m n p t
b 2 2 1 2 1
d 1 2 1 2
m 2 1 0
n 0 1
p 2
13
Feature similarity
# of features in common for [voice], [labial], [nasal]

14. • These are only for consonants in coda position
• Every consonant was presented the same number of times,
and responses were open ended
• Over 34000 trials total (all English onsets/vowels/codas)
Similarity measures
Consonant d m n p t
b 197 46 28 172 16
d 19 53 28 49
m 341 15 12
n 10 15
p 213
14
Perceptual similarity
Number of confusions (Woods et al. 2010:1615)

15. Results in percentages
• The vertical axis in the following graphs represents the
percentage of the trials in which the first pair was chosen
(pooled across subjects)
• For each type of similarity, this is plotted against a comparison
of the relative similarity values for each pair
• These graphs are intended to give an intuitive visualization of
the data
15

16. 16
r = 0.556
p < 0.001
0 20 40 60 80 100
020406080100
% of expected first pair choices based on phonological similarity
%ofobservedfirstpairchoices
bdbm
bdbn
bdbp
bdbt
bmbd
bmbn
bmbp
bmbt
bnbd
bnbmbnbp
bnbt
bpbd
bpbm
bpbn
bpbt
btbd
btbm
btbn
btbp
dbdm
dbdn dbdp
dbdt
dmdb
dmdn
dmdp
dmdt
dndb
dndm
dndp
dndt
dpdb
dpdm
dpdn
dpdt
dtdb
dtdm
dtdn
dtdp
mbmd
mbmn
mbmp
mbmt
mdmbmdmn
mdmp
mdmt
mnmb
mnmdmnmp
mnmt
mpmb
mpmd
mpmn
mpmt
mtmb
mtmd
mtmn
mtmp
nbndnbnm
nbnp
nbnt
ndnb
ndnm
ndnp
ndnt
nmnb
nmnd
nmnpnmnt
npnb
npnd
npnm
npnt
ntnbntnd
ntnm
ntnp
pbpd
pbpm
pbpn
pbpt
pdpb
pdpm
pdpn
pdpt
pmpb
pmpd
pmpn
pmpt
pnpb
pnpd
pnpm
pnpt
ptpb
ptpd
ptpm
ptpn
tbtd
tbtm
tbtn
tbtp
tdtb
tdtm
tdtn
tdtp
tmtb
tmtd tmtn
tmtp
tntb
tntd
tntm
tntp
tptb
tptd
tptm
tptn
Natural Classes Phonological Similarity

17. -2 -1 0 1 2
020406080100
More identical features of A than B
%ofobservedfirstpairchoices
bdbm
bdbn
bdbp
bdbt
bmbd
bmbn
bmbp
bmbt
bnbd
bnbmbnbp
bnbt
bpbd
bpbm
bpbn
bpbt
btbd
btbm
btbn
btbp
dbdm
dbdn dbdp
dbdt
dmdb
dmdn
dmdp
dmdt
dndb
dndm
dndp
dndt
dpdb
dpdm
dpdn
dpdt
dtdb
dtdm
dtdn
dtdp
mbmd
mbmn
mbmp
mbmt
mdmbmdmn
mdmp
mdmt
mnmb
mnmdmnmp
mnmt
mpmb
mpmd
mpmn
mpmt
mtmb
mtmd
mtmn
mtmp
nbndnbnm
nbnp
nbnt
ndnb
ndnm
ndnp
ndnt
nmnb
nmnd
nmnpnmnt
npnb
npnd
npnm
npnt
ntnbntnd
ntnm
ntnp
pbpd
pbpm
pbpn
pbpt
pdpb
pdpm
pdpn
pdpt
pmpb
pmpd
pmpn
pmpt
pnpb
pnpd
pnpm
pnpt
ptpb
ptpd
ptpm
ptpn
tbtd
tbtm
tbtn
tbtp
tdtb
tdtm
tdtn
tdtp
tmtb
tmtd tmtn
tmtp
tntb
tntd
tntm
tntp
tptb
tptd
tptm
tptn
17
r = 0.716
p < 0.001
Features Phonological Similarity

18. 0 20 40 60 80 100
020406080100
% of expected first pair choices based on perceptual similarity
%ofobservedfirstpairchoices
bdbm
bdbn
bdbp
bdbt
bmbd
bmbn
bmbp
bmbt
bnbd
bnbmbnbp
bnbt
bpbd
bpbm
bpbn
bpbt
btbd
btbm
btbn
btbp
dbdm
dbdn dbdp
dbdt
dmdb
dmdn
dmdp
dmdt
dndb
dndm
dndp
dndt
dpdb
dpdm
dpdn
dpdt
dtdb
dtdm
dtdn
dtdp
mbmd
mbmn
mbmp
mbmt
mdmbmdmn
mdmp
mdmt
mnmb
mnmdmnmp
mnmt
mpmb
mpmd
mpmn
mpmt
mtmb
mtmd
mtmn
mtmp
nbndnbnm
nbnp
nbnt
ndnb
ndnm
ndnp
ndnt
nmnb
nmnd
nmnpnmnt
npnb
npnd
npnm
npnt
ntnbntnd
ntnm
ntnp
pbpd
pbpm
pbpn
pbpt
pdpb
pdpm
pdpn
pdpt
pmpb
pmpd
pmpn
pmpt
pnpb
pnpd
pnpm
pnpt
ptpb
ptpd
ptpm
ptpn
tbtd
tbtm
tbtn
tbtp
tdtb
tdtm
tdtn
tdtp
tmtb
tmtd tmtn
tmtp
tntb
tntd
tntm
tntp
tptb
tptd
tptm
tptn
18
r = 0.863
p < 0.001
Perceptual Similarity

19. Logistic regression models
19
• There are various problems that can arise from treating a
categorical variable as a percentage of the total
• Different variances, unbounded predictions, different subject
tendencies, loss of data points
• One alternative way of analyzing this type of data is with a
logistic regression
• For this study, the categorical dependent variable is whether
subjects chose the first pair or not
• A logistic regression attempts to find the best fit (based on
some set of predictors) for the log odds of choosing the first
pair

20. Logistic regression models
20
• Mixed-effects logistic regression models were built using
perceptual similarity and phonological similarity as predictors
• To do this, we need one number to compare the similarity of
two pairs
• Random intercepts and slopes for each subject and vowel
PhonComp = ln
phonological similarity of 1st pair
phonological similarity of 2nd pair
æ
è
ç
ö
ø
÷
PercComp = ln
# of 1st pair confusions
# of 2nd pair confusions
æ
è
ç
ö
ø
÷

21. The models – Summary of
fixed effects
21
Natural Class Similarity Feature Similarity
AIC=4485, BIC=4535 AIC=4205, BIC=4255
Estimate SE Pr(>|z|) Estimate SE Pr(>|z|)
Intercept -0.2135 0.086 0.013* Intercept -0.1760 0.096 0.066
PhonComp 0.7791 0.062 <0.001*
1st-2nd common
Features 0.8841 0.071 <0.001*
Perceptual Similarity Perceptual and Feature Similarity
AIC=3803, BIC=3853 AIC=3803, BIC=3896
Estimate SE Pr(>|z|) Estimate SE Pr(>|z|)
Intercept -0.2839 0.112 0.011* Intercept -0.2846 0.112 0.011*
PercComp 0.8180 0.079 <0.001* PercComp 0.8347 0.084 <0.001*
N=3573 # of Subjects=10
Residuals
of features
-0.1719 0.097 0.076

22. Summary of results
• All models have a negative intercept
• On any given trial, subjects are slightly biased towards choosing
the second pair (they did so in approximately 55% of the trials)
• The three measures of similarity all have positive values in
their respective models
• This shows that subjects are more likely to choose the first pair as
the similarity of the first pair increases compared to the second
pair
• Model comparison with AIC (small AIC means better model)
• Relative likelihood that the natural class metric makes a better
model than features alone is
• Relative likelihood that the metric using features makes a better
model than perceptual similarity is 22
1.58´10-61
5.09´10-88

23. Discussion
• For phonological similarity
• A crude count of features by themselves performs better than a
more complex metric based on natural classes
• Coetzee & Pater 2008; Brown & Hansson 2008 find that the natural
class metric performs poorly for co-occurrence restrictions in Muna
and Gitksan respectively
• A measure of perceptual similarity performs even better than
either of these
• A model that includes both perceptual similarity and feature
similarity did not perform any better than a model based only
on perceptual similarity
23

24. Similarity and half-rhymes
• Phonological similarity does not seem to be useful to language
users who are judging the relative acceptability of half-rhymes
• Whether they are hearing them, or producing (writing) them
• One possible way to give a feature-based similarity a boost
would be to allow each feature to contribute with different
weights, and to allow the phonetic features of the preceding
vowel (such as length and nasality) to be included
• It is not clear that this is any different or better than allowing
language users to reference perceptual similarity directly
• If language users can access a knowledge of perceptual
similarity for composing and judging the acceptability of half-
rhymes, we should allow our theory to reference it directly as
well
24

25. Furtherimplications and questions
• This result does not mean that perceptual similarity is the only
relevant type of similarity
• Other types of similarity (or combinations of them) could be
behind different phonological phenomena
• OCP-Place constraints
• Learning phonotactic constraints
• How is similarity represented? Individual components that
are independent or that make up a whole?
• Does similarity help us to learn categories? And phonological
features?
25

26. In summary
• The biggest problem with the literature relating similarity and half-
rhymes:
• Some consonants that are relatively common half-rhyme pairs are
not phonologically very similar, but they are perceptually similar
• 10 native English speakers completed a forced-choice half-rhyme
judgment task
• Results of mixed-effects logistic regression models show that
perceptual similarity (based on Woods et al. 2010) is better at
modeling subject responses than measures of phonological
similarity
• This is taken as evidence that language users have access to
knowledge of the perceptual characteristics of their sounds
• Further work can be done to determine if they independently have
knowledge of other types of similarity (acoustic, articulatory, or
phonological) 26

27. Acknowledgements
• Gunnar Hansson, Carla Hudson Kam, Kathleen Currie Hall and
Bryan Gick for their many helpful comments
• Michael McAuliffe for script writing and statistical advice
• Morgan Sonderegger for statistical advice
• Various audiences
• UBC Graduate Seminar on Perception and Production
• UBC Phonology Group lab meetings
27

28. References
28
Akaike, Hirotugu. (1980). Likelihood and the Bayes procedure. In Bernardo, J.M. (Ed.) Bayesian Statistics. University
Press, Valencia: 143–166.
Brysbaert, M. and B. New. (2009). Moving beyond Kucera and Francis: a critical evaluation of current word frequency
norms and the introduction of a new and improved word frequency measure for American English.
Behaviour Research Methods 41: 990–997.
Frisch, Stefan. (1996). Similarity and Frequency in Phonology. PhD Thesis, Northwestern University. Evanston, Illinois.
Frisch, Stefan, Janet Pierrehumbert, & Michael Broe. (2004). Similarity avoidance and the OCP. Natural Language and
Linguistic Theory 22: 179-228.
Gallagher, Gillian and Peter Graff. (2012). The role of similarity in phonology. Lingua 122: 107–111.
Johnsen, Sverre S. (2012). From perception to phonology: The emergence of perceptually motivated constraint
rankings. Lingua 122: 125–143.
Kawahara, Shigeto. (2007). Half rhymes in Japanese rap lyrics and knowledge of similarity. Journal of East Asian
Linguistics, 16, 113-144.
Luce, P.A. (1986). Neighborhoods of words in the mental lexicon. Ph.D. Thesis, University of Indiana. Bloomington,
Indiana.
McMullin, Kevin. (2009). Phonological similarity and half-rhymes in Red Hot Chili Peppers’ lyrics. Unpublished
manuscript. University of British Columbia.
Mielke, Jeff. (2008). The Emergence of Distinctive Features. Oxford University Press, Oxford.
Moreton, Elliot. (2008). Analytic bias and phonological typology. Phonology 25: 83-127.
Rickert, William. (1979). Rhyme terms. Style 12: 35–43.
Rose, Sharon and Lisa King. (2007). Speech error elicitation and co-occurrence restrictions in two Ethiopian Semitic
languages. Language and Speech 50: 451–504.
Stemberger, Joseph. (1991). Radical underspecification in language production. Phonology 8: 73–112.
Steriade, Donca. (2003). Knowledge of similarity and narrow lexical override. Proceedings of Berkeley Linguistics
Society 9: 583-598.
Wicklegren, W.A. (1966). Distinctive Features and errors in short-term memory for English consonants. Journal of the
Acoustical Society of America 39: 388-398.
Woods, David, E. WilliamYund, Timothy Herron, and Matthew Ua Cruadhlaoich. (2010). Consonant identification in
consonant-vowel-consonant syllables in speech-spectrum noise. Journal of the Acoustical Society of
America 127: 1609–1623.
Zwicky, A. (1976). This rock-and-roll has got to stop: Junior’s head is hard as a rock. Proceedings of Chicago Linguistics
Society 12: 676-697

29. Results in percentages
• The measures on the horizontal axis of the graphs were
calculated as follows:
• For natural class similarity
• For feature similarity
• For perceptual similarity
29
Expected % =
1st pair similarity
1st pair similarity +2nd pair similarity
´100
Expected % =
1st pair confusions
1st pair confusions +2nd pair confusions
´100
1st pair common features - 2nd pair common features
Example for bdbm
= (0.28/(0.28+0.39))x100
= 41.8% bd choices
= 1 – 1 = 0
= (197/(197+46))x100
= 81.1% bd choices

30. Log odds example
30
• As an example, imagine that we have 100 choices in total
• This solves some of the problems by creating an unbounded
dependent variable
1st pair vs. 2nd pair
choices
Probability of
choosing 1st pair
Odds of choosing
1st pair
Log odds of
choosing 1st pair
1 vs. 99 0.01 1/99 -4.60
25 vs. 75 0.25 1/3 -1.10
50 vs. 50 0.50 1/1 0
75 vs. 25 0.75 3/1 1.10
99 vs. 1 0.99 99/1 4.60
Range: 0 to 1 0 to ∞ -∞ to ∞