Music & Space,  Music Psychology

Those who follow crocodiles – is there more to pitch than high and low?

Hello Dear Reader,

This is likely to be the last blog I write before Music and Neurosciences V, for me the first big music psychology conference of the year. This conference is due to take place in Dijon from 29th May to 1st June. This meeting will focus on “Cognitive Stimulation and Rehabilitation”.  As usual I will be doing my best to report on everything I see there for you.

256687_10100391435178173_1745065238_oBetween now and then I have some time off to spend with my lovely little (at least in age) brother Anthony. I have missed my family very much during the last 8 months in Switzerland. Time away in another country is a good way to focus the mind on what is important in life. I can’t wait to see Anthony and to show him where I have been hiding since September!

In this blog I would like to do something a little different. Rather than present new research I will re-visit one of my favourite papers from the past few years. It undoubtedly has the best title of any music psychology paper…

Beethoven’s last piano sonata and those who follow crocodiles: Cross-domain mappings of auditory pitch in a musical context’ by Zohar Eitan and Renee Timmers. This classic paper presents four tests that explore how we understand musical pitch beyond the sound itself – how we conceive of pitch in our minds.

These four studies reveal some consistency  in the way that we all seem to think about pitch in non-musical ways but also some surprising results that hint at complex and diverse cross-domain pitch mappings.

Cross-domain mappings for pitch rely heavily on metaphor, a type of analogy. Think about it, how would you describe the relationship between two notes to someone who was unable to hear them?

The classic Western culture mapping is “high” vs.”low” But the high/low pitch metaphor is far from universal. Higher pitch has also been associated with the adjectives small, bright, fast and active, while lower pitch has been matched to their opposites.

Crocodylus_acutus_mexico_02-edit1Even more interesting are metaphors observed outside modern Western culture. Ancient Greek theory refers to “sharp” and “heavy”.  The Bashi people of Central America talk of “weak” and “strong”. The Suya people of the Amazon basin use the terms “young” and “old”. And, the inspiration for the paper, the Shona mbira from Zimbabwe include “crocodiles” (low pitch) and “those who follow crocodiles” (high pitch).

The sheer variety of these metaphors suggest that they are learned from within our cultures. However, it may be the case that some metaphors consistently underlie our experience of pitch: Metaphors that perhaps relate to bodily experiences or our physical environment.

up-and-downThe verticality metaphor is no doubt important. That the up-down relationship is core to a much larger metaphorical map – up is more, down is less: up is good, down is bad (our vocalisations and animal sounds, for example)…and so on.

However, another possibility is an intensity metaphor, relating to ideas of tension, brightness and pace.

So, are there latent  metaphors for pitch that have the potential to affect how we think about music? Here is where our study comes in.

Test 1 – Do people consistently match metaphors?

Sixty three participants were presented with 29 antonym pairs (high – low, light – heavy, sparse – dense)  and asked which word was a better metaphor for high pitch. They then marked on a scale of 1-5 how good the metaphor was for pitch. The authors then re-randomised the list and asked the participants to say which word was better for low pitch.

The average level of agreement reached .86, reasonably high. Best agreement was found for alert-sleepy (1.0), thin-thick (.98) and sharp-heavy (.98). Poorest agreements were for fool-wise (.51), pleasant-unpleasant (.53) and little-much (.57).

Musical expertise and pitch direction discrimination ability had no effect on the outcome.

Overall, the authors reported a strong consensus over many diverse metaphors for pitch, suggesting there exists a ‘thick web of cross-domain relationships’.

Test 2 – Do people use these metaphors when they hear real pitches?

Beethoven_2The next step was to test out the metaphors using real music. The authors chose Beethoven’s last piano sonata, Opus 111 – the second movement of which never fails to tug at my heart. Sixty three participants heard two sections of the sonata (37-40sec) with a similar structure but a different pitch register (high/low). Participants had to rate 35 antonyms on a scale of 1-5 as to how appropriate they were for the musical sections.

The antonyms with the most significant differences between the ratings for each word in the pair (indicating a clear preference) included thin-thick, light-dark, sharp-heavy, sharp-blunt, feminine-masculine.

No significant difference was found for pairings like fool-wise, right-left, active-passive or cold-hot.

Tests 1 and 2 suggest that listeners can apply diverse pitch metaphors consistently  in both simple (abstract) and complex (real music) forms.  The data were combined and factor analysed to reveal key dimensions for the consistent metaphor ratings:

1) Potency (weak-strong) 2) Valence (good-bad) and 3) Activity (alert-sleepy).

dogsThere was also a fourth, largest factor which contained the most agreed upon metaphors. All were experientially related to pitch – not cultural conventions but physically relatable. For example, for the most part objects or animals that make higher pitches are thin, sharp, feminine,light smooth and small;  conversely, low pitches are made when things are thick, blunt, masculine, heavy, rough, and large.

The exception in this large final factor was a metaphor for  visual ‘lightness’ (light-dark). This doesn’t correspond to anything in nature. The authors suggest that this concept of Mass-lightness and pitch might represent a latent cognitive dimension of pitch.

Test 3 – Do pitch metaphors derive from spatial height?

As mentioned at the start, the verticality metaphor (high-low) is all pervasive in Western music culture both in terms of how we talk about and visually represent pitch.

Does this dimension represent the true embodiment of musical pitch? Do the connotations from Tests 1 and 2 emerge from this one core dimension?

The authors took the same antonyms from Test 1 and asked participants to apply them not to musical pitches this time, but spatial elevations.

CurvedSopranoAltoTenorSaxophoneComparisonAs in Test 1 the level of agreement as to which word in the pair represented which dimension (high-low) was good. However, several antonyms showed the opposite tendency. For example, in pitch small is high and large is low, whilst in elevation small is low and large is high.  The well-known mapping of “high is more” does not apply to pitch: high pitches are smaller, thinner, sharper and more little in quality.

It appears that metaphors for pitch stem from an interaction of learned and perhaps some more latent factors, rather than a direct mapping of any one dimension.

Test 4 – how does pitch map onto multiple candidate dimensions?

In the final test the authors tested the antonyms on multiple dimensions:

1) Intensity, 2) Mass or size, 3) Valence, 4) Spatial height, 5) Pitch height, 6) Quantity

In the analysis they looked at the correlations between agreements across all dimensions. Of most interest are the partial correlations between pitch height and the other dimensions. The data were summarised for both musicians and non-musicians.

The only notable correlations were for Intensity (positive) and Size (negative). The lowest correlations were for Valence and Quantity. Interestingly, non-musicians had a medium sized correlation with Height, but musicians did not.

So how do we think about pitch?

When added together these four studies blow apart the idea that our mental conception of pitch is a simple, one dimensional idea of verticality – high and low. Rather there is an intricate web of diverse sensory and cultural associations that interact with our concept (and perhaps even our perception) of pitch.

We use the physical: size, mass, visual lightness and texture

We use energy: force, intensity and momentum

We use social concepts: age, gender

We use cultural ideals: beauty, happiness

The high overall level of agreement across so many factors underlies the complex web of cross-domain mappings for pitch. These include embodied dimensions with some physical reality as well as more evaluative and cuturally learned conceptions.

We may favour ‘high’ and ‘low’ in Western cultures and languages but this single dimension hides a wealth of potential non-auditory representations of musical pitch that may exist or can be drawn instantly from our minds.

Including, and never forgetting, ‘crocodiles’ and ‘those who follow crocodiles’…



Paper: ‘ Beethoven’s last piano sonata and those who follow crocodiles: Cross-domain mappings of auditory pitch in a musical context’ by Zohar Eitan and Renee Timmers (2010) Cognition, 114, 405-422.






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