̽��ֱ�� of Cambridge - Centre for Music and Science (CMS)

Pythagoras was wrong: there are no universal musical harmonies, study finds

ta385 — Tue, 27 Feb 2024 09:30:00 +0000

According to the Ancient Greek philosopher Pythagoras, ‘consonance’ – a pleasant-sounding combination of notes – is produced by special relationships between simple numbers such as 3 and 4. More recently, scholars have tried to find psychological explanations, but these ‘integer ratios’ are still credited with making a chord sound beautiful, and deviation from them is thought to make music ‘dissonant’, unpleasant sounding.

But researchers from the ̽��ֱ�� of Cambridge, Princeton and the Max Planck Institute for Empirical Aesthetics, have now discovered two key ways in which Pythagoras was wrong.

Their study, published in Nature Communications, shows that in normal listening contexts, we do not actually prefer chords to be perfectly in these mathematical ratios.

“We prefer slight amounts of deviation. We like a little imperfection because this gives life to the sounds, and that is attractive to us,” said co-author, Dr Peter Harrison, from Cambridge’s Faculty of Music and Director of its Centre for Music and Science.

̽��ֱ��researchers also found that the role played by these mathematical relationships disappears when you consider certain musical instruments that are less familiar to Western musicians, audiences and scholars. These instruments tend to be bells, gongs, types of xylophones and other kinds of pitched percussion instruments. In particular, they studied the ‘bonang’, an instrument from the Javanese gamelan built from a collection of small gongs.

“When we use instruments like the bonang, Pythagoras's special numbers go out the window and we encounter entirely new patterns of consonance and dissonance,” said Dr Harrison, a Fellow of Churchill College.

“ ̽��ֱ��shape of some percussion instruments means that when you hit them, and they resonate, their frequency components don’t respect those traditional mathematical relationships. That's when we find interesting things happening.”

“Western research has focused so much on familiar orchestral instruments, but other musical cultures use instruments that, because of their shape and physics, are what we would call ‘inharmonic’.

̽��ֱ��researchers created an online laboratory in which over 4,000 people from the US and South Korea participated in 23 behavioural experiments. Participants were played chords and invited to give each a numeric pleasantness rating or to use a slider to adjust particular notes in a chord to make it sound more pleasant. ̽��ֱ��experiments produced over 235,000 human judgments.

̽��ֱ��experiments explored musical chords from different perspectives. Some zoomed in on particular musical intervals and asked participants to judge whether they preferred them perfectly tuned, slightly sharp or slightly flat. ̽��ֱ��researchers were surprised to find a significant preference for slight imperfection, or ‘inharmonicity’. Other experiments explored harmony perception with Western and non-Western musical instruments, including the bonang.

Instinctive appreciation of new kinds of harmony

̽��ֱ��researchers found that the bonang’s consonances mapped neatly onto the particular musical scale used in the Indonesian culture from which it comes. These consonances cannot be replicated on a Western piano, for instance, because they would fall between the cracks of the scale traditionally used.

“Our findings challenge the traditional idea that harmony can only be one way, that chords have to reflect these mathematical relationships. We show that there are many more kinds of harmony out there, and that there are good reasons why other cultures developed them,” Dr Harrison said.

Importantly, the study suggests that its participants – not trained musicians and unfamiliar with Javanese music – were able to appreciate the new consonances of the bonang’s tones instinctively.

“Music creation is all about exploring the creative possibilities of a given set of qualities, for example, finding out what kinds of melodies can you play on a flute, or what kinds of sounds can you make with your mouth,” Harrison said.

“Our findings suggest that if you use different instruments, you can unlock a whole new harmonic language that people intuitively appreciate, they don’t need to study it to appreciate it. A lot of experimental music in the last 100 years of Western classical music has been quite hard for listeners because it involves highly abstract structures that are hard to enjoy. In contrast, psychological findings like ours can help stimulate new music that listeners intuitively enjoy.”

Exciting opportunities for musicians and producers

Dr Harrison hopes that the research will encourage musicians to try out unfamiliar instruments and see if they offer new harmonies and open up new creative possibilities.

“Quite a lot of pop music now tries to marry Western harmony with local melodies from the Middle East, India, and other parts of the world. That can be more or less successful, but one problem is that notes can sound dissonant if you play them with Western instruments.

“Musicians and producers might be able to make that marriage work better if they took account of our findings and considered changing the ‘timbre’, the tone quality, by using specially chosen real or synthesised instruments. Then they really might get the best of both worlds: harmony and local scale systems.”

Harrison and his collaborators are exploring different kinds of instruments and follow-up studies to test a broader range of cultures. In particular, they would like to gain insights from musicians who use ‘inharmonic’ instruments to understand whether they have internalised different concepts of harmony to the Western participants in this study.

Reference

R Marjieh, P M C Harrison, H Lee, F Deligiannaki, and N Jacoby, ‘Timbral effects on consonance disentangle psychoacoustic mechanisms and suggest perceptual origins for musical scales’, Nature Communications (2024). DOI: 10.1038/s41467-024-45812-z

̽��ֱ��tone and tuning of musical instruments has the power to manipulate our appreciation of harmony, new research shows. ̽��ֱ��findings challenge centuries of Western music theory and encourage greater experimentation with instruments from different cultures.

There are many more kinds of harmony out there

Peter Harrison

Pythagoras was wrong: there are no universal harmonies! | Cambridge research

Andrew Otto via Flikr under a CC license

A man playing a bonang

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Sing for the win

bjb42 — Sun, 22 Jul 2012 05:00:55 +0000

A new game for the iPhone and iPad called SingSmash is taking an innovative approach to familiarising people with music theory - by sneaking it through the backdoor.

Gamers have to sing into their phone or tablet. By hitting the required note at the right moment, a chunk of translucent wall is briefly rendered impermeable - hopefully in time to bounce a constantly moving ball back at the opposite side, knocking out blocks to progress to increasingly complex levels.

Released today, the game - which is like a handheld mash-up of a brightly coloured ‘Pong’ and an exacting, stripped-down ‘Rock Band’ - was developed by MPhil student Charlie Williams from the Centre for Music and Science as a response to his experiences of teaching music.

Using the game format, the app gets people stretching their vocal chords to ricochet the ball back at opposing blocks - while stealthily introducing them to notation by telling them what they’ve just sung.

“I didn’t want to put theory up front and scare people by stating ‘Now try and sing a harmonic minor scale’ - which can sound pretty daunting,” says Williams. “But if you beat a level, then you find out ‘Guess what? You’ve just sung a harmonic minor scale!’ - people can start to gain confidence, recognise notes and even discover talents with voice and pitch they may have never realised they possess.”

Williams feels that the way a lot of music is taught to beginners can often miss the point: that the first and most important thing with music is to have a go. He hopes SingSmash will help people overcome self-consciousness and get them to do just that, singing an increasingly adventurous series of notes and even licks as they progress.

“In many music lessons, you learn the names for things first and then you learn how to do it - which seems completely backwards and can put people off. When I teach music I try to emphasise actually doing it first, and I wanted to build a game to encourage that and make it fun, while slipping in the educational aspect so that if people want to build on skills they develop through the game then they can,” says Williams.

SingSmash uses inbuilt algorithms and pitch detectors to match the incoming sound to the best fit note within a broad but specified spectrum. To help people stay within the right range, the background music and in-game sounds - such as the collision noise - subtly match the notes of each level.

There is also a cunning secret feature - known in the gaming industry as an ‘Easter egg’ - which gives you a helping hand if you sing in a certain way, although Williams is keen not to spoil the surprise.

̽��ֱ��game starts at a basic level and is very kid-friendly, but employs increasingly complex musical motifs as players advance through the game - to the point where the beta-testers Williams used have yet to crack the hardest level with their voice alone.

“You can play SingSmash using an instrument too, and my most enthusiastic beta-testers said they could only beat the top level with guitar. To my knowledge, no-one has managed to beat it just by singing as yet, so that’s a challenge right there!”

̽��ֱ��app was built by Williams - who has gone from classically trained musician to self-confessed “tech-head” - in collaboration with musician Emma Hooper and graphic artist Jeff Kulak. It will initially cost 69p to download, a decision the team was reluctant to take, but, as Williams points out, “we are desperate to spend more time making games, and that takes money”.

Potential future projects include creating multi-player versions of the game and adapting it to incorporate rhythmic exercises. One of the important aspects for Williams is that SingSmash promotes the making of music, not just emulating pre-existing music. “Most music games - such as ‘Rock Band’ - are imitative. They are really fun games but with SingSmash you are actually making music for yourself,” he says.

“A lot of people who are self-taught are adverse to music theory, it can seem elitist and put people off. I’m hoping that people who play guitar in a band or whatever can use this as a fun way to build up their skills and explore new musical patterns.

“You don’t have to sing nicely, you just have to sing on the pitch - I hope this app will encourage people to not be so self-conscious and just make some noise. ̽��ֱ��best thing about kids is they just go for it right away, people are so worried about doing something wrong - this app is almost like a trick that might get adults to forget they are actually singing!”

A new app game developed by a Cambridge student challenges people to sing the right note at the right time in order to smash down a wall and advance to the next level - surreptitiously engaging them with basic music theory at the same time.

I hope this app will encourage people to not be so self-conscious and just make some noise.

Charlie Williams

Toby Farrell for Watershed Bristol

Testing Sing Smash

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Music of kindness: playing together strengthens empathy in children

bjb42 — Wed, 13 Jun 2012 05:00:06 +0000

Researchers looking at group education sessions for 8 to 11 year old children have shown that engaging in regular music-based activities with others - from ensembles to simple rhythmic exercises - can conspicuously advance empathy development, increasing a child’s capacity to recognise and consider the emotions of others.

A total of 52 children - boys and girls - were split into three groups at random. One of these groups met on a weekly basis to interact through musical games devised by the researchers, while the other two acted as control groups - one met with the same regularity but activities focused on words and drama but not music, the other received no additional activities.

Using standard and novel techniques such as answering questions designed to test compassion, and responding to emotion in facial expressions and movies, each child’s level of emotional empathy was evaluated at the start of the study and then again after a year. ̽��ֱ��researchers found that children in the music-based activity group showed a substantial increase in empathy scores and a higher average score compared to the other groups.

“These results bear out our hypothesis that certain components of musical interaction may enhance a capacity for emotional empathy, which continues outside the musical context,” says Tal-Chen Rabinowitch, from the Centre for Music and Science, who led the study.

“We feel that the program of musical activities we’ve developed could serve as a platform for a new approach to music education - one that helps advance not just musical skill but also social abilities and, in particular, the emotional understanding of others.”

̽��ֱ��activities used in the study were developed to emphasize the components of musical interaction that the researchers believed would promote empathy - fostering greater understanding of shared mental states.

These empathy-promoting musical components include imitation, where children were asked to mimic or match other players’ movements and musical motifs - such as in the ‘Mirror Match’ game - and entrainment, where the researchers used rhythm to encourage synchronised performance - so that children learnt to align and adjust themselves through attending to others.

By engaging with these musical activities, the children were regularly experiencing states of what the researchers describe as ‘shared intentionality’ - an understanding of each other’s intentions through a common aim or object of attention - creating an emotional affinity among the children.

̽��ֱ��team, which also included Professor Ian Cross, head of the Centre for Music and Science at the Faculty of Music, and Dr Pamela Burnard of the Faculty of Education, came up with increasingly complex music games to explore ‘shared intentionality’ - activities included creating music that reflected the perceived emotion of others, or composing music together with a clear theme.

According to the researchers, music and rhythm allows a sense of mutual ‘honesty’ that goes beyond the more precise expression in verbal communication. In essence, everyone can feel a rhythm and respond - sharing an experience regardless of linguistic skills.

“ ̽��ֱ��point about music is that it can make you feel as though you are sharing the same experience, when you don’t need to be doing the same thing or feeling the same way,” says Cross. “There is a strong sense in communal music that you simply do feel you are experiencing the same thing as everyone else.”

̽��ֱ��researchers believe that teaching emotional intelligence should become part of school curriculums, and that music might be a very good way to do it. “Increased ability to empathise may lead to altruistic behaviour that benefits educational environments such as patience and cooperativeness,” says Rabinowitch. “Previous studies have shown that children who score higher on an empathy scale are more likely to help others being bullied for example.”

“Working with children on social and emotional communication allows them to gain confidence in experiencing another person’s emotional state - and producing a supportive emotional response. We believe music to be one of the most welcoming and enjoyable - as well as extremely effective - mediums through which ‘empathy education’ can be achieved.”

“We hope to build on the suggestive results of this study and to replicate its findings with larger groups and in different cultural settings. One of the areas I’m keen to explore is its effectiveness on populations that are seen to have less capacity for empathy - such as those on the autistic spectrum.”

Adds Cross: “Conventional primary music education is thought of as skill or craft based, but in the context of a musical interaction program such as ours it’s not just learning to do something - it’s learning to interact with others. ̽��ֱ��findings show that music as a group medium can give rise to and sustain the development of empathy - but at the same time it is still artistic education, and there’s no reason it can’t be both.”

A year-long study on childrens' music-making indicates that playing music in groups on a regular basis greatly improves a child’s ability to empathise with others.

We believe music to be one of the most welcoming and enjoyable - as well as extremely effective - mediums through which ‘empathy education’ can be achieved.

Tal-Chen Rabinowitch

̽��ֱ�� of Cambridge

Festival of Ideas: Musical mayhem

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