I have been singing in choirs or accompanying one on the piano, from when I was 10 — long before I knew anything about collective phenomena. Recently, I had the opportunity to be the conductor and trainer of the RTMC choir and that is when my right and left brains said eureka in unison! While I have always enjoyed choir music I had failed to notice the connection between choral singing and collective phenomena.
Systems made up of many interacting entities that interact non-linearly, can give rise to a behavior that is characteristic of the whole. Birds flocking together or fish schooling together in water are fine examples of collective behavior; individual organisms do not know the sheer complexity of the shape or dynamical features of the group that may offer them survival advantages. They simply follow a rule and the collective behavior emerges!
In a typical choir, there are four parts: Soprano, Alto, Tenor and Bass. Each part is sung by a group of people who share a common range of pitch (frequency) that they are comfortable to sing. For example sopranos sing high frequencies and hence women whose voices are sharp and shrill take that part. Those with deeper voices sing Alto. Men who can sing higher frequencies take Tenor while the other men who can reach really low frequencies are in Bass. Another way to visualise this, would be to picture the different instruments in a string quartet: violin, viola, cello and double bass.
Choral music is written in such a way that each of these parts can contribute to the song. The tune of the song is usually sung by the Soprano. Other parts do not sing the same notes as the Soprano but rather carefully chosen different notes that, which when put together sounds pleasing to the ear. We call this ‘harmony’. Interestingly, what I realised was that harmony is an emergent phenomena, much like a flock of birds that appear to dance in the sky. The choristers (singers) do not see the grand picture, unless all the parts contribute and the resultant music emerges from this communion. In fact, sung alone, some of these parts may not be interesting at all.
At first notice, choral singing may not appear as a typical example for collective behavior. This is because a choir follows a particular music (notes) where the composer (of that music) has prescribed a certain rhythm, tune and expression for each of the parts. In contrast to systems like a flock of birds where there is no template; a leaderless group can show flocking. In my experience with choral singing, individuals seldom follow the notes to perfection. They may lag behind or race past the right beat, not hit the correct pitch of the note and increase or decrease the volume of singing with delays. During my time as a conductor I noticed how individuals their best to maintain tempo (timing) and pitch by virtue of interaction with their neighbours (of the same and sometimes of different parts). Say for example, if they were lagging behind, they would try to catch up by listening to the singing of the others. Sometimes, when a part has missed their note (pitch) they try to catch up and get their note, and this is typically done by adjusting their pitch to that of the other parts. This kind of interaction is similar to what the fish do when schooling in a puddle of water. They copy the direction of the neighbouring fish and as a result, the group identifies a common direction to move. In the algorithms literature, this is commonly known as the consensus algorithm where a group of agents come to a consensus through interaction.
It has been shown that a single musician following written music would make deviations that had a power law dependence (Hennig et al, 2012). The authors believe that this ‘imprecision’ is inherent in the music played by humans and is what makes music more ‘human’. Simply put, a listener could easily distinguish a computer playing music with high precision from that played by humans. In a choir, where there are repeated interactions between the different choristers, significant deviations from the written music will be inevitable. It will bear signatures of the complex interactions in the system. Characterising these deviations and understanding its structure may help in identifying what makes choral singing beautiful and human.
Another interesting behavior is observed when there are no accompanying instruments. When the choir attempts a song that is high in pitch compared to what is comfortable for the choristers on an average, we would observe a collective pitch change. Choristers who find it hardest to maintain pitch, start to deviate from the pitch slightly lower from the correct one. They try to make amends as and when they hear their neighbours sing differently. However, the neighbours are also influenced by this lowered pitch, as it offers a more comfortable singing experience and hence, very slowly they start to copy and the average pitch starts to fall. This results in a collective pitch change. This transition is very slow and is hardly noticed by the conductor or the choristers. Only when an instrument is used to sound the chord at some-point during the song, the lowered pitch becomes obvious.
Choral singing is collective in nature and the emergent dynamics that is a result of this complex behavior makes a choir an interesting model system for studying collective phenomena. Questions that follows naturally are,
Can one do experiments on a choir to understand how the choristers interact?
Can a novice and an expert choir be characterised from the way they interact?
Can a new learning strategy be developed that can help the choir become better?
Answers to these questions are yet to be discovered!