Xenakis' 'Nomos Alpha' recorded by Arne Deforce, with animation by Marcus du Sautoy & Simon Russell

Iannis Xenakis' 'Nomos Alpha' was performed by cellist Arne Deforce for Birmingham Contemporary Music Group's Music & Maths Festival, celebrating the composer's centenary.

The piece was performed with live animation created by mathematician Marcus du Sautoy and motion designer Simon Russell 29 May 2022 at CBSO Centre, Birmingham.

"'Nomos Alpha' is a perfect fusion of my two passions: the mathematics of symmetry and contemporary music. To celebrate Xenakis’s 100th anniversary I’ve been working with artist Simon Russell to create an animation to guide listeners (and players) through the piece. The composition is based on the symmetries of a cube. There are 24 ways to rotate a cube from its starting position. 'Nomos Alpha' is divided into 24 sections. My immediate thought was there is a section for each symmetry. However as a dug deeper into the piece I discovered something much more interesting is going on.

The piece is divided into 6 groups of 4 sections. The first 3 sections in each group correspond to 3 symmetries of the cube. A label in the animation keeps track of the symmetry being played. The 4th section is more fluid and imagines the cube morphing.

Xenakis places 8 musical textures for cello on the corners of the cube. In our animation these are called S1,…,S8. In each section these corners are played in a fixed order corresponding to two tetrahedra that can be embedded inside the cube. At the end of each section the cube then undergoes a rotation to rearrange the musical textures. The same path is mapped out in the new section but the textures are now played in a new order. A second cube (not shown in our animation) keeps track of the time spent on each corner.

The fascinating thing for me is how Xenakis chooses the symmetries. He starts with two seed symmetries called D and Q12. These control the first two sections. But to get the symmetry for the third section he rotates the cube using symmetry D and then rotates again using the symmetry Q12. The combined effect is a new arrangement that you can get in one go by doing symmetry Q4. For Xenakis each new symmetry is got by combining the two previous symmetries. This is a bit like the way the Fibonacci numbers are defined: 1,2,3,5,8,13…You get the next number by adding the previous two numbers.

It takes 18 symmetries before the sequence repeats. This is the longest cycle of symmetries you can realise in the cube. Some of these symmetries are repeated twice. The animation keeps track of the path that this maps out in the 24 symmetries of the cube.

This idea of a Fibonacci sequence of symmetries is not something that has ever been considered in mathematics. It is a new idea that Xenakis contributes. Often mathematics inspires music but here we see music inspiring new mathematical ideas."

Marcus du Sautoy, Professor of Mathematics, University of Oxford.

Birmingham Contemporary Music Group: Creating music for everyone and reflecting the beauty and challenges of our world today.

Birmingham Contemporary Music Group is a world-renowned new ensemble that has commissioned over 175 pieces of music from the finest composers and emerging talent. They have provided over 400 free music workshops to young people and raised over £325,000 for new music. BCMG believe that music has the power to bring people of all ages and backgrounds together. They build an inclusive community of composers, musicians, and audiences; enabling them to share their spark of imagination, creating beautiful and strange sounds.

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Music taken from Arne Deforce & Ensemble musikFabrik's recording 'Xenakis: Complete Cello Works'.

[mr.p.l.]

This is absolutely incredible! Xenakis has been one of my favourite composers for a while and I've been looking for more videos that explore the complexity of his pieces. This has definitely given me a deeper appreciation for this beautifully complex piece. Excellent work!

[shark_username]

it doesn't make sense at first but actually its as clear as it can get with these kinds of things

[TheFirstSeed]

wow! nicely done!! The visuals are so helpful for structural comprehension !!!

[soundtaxiproject]

You can see to which structure as listener you get in the process of interpretation. - See the music, hear the dance... ✌🎶🖇

[Eden_Laika]

Imagine playing this for Bach. I can't decide if he'd adore it or be terrified!

[DavidPerkins-usrb]

So helpful. Congratulations. A roadmap.

[marcellodantedealmeidanune]

Uma obra incrível associada ao padrão geométrico espacial do CUBO. É pura matemática nas 24 variações. Gostaria de ver como a obra se desenvolve em partitura.
Parabéns ao canal BCMG.

[marioserna]

Muy interesante la union entre las matemáticas, y la música contemporánea.

[ГалинаБельская-лх]

О!! Это теория графов, которой подчинено движение Вселенной. Все зависит от всего и это чарующая музыка зависимости, это порядок Вселенной, где нет ничего случайного.

[joaocorreia]

Ministries of culture or Uni math departaments should fund the math animations for his other pieces, there are only some 2d folios i think

[danlet]

It's like, math and geometry are the languages of the universe but the language is scary.
EDIT: This would make a perfect musical accompaniment to 2001: A Space Odyssey, with the whole *monolith* thing.

[BradEllis]

I have some questions. Some pitches are WELL below the standard range of the cello, and some of what I’m hearing seems to go beyond what can be produced simultaneously just relying on double stops, harmonics, col legno and pizz., etc.
At the end, we seem to be hearing 2 patterns of bowing simultaneously in different rhythms.
What supplemental performing techniques are we hearing?
Thanks in advance.

[juuSilence]

When you are searching for a preset in ableton

[gustavertboellecomposer]

I have never really understood this sort of marriage between maths and music. Like the math is interesting on its own, but it doesn't actually result in meaningful, audible musical phenomena. The quick test would be just to see if you could tell by ear alone if the material was randomly generated or generated with this algorithm. I reckon it is most likely impossible. I have the same sorts of complaints about other types of serialism, or trying to derive form and structure from algorithms.

Maths do absolutely have applications in music, but you have to use the appropriate kinds: You can use maths and physics to synthesize timbres, or maybe do more accurate polyrhythms, or timing different musical events within accelerating tempi, but generating musical material from arbitrary mathematical models seems meaningless to me.

[MegaCirse]

Bir hikayeye yanlış başlarsanız, sanki anlatacağınız konudan kaçıyormuş gibi, ana yoldan çıkıp karanlık ormanlara girip inkar ederseniz sürekli ve sonsuz bir yarışın içinde olursunuz. Yalana inanmak gerçektir. «Xenakis» onu her dinlediğimde beni kendi yalanlarımla yüzleşmeye zorluyor

[MagdalenaBetanzos-ostk]

Se trata de alquimia convertida en musica😅

[lucianogiordana]

Another name for this could be "child playing in Casio keyboard"

[hauthot]

I feel like I can hear some folk influences