A video of the meetup is here: [skillsmatter].
Steven's slides are here: [pdf slides].
Precisely Timed Music
In 1996 Steven read about György Ligeti’s mechanical music. Ligeti's 1962 Poème Symphonique in particular was interesting - a composition for 100 metronomes, each set to different speeds.The piece explored the idea of music from the interplay of precisely timed beats. Importantly, no human could play such music because the accuracy needed is beyond our ability. If you listen to the music above, you'll hear the music change from saturated noise to periods of coherent synchronisation, which disperses again.
There are parallels here to mathematics and physics. In mathematics we have the idea of number multiples, like 2, 4, 6, 8... and 3, 6, 9, 12 ... Sometimes these sequences cross paths, sometimes they overlap completely. Some numbers are always beyond reach - the mysterious primes. In the physical world, we have periodic water waves, which sometimes run past each other, sometimes cancel each other out, sometimes join to reinforce each other .. and sometimes they cause a great non-linear "breaking" wave.
Technology 1962 to 1996
Steven was inspired to experiment creating similar music himself. Ligeti used instruments that were available to him at the time in 1962 - and the metronome was the only reasonable way of generating such precisely timed sound.
Unlike Ligeti, Steven had access to modern (for 1996) technology like computer-based music sequencers and MIDI.
Today, Steven also uses software he developed himself, a javascript and C based MIDI library.
The Process of Idea to Music
Steven gave several examples of the work that goes into building from a core mathematical idea to creating a piece of music that actually sounds like music and is interesting to listen to.He started with a very simple example.
The above shows a rhythm with 1 note per bar, then 2 per bar, then 3 per bar, 4 per bar, then finally 5 per bar. As a mathematical idea that is simple and rather pleasing. In this particular example, each bar is repeated twice.
If only it were that easy to make successful algorithmic music!
Steven underlines this point and discussed how we need to think about several questions, such as:
- which notes (frequencies) we want to place at each of those dots marking the rhythm?
- how many notes to choose from?
- which instruments?
- any fades or transitions?
- vary speed over the piece too?
Steven chose to transition between a piano and a harp, with variations in speed. You can hear the piece in the video at about 9m50 [video]. The result is a very interesting and engaging!
MIDI Libraries
Instead of having to play music himself by hand, Steven wrote his own libraries for writing MIDI files.MIDI is a technical standard for communicating music between tools and instruments. MIDI files can contain music, but a common misunderstanding is that they are like mp3 files. MIDI files contain information about which notes occur when, and how they occur (eg loudness, duration). The sounds themselves are separate, but a MIDI file will refer to sounds and instruments for playback.
MIDI libraries allowed Steven to create these MIDI files from his own programs. Those MIDI files could then be played back, or modified, by other music tools.
See the resources below for links to a javascript and a C based library.
MIDI Process
Steven went on to explain his process with an example of MIDI generated by his own computer program. He explained that too often the result of directly playing back music created like this something that sounds horrible.Again, he came back to the theme of having to put in additional work to turn the output of simple algorithms into something listenable. He explained additional things that needed to be thought about when developing the first raw MIDI from a mathematical idea:
- relative volumes of different instruments, and individual notes to avoid them being hidden in the noise
- introductions / outros
- changing sounds/instruments so they work better - pianos don't sound like harps, which don't sound like human voices - they have different timbre.
For me personally, the amount of work involved in sound and music "direction" was something I was previously unaware of.
Fractal Music
Steven demonstrated another idea where he started with a melody of notes, and for the next accompaniment he took every second note, and repeated this idea.
This is similar to the process of creating mathematical fractals - self-similar Cantor sets for example.
The result of taking out every other note, repeatedly, is a melody that's the same as the original - which you can see visually above.
From an algorithmic perspective, this seems like a great idea. Steven played a version of music based on this theme (at 32m50 in the video). It sounded fantastic - but only after a fair bit of human work:
- orchestration to choose which instrument when
- which parts to repeat as a motif
- add elements like a cymbal crash to highlight repeats
- overall structure of 5 repetitions
- play the 2nd repeat backwards
- relative dynamics and emphasis - eg building to a climax
- remove notes towards the end when they oversaturate
Written But Not Recorded
After taking us through some more examples of algorithmically based music, Steven took us through an often overlooked step - that of actually recording and producing music.The central point is that what we might produce at home will very likely sound different when other people listen to the music on their equipment.
Part of the approach is to use high quality equipment and sounds to recreate the music with high fidelity - the master. From this master, versions can be produced for listening on personal audio players and tiny headphones. In addition, recording studios will have expertise in avoiding sound which works in the studio but won't on cheaper and smaller equipment.
Conclusion
The main point for me was that it is great to have mathematically interesting ideas for creating music - but it can only be a starting point, a basis even. Once the theme has been set, a human artist does need to put in a fair bit of work to create works that are listenable music.Having said that, some of the algorithmic themes are really interesting - the fractal music was really interesting and very pleasing too.
Symphony No. 1 in C# Minor
You can listen to Steven's impressive symphony at his website. Click the following to be taken to Steven's site.
Afterthought: 2001 A Space Odyssey
Steven's talk inspired me to explore Ligeti and I found that his music was used by Stanley Kubrick. I hadn't realised that the haunting Lux Aeterna used in 2001 A S[ave Odyssey was created by Ligeti.Resources
- http://marquisdegeek.com/music - Steven's website, music section
- https://github.com/MarquisdeGeek/sml - Steven's javascript midi library
- https://github.com/MarquisdeGeek/midilib - Steven's pure C midi library
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