Music, Maths, and Mash-Ups

It’s been a huge pleasure and a lot of fun to host Esa Räsänen and George Datseris here at Nottingham over the last few days. Once the video of George’s seminar, “Music Time Series Analysis: Universal Structure and Its Impact on the Listening Experience“, is edited and uploaded, I’ll write a longer post expanding on Esa’s and George’s work and the reasons why they both spent some time visiting our group at Nottingham. (I’ve been following Esa’s work for quite some time now…)

In between our discussions of 1/f noise, microtiming deviations, and power spectra, Esa introduced me to some classic compositions in the “mash-up” genre, of which I was previously only vaguely familiar. That meant that I was missing out on gems like this ground-breaking Bangles-Slayer collaboration…

Thank you, Esa, for expanding my musical horizons!

More soon on the physics behind Esa and George’s visit, but for now I’ll leave you with George’s wonderfully monikered (and logo-ed) band, The Max Funk Institute. George, a professional drummer, has recently completed his PhD at, you guessed it, the Max Planck Institute. He’s clearly a polymath; music, physics, and — as the first few seconds of the video below show — acting all fall within his sphere of expertise….

“The drum beats out of time…”

Far back in the mists of time, in those halcyon days when the Brexit referendum was still but a comfortably distant blot on the horizon and Trump’s lie tally was a measly sub-five-figures, I had the immense fun of working with Brady Haran and Sean Riley on this…

As that video describes, we tried an experiment in crowd-sourcing data via YouTube for an analysis of the extent to which fluctuations in timing might be a signature characteristic of a particular drummer (or drumming style). Those Sixty Symbols viewers who very kindly sent us samples of their drumming — all 78 of you [1] — have been waiting a very, very long time for this update. My sincere thanks for contributing and my profuse apologies for the exceptionally long delay in letting you know just what happened to the data you sent us. The good news is that a paper, Rushing or Dragging? An Analysis of the “Universality” of Correlated Fluctuations in Hi-hat Timing and Dynamics (which was uploaded to the arXiv last week), has resulted from the drumming fluctuations project. The abstract reads as follows.

A previous analysis of fluctuations in a virtuoso (Jeff Porcaro) drum performance [Räsänen et al., PLoS ONE 10(6): e0127902 (2015)] demonstrated that the rhythmic signal comprised both long range correlations and short range anti-correlations, with a characteristic timescale distinguishing the two regimes. We have extended Räsänen et al.’s approach to a much larger number of drum samples (N=132, provided by a total of 58 participants) and to a different performance (viz., Rush’s Tom Sawyer). A key focus of our study was to test whether the fluctuation dynamics discovered by Räsänen et al. are “universal” in the following sense: is the crossover from short-range to long-range correlated fluctuations a general phenomenon or is it restricted to particular drum patterns and/or specific drummers? We find no compelling evidence to suggest that the short-range to long-range correlation crossover that is characteristic of Porcaro’s performance is a common feature of temporal fluctuations in drum patterns. Moreover, level of experience and/or playing technique surprisingly do not play a role in influencing a short-range to long-range correlation cross-over. Our study also highlights that a great deal of caution needs to be taken when using the detrended fluctuation analysis technique, particularly with regard to anti-correlated signals.

There’s also some bad news. We’ll get to that. First, a few words on the background to the project.

Inspired by a fascinating paper published by Esa Rasanen (of Tampere University) and colleagues back in 2015, a few months before the Sixty Symbols video was uploaded, we were keen to determine whether the correlations observed by Esa et al. in the fluctuations in an iconic drummer’s performance — the late, great Jeff Porcaro — were a common feature of drumming.

Why do we care — and why should you care — about fluctuations in drumming? Surely we physicists should be doing something much more important with our time, like, um, curing cancer…

OK, maybe not.

More seriously, there are very many good reasons why we should study fluctuations (aka noise) in quite some detail. Often, noise is the bane of an experimental physicist’s life. We spend inordinate amounts of time chasing down and attempting to eliminate sources of noise, be they at a specific frequency (e.g. mains “hum” at 50 Hz or 60 Hz [2]) or, sometimes more frustratingly, when the signal contamination is spread across the frequency spectrum, forming what’s known as white noise. (Noise can be of many colours other than white — just as with a spectrum of light it all depends on which frequencies are present.)

But noise is most definitely not always just a nuisance to be avoided/eliminated at all costs; there can be a wealth of information embedded in the apparent messiness. Pink noise, for example, crops up in many weird and wonderful — and, indeed, many not-so-weird-and-not-so-wonderful — places, from climate change, to fluctuations in our heartbeats, to variations in the stock exchange, to current flow in electronic devices, and, indeed, to mutations occurring during the expansion of a cancerous tumour.  An analysis of the character and colour of noise can provide compelling insights into the physics and maths underpinning the behaviour of everything from molecular self-assembly to the influence and impact of social media.

The Porcaro performance that Esa and colleagues analysed for their paper is the impressive single-handed 16th note groove that drives Michael McDonald’s “I Keep Forgettin’…” I wanted to analyse a similar single-handed 16th note pattern, but in a rock rather than pop context, to ascertain whether Procaro’s pattern of fluctuations in interbeat timing were characteristic only of his virtuoso style or if they were a general feature of drumming. I’m also, coincidentally, a massive Rush fan. An iconic and influential track from the Canadian trio with the right type of drum pattern immediately sprang to mind: Tom Sawyer.

So we asked Sixty Symbols viewers to send in audio samples of their drumming along to Tom Sawyer, which we subsequently attempted to evaluate using a technique called detrended fluctuation analysis. When I say “we”, I mean a number of undergraduate students here at the University of Nottingham (who were aided, but more generally abetted, by myself in the analysis.) I’ve set a 3rd year undergraduate project on fluctuations in drumming for the last three years; the first six authors on the arXiv paper were (or are) all undergraduate students.

Unfortunately, the sound quality (and/or the duration) of many of the samples submitted in response to the Sixty Symbols video was just not sufficient for the task. That’s not a criticism, in any way, of the drummers who submitted audio files; it’s entirely my fault for not being more specific in the video. We worked with what we could, but in the end, the lead authors on the arXiv paper, Oli(ver) Gordon and Dom(inic) Coy, adopted a different and much more productive strategy for their version of the project: they invited a number of drummers (twenty-two in total) to play along with Tom Sawyer using only a hi-hat (so as to ensure that each and every beat could be isolated and tracked) and under exactly the same recording conditions.

You can read all of the details of the data acquisition and analysis in the arXiv paper. It also features the lengthiest acknowledgements section I’ve ever had to write. I think I’ve thanked everyone who provided data in there but if you sent me an MP3 or a .wav file (or some other audio format) and you don’t see your name in there, please let me know by leaving a comment below this post. (Assuming, of course, that you’d like to be acknowledged!)

We submitted the paper to the J. New Music Research last year and received some very helpful referees’ comments. I am waiting to get permission from the editor of the journal to make those (anonymous) comments public. If that permission is given, I’ll post the referees’ reports here.

In hindsight, Tom Sawyer was not the best choice of track to analyse. It’s a difficult groove to get right and even Neil Peart himself has said that it’s the song he finds most challenging to play live. In our analysis, we found very little evidence of the type of characteristic “crossover” in the correlations of the drumming fluctuations that emerged from Esa and colleagues’ study of Porcaro’s drumming. Our results are also at odds with the more recent work by Mathias Sogorski, Theo Geisel, Viola Priesemann (of the Max Planck Institute for Dynamics and Self-Organization, and the Bernstein Center for Computational Neuroscience, Göttingen, Germany) — a comprehensive and systematic analysis of microtiming variations in jazz and rock recordings spanning a total of over 100 recordings.

The likelihood is that the conditions under which we recorded the tracks — in particular, the rather “unnatural” hi-hat-only performance — may well have washed out the type of correlations observed by others. Nonetheless, this arguably negative result is a useful insight into the extent to which correlated fluctuations are robust (or not) with respect to performance environment and style. It was clear from our results, in line with previous work by Holger Hennig, Theo Geisel and colleagues, that the fluctuations are not so much characteristic of an individual drummer but of a performance; the same drummer could produce different fluctuation distributions and spectra under different performing conditions.

So where do we go from here? What’s the next stage of this research? I’m delighted to say that the Sixty Symbols video was directly responsible for kicking off an exciting collaboration with Esa and colleagues at Tampere that involves a number of students and researchers here at Nottingham. In particular, two final year project students, Ellie Hill and Lucy Edwards, have just returned from a week-long visit to Esa’s group at Tampere University. Their project, which is jointly supervised by my colleague Matt Brookes, Esa, and myself, focuses on going that one step further in the analysis of drumming fluctuations to incorporate brain imaging. Using this wonderful device.

I’m also rather chuffed that another nascent collaboration has stemmed from the Sixty Symbols video (and the subsequent data analysis) — this time from the music side of the so-called “two cultures” divide. The obscenely talented David Domminney Fowler, of Australian Pink Floyd fame, has kindly provided exceptionally high quality mixing desk recordings of “Another Brick In The Wall (Part 2)” from concert performances. (Thanks, Dave. [3]) Given the sensitivity of drumming fluctuations to the precise performance environment, the analysis of the same drummer (in this case, Paul Bonney) over multiple performances could prove very informative. We’re also hoping that Bonney will be able to make it to the Sir Peter Mansfield Imaging Centre here in the not-too-distant future so that Matt and colleagues can image his brain as he drums. (Knock yourself out with drummer jokes at this point. Dave certainly has.) I’m also particularly keen to compare results from my instrument of choice at the moment, Aerodrums, with those from a traditional kit.

And finally, the Sixty Symbols video also prompted George Datseris, professional drummer and PhD student  researcher, also at the Max Planck Institute for Dynamics & Self-Organisation, to get in touch to let us know about his intriguing work with the Giesel group: Does it Swing? Microtiming Deviations and Swing Feeling in Jazz. Esa and George will both be visiting Nottingham later this year and I am very enthusiastic indeed about the prospects for a European network on drum/rhythm research.

What’s remarkable is that all of this collaborative effort stemmed from Sixty Symbols. Public engagement is very often thought of exclusively in terms of scientists doing the research and then presenting the work as a fait accompli. What I’ve always loved about working with Brady on Sixty Symbols, and with Sean on Computerphile, is that they want to make the communication of science a great deal more open and engaging than that; they want to involve viewers (who are often the taxpayers who fund the work) in the trials and tribulations of the day-to-day research process itself. Brady and I have our spats on occasion, but on this point I am in complete and absolute agreement with him. Here he is, hitting the back of the net in describing the benefits of a warts-and-all approach to science communication…

They don’t engage with one paper every year or two, and a press release. I think if people knew what went into that paper and that press release…and they see the ups and the downs… even when it’s boring… And they see the emotion of it, and the humanity of it…people will become more engaged and more interested…

With the drumming project, Sixty Symbols went one step further and brought the viewers in so they were part of the story — they drove the direction of the science. While YouTube has its many failings, Sixty Symbols and channels like it enable connections with the world outside the lab that were simply unimaginable when I started my PhD back in (gulp…) 1990. And in these days of narrow-minded, naive nationalism, we need all the international connections we can get. Marching to the beat of your own drum ain’t all it’s cracked up to be…

Source of cartoon: https://xkcd.com/1736/


[1] 78. “Seven eight”.

[2] 50 Hz or 60 Hz depending on which side of the pond you fall. Any experimental physicist or electrical/electronic engineer who might be reading will also know full well that mains noise is generally not only present at 50 (or 60) Hz — there are all those wonderful harmonics to consider. (And the strongest peak may well not even be at 50 (60) Hz, but at one of those harmonics. And not all harmonics will contribute equally.  Experimental physics is such a joy at times…)

[3] In the interests of full disclosure I should note that Dave is a friend, a fan of Sixty Symbols, Numberphile, etc.., and an occasional contributor to Computerphile. He and I have spent quite a few tea-fuelled hours setting the world to rights

 

 

The Rhythm Method: Crowd-sourcing Drum Science

It’s always fun making Sixty Symbols/Numberphile videos with Brady Haran but the most recent filming brought together quite a number of my core enthusiasms — Rush, physics, drums, and noise (in all senses of the term) — and so was even more enjoyable than usual.

Brady uploaded the videos this morning (here and here). The first discusses a fascinating recent paper by Esa Räsänen and colleagues which focuses on the fluctuations in timing in the virtuoso drum pattern played by Jeff Porcaro in Michael McDonald’s “I Keep Forgettin’ “. I’m not a huge fan of the song but Porcaro’s groove is certainly infectious. He’s also responsible for the fantastic drumming in this classic, among so many other others. (Please excuse the excruciatingly high cheese factor in that Toto video. It was the Eighties.)

Fortuitously, I read the paper by Esa, Holger and their colleagues at around about the time an e-mail arrived asking for suggestions for undergraduate projects. As Esa et al. state in the conclusions of their paper, there is particularly exciting scope to extend their analysis to other songs, drummers, and styles. So I proposed an analysis of fluctuations in drum beats as an undergraduate project and was delighted when two 3rd year Physics students at Nottingham, Easel Kandola-McNicholas and Adeel Bokhari, selected the project.

What we want to do is analyse the fluctuations in timing/rhythm for not just one drummer — as Esa, Holger et al. did — but for as many drummers as possible. Enter Sixty Symbols. While we could have stuck with an analysis of the Porcaro pattern — and, indeed, if you’re a drummer, please feel free to send us your version of “I Keep Forgettin’ ” to the address below — there’s another single-handed 16th note pattern which is very famous among drummers: Rush’s “Tom Sawyer”. Neil Peart is widely recognised as among the very best rock drummers in the world, and there are very interesting parallels with the Porcaro track in terms of the way the 16th note pattern is played, so, in many ways, “Tom Sawyer” is a natural choice. (My love of Rush is, of course, entirely coincidental…)

I put together this short video (using the wonder that is Aerodrums — see below) to show some examples of the 16th note patterns in “Tom Sawyer” and to explain what we need for the analysis.

Our aim is to publish the analysis and include the names of all those who contributed their version of “Tom Sawyer” (and/or “I Keep Forgettin’ “) in the paper. If you’re a drummer and you’d like to contribute please e-mail your WAV, MP3, or MIDI file (or any other appropriate file type) to drumsciproject@gmail.com. There’s no deadline — we’ll accept drum tracks for as long as it takes to get good statistics for the analysis. The more, the merrier.

By the way, Aerodrums are available here. I enthusiastically recommend them! I’m not a drummer and so Aerodrums are ideal for learning to play and for putting down rhythms when song-writing or demoing tracks. But they’re much more than this — in very many ways, Aerodrums are just as good as a real kit, as this impressive example of virtuoso aerodrumming shows…

[A huge thank you to the University of Nottingham BandSoc and, in particular, Jedd Bellamy-Carter for providing the practice room for the video and for all their help with equipment].