It’s been over a decade since I collaborated on this metallized paean to the golden ratio. Ever since, I’ve wanted to adopt a similar approach to a quantum physics-inspired metal song, but, as Mr. Waters puts it in that timeless Floyd classic, “Every year is getting shorter, never seem to find the time.” The pandemic finally gave me the opportunity to organise and demo some ideas, but it’s then taken a couple more years to claw enough time to finally track, mix, and master the song in question. En route, we had a bass-playing physics teacher (thanks, James!), a guitar-playing physics research fellow (thanks, Chris!), and a “choir” of Nottingham’s undergraduate physics students (with just a few non-physicist interlopers….shhh) contribute to the song. Thank you all!
The video for the resulting song, “Shut Up And Calculate”, was finally uploaded to Sixty Symbols today:
I owe an astronomical debt of gratitude to both Sean Riley and Dave Fowler for their herculean efforts on the SUAC project. Sean, whose day job is with Computerphile, had the unenviable task of sifting through gaggles of gigabytes of video footage to produce the final video, while Dave had the equally arduous task of having to deal with mixing and mastering my sloppy recordings. What’s frankly astounding is that he did a great deal of that mixing work with a broken arm.
I’ve waxed lyrical before about Dave’s many talents — guitarist (not least with the Australian Pink Floyd Show), songwriter, producer, sound engineer, videographer, blogger, coder etc.. etc… — but I thought that one-armed mixing with Cubase would be beyond even Dave’s other-worldly skills set. I was wrong. (Here’s Dave in action with both arms in full working order, by the way:
And, of course, thank you, Brady, for indulging another metal-physics mash-up for Sixty Symbols.
For the golden ratio song, we revealed the links between the maths and the music at the same time as we uploaded the video. (For the more musically inclined, there’s more detail, and tabs, here.) With Shut Up And Calculate those links are instead hidden, for now, as physics “Easter eggs” in the riffs, rhythms, FX, and lyrics of the the song. Our hope is that Sixty Symbols viewers will discover the physics-music links for themselves. (All will be revealed in a future blog post and/or video.) Some of these are rather subtle. Others, less so.
This doesn’t mean that every single note in the song somehow relates to a physics equation or constant, however. I’ve got to thank an alumnus of the Nottingham Nanoscience Group, Alex Allen, for reining in my tendency to let the physics override the music — his extensive feedback on a first “draft” of SUAC was immensely helpful in letting the music breathe rather more. Some of the physics links are recurring motifs in the song, whereas others happen only once.
Although an initial idea to embed a physical constant as a modulated waveform throughout SUAC didn’t make the final cut, one particular sound effect was lifted directly from a quantum mechanical simulation. The “squelchy”, seventies sci-fi-inspired waveform that appears during the middle section of SUAC is taken directly from an audio encoding of the evolution of a superposition state in the infinite potential well. It’s not quite in the same league — or should I say the same universe? — as the fascinating musical encoding of quantum information that Philip Ball described in a recent issue of Physics World, but it’s still, nonetheless, an audio representation of the dynamics of an archetypal quantum system: the particle in a box model so beloved of physics undergrads.
The lyrics for SUAC are at the foot of this post. In addition to the references to quantum concepts and some wince-inducing physics puns, there are a couple of allusions to major musical inspirations for SUAC, namely Rush and Black Sabbath. The latter’s classic Mob Rules had a particularly strong influence on the writing of SUAC.
“Everything louder than everything else”
If I hadn’t opted to do a PhD, I’d have almost certainly aimed to find a career in sound engineering — I have always been fascinated by recording, mixing, and mastering techniques and processes. The “Classic Albums” BBC series, which dissects the music and production of, um, classic albums, has always been essential viewing — I’ve lost count of how many times I’ve watched the Number Of The Beast, 2112, and Rio episodes. (At the risk of sinking my metal credentials without trace, I’m a big Duran Duran fan. They’re superlative songwriters — Save A Prayer alone is enough to afford them iconic status in my book.)
Sound engineering is underpinned by a great deal of physics, aspects of which Dave and I discuss in the accompanying “Making of…” video for SUAC. But there’s also quite a bit of rather less-than-scientific thinking out there. Glenn Fricker, audio engineer at Spectre Sound Studios, has a popular YouTube channel where — when not yelling at 140 dB about tone-deaf bass players or egomaniacal singers — he critiques the “received wisdom” on a variety of sound engineering topics, including, in particular, guitar tone. Fricker adopts a refreshingly objective and science-driven approach in analysing the contributions of tonewood, pickups, amplifier tubes (i.e. valves, as they’re known this side of the pond) etc.. to the sound of a guitar in a metal/rock context. (Remarkably, some have even claimed that the type of battery in a guitar pedal has a discernable effect.)
As Fricker points out, there are a lot of frustrating myths — and a great deal of snobbery (surrounding expensive gear and instruments) — behind many of the claims about the nuances of guitar tone. He has aimed to debunk some of these in a series of videos, including this:
It’s fair to say that Fricker’s arguments have met with a robust response across the guitar/sound engineering communities. Regardless of whether we agree with Fricker or not, however, his systematic approach to tackling this age-old question is to be applauded. (For what it’s worth — and I’m certainly not a professional — I have a great deal of time for his stance. There’s also a direct link between Fricker and Shut Up And Calculate: his Spectre Digital company’s Extinction Level Event library was used, in conjunction with Aerodrums, for the drum tracks.)
More generally, the question of subjective perception vs objective signal processing in mixing and mastering music is, to put it mildly, vexed. What we hear depends very much on the environment in which we’re listening and on the volume of playback. The latter is especially problematic when it comes to trying to “objectively” mix and master a track so that it will sound the same regardless of the listening conditions. Essentially, it’s impossible to do this, not least because of the insights of physicists Harvey Fletcher and Wildon Munson almost a century ago. (According to Wikipedia, Fletcher is known as the father of stereophonic sound. His PhD thesis advisor was Millikan, of oil drop fame.)
The Fletcher-Munson curves shown below, taken from their influential 1933 paper, “Loudness, its definition, measurement and calculation” [J. Acoust. Soc. Am. 5, 82 (1933)], demonstrate how our perception of sound depends critically on frequency and volume. I’ll save a detailed discussion for a future post, but the central message from that graph is that the volume at which we play a song has a significant influence on our perception of different frequency ranges. So too, of course, does the sound system/monitors/headphones on which we’re listening. (Another piece of received wisdom in the sound engineering community is that mixing on headphones is very much frowned upon. I’ve never really quite understood this, for all of the reasons described here.)
While there are many arguments and debates about the minutiae of mixing music, one widely accepted premise is that louder is better. Stories abound of musicians bitterly complaining to a producer about a mix, only to be completely happy with exactly the same mix when they returned an hour later. In the intervening sixty minutes, all that happened was that the producer pushed the master volume up a few dB. One reason for our preference for loud music can again be gleaned from the Fletcher-Munson curves above: louder means, for one, a much less rapid fall-off in low end frequencies, improving our overall perception of the audio spectrum. However, as much as we may, to quote Simmons et al., love it loud, there are limits to just how far the loudness can be pushed. This is true even for — indeed, especially for — metal fans.
The so-called loudness wars took this premise to an extreme end: all the dynamics — all the life — was sucked out of music in a quest for ever-louder tracks (as these would grab more attention on streaming platforms). Metallica’s Death Magnetic is generally held up as the worst culprit but, for me, the biggest victim of the loudness wars is the music of Baroness, especially on their Purple album. This is pushed to the limit of clearly audible audio distortion and clipping — hear for yourself — and makes the album virtually unlistenable. I don’t quite know why the band would allow their carefully crafted music to be butchered like this.
In the last couple of years streaming services have imposed loudness limits using the LUFS (Loudness Units relative to Full Scale) standard. On YouTube, for example, tracks that have an integrated LUFS above a value of -14 will be turned down. Some claim that this represents the end of the loudness wars. I’m not so sure. For one, streaming services don’t always implement the loudness limits. Moreover, automated/AI mastering services tend to still offer a variety of loudness options. eMastered, for example — which I used to make reference masters of SUAC before Dave wove his magic — has loudness options ranging from “Normal” to “Extreme.” Here’s how they look:
Those are the stereo mastered tracks over roughly the same timespan of ~ 1 minute, on the same y-axis scale. Note how the lower pair of waveforms show a great deal less variation in amplitude, and thus have a much higher integrated loudness. Each of the mastered tracks is linked below, for comparison.
Normal volume eMastered master of Shut Up And Calculate
Extreme volume eMastered master of Shut Up And Calculate
Fortunately, we don’t need to worry about quantum loudness wars just yet —quantum music is in its infancy. I look forward to the day when the first metal track is produced by an AI-driven quantum computer. Just as quantum computing won’t, however, completely supersede and replace its classical counterparts (despite many pundits’ excitable claims to the contrary), I’m sure that quantum and classical metal will be able to peacefully loudly coexist.
I’ll close with the lyrics to SUAC, as promised. Despite the traditional advice, this time I’ll be reading the YouTube comments with quite some interest!
Bracket the vector, apply operator
Bit by bit, by bit by bit … how low can we go?
Bit by bit, by bit by bit… in thine eye, in thine i
It’s just a phase that you’re going through
The action speaks louder than surds
Don’t question the direction
Or all is scattered on the shore
Shut up and calculate… the numbers don’t lie
This is the root, the root, the root of all things….
You will never deviate from the norm
You will never deviate from the norm
You will never deviate from the norm
You will never deviate from the norm
