The Exchange: Chorusing and John Smith discuss acoustics and shaping songs.

The Arts and Sciences used to share much of the same intellectual space. Only recently have they diverged to the degree that they seem diametrically opposed. The Exchange is our attempt to rekindle some of the dialogue that occurred between the two fields.

In this installment, we’ve brought together Western Vinyl’s Chorusing and John Smith, an experimental physicist at the University of New South Wales.

Matthew O’Connell aka Chorusing is Western Vinyl recording artist based out of North Carolina. His debut album, Half Mirror, superimposes warm analog synths onto self-described “confessional folk” with a simultaneously cosmic and earthly outcome. Tracked at home in the mountains of North Carolina using a vintage tape delay, electric guitar, and a self-designed synthesizer named ‘Balsam,’

O’Connell also spent some time working at Moog. He described his experience there to Brooklyn Vegan: “One of my tasks at Moog Music was to test vintage bucket brigade chips to use in their delay units. I would spend all day sitting in front of a spectrum analyzer, passing pink noise through them, seeing what came out on the other end. I still have a prototype delay from that era, which I used all over Half Mirror. It’s a special object to me, and it adds a nice analog haze to anything it touches.”

John Smith is an experimental physicist who has spent his academic life working in Sydney. Currently, he conducts his research at the University of New South Wales. His main research interest in recent years has been the development of new techniques for the rapid and precise measurement of acoustic impedance spectra with a very large dynamic range.

In the last few years his research has focussed on the acoustic properties of the human voice and musical instruments, and how the vocal tract of a player can interact with their instrument.

Along with his long-time colleague, Joe Wolfe, Smith maintains a popular website called Music Acoustics that deals with their research and musical acoustics in general.

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MATTHEW O’CONNELL: Lately I’ve been experimenting with old digital samplers in my music (Casio SK-1s, Yamaha VSSs, etc). They’re cheap, fun, and not too hard to come by if you frequent the right thrift stores. Part of the appeal is that these keyboards seem to add strange, ghostly harmonics when you play back samples through them. I read that these harmonics might be a result of a phenomenon called aliasing or folding. Could you explain what that is and how it affects digital audio?”

JOHN SMITH: Aliasing can occur when we measure a signal at a number of discrete instants in time. This is called the sampling frequency, and for audio measurements it is determined by the recording electronics. If we start by considering a simple sine wave as the input signal, we can only describe it accurately if we make at least two measurements every cycle. This means that any signal we sample with a frequency that is greater than one half of the sampling frequency, will not be well defined. This upper frequency limit is known as the Nyquist frequency. 

So, for an example, let’s assume that we make measurements with a sampling frequency of 8 kHz. The Nyquist frequency will thus be 8 /2 = 4 kHz.

If we sample a pure sine wave of frequency 3 kHz, this is less than the Nyquist frequency of 4 kHz and it will be reproduced accurately when played back. However, if we sample a 5 kHz sine wave it turns out that the measurements will be exactly the same as when we measured the 3 kHz sine wave – this 3 kHz signal is an ‘alias’ of the original 5 kHz signal. 

So, if we now play back our recorded 5 kHz signal we get a 3 kHz signal rather than the original 5 kHz input signal; it has been ‘folded back’ at the Nyquist frequency.

Indeed, for a sine wave with a frequency that lies between the Nyquist frequency and the sampling frequency, the alias will be a sine wave with a frequency that is as far below the Nyquist frequency as the input signal was above it. Another way to think of this is that the alias will be at a frequency given by the sampling frequency (i.e. twice the Nyquist frequency) minus the input frequency.

So far we have considered only a simple sine wave input as the input, however most input signals will be more complicated and contain harmonics. Now the consequences of aliasing can become much more interesting.

For most sounds with a fundamental frequency of frequency f, these harmonics will be in the ratio f, 2f, 3f, 4f, etc; the usual harmonic series. However, once aliasing occurs, the higher harmonics need no longer be in the harmonic series.

Let’s consider an input signal with fundamental frequency of 1.5 kHz that contains 4 harmonics; the frequencies will be 1.5, 3, 4.5, and 6 kHz. The frequency ratios will be 1:2:3:4 and it will sound like a normal instrument. If it is sampled at 8 kHz, the component at 4.5 kHz will have an alias at 3.5 kHz (i.e. 8kHz – 4.5kHz) and the component at 6 kHz will have an alias at 2 kHz (i.e. 8kHz – 6kHz). The playback sound will thus contain frequencies at 1.5, 3, 3.5, and 2 kHz; certainly not the harmonic series in the original sound, and it can have a quite different sound. 

Interesting things will happen if the fundamental frequency changes; if it increases the aliases of harmonics above the Nyquist frequency will actually decrease in frequency, and vice versa.

So far we haven’t considered how strong these aliased signals will be – ideally the input signal will be low-pass filtered so that frequencies above the Nyquist frequency simply don’t get through to be measured, and so don’t contribute to the output sound. However, this requires additional electronics and involves extra cost; an inexpensive sampler might skimp on the filtering and so input frequencies above the Nyquist frequency could produce strange harmonics in the output sound. Indeed, I suspect that these unexpected strange sounds can be part of the fun.

Aliasing shouldn’t normally be a problem in professional audio. A very high sampling rate is used, usually 44.1 kHz or 48 kHz. The means the Nyquist frequency will lie well above the standard audio range. Just in case there are some ultrasonic components present in the input signal, the input is drastically low-pass filtered so that only signals in the audio range can get through to be measured.

JOHN SMITH: Your songs have many important elements: there are the lyrics and the tune, there are often repeated riffs in the background and often an overall ambience generated by electronic or more conventional instruments. I’m interested to know more about your creative process and inspiration. Is there a common starting point, perhaps the idea for the lyrics, that you then develop and embellish?  Or is there a particular overall sound that you work towards by combining various elements?

MATTHEW O’CONNELL: I’m still very much learning how to write and record music, so I usually rely more on instinct than any specific technique. Everything I’ve ever recorded has taken shape in its own idiosyncratic way, and I try to go along for the ride and stay open to however it unfolds.

When I was recording Half Mirror I was reading Zen Mind, Beginner’s Mind by Shunryū Suzuki.  The recurring guidance he offers is to stay present with every experience as if it’s entirely new, bringing none of your conditioning along with you. I’d never made a record before, so that wasn’t too much of a stretch for me, but the idea that I could take my ego and expectations out of that process was inspiring. I would just write and record what came up, trying not to get too involved in whether or not it was “good” or exactly what I was creating.  

All of the songs on that record were written and recorded as part of the same process. Each one would start out as a lyric or a melody that evoked a time or place for me. (Sometimes they would illustrate a real, autobiographical event. Sometimes they were imagined timelines that brought to light a more hidden, elusive experience.) Once I had that sense of place and mood, I would decorate and record in that spirit — writing more lyrics, overdubbing new sounds and textures, subtracting elements that sounded too boring or traditional, again trying to stay specific to the mood of the song. So in a way, I didn’t have any overarching sound or concept that I was working towards, it just sort of emerged from experimentation.

I know that might be a bit of an elusive answer to your question, but it’s really true that I don’t know what I’m making until I’m finished making it. I think that mystery of creativity gets at why art can be so fun and therapeutic for us humans. We get to tap into these hidden currents that we can’t really explain or map out with our logical minds.

Thanks so much for the question and for your sound explanation!

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