And, it just doesn’t make sense to take the sound made by plucking a common, run-of-the-mill string and then post-processing to sculpt it into something more interesting. Where’s the inspiration coming from in this process? Surely it’s more likely Derbyshire would have started with an interesting ‘found’ sound as a basis for the bass note. This ties in with Mills’ explanations, both of which recount the use of, “19″ jack-bay panels,” and, “metal channelling”. Further, Mills more recently expanded on this with, “A simple steel wire was tensioned along the length of a standard 19” blanking plate from a jackfield bay,”. According to Radiophonic Workshop technician, Brian Hodgson, “Dick (Mills) is the only person who would really know.”.
So, could it be that Derbyshire was exploiting the resonant properties of a metal panel to amplify and modify the timbre of the string in the same way that a soundboard does on an acoustic guitar—accentuating frequencies in the region of the 8th harmonic acoustically, rather than electronically? This seems a more realistic proposition and, technically, it should work. It’s easy to imagine how Derbyshire could have removed the front or top panel from one of the Radiophonic Workshop’s 19″ rack equipment cabinets and stretched a guitar or piano string between the two side panels. The base, sides and/or front panel would have acted as a soundboard and a microphone placed in proximity to the panel to capture the sound.
To have any significant effect the level of that 8th harmonic the rack panel(s) would need to have a resonant frequency at, say, around 650Hz. Now, a panel with a finite boundary will vibrate at a fundamental frequency (and at mathematically related harmonics of the fundamental). If the panel is flat and rectangular—19″ rack panels normally are!—and the thickness and material it’s made from are known we can determine its resonant frequency using the formula below:
Fr = 0.45 × vl × t × ((r/w)² + (r/h)²)
For example, the resonant frequency of a 1¾” high 1U rack panel can be calculated where, vl is the longitudinal velocity of sound in the panel = 5960m/s for steel, t is the panel thickness = 1.5mm (0.0015m), w and h are panel’s width (19″ = 0.483m) and height (1¾” = 0.044m) and r is harmonic number (1 gives the fundamental frequency, 2 gives the 2nd harmonic, etc).
Fr = 0.45 × 5960 × 0.0015 × ((1/0.483)² + (1/0.044)²) = 2095Hz
The calculated frequency is substantially higher than the 650Hz needed to excite the 8th harmonic, however if the base and sides of the panel are added into the equation they will lower the resonant frequency. Taking a standard 1U rack shelf of width: 48cm and depth: 21cm:
Fr = 0.45 × 5960 × 0.0015 × ((1/0.48)² + (1/0.21)²) = 110Hz
Now the calculated resonant frequency of the panel is far too low. At this point it’s tempting to begin arbitrarily tinkering with different panel dimensions until the desired frequency pops out of the equation. But there’s no need to resort to such result fiddling, yet. Keep in mind Derbyshire and Mills repitched, slowed or sped up, the Doctor Who bass note by some amount. This would have also altered the estimated 650Hz panel frequency—whether it was pitched up or down is impossible to determine from our calculations as the answers lie above (≈2KHz) and below (≈100Hz) this. The time has come to try and replicate what Derbyshire did with a string and panel—basically build it and see.
