The Reese
Two saws seven cents apart, into a lowpass, into saturation. The bass under most of jungle, built from the last four parts. Saturation flattens its swell from 6.4 dB to under 1, and cannot stop the sub vanishing 60 dB down every four and a half seconds. That is why there is a sine under every Reese.
What it is
The Reese. Two of the saws from part one, seven cents apart as in part four, through the lowpass from part two, into a tanh. That’s the whole recipe, and it has been the bass under a very large share of jungle and drum and bass since 1988.
The four parts before this measured each stage on its own. This one measures what the last two stages do to the movement the first one makes. The strip in the middle of the page is eleven seconds of level: the whole sound in amber, and the fundamental, the sub, in ember. The finding is in the gap between those two lines.
Raw, the whole sound swells 6.4 dB once every 4.5 seconds and the sub disappears at the bottom of every swell. Saturate it and the swell flattens to 0.7 dB, the loudness stops breathing, and the sub still disappears, 60 dB down, every 4.5 seconds, as if nothing had been done.
How it works
Everything in the picture is measured live. The recipe is synthesised sample by sample as the clock runs, through a stateful copy of the same filter and the same saturation the audio graph uses, and the last stretch of it’s read each frame for its overall level and for the fundamental’s level under a Hann window. Eleven seconds of both are kept, and the swell and the speed on screen are read off that history rather than asserted.
The raw swell is a fixed number and it comes from part four. When the two fundamentals cancel, the two saws are half a cycle apart at the bottom, which puts every odd harmonic in antiphase and every even harmonic in phase. The sound at that instant is the even harmonics at full strength and nothing else, and the ratio of all the harmonics’ power to the even ones’ power is four, which is 6 dB. Measured, 6.4.
Saturation squashes peaks. The in-phase moments have the biggest peaks, so they get squashed hardest, and the level swing closes: 4.4 dB at drive 0.5, 2.4 at 1, 1.1 at 2, 0.5 at 4, 0.2 at 8. The speed doesn’t change, 0.223 Hz throughout, because the loudest thing in the sound is still the fundamental and its beat still sets the rhythm.
The real Web Audio chain the page plays through, two oscillators into a lowpass into a WaveShaper, was rendered offline and measured the same way. Swell 6.4, 0.7, 0.4 and 6.6 dB against the maths’ 6.4, 0.7, 0.4 and 6.6. Sub swell 62, 61, 61 and 66 dB against 62, 61, 61 and 66.
What surprised me
That saturation can’t save the sub, and the reason is exact rather than approximate.
At the fundamental’s null every odd harmonic is at a null with it, so what is left going into the saturator is only even harmonics. A tanh is an odd function, so it can only make odd order products, and an odd number of even harmonics added and subtracted is always another even harmonic. There is no way to get back to 55 Hz from what is there. The sub swell measures 62 dB at drive 0 and 61 dB at drive 8. Drive does nothing to it, to within the measurement.
So the Reese, driven as hard as you like, has a sub that drops out completely once per beat, while the rest of the sound sits steady within a decibel. Producers have layered a clean sine under Reese basses for as long as there have been Reese basses. The page has a button for it, and with the layer in, the sub swell drops from 61 dB to under 6. I knew the practice. I did not know it had a proof.
The other finding is a negative one. I went in expecting the filter to change the speed of movement, since the tenth harmonic beats ten times faster than the first and the filter is what removes the tenth harmonic. It does not. The dominant speed of the overall level is 0.227 Hz at every cutoff from wide open down to 200 Hz, because the fundamental’s beat was always the biggest movement in the level and the shimmer above it was never more than a flicker on top. The filter takes the shimmer away. It doesn’t slow anything down.
The instrument failure this time was in the sound rather than the picture, and I only know about it because the sound gets measured against the maths as a matter of routine now. A Web Audio WaveShaper clamps whatever goes into it to the range of its curve, minus one to one, and two saws in phase peak near 3.6. With an identity curve, that clamp is a hard clipper. The “clean” setting was measuring 1.6 dB of swell where the maths said 6.4, while every saturated setting agreed perfectly, because at drive 3 the clamp sits where the tanh has already flattened. The picture said unsaturated and the audio was clipping hard. Scaling into the shaper and writing the curve in the signal’s own units made the audio path the same function as the maths, and the 1.6 became 6.4.
What I would do next
Part six is the 808, and the measurement I want there is at what frequency the sub stops existing on a phone speaker, which is a question about the speaker rather than the synth and matters more to how a track lands than anything about the patch.
The sub layer here is a plain sine mixed in afterwards. The more interesting version is the one where the layer is a third saw, not detuned, so the fundamental never nulls but the harmonics above it still beat against the pair. That’s three oscillators, which is where a lot of real Reese patches end up, and it would put a number on why.