The 808 on a Phone
A phone speaker hears one per cent of a clean 808, and 93% of that is the first 60 milliseconds. Saturation does not bring the energy back, it moves it later into the body of the note. Drive makes a sub last on a phone. It does not make it louder.
What it is
An 808. A sine that starts at 220 Hz and falls in thirty milliseconds to 50, with a half second decay on it, hitting on a loop. On a big system it’s the whole track. This page lets you hear it through a small speaker instead, and measures what gets through.
The speaker is a stated model rather than a measurement of any real phone: a two pole highpass at a corner you pick, 150 Hz for a laptop, 300 for a phone, 500 for something tiny. Every small speaker has that shape, twelve dB an octave below its corner, and the corner is the one number you have to state. I’ve stated it.
Through the 300 Hz one, 1.1% of the hit’s energy survives, and 93% of what survives is the first 60 milliseconds. A phone hears the knock and then nothing.
How it works
The knock is the start of the pitch glide. For its first few tens of milliseconds the 808 is up around 200 Hz, which a phone can just about reproduce, and then it falls under the corner and is gone. The trace on the page shows the full hit as a ghost and the heard version in amber, and the amber one stops where the ghost carries on.
Every number is measured off a rendered hit. The pitch glide is read back from the spacing of zero crossings and agrees with the design to 0.2 Hz all the way down, 182.3 against 182.1 at 8 ms, 83.9 against 83.7 at 49 ms, 50.0 against 50.0 at 400 ms. The surviving energy is the hit through the highpass over the hit without it, and the knock share is how much of that sits in the first 60 ms.
The audio path is the same recipe with the real nodes: a fresh oscillator whose frequency approaches 50 Hz with setTargetAtTime, which is exactly the exponential the maths uses, a gain that decays the same way, a tanh shaper and a highpass. Rendered offline and measured, it agrees with the maths in every case to the digit shown: -19.6 dB and 93% for a clean 808 on a phone, -17.7 and 49% at drive 8, -11.5 and 37% at drive 8 on a laptop.
What surprised me
I went in believing the thing every producer believes, that you saturate a sub so it translates to small speakers, and the measurement made me say it more carefully.
Saturation doesn’t bring the energy back. Through the 300 Hz speaker a clean 808 survives at -19.6 dB and a hard driven one at -17.7, a gain of 1.9 dB for drive 8, which is barely anything. Through a 150 Hz laptop speaker drive makes it slightly quieter, -10.8 to -11.5, because the tanh takes the peak off the sub and the harmonics it adds are still under the corner. If saturation is making your sub louder on a phone, it isn’t by much.
What it does is move the surviving energy later. Clean, 93% of what a phone hears is the knock. At drive 2 that’s 85%, at drive 4 it’s 70%, at drive 8 it’s 49%. The body of the note goes from 7% of what gets through to more than half, at the same total. Drive doesn’t make the sub louder on a phone, it makes it last.
The mechanism is the one from part five. A tanh is odd so it adds odd harmonics and nothing else, and the odd harmonics of a 50 Hz sub are at 150, 250, 350, 450. The measured spectrum of the settled note at drive 8 has the third at -12 dB, the fifth at -19, the seventh at -27 and the ninth at -34, and every even one below -95. The third and the fifth are still under a 300 Hz corner. The seventh and ninth are above it, and those two lines, spaced 100 Hz apart, are what the phone gets of the note’s body. The ear reads the spacing as the pitch, with the fundamental missing entirely, which is the same trick a small radio has always used.
There was no instrument failure on this day, which is the first time in the series, and I think it’s because the measurements are all ratios of the same rendered hit. Nothing had to be windowed on the right period or kept inside a shaper’s domain. The lesson from the last five parts was already built in.
What I would do next
Part seven is the supersaw, and the question is where stacking saws stops getting fatter.
The honest gap here is a real phone. The model is the right shape and the corner is stated, but a phone speaker also has a resonance near its corner, a peak a few dB tall, and that peak sits right where the 808’s knock is. Measuring one with a microphone would say whether the knock gets through better than the model says, and I suspect it does.
The other measurement is the one producers argue about in comment sections: whether a sub layer or a driven sub translates better. Both are on this page. Putting them through the same speaker and reading the same two numbers would settle it for at least one 808.