You can date a TR-808 from a recording by fitting the shape of its TONE knob
I am modelling a TR-808 from the service notes, stage by stage, and while doing the snare I ran into something I did not expect: two independent ways to tell which production revision a recording came from, one of which is just the response curve of a potentiometer.
Background. The 808 snare is two bridged-T resonators in parallel, one for he shell body and one an octave up, mixed by the TONE control, with the noise ("snappy") path summed in separately. Mid-production Roland changed four parts in that voice. The service notes list them as a PORTION CHANGED
annotation:
C58 .027 to .056
C61 .0068 to .015
R191 8.2k to 10k
R200 47k to zero
The caps are the obvious half. Only one cap of each bridged-T pair changes, so the frequency ratio is sqrt(27/56), not 27/56:
resonator 1: 249.63 Hz -> 173.34 Hz (-6.29 semitones)
resonator 2: 499.00 Hz -> 335.98 Hz (-6.85 semitones)
So an early 808 snare sits about a fifth higher, and because the two shifts differ slightly, the pair goes from an exact octave to a flat one. Q drops a little too (17.4 -> 16.3 and 10.7 -> 9.9), so the shell also rings around 35% longer after the change.
Now the part I thought was neat. R200 sits in series between an op-amp output and one end of the TONE pot. Since 47k is comparable to the pot's 100k, it is not a level trim: it changes the SHAPE of the crossfade law across the whole sweep. Deriving both cases:
R200 = 47k -> TONE spans 16.8 dB
R200 = 0 -> TONE spans 26.8 dB
The recordings I have span 26.4 dB measured. Fitting the derived law against ten measured amplitudes with a single common gain and nothing else fitted gives 1.16 dB mean error for R200 = 0 against 6.62 dB for 47k. That is a clean verdict, and it identifies the machine's revision without looking at the resonator frequencies at all. Then the frequencies agree independently: measured 172.0 and 339.5 Hz against derived 173.3 and 336.0 for the late version.
Two consequences that might be useful to others:
A control law is a fingerprint. We normally treat pots as "the user's problem" and model them as a gain or a simple taper. But when a series resistance is comparable to the pot's own resistance, the law is a property of the circuit, it is measurable from audio, and it carries information the spectrum does not. I would not have thought to look if the two cap values had not sent me to check what else changed with them.
Watch out for manuals describing a different machine than the one in front of you. Roland's own printed spec quotes 476/238 Hz for this voice, which is the early revision. Earlier in the same project I found their printed bass drum tuning (56 Hz, and 62.5 Hz in the prose) disagreeing with both my derivation from the component values and the hardware, which both land at 49.5. Component values have been right every time so far;
printed prose has been wrong twice.
Method note, since it is the part that actually matters: I derive each stage symbolically from the drawn component values, then measure real hardware recordings, and I only trust a number when the two agree. Where a published academic derivation of the same circuit exists I use it as a third reader, and that has caught mistakes in both directions, including three errata in the paper.
Disclosure: I make a drum machine plugin and this work goes into it. Not linking it, this is about the circuit.