I built an audio timegrapher feature for my watch accuracy app, ChronoLog. Professional timegraphers use a piezo contact sensor and can cost upwards of $1,000. I wanted to do it with a phone mic.

The problem: an iPhone's built-in microphone picks up a mechanical watch's tick at about 1.5 dB SNR. The solution turned out to be epoch folding — the same technique radio astronomers use to find pulsars. Stack 100+ tick periods together and you get +20 dB of effective gain, enough to reliably measure rate and beat error.

The post covers the full DSP pipeline — bandpass filtering, epoch folding, autocorrelation (and why it finds harmonics before fundamentals at low SNR), Kalman filtering for convergence — and what I learned from five rounds of device testing.

Fantastic post. As a mechanical watch collector / enthusiast, I enjoyed reading this.

When you say "phone mic" do you mean the embedded one, or an external one?

This is a fascinating read but what do you do with this information? Is there a threshold at which you need to take the watch apart and fix something or is this just useful info to know about your watch?

Neat, but I wish this wasn't a phone app (and Apple exclusive at that). My computer already has a high quality microphone that I assume would be more suitable for this purpose.

I've tried these as apps before, and they never worked that well unfortunately. Perhaps the ticks aren't loud enough, or phone mics aren't that great, or background noise gets picked up as ticks, who knows.

I bought and use the item linked below. It's big, and feels like tech straight out of the cold war era, but works great.

https://www.amazon.com/gp/aw/d/B0081SSJZG

If the signal is periodic and the tick structure is stable, you might also be able to improve SNR further by aligning the detected peaks and averaging them rather than just stacking raw samples. That sometimes helps suppress random noise even more when the waveform shape is consistent.

Not sure how stable the waveform is across ticks in a mechanical watch though.

Wow I’m a watch guy and this was a fun read. I used a couple of similar apps and they work ok. I wonder how yours stack up. You can get these cheap piezo ones for $150 but unsure how those perform either.

How accurate are the clocks driving the DACs? Presumably the algorithm assumes that the audio is sampled at 48khz (or something) but that sample rate is unlikely to be perfectly exact?

Old mechanical watches and clocks had an adjustment with which you could change slightly the oscillation frequency of the balance wheel (usually by changing the tension of the balance spring).

You used a device like that described in the parent article to measure the deviation from the correct frequency and you adjusted the frequency with a fine screwdriver or a similar tool, until measuring the desired nominal frequency.

Watches are precise machinery that require maintenance and well known watch brands take great pride in the longevity of their pieces, meaning they provide support for the lifetime of the watch (you will pay for this though). Typically, every 5-10 years you send them in for a service. Overtime, the little pieces and minuscule drops of lubricant wear and age and need replaced. Visibility into these metrics can help you keep an eye out for problems.

Higher end watches also get external certifications that reflect different precision standards. Some examples: METAS, COSC, or Rolex Superlative Chronometer if you are Rolex and need to be special. They have different specs, Superlative Chronometer is +/-2 sec per day. If it's out of spec and you're under warranty, you may be entitled to a free adjustment by a service center. Otherwise, overtime, as the performance degrades, it's a signal you may need a service.

There's also the risk of magnetization. If the delicate machinery becomes magnetized, you'll see BIG swings, like +/- minutes per day. Demagnitization is something any watchmaker can do quickly. (There is inherently some risk posed by the phone itself having a lot of magnets, but modern watches are typically built to resist magnetization to varying degrees -- look at the Rolex Milgauss as an example of best-effort magnet resistance)

Watches will also perform variably depending on position. If you know your watch is -4sec/day on your wrist, but +6sec/day face down, you can effectively manage it's accuracy by placing it face down over night and never have to unscrew the crown but keep a true time. This is a very common use case.

Hope that covers the general cases. This app avoids a lot of even deeper complexity, like beat error and amplitude which are deeper metrics describing the movements performance and guide watchmakers to know which screws to adjust which way.

It tells you for how long the time displayed by the watch is valid. If a watch loses ten seconds per day, in a month it will be about five minutes off.

The objective is to minimize this number as much as possible. The open source sensor watch has a temperature sensor and software which turns it into a temperature compensated quartz watch. Mine loses time every year instead of every day or every month.

It is actually pretty useful if you own a few mechanical watches. Daily rate tells you how annoying the drift will be, beat error can hint that regulation or service is due, and measuring in different positions gives you a decent sanity check on movement health. Even if you never open the watch yourself, it is a much better baseline before taking it to a watchmaker.