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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.

If you know the structure of the “tick”, you can apply the technique of a correlation receiver. It can dig up signals below the noise floor and is used in GPS reception.

I'll do some research on this! I have a nagging feeling that there is more I can do to get the most out of this, but struggle with knowing where to look since this is not my background. I'm learning a lot as I go!

Did you consider trying the iPhone accelerometer? Perhaps lay the phone face down on the table and then lay the watch on the back? Wondering if this would have higher or lower SNR.

I don't think it would work because the accelerometer updates are at too low a frequency. Apple's developer info says:

``` Before you start the delivery of accelerometer updates, specify an update frequency by assigning a value to the accelerometerUpdateInterval property. The maximum frequency at which you can request updates is hardware-dependent but is usually at least 100 Hz.

```

100Hz is way too slow. Presumably some devices go higher but according to the article the peak signal is in the 3kHz to 15kHz range.

How does it compare to other apps ("watch accuracy meter" for example) on android?

I have this in open beta on Android right now so you're welcome to give it a shot and let me know :)

One difference is cost. I know that mine is lower cost, and is a one time unlock -- no subscription. So there's that. I'm also therefore positioned a little bit more towards the casual user, I prioritize speed of completion which means I need high confidence in a good signal quickly and don't hesitate to cancel mid-flow.

I think one thing alternatives offer is the ability to run for longer -- like a 10 minute check for instance. There are marginal gains in precision for every additional second, but they seem to diminish pretty quickly past 30 secs or so. But that's one difference I'm aware of.

>One difference is cost. I know that mine is lower cost, and is a one time unlock

The one I'm talking about is free, so not sure about that. Not sure if I will pay for beta testing : )

Awesome writeup! I wonder whether with a real contact mic (Korg offers one for about 20 bucks) you could get much better results. Due to no 3,5mm on phones anymore it might be easier to use a sound-enabled SBC though.

This is definitely the way. Even the old wired mics Apple phones used to ship with that had the little rectangle mic works better because you can press it right up against the case back.

10 seconds per day is a little over 115 ppm. What is the frequency error of the reference clock that ultimately drives the ADC connected to the microphone?

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?

It uses the built-in one. But as discussed in the article they ran into the problem where even when you try to force using the internal mic, iOS will silently switch to the mic on a pair of AirPods if there's a pair connected.

This is designed to be used by the internal device microphone. And this is in my write up, but if you have Airpods in all the time (like me), it will try to use that microphone and it will not work, and it will cause you to lose a day in frustration if you are working on something similar

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

This is the way. I got one as well to validate my results. Cost is the difference. If you're okay with close-enough and saving $145, I think the apps fit in a nice place.

I will say, this flow is not the primary concept for the app. My intended design, and what it's been for 2+ years, is a tool that provides structured flows for inputting the time on your device and comparing it to atomic time (provided in my app). If you stagger these measurements over 6 or so hours for a day or two, you get a very precise reading and I still recommend this approach as being better.

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?

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.

Piezo mics are pretty cheap, and if wired up to the microphone input of a computer or phone you could probably get better accuracy as well if you used the same signal processing techniques.

Seems some people have done this already with a PC app: https://timeandtidewatches.com/how-to-make-your-own-timegrap...

I used flutter so maybe some day!

It's in open beta testing on the Play Store for Android. You can also find low cost external mics for your devices that work well.

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?

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.

Practically speaking, unless you only own a single mechanical watch you really only care about the per day loss.

You know what they say. Man with one clock, always knows what time it is.

Man with two clocks, never quite sure...

This is my motto (data engineer frequently dealing with "but this source says...")

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.

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