Methods of Dealing with Temperature
Let's not beat about the bush: temperature is the one thing that most affects the accuracy of quartz watches. It has to be dealt with. But how?
There are several approaches:
Let's take those one-at-a-time:
You take a 32 kHz quartz crystal (XO) and programme the integrated circuite (IC) to count the number of oscillations and divide down to 1 Hz. That 1 Hz signal is delivered to the stepper motor and the stepper motor moves the second hand. This actually works but it is rather crude. Every time the temperature changes, the oscillator frequency changes and that means that the count changes and that means that the pulse gets sent to the stepper motor at the wrong time. In my collection, I have seen evidence of this approach only in my cheapest Casio quartz watches, with the second-by-second the SPM values returned by analysis of the oscillator frequency remaining steady over several minutes and exactly matching the values returned by the stopwatch method.
It surprised me to learn that most XOs are actually set to run slightly faster than 32 kHz. Every ten seconds (it's usually ten seconds), the IC inserts a 'correction' into the frequency count, deducting a certain value. This is called 'inhibtition'. I think someone once tried to explain it to me but I really can't claim to understand why this approach is taken or how it works. I do know that when I put certain watches on my timing machine, I see regular corrections at ten-second intervals. In fact, the ten-second correction also seems to be built in to several (and possibly all) models that also use longer inhibition periods coupled to measured temperature. In such cases, the 10-second correction may be thought of as a 'minor' inhibition cycle, whilst the TC-related correction would be the 'major' inhibition cycle.
Besides the regular ten-second corrections, my MicroSet timing machine also seems to show that many non-bargain-basement watches have a variety of regular tick patterns. That is to say that within the ten-second inhibition period, some seconds are regularly faster or slower than others. Often this is presented as simple pattern of one fast tick followed by one slow tick. Someone once explained to me that this is probably because of a mathematical problem of division - in order to deliver each tick at exactly the right interval, the IC may need to make a count correction of half a hertz (or some other number that doesn't divide particularly well from the 32 kHz baseline frequency), which it may not be possible to resolve. In this case, the IC would deduct different amounts, tick-by-tick, to land one tick above the target rate and the following tick below, averaging out at the proper rate. It occured to me that this strategy might not simply be due to difficulties in dividing count, but, if the ticks are far enough apart, it may also be a deliberate attempt to reduce the impact of relatively small changes in temperature by spreading the count deduction across more of the arc of an oscillator's thermal performance graph. That's just me think out loud, though. The simple fact is that many watches that aren't absolutely as cheap as chips incorporate some form of count correction, but this pattern is not adjustable. No doubt some very clever calculations are made to create a count pattern that will deliver reliable accuracy for a reasonable range of temperatures, but once this has been set in the factory, it cannot be changed.
Another approach to the problem is to fine-tune the frequency of the quartz oscillator. This is sometimes referred to as a Voltage Controlled Temperature Compensated Crystal Oscillator (VCTCXO) approach (also sometimes referred to as TCVCXO). First, you would need to measure the thermal performance of the XO across a range of temperatures that the watch might typically expect to encounter. Then you can programme the IC to make micro-adjustments to the power being fed into the XO as changes in temperature are detected. Since quartz crystals oscillate in response to current, a fast-running XO (in cold conditions) could be slowed down by reducing the current being fed into it. Rolex took this approach with their Oysterquartz and it has been suggested that Citizen might be in on the act, too. In fact, if a theory I have recently read holds true, it may even turn out that VCTCXO (or some variation on the theme) might be more widely used than previously thought, as count adjustment could be limited to just the Swiss.
Another approach is to adjust the count. For this you still need to determine the thermal performance of the XO, as in approach 3, above. You also need some way of determining the temperature (either a thermistor or a second XO). But instead of adjusting the frequency of the XO, you simply deduct a certain count of oscillations corresponding to the surplus that the XO is calculated to have produced at the determined temperature. This, of course, is the inhibition approach described in approach 2, above, but with on-going fine-tuning of the count deduction value. Given that count is deducted and not added, this approach wouldn't work if the temperature of the watch were to rise above a certain level, but since that level would be pretty darned hot, it's not so much of an issue.
These days temperature is measured by a thermistor, but there was a time when it was fairly common to have a second XO to solve this problem. Seiko labelled it their 'Twin Quartz' range, and their best examples were rated to 5 SPY. ETA also had a brief experience with a dual oscillator, as they collaborated with Longines. The Longines / ETA dual oscillators didn't exist for nearly as long as the Seiko variants, but I believe the underlying principles were the same. That is to say, the temperature was determined by measuring the difference in count between the two oscillators. As the temperature changed, each oscillator would be affected in a different way, with the higher frequency oscillator seeing a smaller change in frequency than the lower frequency crystal. I am not sure why this approach was abandoned, but I have read that crystals of different frequencies may experience markedly different ageing characteristics, so it is possible that the accuracy of the temperature measurement could not be maintained over time.
I once believed that count correction wa the predominant thermocompensation method found in HAQs, today, and served all of the top-performing movements. It might turn out that count correction is, in fact, used only by ETA, and that all other manufacturers use VCTCXO or some other approach.
So, if higher frequency oscillators are less affected by temperature changes than low frequency oscillators... why not just use a really high frequency oscillator? The answer is probably 'power consumption'. Omega, Citizen, Casio and Junghans all produced watches with oscillators in the MHz range, but they were power-hungry and didn't exhibit very much greater accuracy than dual oscillator or thermistor approaches.
Besides the MHz watches, Seiko have used 196 kHz oscillators in their 8F range of movements and, through their Pulsar subsidiary, in the Y301 and Y302 calibres. These movements simply could not stick to spec. as their crystals aged. It didn't take long for their stated accuracy to become something of a joke in HAQ circles.
Bulova use a 262 kHz oscillator and this is also coming in for stick for not living up to spec.. This is made worse by the fact that the fancy sweeping second hand on the high frequency Bulovas renders the battery flat in about a year. And yet, some people are reporting that their Bulova Precisionists and Accutron IIs are living keeping quite good time. That may in part be due to the higher frequency, and possibly also due to the final approach...
I won't pretend to understand this, but it was explained at great length in a paper that Seiko submitted to the Symposium on Frequency Control, in 1980. Bulova are using it in their high frequency, tri-pronged crystals and Seiko used it in their Twin Mode quartz movement. While the scientific stuff is all Greek, to me, I do believe that this is an approach to thermoinsensitivity, rather than thermocompensation. That is to say, it is another means by which the XO can be rendered less susceptible to the effects of temperature changes.