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Even and Odd numbers

In the benchmarks shown, I have concentrated on the 100, 133, 154 and 166 MHz memory bus speed, leaving aside completely the 143 MHz setting that, with a 7 x multiplier, also yields a 1 GHz clock speed. There are certain reasons for that, though.

About two years ago, we first reported a rather strange phenomenon. It all started out with a discussion on Tom's Hardware's Forum, centering around the observation that certain DIMMs would not work at 75 MHz but had no problems at 83 MHz. Adding to this phenomenon was the observation that quite a few Intel Pentium II CPUs (66 MHz specified bus speed) would not even post at 112 MHz bus speed but work reliably at 117 MHz and even get into Windows at 133 MHz. Needless to say that, in those instances, the 120 or 124 MHz bus frequencies were a no-go. A closer look at the working vs. non working frequencies showed that all viable settings were either multiples or second order harmonics of the standard PCI frequency of 33 MHz.

What is a harmonic frequency?

Harmonics are multiples of a base frequency, meaning that every frequency (f) is harmonic to its octaves or f*2ⁿ Hz. There are also higher order harmonics where the frequency multiplier can be an odd number or, by extension, 1/2 of the odd number. Examples are 100 MHz (33.3 MHz x 3) or 83 MHz (2.5 x 33 MHz or 5 x 33 MHz / 2). If this principle can be applied to PCs, 33, 66, 100, 133, 166 MHz are among the favorable frequencies, followed by 83, 117, 150, 183 MHz whereas everything in between would be a higher order harmonic and, therefore, be prone to cause runaway frequencies escaping termination designed for specific harmonics of the PCI bus frequency.

Why would this be important?

Electronic devices, including CPU, chipset and mempory, follow rules that optimize them for specific operating frequencies. Among the considerations are trace length, signal termination and so on, but the one thing they all have in common is that a deviation from the optimal frequency can cause some resonance problems with feedback signals (even though elimination of those is exactly the purpose of termination resistors). Most peripherals nowadays are designed around an optimal operating frequency of 33MHz or its multiples. In any event, what came out of several thousands of benchmarks we have run since, was that staying within the harmonic frequencies of the PCI bus consistently yielded the highest performance, in other words, even with a nominally higher clock frequency, the overall system performance often lagged behind the "less MHz" settings.

These factors are extremely difficult to document, especially, since, to the best of our knowledge, there are no precedents. Moreover, most benchmarks don't show a linear performance increase with clockspeed, making it necessary to interpolate data which, by itself, opens up yet another can of worms.

The current set of benchmarks, however, offers exactly this opportunity. If our idea about harmonic frequencies were correct, we would expect that, instead of showing an increase in performance that fits into the expectations derived from the other 1 GHz settings, the 143MHz x 7 setting would reveal a performance hit of some kind.

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