The reason Commodity prices are so important to the Market Correlation picture is that they play a major role as a leading indicator of Inflation. And inflation is the general increase in prices over a 12 month period.

If Commodities start to rise, that means economic strength and that will push Bond prices lower and Interest Rates higher. On the other hand, falling Commodity prices means economic weakness.

A period of rising Commodity prices arouses fears of Inflation which prompts monetary authorities to raise Interest Rates to combat that inflation. Eventually, the rise in Interest Rates chokes off the economic expansion which leads to the inevitable economic slowdown and recession.