If it is true that total pool of currency needs to be able to grow with the economy then the rate one variable grows must be linked to the rate the other grows. If there is no link then there is no relationship.
The great depression was caused by a stock market over inflated with leverage. This has nothing to do with the gold standard.
And notice how we have deviated from the topic of deflation. It's a topic built on myth and misunderstanding that easily slips out of focus.
There is absolutely no evidence that deflation itself is bad. The great depression occurred because there was too much debt. Japan suffered in the 90s because it had too much debt. Deflation/inflation just measures who gains more over time, debtors or lenders.