Under a gold coin standard, the name dollar is defined as a weight of gold. So there is no dollar price of gold. There are only dollar prices of goods and services. Once defined, the dollar equivalent to gold does not change. If ten dollars is a defined as equivalent to a half ounce of gold, then a half ounce of gold cannot fall from $10 to $9. A half ounce of gold can fall in purchasing power relative to goods, but not in a dollar defined name.
If one foot is defined as equivalent to 12 inches, then the “value” of the foot cannot fall to ten inches. Feet and inches are just two different names for an equivalent length. A person’s height could change from 5′ to 6′ but that would still be equivalent to a change from 60″ to 72″. So the price of a month’s rent could change from a half ounce of gold to an ounce of gold, but that would be equivalent to a change from $10 to $20. Gold ounces and dollars are merely two different ways of referring to the same thing.
Under a gold coin standard, a bank note is not traded for a gold coin. A bank note is redeemed by the issuing bank for the equivalent amount of gold. This is what makes bank notes a substitute for gold coins. Merchant accept either a half ounce gold coin or a $10 bank note because they know that the bank that issued the $10 bank note will redeem it for a half ounce gold coin. So gold coins and bank notes both trade for goods and services, but not for each other. The legal way of seeing the relationship between bank notes and gold coins is that bank notes are titles of ownership to gold coins. A $10 bank note issued by the First National Bank is a legal title of ownership to a half ounce gold coin. The FNB stamps this fact on the bank note. For example a $10 bank note might have the words, “pay to the bearer of this note, $10 in gold” stamped on it. So, the value of a bank note in terms of gold is fixed contractually by the issuing bank. The bank does this to create general acceptance of its bank notes as a substitute medium of exchange for gold coins.