A scale is a short list of permitted sizes. Its value lies less in mathematical elegance than in the fact that a designer stops choosing sizes and starts choosing steps, which makes different pages agree without anybody comparing them.
Try it
Pick a ratio and every size moves together. A tight ratio suits many levels of heading; a wide one suits few.
Ratio
Pick one ratio, multiply your base size by it repeatedly, and use only those sizes. The sizes are then related to each other instead of chosen one at a time, which is the entire benefit, and it is a real one, because most muddled-looking pages are muddled in their size steps rather than in their fonts.
The ratios are borrowed from musical intervals, and the golden ratio is on the list because it always is. None of them is correct. A tight ratio like 1.125 suits an interface with many levels; a wide one like 1.5 suits a poster with three. Choosing a wide ratio and then needing six levels is how people end up back where they started.
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