re: for the joy of beauty...

Thanks for posting this presentation of the Golden ratio scale. I have made these scales and used them and the Golden Ratio many times. Though Leonardo may have made this commonly known to man he is not the creator or the first to use it.  It is the work of a Holy God the creator of the Earth and all there is in it. You see this ratio all through Nature I have enclosed a link to just a few of the proven examples below. You can find many other such evidences all around if you will take notice of the Creation.
https://www.mathnasium.com/examples-of-the-golden-ratio-in-nature