“I tried to follow this distinction beteen notes which are chromatically they same yet differnt but I just couldn’t. it was all greek to me.”
Pitch is like real numbers. Between 1 and 2, there are an infinite number of numbers, like 1.1 and 1.02976 etc. Between C and C#, there are an infinite number of possible pitches (you hear it when a blues singer goes a little flat on a note and it sounds good or when a guitar player “bends” a note by pushing on a string while it is vibrating).
So the pitches on a piano keyboard are particular spots on that continuous line of possible pitches that have been picked out for common use because of their versatility in different keys.
The term “well-tempered” (Bach’s The Well-Tempered Clavier is probably the most famous use of the term) is a selection of pitches for the notes in a scale so that the same instrument can play compositions in different keys and not sound stupid. Pianos are usually tuned to a well-tempered scale. The intervals between notes in a well-tempered scheme are set just so and they are a little different from note to note. There are a lot of different “well-temperment” schemes and each sounds a little tiny bit different. The Pythagorean temperament discussed in the article is one example.
However, the result of that is that different keys for compositions have a different feel as the interval between the notes changes just a little depending on what key you are in.
BTTT for the Pythagorean comma!