A few questions:
1) Is there a preferred or standard tuning system (e.g., even-/just-tempered, etc.) for modern western music or, perhaps a more appropriate question, what is your ideal tuning system?
2) Is it possible to formulate a mathematical expression for the intervals in any given tuning system, or are they set a little more arbitrarily?
3) How do intermediate intervals change when using the fractional definition of a fifth interval (3/2)?
Looking at the wiki page it says that equal temperament "...is the most common tuning system used in Western music, and is the standard system used as a basis for tuning a piano", but I have read elsewhere that this is not the best option.
I'm currently trying to code an open-source tuning app and have stumbled so far into the nether zone that I'm now more confused about what I'm trying to achieve than how I will achieve it.
Any advice/opinions would help a great deal.