Confused about Sharps and Flats
General mountain dulcimer or music discussions
It boils down to the fact that the frequencies of the notes are not exact/even and do not double [times 2] as is commonly accepted. This is the basic reason the frets are not evenly spaced and results in the 'Rule of 18' and '12th root of 2' for fret placement. I think 'wolf notes' are also part of this.
When the "G#" frequency approximately doubles, the frequency is not the same as the doubled frequency of the Ab. This difference is/can be audible.
When 'equal temperment' was developed, this difference was, essentially, eleminated.
Most of the other 'temperments' are attempts to modify this difference.
updated by @skip: 09/01/23 04:02:23PM