Major 3rd Problem of All Guitars in the World
Why Music: Practice & Theory Stack Exchange recommends it
Music Stack Exchange users link it when discussing just intonation, tuning and moveable-fret guitars, as a clear demonstration of why standard frets cannot give pure major thirds.
Recommended by 1 people across 1 different months, 2017 to 2023.
What it is
A short explainer by microtonal guitarist Tolgahan Çoğulu on why equal-tempered fretted guitars cannot play a pure (just) major third in tune. It comes from his research at the University of Bristol and demonstrates the problem and his microtonal guitar approach.
What people said
Recommends Scott Wallace · 2023-05 · Music: Practice & Theory Stack Exchange · on “guitar - open strings in just intonation”
@Tom - as phoog said, you need to decide what your priorities for just intervals are, and that's not a simple question. You might also be interested in the work of Tolgahan Çoğulu, a guitarist who has developed a guitar with moveable frets to explore a wide range of tunings. This is a good place to start, as it is expressly devoted to the problem phoog mentions: [this video]
Cites Dave · 2017-06 · Music: Practice & Theory Stack Exchange · on “Is it possible to change the position of the frets of an electric guitar?”
Note: he's also done some work on just adding additional partial frets to, what seem to me to be, standard guitars. [this video]
Cites phoog · 2021-11 · Music: Practice & Theory Stack Exchange · on “Do chords introduce interference/beating?”
There are no semitones in a C major chord -- and some semitones are in fact integer ratios. Two tones sounding simultaneously beat according to the difference of their frequencies. If you have one tone at 440 Hz and another at 441 Hz, you'll hear one beat per second. Raise the frequency of the higher tone to 442 Hz and you'll hear two beats per second. Now an acoustically tuned A major triad comprising A4, C♯5, and E5 has the frequencies 440 Hz, 550 Hz, and 660 Hz. If there is interference, with what frequency should we expect to hear beating? 660 - 550 = 110 660 - 440 = 220 550 - 440 = 110 The beating is so fast that it sounds like another tone, or rather two other tones, one an octave belo