Mr Kite wrote:
Luis_Br wrote:Fifths are not in correct tune for the tempered scale
I was just wondering about this and by my calculation the perfect fifth is about 2 cents flat and the major third is about 13 cents sharp. That seems to mean that the difference between ET thirds and just thirds is too big for intonation to make any appreciable difference but that it might make a difference to the fifths.
I think one single fifth tuning is not a big issue and we can use, but we must be careful that the difference might propagate and accumulate from one string to the other, depending on the tuning strategy, then it might make a difference. For example, if you simply tune in fifths from each string to the other, starting from 6th string toward the first one, then error from string 6 to 1 will become 2 cents times 5, or 10 cents, assuming your cents calculation is right (I haven't checked that). 10 cents generates around 1.5 Hz frequency beat, which is ok for a third, which has a more complex harmonic subset, but it is a bit annoying for the pure octaves of both open E (1st and 6th strings). By the way, check wikipedia for a sound sample on 10 cents beating of the same notes:
Propagation becomes even worse on that tuning in fourths from one string to the other, which is certainly a bad tuning strategy. Those tuning this way certainly improve intonation checking chords, some adjust both open Es at the end.
When tuning by ear, comparing strings, I recommend using a single string as reference and using octaves and a few fifths (attention to avoiding fifths error propagation), avoid other intervals, except for specific chord/key adjustments in the piece.
I normally tune 5th A string to the reference.
- 3rd string 2nd fret with 5th string open (octave)
- 2nd string open to 5th string second fret (octave)
- 1st and 6th string to 5th string seventh fret harmonic (fifth)
Notice those string tuned to the same 5th string reference, to avoid error propagation, both from temperament or my imperfect ear.
- 4th string depends on guitar. Sometimes its seventh fret (A note) to 5th string harmonic 12th fret (octave). But using higher fret might be tricky, so in this case I might use harmonics (fifths), fourths or another string.
After that I might do some chord/key adjustment for a particular piece, but I seldom use this. I would use it more for a pro recording, tuning to specific passages played as different takes. It is an artificial result, but recording is artificial anyways...
I used to prefer manual tuning to the regular automatic tuners around, but I recently found a stroboscopic tuner which is pretty good and after some practice I've became addicted to it. I hope my ears do not start degrading...