Is it better to tune an instrument by procedure, or while playing?
I'm an amateur Guitar player. When I want to tune my Guitar, I follow this formula:
Use a diapason to tune the A note on the third string, second fret
Tune the second string by help of the B on the third string
Tune remaining string (1st, 4th, 5th, and 6th) by help of their top string's fifth fret note
But I recently saw a guy who didn't follow this formula. He simply picks a Guitar, starts playing a melody, and by help of that melody, he tunes the Guitar. This seems genius to me. How can one get this ability? Or more broadly, should we try to tune our instrument by playing a melody, or by following the formula?
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First, kudos to you for wanting to use your ear to tune - if you don't practice this essential skill as much as possible, and instead always start with a tuning device, when the chips are down you'll be fff* - well, in a bad way. It's great to check yourself after tuning by ear with one, though.
So - it depends very much on the music. If you are playing with other instruments with fixed pitches (for example, keyboards), they will almost always be using "tempered tuning". This ensures that, no matter what key (C, A-flat, F#, whatever) they are in, they are all equally in tune (or out-of-tune, actually - for TMI, Google "Pythagorean comma"). So you had better tune your guitar using tempered tuning as well - use the classic fifth-fret pattern (or a usually more accurate and reliable approach using octave harmonics).
If you are playing jazz or classical solo guitar (as I do), particularly jazzy or contemporary pieces (that use lots of different keys), then you'd better temper your tuning as well.
BUT - if you are playing by yourself, or singing with the instrument, or playing songs that stay in one key, then you can use a much purer tuning approach - the fifths won't be flat, the thirds can sound less muddy - that, I'm guessing, is what the fellow was doing that tuned to a particular chord. For example, when I play flamenco, I usually tune to open fifths and octaves on E and A, since flamenco, for all its complexity, stays always very close to "open string" harmonies on the guitar, and relishes the dissonance that comes with a purer tuning. Using the harmonics at V and VII will give you this purer result as well, but can get tricky.
So, to build your ear and emulate your friend, play around with getting a chord sounding right, and checking your results. Then get two different chords to sound right, and check your results. Using E and A will give a purer sound, E and C a more tempered result.
Hope that helps - and keep tuning using your ear!
I think it also depends of instrument. Perfectly intonated guitar is rare thing. After reading Your question i realized i tune-up each of my guitars in a different way - and those are:
Using tuner - tunning open strings
Using open position D - chord along with blues riff for lower strings
Using natural Harmonics on 5th, 7th and 12th fret
And finally formula You described when i tune up unfamiliar guitar.
I think in the final analysis, as long as you start with an un-tuned guitar, and end up with a tuned guitar, it really doesn't matter how you go about doing it. Personally, I use a tuner and tune open strings. Once I get the guitar close to tune, I'll start using fretted notes to get the strings in tune with each other. Typically I'll start with 6th string, 5th fret and open 5th string. Repeat until reaching 1st string. Then hit 6th string, 12th fret and 1st string open (since I have difficulty hearing the extra octave when using 6th string, open). Once every string is in tune to pitch (according to the tuner) and in tune to the other strings (according to the fretted notes/open strings), then it's time for the hard part of practicing.
Using the method described, you can end up with an instrument that's in tune with itself, but quite a bit off to say, a piano.
People have different hearing abilities, and those few gifted with absolute pitch can manage nicely without aids.
Those of us with less-than-perfect hearing find electronic tuners a godsend.
For acoustic guitars I tune using chords, eg an open E chord, which is a very simple one to highlight out of tune strings - this requires you to have a good feel for how the chord should sound, but is quick and easy once you have one string tuned.
For my electrics I use the 5 and 7 fret harmonics.
On stage I usually use a tuner, as it is often difficult to hear. I may check between songs with powerchords.
As @pulsehead points out, it doesn't really matter as long as it works for you.
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