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The advantage of this method is that the pure intervals give the guitar a very pleasing, resonant, in-tune sound on chords that have plenty of open strings, like E minor and G major. Tuning strings to other strings is also pretty easy once you've practiced a little.
The disadvantage is that, since you are not using equal temperament, some chords are going to sound more in tune than others. Experienced guitarists simply tweak the tuning by ear as they change keys (for example, one might adjust the third string to give a better E major chord when playing in A major or E major). You may also find that your guitar sounds slightly out of tune when playing with a piano.
Many experienced guitarists become so comfortable with hearing the pure fourths and third that they can tune simply by listening to the interval between the strings, rather than using the fifth-fret/open string unisons .
Some advanced guitarists prefer to tune using string harmonics , which cut out some of the string overtones , leaving a clear, easy-to-hear pitch . This is a little tricky to learn, but it gives a very accurate, resonant, pure-interval-based tuning.
Because it is very easy to hear the pitch of the high, clear string harmonics, this tuning method gives a very accurate, pleasing tuning that takes advantage of pure intervals (fourths) to give the instrument a more resonant, vibrant sound (because pure intervals support and resonate with each other better).
Harmonics are played by touching the string very lightly at the fret, rather than holding it down just below the fret. You must be comfortable with playing harmonics to use this tuning method; it is not recommended for beginners.
All of the above discussion assumes that you want a standard guitar tuning, but there are many other possible ways to tune a guitar. For example, Slack key tuning, popularized by Hawaiian guitarists, involves tuning some of the strings lower (or "slack", because they are looser when lower) than standard tuning. The resulting tuning often (but not always) gives a major chord when all of the open strings are played. For example, one popular slack key tuning involves lowering both E strings to D and lowering the A string to G. The result (DGDGBD) is a G major chord. Slack key tunings will usually sound best using pure fifths and thirds, rather than equal temperament . The major chord will be easy for most experienced guitarists to hear accurately, so many players will be able to do this tuning by ear.
Another popular tuning, found in styles as different as classical and rock guitar, is D tuning . This involves tuning the lowest string to D instead of E, which gives an unusually resonant sound when playing in the key of D. Tune the guitar as usual, then retune the lowest string using the open 4th string D. (Tune the 6th string to an octave below the 4th string.) Check your tuning using a chord of D's and A's.
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