When playing the guitar, I find it difficult to fret a string without touching the string on either side and ruining the sound. Open tunings make it very easy to play one type of chord by barring across a single fret, but make it almost impossible to form any type of chord that would require 'lowering' a note. Are there any tunings that allow for a variety of major, minor, and seventh chords without having to fret strings further up the fretboard than the strings on either side?
If one is aspiring to become a good guitar player, there really is no alternative to learning to finger cleanly. On the other hand, if one wants to simply have fun playing the instrument, and play chords to back one's favorite songs, alternative tunings may reduce the level of technical proficiency required.
One tuning which makes it very easy to play a wide variety of four-finger chords is minor thirds tuning (tune all strings at intervals of minor thirds). If one keeps D where it is, a minor thirds tuning would be G#-B-D-F-G#-B, though in practice D-G#-D-F-G#-B would be just as useful (it sounds a cool full diminished 7th when strummed) and would avoid over-stressing the lower strings.
Every 4-note closed form of a major or minor triad, in any inversion, consists of a minor third, a major third, and a perfect fourth, in some order. Playing the same fret on two adjacent strings will yield a minor third. Fretting the upper string one fret higher will yield a major third. Any stacked combination of these intervals can be played using four consecutive strings without fingers having to cross over live strings. In addition, a true closed-form 7th chord may be played by barring the top three strings one fret higher than the fourth. This form has a sweet delicate sound when it leads into a second-inversion major or minor chord.
Unfortunately, while there are some styles of music where the four-chord barre chords made possible by minor-thirds tuning sound nice, the tuning effectively turns the guitar into a very-easy-to-play four-string instrument. While continuing the minor-thirds tuning into the lower string would allow one to use the same chord shapes on any group of four strings, trying to strum the middle or bottom four strings would be somewhat awkward, and the downward range of the instrument would still be very limited. Likely for this reason, comparatively little attention seems to have been given to minor-thirds tuning.
It's worth noting, though, that despite its limitations, straight-minor-thirds tuning, using the top four strings, does allow some nice musical possibilities. For example, Andrew Lloyd Weber's "Mermaid Song" from Aspects of Love, may be played using four chords in third position (listed alphabetically)
and three chords in fourth position
After the key-change, use the above chords up a half step. An excerpt from the chord progression is
Bbm F Bbm Gb Db Ebm Db F Bb F F7 Bb
(note that the B chord is used in the bridge, which is not included in this excerpt but may be played by anyone who knows the tune). Note that unlike most guitar chord sequences there the notes leap all over the place, here notes which are common to two chords will stay put. An interesting style, and one which may be worthy of more exploration than it has received.
Since the top four strings of a minor-third tuning make a very nice four-stringed instrument, which can even do some things a conventionally-tuned six-string guitar can't (e.g. play the closed-form F7 chord above), a natural question becomes what to do with the bottom two strings. Continuing downward by minor thirds isn't very useful, so what might work better?
Tuning the fifth string to be down a fifth rather than a minor third (i.e. to G) leaves it rather useless for many chords, but greatly improves the sound of second-inversion chords (simply bar it on the same fret as the fourth string). An alternative which sounds great for root-position chords, and decent for first-inversion chords, is to take the fifth string down to D. Unfortunately, doubling the bottom note of second-inversion chords vastly overemphasizes the fifth (e.g. a second-inversion C chord would be spelled G g c' e' g').
If one takes the sixth string down to D and the fifth string down to G, this will allow bass/strum chord patterns to have a good-sounding bass to root or second-inversion chords, simply by extending the first finger. Unfortunately, it's difficult to make a good sounding strum while skipping a string. Fortunately, there's a way--albeit unorthodox--to fix that.
If one swaps the position of the D and G strings, such that the sixth string is a G and the sixth string is a low D, then one will be able to make root-position chords sound nice using five strings, rendering them as a four-note chord, plus the lower note doubled down an octave. Second-inversion chords play all six strings. The sixth string, which is strummed earliest, supplies the root. The fifth string is lower, playing the fifth of the chord, but since it is strummed later, it's less prominent.
Adding the lower two strings makes first-inversion chords not sound as good as they would with just the top four strings, but the extra bass they offer makes the tradeoff worthwhile in most cases. A chart of fingerings for the tuning appears below. Although each chord is only shown in one form, other forms are possible as well.
The upper four strings in open G (D G D G B D) comprise a harmonic series and offers shapes with some of the advantages of supercat's fine answer.
Since the spine is a major chord, deviations and substitutions are pretty straightforward and there are myriad possibilities for inversions due to the close intervals at the top.
Similar shapes are available in "Double-Drop-D" (D A D G B D), by adjusting the fifth string to the nearest chord tone.
Perfect fifths tuning allows four-string movable "open" chords to be played with fingerings that are similar to those of minor-thirds tunings; if the bottom string is tuned the same, the six fingerings will generate the same six chords, but in a different sequence
- frets m3 tuning P5 tuning - open D F G# B D A E B - 1124 Eb Gb Bb Eb (Ebm) Eb Bb Gb Eb (Ebm) - 1224 Eb G Bb Eb (Eb) D# B F# D# (B) - 1134 D# F# B D# (B) Eb Bb G Eb (Eb) - 1244 Eb G C Eb (Cm) Eb Cb Ab Eb (Abm) - 1334 Eb Ab Cb Eb (Abm) Eb C G Eb (Cm) - 1344 Eb Ab C Eb (Ab) Eb C Ab Eb (Ab)
Whereas all six of the chords in m3 tuning sound pretty good, and some of the chords in P5 tuning also sound pretty, though in a different way, the sparseness of the chords in the P5-tuning chords makes some of them sound a bit harmonically vague. Having an "octave fold-back" (e.g. so the second string was a major second above the fourth, and the first string a major second above the third) might be interesting, but I've not explored such a thing.