I understand the difference between open tuning (all 6 open strings play a chord) and regular tuning (the intervals between strings are the same). I would like to know if it is possible to have both, that is, a tuning with equal intervals between strings that when played open gives a major or minor chord. Is this actually possible?
Is [...open tuning...the intervals between strings are the same...when played open gives a major or minor chord...] actually possible?
In terms of "stacked" intervals major and minor triads are not "regular" interval stacks. Those chords alternate major and minor thirds. Additionally when the chord root is repeated at the octave it will be a perfect fourth above the chordal fifth. So, that's three different interval types involved in the stack to build major and minor triads.
If you stacked only major thirds for an open tuning, the resulting chord would be an augmented triad.
If you stacked only minor thirds for an open tuning, the resulting chord would be a fully diminished seventh chord.
If you stacked only perfect fourths for an open tuning, you would have six of the seven tones to get a complete diatonic set. Arranged as all perfect fourths you might call it a very large quartal chord, but those chords tend to be only 3 or 4 perfect fourths stacked up not six.
Of course just because those tunings don't form either a major or minor triad does not mean you can't use them. An interesting thing about alternate tunings is there are some that are very common, like "drop D" or "open G", but you can make up any tuning you want.
Regular tuning gives P4 between all strings except 3rd-2nd, which is M3.
Basic major chords are made up from M3, m3 and P4, while minor chord are similar, but m3, M3 and P4.
Thus the answer is no, as there can't be a mix between regular/major or regular/minor. There could be say, bottom 3 give major, top three minor, but then you've lost the regular tuning.
Any alternative tuning will mean having to use different fingering anyway, but using a 'Spider Capo' may give some inroads to what you're after.
This is probably not what you are looking for, but:
If you have the same diatonic interval (e.g. a third or a sixth), you could have a "regular" tuning that gives open triads. Say we pick the key of G:
- Thirds: C - E - G - B - D - F♯ – Contains both C major, G major, E minor and B minor triads.
- Sixths: F♯ - D - B - G - E - C – Contains the same, but inverted (and probably not in a musically useful way).
In either case, you won't get a full chord across all the strings. You have to play a 3-adjacent-string subset only. If you have a 3-string instrument, it does fit the definition.
If you build a regular tuning with seconds, fourths, fifths, or sevenths, you can also get the notes of major and minor triads, but the notes to form them will not be on adjacent strings.
Another thought: You did say "a major or minor chord". You could make a 3-string instrument with a neutral third of about 350¢ between strings. Depending on context, that might be heard as "major or minor", though it's probably more correctly described as "neither major nor minor".
;tldr: You can't get major or minor chords in a tuning where all intervals between consecutive strings are the same, but you CAN get other nice sounds.
As previous answers have pointed out, getting all the open strings to sound a major or minor chord while keeping the intervals between strings the same is impossible.
The intervals between consecutive notes in a major or minor chord which extends over several octaves are minor thirds, major thirds and fourths; 3, 4 and 5 semitones, respectively; and you need all three of them to make the chord. You could try to get around this by imagining larger intervals between consecutive strings, like an octave + a third, but it turns out you still need three different intervals to get complete chords.
To put it simply, what you ask for is impossible.
Others have pointed out that some intervals can be stacked to make chords other than major or minor chords. The most obvious one would be the diminished and augmented chords, made from all-through minor thirds and major thirds, respectively. This can work, but they do contain notes outside your desired major and minor chords. More importantly, these chords are not ones that are comfortable to listen to when you strum them for a long time. I thus think they sort of miss the point of an open tuning!
There is a way (in theory two ways!) to tune you guitar in a completely regular way which allows for pleasant open chords!
There are two intervals that can be stacked indefinitely and still make good sounding chords: The unison and the octave!
Tuning all notes to the same note makes it very regular, and all notes work well together. In fact, all notes are part of the same major or minor chords, and this is the best you can hope for. I'd definitely say it's an open tuning.
To achieve unison tuning, you could simply restring the guitar to have only one type of string, e.g. only A strings. This can be quite a cool effect, like a chorus, and it can bring out overtones in interesting ways. To get an idea, have a look at so-called monochords (e.g. this one from Thomann). The clips at the site is quite nice actually, and more clips can be found if you check out their other monochords.
If you're tuning all strings an octave apart you'd definitely need to change strings. I'm quite sure you can't actually find such a range of strings, but just maybe if you look around among strings for various instruments and get really creative. It would be fun to see someone do this if it's possible.
You could also cheat a bit and mix among unisons and octaves. The patterns to play chords would be the same as for either of the other two types, and it would still sound cool. It's not even totally unheard of, and something sort of like it was famously used on the song Iris by the Goo Goo Dolls. (Though I think they cheat even more and have one string tuned to a different note..)