How does the F# tuned up to a G (creating a Dsus4) work to create that "celtic" music kind of sound?

I'm currently learning to play in Open D (building the chords myself), but this DADGAD tuning caught by attention.
It doesn't. There's nothing Celtic about F# or G. It's the fact that it's an open tuning at all. Open tunings lend themselves very well to long sustained drones. Drones are a very common element in ancient music i.e. before harmony and counterpoint were developed.
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The tuning just makes you play in a certain way. The open strings are different (than in standard tuning) so people use them differently which makes the tuning sound a certain way. And there are own kind of chord voicings. The tuning may just fit Celtic kind of music.
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Not related to your query about celtic music, but two of my guitars live in DGDGAD which obviously is close to DADGAD, albeit with the A dropped to G. I believe that makes it an open Dsus2. It’s my absolute favorite alternate tuning - very droney but also lending itself to soloing in sort of a classical style. Theres only so much you can do with it I feel, but maybe that’s just a limitation of mine though.
Yes I do, good catch. And upon googling that I just found a list someone made of chords in that tuning here
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How does the F# tuned up to a G (creating a Dsus4) work to create that "celtic" music kind of sound?

I'm currently learning to play in Open D (building the chords myself), but this DADGAD tuning caught by attention.

Interestingly, DADGAD was invented (it is believed) by Davy Graham to help a guitar play middle-eastern music - the idea was to play with/replace the Oud.

The sense we have of that being a celtic folk sound comes in large part from Davy and his disciples (particularly Bert Jansch) who were playing that kind of music and inspired by Graham.

However, it is well-suited to that kind of music, and probably more so than open D. Part of that is become DADGAD puts less of an emphasis on the major tonality, and a lot of the folk songs that Jansch, Graham, and others were inspired by were written modally - the tonal harmony we're used to wasn't organic to those songs. DADGAD makes strums or runs across those bottom strings NOT major - the major (or minor) tonality is something you now have to chose.

The G note ends up being more flexible than the F# if you don't want to be locked into a major tonality. DADGAD lets you imply a major or a minor tonality by finding Fs or F#s elsewhere on the fretboard, and you don't have to worry about an open F# string always pulling you back to major.

Also, a lot of DADGAD playing involves keeping a bass line going on the three low strings, using the top two strings to fill in the harmony, and plays melody lines on the third string. And it turns out that having an open G note there is just more useful than having an F#. eg, that G note is a sus4 to a D chord, a root to a G chord (G, being the IV, is very common in both D major and D minor) and the 7th to a V7! Super useful on your most common three chords, in both major and minor!

Whereas an F# is a maj7 to a G chord (and thus something you'll almost never use in G minor) and a 6th to an A chord - much less useful than the 7th.

So now if you move your melody playing to the second or the fourth string, that open G string is still a useful note. Whereas if it were an F# instead, you'd have to avoid that string unless you were fretting it.
Off subject, but I love DADGAD tuning. I just learned to play Tool 46&2 bass, guitar, and vocal notes at the same time(See Ernesto Schnaak version on Youtube). I dont quite play it as well as him, but im gettin it down. Also found that Deftones Change sounds better in that tuning. You play it the same, but it just sounds better the way the strings ring out. You can do alot more with this tuning thatn what you see in the Youtube vids under DADGAD. Ernesto hnaak is who first comes to mind who uses this tuning alot.