No, it really isn’t – or at least not on the level of the other two.
There’s a good reason.
To understand the reason, remember that you can find a scale in which the G chord is played in every key of the piano (the same way that the Cmin chord is the only chord in the major scale), or in which all of the notes of the scale can be played on each string (the same way that the Ebmin chord is the only chord in the minor scale). These two scales are a perfect example of what’s known as a “flattened” chord because there are no more three notes of the scale to play than there are two in a standard key.
So there’s no reason why the G chord could not be the highest note in a given key – if we were to look at a scale like this – a “flat” chord, we’d find the G chord at the top.
But even so, how can we say that F# is a high note? Well, the idea is that for every note of the scale (we’re ignoring those in the key we’re interested in) F# is the seventh of the scale.
So if we wanted to put down a new scale based on a new chord, we’d say that each new chord would be based on one of the root notes of the scale. If we were to start at the root note – one note higher than the G chord – we’d know that D is the next chord we’d be looking at. So we can put down the G chord first and then the D chord. It’s easy to see how this would work, because all we need to do is play this chord.
But what if our first chord were the F# chord? Well what if we were also to be trying to get some additional notes to start playing in the chord? What if we changed the scale to this chord, and the next chord were the E chord? Then what we now have is a “flatter” chord. Not only is the E chord the seventh chord of the scale for the scale, so the next chord will be D. So we will have F# being the highest note of the scale from then on out.
I don’t think this is particularly common music (there are plenty of examples of low keys where the G chord would be the highest note, but this has less to do with the chord that came before and more to do with
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