Can an Augmented triad be called a Quartal chord?
Since a Quartal chord can be defined as diminished, perfect or augmented fourths, can an augmented triad be analysed as a quartal chord with stacked diminished fourths enharmonically?
Also is the chord D/E voiced as E-A-D-F♯ a quartal chord?
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I tried working out a possible quartal scenario using a diminished fourth, sort of along the lines that @IndroneilKanungo described, creating a scale with E A D Gb.
First I compacted the chord and arranged the two fourths by step D Gb and E A. It seem sensible to add fourths above at C (natural because the G was already altered) and B below (natural to make a P4 with the E.) The remaining tone to fill in was F (natural to not enharmonically duplicate E or Gb.)
Unless I missed something I found only one four voice stack of perfect fourths starting on B. I made that the sort-of-tonic and then made two parallel chord lines going up and down to the B chord.
I marked the complete, perfect quartal chord with *, the chord with the not-a-third-but-an-diminished-fourth I marked M, and two dominant-like chords I marked D.
It's interesting how the diminished fourth appears in 3 of the 7 chords with a kind of tertian sound yet there was only one full, perfect fourth chord. In a plain diatonic scale you get 4 out of 7 full, perfect fourth chords.
Would this work as quartal harmony? I don't see why not. But you would probably want to avoid emphasis of the tertian tinged chords.
There's 'Quartal harmony' and there's 'Quartal voicing'. The first is a conscious attempt to get away from triad-based tonal harmony. The second is a very standard and unremarkable way of voicing tonal harmonies, particularly when sus4, 9 and/or 13 extensions are used.
Scriabin based whole pieces around this sort of chord, (and he didn't use it as an extended C7!)
Most pianists would consider using this RH voicing for F13 pretty mainstream.
Both can be described as 'quartal'. If you use the term, make sure it's clear which you're talking about!
It would at best be a stretch. Typically in quartal stacks, you only use perfect and augmented 4ths for obvious reasons (diminished 4ths sound like major 3rds in equal temperament). Same goes for quintal as you typically only use diminished and perfect 5ths. When diminished 4ths are used they are used sparingly so trying to do two in a row would very much be an outlier and wherever you are in your stack it will take a more terian harmony turn.
Maybe to put it the best way, there's a whole class of chords called suses which are for when there's no third and it has been replaced by a major 2nd or perfect 4th. You could spell them so you're dealing with a diminished 3rd or augmented 3rd, but they are never interpreted nor spelled that way because they are subverting the terian system not forced inside of it.
This is the same thing with your proposal. While possible, you are bending the spelling and what the typical bounds of what is considered quartal via enharmonics which could be done.
In theory whenever there is an ambiguity regarding two notes that are enharmonic equivalents, it can only be resolved with the help of the context.
For instance a tritone by itself can be a #4 or a b5 but when you play the rest of the notes of the scale, it clears things up. You can make the same note sound like the fourth degree in lydian or the 5th degree in locrian and they both feel very different from each other. In fact just playing the major 3rd would make it feel like lydian (#4), and a minor 3rd would make it sound locrian or diminished (b5).
So in situations like this, try to think what scale your chord comes from. If you say an augmented chord can be considered a quartal chord, it means it contains 2 diminished fourths. So the scale would have to look something like 1 b2 b3 b4 b5 bb6 bbb7. Even if the scale has its name it's got to be so rare that when you hear the augmented chord by itself, you'd much rather see it in the context of the whole tone scale or perhaps lydian augmented. Which are far more common than the monstrosity that that scale is with the bbb7.
Similarly if you're imagining [E-A-D-F#] this chord as a quartal one, firstly you'll have to call the F# a Gb, and then you'd have to visualize a scale which contains [ D E F Gb A ].
You could do that. But I'm pretty sure that it won't be a common scale and it won't be easy to capture the sound of the scale. And in any case, it certainly won't be as easy as hearing the D major scale. As a result when you hear those notes, your brain would much rather hear a F# at the top than a Gb because then that chord appears in numerous common scales.
So to answer your question, in summary, by default they're not to be considered quartal chords, however, you can try to make them sound like one though that could be very difficult.
Actually I don't know. But as you ask:
Can an Augmented triad be called a Quartal chord?
The answer is: Yes, we can.
somewhere even the Tristan chord is mentioned as a the root of the quartal chords:
The bottom two notes make up an augmented fourth, while the upper two make up a perfect fourth. This layering of fourths in this context has been seen as highly significant. The chord had been found in earlier works (Vogel 1962, 12), notably Beethoven's Piano Sonata No. 18, but Wagner's use was significant, first because it is seen as moving away from traditional tonal harmony and even towards atonality, and second because with this chord Wagner actually provoked the sound or structure of musical harmony to become more predominant than its function, a notion which was soon after to be explored by Debussy and others.
But the opinions differ:
Despite the layering of fourths, it is rare to find musicologists identifying this chord as "quartal harmony" or even as "proto-quartal harmony", since Wagner's musical language is still essentially built on thirds, and even an ordinary dominant seventh chord can be laid out as augmented fourth plus perfect fourth (F–B–D–G). Wagner's unusual chord is really a device to draw the listener into the musical-dramatic argument which the composer is presenting to us.
At the beginning of the 20th century, quartal harmony finally became an important element of harmony. Scriabin used a self-developed system of transposition using fourth-chords, like his Mystic chord (shown below) in his Piano Sonata No. 6.
Read more about Quartal chords:
Quartal and quintal harmony (wikipedia)
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