Why do quartal progressions typically not utilize common tones?

Question

Typically chord are built in thirds, but in quartal harmony chords are built in fourths instead. One pattern in quartal harmony I noticed was chords tend to move completely in parallel even if common tones exits between notes as demonstrated in this Debussy passage:

And this Jazz guitar passage:

In standard harmony one would want to utilize common tones between chords, but it seems even when there are common tones between chords, parallel motion is instead preferred. What is the reasoning behind this complete parallel motion between chords?

Answer 1

I think there are some assumptions in your question that are false.

First: Quartal harmony emerges and starts getting used extensively in Western music in the late-19th-, early-20th century. At the same time, many composers were also exploring different ideas about how chords can connect, including chord planing, which involves holding the same chord structures and simply moving them up and down in parallel as opposed to the more traditional voice leading that would avoid parallel 5ths and 8ves and that would tend to use common tones. Debussy, the composer of your first example, uses chord planing techniques in a huge chunk of his music, regardless of whether he's using triadic or quartal harmony. I think the phenomenon you're pointing to is more likely just a confluence of two different aspects of chord usage around the turn of the 20th-century.

Second: Although I see why you are pointing to The Sunken Cathedral as an example of quartal harmony, it actually isn't a very quartal passage. The first measure is chord planing of harmonies that involve m3s and P4s above a root. This is just as close to being a triadic harmony (minor seventh with missing third) as it is to a quartal one (D-G-[missing C]-F. The second measure only has two unique pitches in every chord, just parallel 4th intervals with octave doubling, and doesn't really qualify as a full blown quartal harmony, which would really need at least one more fourth added to the stack.

Third: If we're being fairly loose about what constitutes a quartal or triadic harmony (that is, allowing skipped notes in the stacking) then the harmonies are actually relatively hard to distinguish from one another. The more triadic extensions you have, especially with any skipped notes, the closer your harmony becomes to being conceivable as a fourth or fifth stacking. As an extreme example, a C9 chord without third or seventh (C-G-D) is identical to a fourth or fifth stack, and a diatonic C13 chord with all notes (C-E-G-B-D-F-A) is indistinguishable from a quartal harmony except in voicing (B-E-A-D-G-C-F).

These caveats being made, I think it is possible that common tones would be less bountiful in a quartal universe because, unlike thirds which can be major or minor without utterly changing their function or overall sonic quality, fourths and fifths have to be one quality, perfect, lest they sound like a completely different interval. Changing from a M3 to a m3 or vice-versa is just a shift between two different consonant qualities. Changing from a P4 to +4 or P5 to °5 is a shift between an extremely stable consonance to an extremely unstable dissonance. Moving in the opposite direction by one half step—P4 to °4 or P5 to +5—is a shift into chords that just sound like enharmonically misspelled 3rds and 6ths. As such, there are somewhat fewer harmonies available involving the same tone, especially new harmonies that will involve smooth motion in the non-common-tone voices. [Your guitar example does involve the occasional tritone, but I don't think that's very idiomatic to a quartal harmonic universe.]

If I try to imagine an alternate universe in which Western harmony never gravitated toward thirds as a consonance (perhaps a universe in which Ptolemaic tuning was never pursued, and composers had stuck with a purely Pythagorean tuning), then I picture a world in which voice-leading as we know it would not exist in any sort of recognizable way at all. With only a few exceptions, I think composers would be choosing between smooth, conjunct writing without common tones and rough, disjunct writing with common tones. It's an interesting thought experiment, but I think that the grammar of common-practice tonality only evolved because of the triadic vocabulary already being pursued, different vocabularies would have developed different grammars.

Answer 2

I'm not sure that parallel motion is invariable - I think back to a lot of middle period Bartók (although he almost invariably spices the harmony with augmented fourths) - but I think in situations such as the examples you have given here, the colour, the sonority of fourths is a consideration. These are essentially melodic gestures that are coloured by the consistent use of stacked fourths. Consider what happens when you hold over the common notes: you end up with inversions, and other intervals that are latent in the stacked fourths start coming to the fore, so you start losing that distinctive sonority.

Here's more or less what I mean:

Before the double bar line is a pretty straightforward progression of parallel fourths not unlike your guitar example. After the double bar line is the same progression holding common tones. Note the pitches within the brackets at (a) and (b). (a) is embedding a 2nd inversion E Major chord; (b) is embedding a first inversion A minor chord. Those are definitely going to have an effect on the sonority.

Note too that the suggestions of functional harmony are even somewhat different. In the first example, all the voices are outlining a melodic half-cadence. In the second example, leading tone movement between the end of the first bar and the beginning of the second create a similar suggestion of dominant to tonic movement, but that suggestion is strongly reinforced by the embedded triads, and the F-B drop in the top voice does little to dispel that - the impression is closer to a quasi-authentic cadence.

This is a contrived example, but it illustrates that, when you are trying to set up a desired harmonic allusion by purely melodic means with colouration provided by a set vertical sonority, holding the common tones might disrupt the colouration and add a set of (more functional) harmonic implications that might differ from what the melody implies. None of that is necessarily a bad thing, but I don't think it was what your examples were aiming for.

Answer 3

I would make one distinction here in particular. Though not necessarily always the case, often times chords such as this are not so much quartal chords as they are quartal voicings. This is a good bit more obvious in the Jazz example. The example you provided also shows the chord symbols above, which are all indeed traditional triad based chords within the Jazz idiom. If you were to hang onto common tones between chords, it would completely subvert the quartal voicings. Miles Davis did a wonderful job with Kind Of Blue in utilizing a quartal voicing for triad based chords. I like this example because it really spells out the concept of available tensions, ie, within Dorian, all tensions (9/11/13) are considered available and by stacking the fourths all the way up, you can hit each of them. Although, if I remember correctly, he threw a third on the top of those chord voicings. I believe this would be to prevent the b9 dissonance that would occur between the 9 and 3 of the chord, or the 13 and 7, as well as the ability to move the voicing around as he does.

As others have mentioned, this can also happen with chords that would fall more in the category of quartal chords but by a slightly different means. Essentially hanging onto the common tones can spell out other triadic relationships in such a way that it could subvert the quartal intention. I would not consider myself well versed enough to dive into planing as Patrx2 did and would find it unnecessary with the explanation he gave being quite good.

Answer 4

While not present in these examples, the inversions of the quartal triad (a stack of three perfect fourths) often go unnoticed and are, in fact, essential to utilizing common tones in quartal harmony.

Consider the chord (from lowest to highest) A-D-G. If we consider this to be the root position of the quartal triad, then its first inversion is D-G-A (known colloquially as a sus4 chord), and its second inversion is G-A-D (known colloquially as a sus2 chord).

Why is this important? Well, consider how we use common tones in traditional tonal chord progressions:

Take a V-I cadence of G resolving to C. We would typically resolve G-B-D by keeping G where it is and then resolving the other voices upwards to spell G-C-E. We don't see it often because of the old prohibitions against parallel fifths, but in a free harmonic context we could simply move G-B-D up a fourth to C-E-G. This is the type of planing we see above; if common tones are available when moving from one quartal chord to another, then the ONLY way to hold the common tone over is to invert one chord, the other, or both (The only exception being if you move up or down by one or more fourths, such as A-D-G moving up to D-G-C).

Consider this jazz piano example:

  One voicing of an Am7 with an added 11th would be A-G-C-D. Note that this is an inverted quartal 
  stack (A-D-G-C). If we wanted to resolve to Dm7 (with another added 11th), we could plane up to 
  D-C-F-G (again, an inversion of the quartal stack D-G-C-F), but it would be a more comfortable
  and idiomatic to voice the chord as D-F-G-C, keeping the G as a common tone.

This is all done by way of inverting quartal stacks. In the case of the guitar chords, they are planed in this manner because, as was the case with the piano example, it is more comfortable and idiomatic to play the chord progression as a series of quartal stacks. Since guitar strings are (mostly) tuned in fourths, playing two different stacks of fourths is as simple as moving up or down a fret. On the piano, large stretches of a tenth or more typically necessitate a rearrangement of the quartal chord in order to comfortably play the chord.

As for Debussy, planing is a hallmark of his style. More over, he was evoking a style of medieval music known as organum. Organum consisted of a single perfect fifth/fourth doubled over several octaves, and most textbook examples of the style are nearly identical to the chords and voicings Debussy used in measure three.

Lastly, planing of this sort is not limited to 20th century quartal chords; see the opening measures of Beethoven's Piano Sonata No. 3, mvt. 4 for an example of diatonic planing by similar motion :)

-As a side note, it is worth noting that extended minor seventh chords and major seventh chords get some of their cadential stability because they are inverted quartal stacks:

  -Am7 add 9, 11, +13 = A-C-E-G-B-D-F# rearranges to: F#-B-E-A-D-G-C
  -CM7 add 9, +11, 13 = C-E-G-B-D-F#-A rearranges to: F#-B-E-A-D-G-C