Quartal harmony… or the search for the grail

Debussy's opening to 'The Sunken Cathedral' (La Cathedral Engloutie) employing the use of parallel fourths, also known as 'planing'.

Debussy’s opening to ‘The Sunken Cathedral’ (La cathédrale engloutie) employing the use of parallel fourths, a technique also known as ‘planing’.

I’m following on from a previous post, Harmonics, Fourths and Fifths, where I had discovered that I was inadvertently drawn to a particular type of harmony based on intervals of perfect fourths and fifths, especially when these intervals are ‘stacked’ and become the basic unit for constructing harmony. In the Western tradition, our sense of harmony is usually based upon stacked intervals of a third, which gives western music its particular ‘colour’ or sound characteristic, and leads us to label chords as having either a ‘major’ or ‘minor’ tonality. Over many years of playing and listening to music, I’ve found that as well as the Western harmony that I’d grown up with, I was also often drawn to what I perceived as a more intriguing and interesting sound, that of the open and more ambiguous harmony of fourths and fifths. I found this in the most diverse of places – in medieval music, sometimes in British pop music from the 1960s, sometimes in Scottish bagpipe music and Irish traditional music, in Georgian and Bulgarian vocal music, and more recently in some of the music of Debussy, Bartok and Copland. Quite often this music would be underpinned by a drone or continuous tone, against which these intervals would be stacked to form odd sounding but rather compelling harmony. I enjoyed the sound of these chords, which in conventional western harmony usually had exotic names like C7sus4 or Gadd69. But of course, these are seen as aberrations in harmony based on the principle of thirds, and it’s been only recently that I’ve discovered that this type of harmony indeed has a name, and is a perfectly legitimate (and alternate) method of writing music.

Known as quartal or quintal harmony (as opposed to the Western tertian harmony approach), as a writing system, quartal harmony has been around in various forms since the Middle Ages (though in traditional musics throughout the world it appears much longer) and interestingly, a fourth was considered a consonant interval up until the common practice period (from Baroque through until late romanticism in western European music) when it became to be considered as dissonant, as a suspension that necessarily need to resolve to the third degree of a scale, unless it was the interval between the fifth degree and the octave. I’d actually like to believe that the fourth can be recognised as an interval worthy of constructing a system of harmony upon (and the fifth, being inverse intervals of each other) in it’s own right – it has a purer tonal characteristic and of course is more naturally related to the natural harmonic series and just intonation, as opposed to the thirds and sixths of 12 tone equal temperament which have had to be adjusted (albeit notionally) to accommodate changes in key. It also has an ambiguous quality that seems to hang indeterminably in air, like sunlight or activity, life itself – the opening to Stravinsky’s Petrushka is a good example of this, but other composers such as Bartok and Copland have also exploited this quality.

It was quite a revelation to discover all this only recently: after 30-plus years of playing and listening to music, it was almost a holy grail moment to discover what I thought I was imagining actually did exist, and indeed had a name. I’d been hearing snatches of quartal harmony for years, darting fleetingly in and out of the various musics I thought possessed  the quality I was looking for – I almost stumbled across it last year through my research into the harmonic approach of the Beatles (see my essay “The Harmonic Series in the Music of the Beatles“) where I thought this phenomena had to do with relating tones back to natural tones within the harmonic series – as it turned out, I wasn’t that far off the mark. But now I have a name for this, and it makes sense in so many ways in relation to what I’m investigating, the idea of composing a ‘vertical’ music that negates the sense of time passing

The sound of quartal harmony is very different to tertian, or thirds-based harmony – without the notion of a third, there is a very open quality, conveying almost a bell-like ‘ring’ to chords built upon this interval. It also makes for some interesting chords: dominant7 suspended4 chords are the most obvious example (for example, C, F, G, Bb, low to high) but by logical extension using fifths, you also get add 6/9 chords (C, G, D, A, low to high) and the various inversions of these. Of course, by using this kind of terminology (suspensions, ‘add’ chords), it implies that these are chords that would normally fall outside standard Western harmony standards, and herein lies a problem: what do we call these chords if we aren’t relating them back to a western system based upon thirds? Musicologist Phillip Tagg has very recently addressed this problematic in an entire chapter devoted to quartal harmony for an upcoming book, Everyday Tonality 2. He suggests that if we are to use quartal harmony as our approach, that we need to think of chord names in particular in quite a different way. As he puts it:

“if there’s nothing suspended, added or omitted about a chord, it’s perverse to designate it as if there were” (Tagg, 2014, p. 259).

He suggests ‘sus’ and ‘add’ are clumsy and should not even be used in a quartal harmony context, instead labelling chords simply ‘C4’, ‘C2’ and using up or down arrows to indicate the direction of stacked fourths, i.e. G4↑ would indicate G, C and F, with G the lowest note of the triad: F5↑ would indicate F, C and G, with F the lowest. (p. 260).

The most interesting aspect of quartal harmony from a compositional perspective for me however, is that modulating, or changing key, dictates a completely different, and quite subtle approach. Being based on fourths, it naturally relates closely to the circle of fourths or fifths, and allows for quite understated, sideways movement into a new ‘key’ (for want of a better word) by altering only one note. Moving this way in western harmony would dictate that two notes would need to change, and the shift is far more obvious. There’s nothing of course in standard harmony that would stop one from changing key by changing only one note of course (i.e. from C major to A minor, or perhaps C Major to C minor) but this is usually fairly obvious – there is a distinct mood change. In quartal harmony, this change is quite subtle, and given the ambiguous quality of this harmony, it becomes almost imperceptible – there is a sense that something has changed, but you’re not quite sure what it is.

Of course, if we include five notes of stacked fourths, we now have the notes of a pentatonic scale, and we can hear the relation back to many traditional folk musics throughout the world, which, given the harmonic materials we’re working with here, makes a lot of sense – this relates back to Pythagorean theory on the construction of early musical scales. But if we limit ourselves to only four notes in a chord, the sense of ambiguity and suspension is retained – and for a project that centres on a ‘timeless’ approach to composition, I believe I’ve stumbled upon a very useful and appealing system of harmony to use, at least to my ears. Like the proverbial elephant in the room, it’s been staring at me for many years, enticing me with an enigmatic quality that I never entirely recognised or understood, and now it’s been handed to me like a gift. A holy grail indeed…

More musical developments as they come to hand. Until next…

References

Tagg, Philip (2014). Everyday Tonality II; provisional text, 2014-05-07; http://tagg.org/bookxtrax/FFabBk08/FFabBk08.zip [accessed May 21, 2014]

Advertisements

Harmonics, fourths and fifths

Fourths and fifths - a spectral analysisI’m having several different ideas of where to go with this honours year spectral music project at present, and my thoughts have been a little scrambled. From where I was coming from originally, and trying to use a compositional method that related everything back to the harmonic series, I’ve been feeling a little boxed in – to compose completely in this style throws up two challenges:

  • as pointed out in a recent paper, ‘The European Folk Scale’ (Hirt, 2013), if I’m to truly use the series as a basis for composition, notes ideally need to follow the order of harmonics as they evolve, i.e. in the key of C, it would follow C1, C2, G2, C3, E3, G3, Bb4, C4, D4, E4 etc. Any transposition down or up an octave is pointless, because there was no ‘octave’ equivalence on early instruments, one had to work with natural overtones inherent in the instrument.
  • if I’m to be true to this method, I would really need to start writing in just intonation; apart from being particularly limited (as a guitarist and keyboard player, tuning to just intonation is more than a little awkward, especially on piano) and essentially limits you to only one key.

In a way I feel I’m confining myself, yet a core part of my reasoning behind this idea of using the harmonic series is to get back to some basic harmonic ‘truths’. When I first started investigating using the harmonic series as a compositional method, it was pointed out that I should look to the French Spectral School of composition, as the main proponents, Gerard Grisey and Tristan Murail, were chiefly concerned with representing the often very detailed information contained within Fourier transforms (a spectral analysis) of musical instrument tones. The results were, to my mind, interesting as they represented, in great detail, the partials evident within say, a trombone note (e.g. Partiels). Although initially very striking, I generally found these pieces both difficult to listen to (the upper partials being represented in the woodwind section of the orchestra became increasingly dissonant) and exceedingly complex: an analysis by François Rose, Introduction to the Pitch Organisation of French Spectral Music, was enough to convince me that this was not a path a wished to pursue. It was getting further and further away from where I wanted to go, which was more a preoccupation with tone colour and the compositional possibilities offered by the harmonic series, rather than a need to replicate it.

One thought that occurred was that I didn’t have to necessarily represent every harmonic. Some time back I decided that everything past, say, the 12th harmonic I could disregard, as the overtones were becoming so tightly packed that their usefulness became questionable, not to mention fairly unpleasant to the ears – these were also beginning to get out of the range of what could be physically ‘played’ (on guitar, it’s very hard to obtain natural harmonics past the 12th partial anyway). In this way, it occurred to me that it was perhaps more the phenomena of the series I was interested in, and my focus shifted to timbre, and tone colour. It also seemed to be particular tone colours I was interested in, in particular metallic sounds – electric guitars and string instruments, pianos, chimes, bells, even xylophones and marimbas. It was also the ring of overtones that got me, the sound one gets with open fifths and fourths, open ninth chords, which are stacked intervals of a fifth anyway, and… perhaps it was the intervals themselves contributing to this phenomena?

I tried some recording experiments with open guitar tuning back on March 5, which were interesting – apart from experimenting with slide rubbed back and forth across the strings in the manner of a violin bow (which brought about some natural harmonics) I also tuned the guitar to open fifths, in the manner of an Indian classical drone instrument such as a tanpura – although the original intention was to exploit the use of slide to find harmonic tones naturally, I gradually moved to using the slackened G string (now tuned to an E3) as a highly nuanced melodic string, with the other strings acting as sympathetic drones. Not unusually, this sounded somewhat like a sitar, and also not unnaturally considering the tuning, I started to come up with melodic lines that emulated sitar ragas, especially with the use of a flattened 5th and microtonal bends. I noted that if I abstained from using the 4th degree of the scale and stayed with notes contained within the harmonic series in order of their appearance, the resultant sound was very much like Indian classical music. Which was not exactly what I had in mind, but led to another idea…

On a hunch, today I re-listened to a number of pieces that I felt encapsulated to some extent the quality I was after. Aaron Copland’s Fanfare for the Common Man and Debussy’s La Cathédrale Engloutie, both struck me as exemplifying what I was actually hearing in my head, without knowing exactly why. Once I examined the scores for both, it started to become more apparent. Both pieces make extensive use of open 4th and 5ths, often consecutively. This gives, to my ears anyway, a kind of bell-like, ringing quality, and emphasises overtones without having to actually play them. I noticed this with my Indian-esque noodlings too; the buzz of overtones was quite apparent with the sympathetic open strings picking up on what was played on the ‘melody’ string. But the difference of course with both the Copland and Debussy pieces, were neither were chained to one key: both modulated several times, and both strikingly so, with some faraway excursions to distant keys. Evidently, it was the quality of the intervallic nature of the pieces that was attractive to me; once this particular penny had dropped, it became quite apparent in music where I had perceived this quality before: in the Georgian male vocal tradition, in some Bulgarian music, in fact a whole range of popular music which had started this investigation in the first place – the vocal harmonies of the Beatles and those that came after them, and in fact much of the Indian-influenced ‘raga-rock’ and psychedelia that appeared in the mid 1960s. Many of these musics employ the use of ‘stacked’ 4th and 5th intervals to produce a particular ringing kind of harmony, often against a common ‘drone’ tone which carries through a chord sequence – the result are chords that will often contain suspensions and a mix of sixths and ninths, often without the third degree of the scale, which lends them a floating, unresolved quality.

I suspect in some ways I have known this all along, and have in fact experimented with similar tonalities previously (see Grass, Desert, Earth and Air). But it has taken this long to confirm my thoughts, and I hadn’t realised the importance of the intervallic nature of the fifths and fourths – it also implies pentatonic modes (travelling by fifths/fourths eventually produces a pentatonic scale) and the cycle of fifths itself. So in a way, I’m tapping into something quite fundamental and possibly rudimentary… but it feels like I’m finally on the right path.

I will press on with a few more audio experiments… more later