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

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9 thoughts on “Harmonics, fourths and fifths

  1. Interesting stuff!

    Personally, the idea of composing around the harmonic series fills me with dread. With regard to the use of fourth intervals, this is a natural step from the use of thirds in ‘conventional’ music, resulting from the omission of every other note in the particular mode/scale we use to produce the harmony scale from which harmonies are built. Without this expansion the notes played in simultaneity (chords) would have seemed useless, although we make use of these so-called ‘cluster’ chords nowadays for colouristic purposes.

    When we choose to devise chords from the scale/mode in its second expansion, now omitting two notes each time, we have a system that has the same right to exist and any deviations from what we’re used to – the omission of the third and the suspensions you refer to – are, strictly speaking, irrelevant, although I admit that, because of our conditioning, the effects create a similar response, nevertheless. Conditioning, in my opinion, is the most powerful force in art appreciation and the idea has led to some interesting exchanges here on WordPress regarding the question of music being an international language – or not. (See Jonathan Friedman’s posts where my responses appear).

    Further expansions of scales/modes are less likely to be useful.

    I use fourth intervals a lot. Chord transformations (voice leading), if required, may be handled with a systematic technique that is consistent within the style, making no reference to classical forms.

    This particular matter can be developed considerably, but I won’t go into that here.

    Thanks for this input.

    • Thanks for your thoughts John, apologies for the length of time in replying to this. I agree with much of what you’ve mentioned, although I don’t necessarily feel the same dread in contemplating the series for use in a composition, just a sense of limitation. I suppose it all gets down to how much we wish to ascribe to a particular system, and at what point we start to bend rules for our own purposes – for myself, I’m finding diatonic harmony increasingly constraining, hence my search for different ways of opening up my auditory palette and my current predisposition toward timbre as a device. Stacking 4ths and 5ths is an alternate method and a logical step from our western use of thirds as you’ve correctly pointed out, and one that excites my ears at present – however, I’m open to all possibilities that may arise from the approach I’m currently undertaking.
      I also agree that conditioning and also cultural influences plays a large part in our apprehension of certain tone ‘colours’: certainly the people of Indonesia have a very different take on what they perceive as ‘harmony’ due to the influence of the gamelan (William Sethares has written an interesting book on this) – music may be an international language, but it has many varied and interesting regional differences. The stacked fourths and fifths I attribute mainly to the Georgian vocal tradition, which is a fantastic sound and one I’ve been exposed to through the choir I sing with here in Australia (The Spooky Mens Chorale), but you can also hear aspects of this in the harmonies of mid-1960s vocal groups, i.e. the Beatles, Kinks, Byrds, Beach Boys et al… music crosses many boundaries.
      Glad you enjoyed the post – I’ll certainly check out Jonathan Friedman’s blog, and by all means if there’s other you could recommend, I’d be more than happy to follow those as well.

      • Thanks for your continued interest. I find that diatonic harmony is far from exhausted. There are 36 seven note scales with their modal derivatives plus scales of 3,4,5 and six notes, and their modes – many hundreds of them. Freshness may be achieved by departing from inherited ideas about chord sequences/transformations and formal structure. You might be interested in ‘Los Jardines De Espana’ at https://soundcloud.com/john-morton-10/tracks
        The melodies, harmonies and rhythms are based on the Fibonacci series (they’re therefore ‘diatonic’). This composition was largely ‘constructed’ (because of the lack of a traditional hierarchy to draw from) but I don’t think it sounds that way at all. Keep in touch, J.M.

  2. I’ve just followed this blog. Interesting stuff indeed.

    Another P.S.:

    Shortly after I last wrote I thought of a good example of what I meant (when I said that traditional resource is not exhausted) in the form of the music to the films ‘The Green Mile’ and the ‘Shawshank Redemption’, both written by Thomas Newman. This music is childishly simple and uses no new approaches or techniques but its impact is very powerful and fresh. It knocks me for six every time I hear it. The simplicity is deceptive, of course, in the tradition of ‘less is more’. The transparency of the music is one of its most obvious characteristics.

    • Thanks John – I wasn’t familiar with either of these pieces, but now glad I’ve acquainted myself. The main theme from the Shawshank Redemption is particular powerful, and has that lovely ‘open’ feel with some widely spaced intervals (what I presume you’re referring to as transparency). Quite often less is more, as they say!

  3. Pingback: Timbre and ‘spectral’ colour – just so we’re clear… | Adventures In Sound & Vision

  4. Pingback: Quartal harmony… or the search for the grail | Adventures In Sound & Vision

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