A HARMONIC VIEW OF RHYTHM: PART 1 of 3

INTRODUCTION

This whole journey started for me with hearing one statement: “Rhythm is just harmony slowed down”

From there, with some basic knowledge of physics, you can start seeing a) how this is the case, and b) how you can start applying all the centuries of study on harmonic theory and composition, to rhythmic composition.

In this series I’m going to try and summarise some of my thoughts and ideas about how I look at the underlying structures of rhythm, and how we can actually put to use what is now becoming a much more mainstream school of thought – featuring the likes of harmonic polyrhythms and microtiming.

We’ll look at transposing concepts of harmony down to the rhythmic level such as melody, chords, scales, and timbre/texture*.

*OK, this isn’t a harmonic concept, but it’s still applicable!

PART 1 will talk about where rhythm lies on the frequency spectrum and so what to focus on.

PART 2 is some fundamental thoughts on pulse, perception, and the ‘tonal center’ of rhythm.

PART 3 starts to dive in to some practical applications.

Just a tiny disclaimer before we start… I’m going to assume a certain amount of musical knowledge, as otherwise this would be stupidly long, plus there are numerous places you can learn that stuff for free that will explain it far better than me anyway.


THE FREQUENCY SPECTRUM

I’ve been toying with the ideas of harmony in the realms of rhythm on and off for a good few years, and after a while of making chaotic sounding messes of polyrhythmic triads (in which, to be fair, there is a kind of beauty, it might just take a while to hear it), I realised quite an important aspect of this whole area of study: the position of rhythm on the frequency spectrum, and how that affects its functions and your musical choices.

Often when people talk about the frequency spectrum (in relation to music), they’re talking in terms of the whole range of frequencies we humans can hear – roughly around 20Hz – 20,000Hz. 

When you hear a voice or a musical instrument sound a note, you’re hearing something vibrate at both a fundamental frequency (a pitch), and also multiples of that frequency at the same time. This pattern of additional frequencies – harmonics – is known as the harmonic series, and it applies to all resonant objects that make sound. So you have these layers built up from a fundamental note – and it is essentially those fundamental notes that is the focus when composing harmonically.

You could see the two sides of this as the fundamental frequency being the ‘note‘ in terms of pitch and function, and the harmonics the ‘detail‘, the patterns of harmonics in differing intensities giving you information about the sound source – how bright or dark it is, whether it’s a cello or a flute, and so on.

To give you an idea of how these notes fit into our hearing range, the fundamental frequency of the low E on a bass guitar is 41Hz, and Soprano C (two octaves above middle C on a piano) is a little over 1000Hz. Musically, that is a very wide range of notes, though in our hearing range of 20-20,000Hz that leaves a lot of room for the detail in what we hear – the harmonics. However, even within this relatively small range of frequencies, different sub-ranges of this have very different characteristics and effects (this is what sound engineers spend their time worrying about).

The interpretation of a harmony is often defined by both its context in the long term (e.g. tonal centre, modulations), and also in the short term (the specific notes making up a chord). A very strong influence on how a chord is felt/perceived is the bass note. For example, play a C triad with a C 2 octaves below, and it will still feel like C. Change that low bass note to a G or an E and the chord will still be C, but feel less stable. Or even, change the bass to a note that isn’t in the triad and it is perceived as a new root: change the bass to A to make an Am7, change it to F to make Fmaj7add9, and so on.

Tight harmony (simultaneous notes in close proximity) in the lower ranges is often avoided, partly due to the fact that it’s often trying to make a stable ‘base’ for the higher notes, but also because it can easily sound unclear, or ‘muddy’. We can’t discern as much detail and separation in those lower ranges as we can for higher pitches.

So rather than trying to force certain musical/harmonic ideas into somewhere they don’t sound so great, you instead use a range based on its strengths. Composers have used the bass for years to make movement, guide chord progressions, add variation, create stability, instability, weight, power, aid modulations, slow or quicken the harmonic rhythm/perceived speed of the music.. many things that bass is very useful for and very good at, and most importantly, different from what mid- and higher-range notes are good for.


RHYTHM ON THE FREQUENCY SPECTRUM

All of these audible frequencies we call notes are just regular vibrations, occurring at a speed where we can’t make out the individual events, but instead perceive them as a pitch. Much the same as when a screen of individual images changes them fast enough, we ‘glue’ them together and perceive a moving image. If we slow down musical notes far enough, that moving image becomes ‘unglued’ and we start seeing (hearing) the individual images (pulses). For example if we take that low ‘E’ on the bass guitar (41Hz – 41 cycles per second) down an octave (half the frequency) we end up with pulses at around 20Hz. Another octave down and we’re at 10Hz, or 10 pulses per second. Now we’re well into the realm of being able to hear a stream of individual pulses we can tell apart from each other. We’ve reached Rhythm on the frequency spectrum.

60bpm is 60 crotchets (1/4 notes) per minute, or, 1 per second. We could say crotchets at 60bpm have a ‘note rate’ of 1Hz.

Let’s say you play semiquavers (1/16 notes) at that speed. Four notes per beat, you’re now playing notes at a rate of 4Hz. Still very low.

Let’s say you’re playing constant semiquavers (1/16 notes) at 240bpm. Musically, this is extremely fast. It’s four times the speed of 60bpm, so you’d now be playing notes at a rate of 16Hz.

The reality is that, because these events are now happening slow enough that we can perceive them separately (the separate frames in the movie), we can have more fun with them than just playing constant rates. For example you might play a combination of crotchets, quavers and semiquavers across different instruments, or even simply within each voice.

This is where we come back to harmony. Crotchets, quavers and semiquavers are all related very simply to each other, in factors of two. Semiquavers are twice the speed of quavers, which are twice the speed of crotchets. In terms of pitched frequencies and harmony, they are all ‘octaves’ apart – if you double the frequency of a pitch, you raise it by one octave. If one of these ‘rhythmic notes’ were a C, all the others would also be C.

If these ‘C’s were played simultaneously, on top of each other, in harmonic terms this is basically nothing – it’s not a chord, it’s just one note with reinforced ‘harmonics’.

If you played them in a series – changing between them one after the other – you would make a rhythmic ‘melody’ that was also very dull to listen to if you played the equivalent notes, say, on a piano. However, rhythmically, you can find this as the entire rhythmic pallette for countless songs and pieces of music, from centuries ago to the present day*.

* A comment on microtiming: often what appears (or can be simplified) to be a basic rhythm like this, will be inflected with very small but specific shifts in the timing. This is one of the particular bits of fun that can be had with this range of the frequency spectrum, and can have a profound effect on the feel of a rhythm. I dive into this a lot further here.


As we go down into these lower frequencies, the duration of the cycles becomes longer (in physical waves this is known as the wavelength). You need to hear at least a full cycle of a frequency to be able to tell what frequency it is, in the same way as you don’t get the full picture of a phrase or a chord sequence until you’ve heard the whole thing. This also goes for the complexity of what’s being presented – simple ideas can be digested more quickly than more complex ones, and so for example a very dense chord might need more time to be appreciated, than a simple triad. Similarly, a simple rhythm can be picked up quickly by a listener, whereas a more intricate rhythmic phrase, or nuanced groove might take more time to really appreciate.

For a lot of music, this is really the function of rhythm: where bass gives a solid grounding for the harmony, rhythm gives a solid grounding for the overall feel. That goes for tempo, subdivisions, swing, accents and more. This is what’s meant when people talk about ‘groove’ – like the groove on a record that the stylus rests in, it’s something everyone can sink into, a bed for the rest of the music to grow out of. A lot of music is based on the principle that once the groove is set up, breaking away from that will break the spell and ruin the magic. Look at any form of dance music to see this in action. Or on the slower end of things, something like reggae/dub. Of course rhythm is just one player in this – a lot of music will aim to be very focused in what emotion it’s getting across, and breaking that flow can kill it very quickly.


So, to sum up: rhythm is just another range on our spectrum of musical players, ranging from the atmosphere and detail of the high frequencies, down to the fleeting and melodic higher musical notes, to the deep bass notes that support the harmony and make your trousers flap, right down to these separate pulses that we perceive in a different way, but are nonetheless still related (albeit not quite as closely as the other players – rhythmic frequencies can’t be ‘out of key’ with the tonal elements in the same way as they can with each other).

The nature of how we perceive these lower frequencies, which have longer durations, lends itself to slower changes, broader strokes, defining feel.

Rhythm however is also the structure on which we lay the notes that are played. How a succession of notes appear in time is as important as the notes themselves.. so it’s worth looking at.

In Part 2 we’ll look at the ‘tonal center’ of rhythm. See you there!


Leave a Reply

Your email address will not be published. Required fields are marked *