A few years ago I went back to college and did some postgraduate study. I didn’t really know why at the time. I had considered the possibility that this was some kind of vindication, an opportunity to prove to myself what I could achieve if I actually applied myself academically; a thought which gave way to the more valid inclination that this was actually an elaborate means of hanging with college chicks. Through the course of my study however, I realised the reason I had enrolled was to search for meaning in art. I don’t mean warm and fuzzy ‘it makes u feel good’ (subjective) meaning; what I was searching for were tangible objective points as to why we play and why it is essential to us as a species.
The course was a Post Graduate Diploma in Performance; it’s basically a baby Masters Degree and it gave me the opportunity to research and present two papers: Why Music Exists: An Exploration of the Lexicon of Sound and Bass Guitar: The Influence of Design, Industry, Genre and Technique on Performance Practice. In writing these papers, I stumbled on some facts, both concerning the ‘nuts and bolts’ of music theory/sound and concerning music as an art form. The points raised in these papers are, to me, extremely relevant to the modern musician and yet very rarely taught in music education.
Some points raised address musical understanding. For example, how many musicians were ever taught why the octave exists at all in music theory? Is it an abstract concept or is it based on measurable, explainable phenomena? Why does a b9 chord sound different (darker/more complicated) to a major 6 chord? Some of the points address issues of musical performance. For example, what are the ramifications of electronically amplified sound versus acoustically amplified sound (or why do bass players get no TV time)? And what exactly is music? I mean where did it come from in the first place, and does this explain why we continue studying and creating it despite comparatively menial economic returns and social marginalisation?
What I intend to present here over the coming months are articles based on my findings – sans academic hyperbole. Topics covered include: The Birth of Music, The Syntax of Music, The Influence of Design and Technology on How We Play, Art vs Super Mart and anything else that seems relevant. Beyond that I’d like to share a few things I’ve learnt over the last 20 years of playing and teaching bass.
So what’s first? Well I think as good a place to start as any, is the very beginning.
The Harmonic Series – Syntax of the Musical Language
I’ll tell you what is absolutely nuts. Bonkers. CRAY – CRAY! Because you are a product of the universe, you can not observe it objectively as a third party – your tools of perception are a product of the elements you are observing. What the hell do I mean? Ok, take waveforms. If you emit a sound wave, the rippling sympathetic sound waves which are generated occur at a consistent set of incrementally smaller ratios known as the Harmonic Series. You may not always be able to pitch these sympathetic sound waves themselves, however you will always hear the richness and colour these overtones bring to the fundamental tone (‘Man this bass sounds fat!’ etc).
This is the nutso bit: your ears perceive pitch based on the same values as the Harmonic Series. This might sound obvious (pun unintended – yet charming) but think about it – if you perceived pitch linearly, this whole universe would sound, well, like poop. What is the Harmonic Series exactly? Let’s use an example that is not music – just noise…
If I strum a banjo string, not only will Cletus mute the Nascar coverage (Bazinga!) but the string will almost instantly start oscillating at smaller and smaller increments. The first oscillation is the full length of the string, the next oscillation is half the length of the string, then a third, quarter, fifth etc. These sympathetic oscillations might be almost impossible to hear, but they are there and continue to generate until the energy in the string is exhausted.
You can see similar phenomena with other waveforms, for example, if you throw a TV playing Nascar footage in a pond, the wavelets will radiate outwards and decrease in size at predictable ratios until the energy is expired. It all depends on the size of the TV.
In reality, it’s pretty self explanatory (to a point); we evolved in a logarithmic universe and thus our faculties evolved in a similar fashion. But it is worth taking a closer look at the Harmonic Series because understanding it is the key to understanding why music theory makes sense.
Let’s take a musical example….
If we pluck a 1960s P Bass A string at the third fret, we generate a concert C note. This is our ‘fundamental’. Almost instantly, a sympathetic wave half as long (= twice as fast) is generated. Because our ears analyse data logarithmically, they understand pitch in comparative ratios. In other words, if the first C note is 65.4hz and the first sympathetic sound wave is 130.8hz, our ears instantly recognise that the second wave is exactly twice the frequency of the first, and such an easy-to-process ratio relationship that the second note is directly related to the first – even if it is higher in the audio spectrum. That is what an octave is; the ear saying ‘hey I find those two pitches really easy to relate and compare…. what a positively non-confronting ratio!’
Maybe a good visual equivalent would be looking at a chair from 50m and then placing another chair 100m away within eye sight of the first. You know you are looking at two different chairs and you know the second is far too small for Cletus to sit on, but they are both chairs nonetheless and you’re satisfied. Satisfied? Good.
So what happens next? We have our first two sound waves of the harmonic series: C1* the fundamental and C2* the octave above that. Well let’s think about it. The next sympathetic sound wave is 3 times as fast as the first. Think about music theory and this riddle can be solved rationally with no science necessary. Next to an octave what is the simplest, most common interval? Let’s go back to Cletus… When he picks up his cousin’s rum-stained acoustic and plays Sweet Home Alabama, what chord voicing does he use? Keep in mind Cletus doesn’t really know what he’s doing; he’s just following his intuition and punching out thick sounding bar chords. Well, I think he’s probably going to reach for ‘power chords’ voiced 1 – 5 – 1 or even just 1 and 5. This is because the 5th is almost as simple a ratio as the octave and yet harmonious enough to pass the mustard as a chord tone.
So we have our first three pitches of the Harmonic Series:
- the root or fundamental – C1
- the next wave vibrating 2:1 times as fast as the first = C2 (octave above C1)
- the third vibrating 3:2 as fast as the second = G (fifth above C2)
Because I’m using a musical example, it creates the illusion that the Harmonic Series is a man made musical theory concept. But remember THIS IS PHYSICS! Sound just works this way! As the ancients tried to understand sound, they stumbled upon the same phenomena I am now describing and they did so purely intuitively; but that doesn’t diminish the science of it – it only serves to prove it.
For example the oldest playable harmonic instruments ever found are from Henan Province, China, and date back as far as 9,000 B.C. The collection of flutes feature five to eight holes:
“Tonal analysis of the flutes revealed that the seven holes correspond to a tone scale remarkably similar to the Western eight-note scale that begins “do, re, mi.” This carefully selected tone scale suggested to the researchers that the Neolithic musician of the seventh millennium BC could play not just single notes, but perhaps even music (harmonies).”
~ Juzhong Zhang, Wang, Kong and Harbottle
What is perhaps more provocative, is that there is evidence of the instruments being altered after their initial construction for tuning purposes. These early musicians had more pride in their intonation than some pub singers!
If we were to continue working through the Harmonic Series and reverting the pitches back to music theory, we would come up with a scale that approximates the major scale very closely (actually the 7th we arrive at is very flat, making the scale closer to a mixolydian scale). Eventually, the increments become smaller than our 12 tone tuning system can easily document. See the figure below (wiki): the numbers above each pitch indicate how out-of-tune with tempered concert pitch they are.
Here’s the thing. You can actually explain our perception of pitch without referencing the harmonic series; you could say we hear logarithmically, and therefore harmonic relationships are really ratio relationships – and that’s that. But this does little to explain why we evolved to hear this way in the first place and it doesn’t address the fact that musical harmony (in terms of music theory) is a phenomenon occurring naturally in nature. Even within a single note.
The fact is that within every tone, the macro goings-on which we can clearly witness (the sound of harmony) also exist – even if imperceptible to most people at most times – and I believe this goes a long way in explaining just why it is that our sense of hearing and perceiving pitch developed the way it did.
What the Harmonic Series represents to me is two things:
- an example of the subtle, constant pressures of the universe influencing the evolution of life within that universe: every sound wave has exerted the Harmonic Series since the dawn of time and therefore informed life as to how to perceive sound.
- the smallest possible nugget of musical syntax present in nature; that is the DNA of music
Now what does all this mean for you the musician? First of all, if you’re an electric bass player, you can have some serious fun with the Harmonic Series. You play the most apt instrument for exploring it. The register of the instrument, the mode of sound production (plucked strings) and the fact that it is amplified means it can produce clear, ringing harmonics better than just about any other instrument. Whenever you have a length of string (it’s only more common to play harmonics on open strings because most of us only have two hands), you can ascend the Harmonic Series (relative to the fundamental – the pitch of the open string) by dividing it into incrementally smaller fractions. So if you play an A string and then lightly touch it at the 12th fret (half way) and play that harmonic, you will hear the second pitch of the harmonic series based on A1 – A2. Again, if you lightly touch the A string at the 7th fret (a third) and play that harmonic, you will hear E2 (a 12th or Octave + a 5th above the open A string), and so on.
Also, understanding the logarithmic nature of pitch recognition explains why harmony is relative; why for example an F# over a D wants to pitch slightly flatter than an F# over a B. If you have a fretless bass try this out for yourself: if you are really listening (and you’ve tuned up, Cletus…) you will notice that to get a truly harmonious Jaco moment going on, your F# finger will need to ever so slightly change position over each bass note (D and F#). As we start playing in ensembles and richer harmonies we (well I do…) surrender to tempered harmonic standards and battle onwards.
So do you get it? What we do as musicians is deal with a language unlike any other. The written and spoken word are a series of arbitrary symbols organised by arbitrary systems, and thus 1000s of languages populate this green earth. Music on the other hand is codified by laws of physics – and is thus truly universal! Cool hey? Better than Nascar even! Despite the fact that I might enjoy the ratio-istic orgy of an altered chord, and Cletus might prefer the down home honesty of a power chord, we are both perceiving the data the same way; both understanding in an intuitive manner the syntax of the musical language.
*Throughout the article I refer to the tones of the Harmonic Series by their note name and octave (relative to the fundamental tone of that Harmonic Series). For example the Harmonic Series in C would be C1 – C2 – G2 – C4 – E4 etc.
PW Farrell is an Australian session musician and solo artist. His critically acclaimed debut album is available on iTunes.