My writings on the value and practice of music.

Strings: Just Intonation, Harmonic Series, Standing Waves Part 1

It’s not totally clear to me why I chose the guitar as my first musical instrument. It’s a toss up between listening to my father sing while strumming his Martin acoustic guitar (as a very young child) and watching heavy metal music videos on MTV around the time I reached adolescence.

I suppose the guitar seemed like a hero’s instrument, the way it’s handled and slung about the body like a sword or bow. Beneath that slightly puerile visual attraction that certain sound the guitar made happened to light up my young receptors. Since the time I first picked up a guitar and began my relationship with music (age 11 or so) I have played a variety of instruments;  Bb and Bass clarinet in high school, drum-kit and various percussion and I would also consider myself a competent pianist.  None of these other forays ever stole me away from the guitar though, piano is a close second but I view piano and guitar as cousins of a sort.  The only other instrument that may be more important to me is my own voice although I don’t perform as a vocalist. It has always been a curiosity of mine as to why a musician gravitates towards a given instrument or family of instruments. It’s probably a more complex question than it appears but for whatever reason, as a player strings seem to do it for me.

Going back for a moment to my battlement analogy, all string instruments are in fact like a bow. The most primary characteristic of any of the strung instruments is that there is a frame of some sort and stretched cross the frame is a string set with the necessary amount of tension to produce a recognizable tone when plucked or struck.  The iterations of stringed instruments have evolved over the years from instruments that actually did resemble a weaponized bow to the guitars, violins and other string instruments we are familiar with today.

Early Stringed Instruments, ancient string instruments, string family of instruments

Depiction of the String 'Family Tree'

In the case of the guitar each of the six strings are stretched across two focal points of tension, the “bridge” attached to the body of the instrument and the “nut” which is essentially the topmost part of the neck.  These two points suspend the tension filled string above the body and neck of the guitar and allow the player to interrupt the span of the string by “fretting” with their left hand.  Although this description may seem tedious to anyone with even a remote idea of the instrument I feel it is important to see that in essence the guitar is just a taught length of string, or rather six.

Not just any string will do though, the strings used in the manufacture of musical instruments have very particular characteristics. They have to be dense enough and strong enough to bear a considerable amount of tension, yet they also have to be slight and highly elastic so that they move easily and can sustain motion.  The motion of the string, in turn moving particles of air around it which issue outward (in fact they explode spherically outward) as highly organized waves of air  that carry to our hearing organs, is what creates the sensation of pitch. Tuning forks, strings, tines, bells and other musical instruments that are made with materials that give a reliable pitch when struck (or plucked) all share a commonality–when the object is struck it vibrates at regular intervals and in turn pushes the air around it into regular wave patterns.  The vibration is happening too fast for our eyes to track as a regular back and fourth or up and down pattern and  our ears don’t hear each individual wave or beat of air but the sum effect of those highly regular beats of air against our ear drum is a stable pitch. Motion with this equality and balance is called “periodic motion”. The object must have an equilibrium (state of rest or inactivity), in a string this is it’s taught resting state before it’s ‘distorted’ (in other words set into motion). Then it must have “elasticity”, this means that when the object is distorted (again struck, plucked or bowed) it will seek (restoring force) to return to the precise state it started in. In musical strings the struggle the string goes through after being plucked to regain equilibrium is the life span of the audible pitch, in other words when the note has fully decayed and we no longer hear it that means the string has found it’s original state or equilibrium. Again though it is not enough for the object or to vibrate and then come to rest, it has to vibrate at very regular intervals in order to be heard as a stable pitch. Let’s borrow a few visual aids to help clarify.

Here is a rubber band being displaced (plucked/distorted) and released in slow motion…

I would have preferred that this video allowed the string to complete a single “cycle” of motion and showed the full return force of the band but it still serves as a good visual.  If the video had not been edited you would see the wave form continue to go up and down until the equilibrium  robbed the distortion of it’s initial energy, very much like  a rubber ball being dropped from a height and eventually coming to rest on the ground.

Here is a very clear vintage video that shows the how tuning forks behave when struck and how they create very regular wave forms, the regular motion of a struck tuning fork is even more precise and reliable then that of a string…

The “oscillogram” that is shown at the beggining of the video is a very helpful visual aid, it is a two dimensional representation of the amplitude (size) and frequency (waves per second) of sound waves. Although it couldn’t really convey what the waves of air actually looked like exploding outward in three dimensions it is still a usable model for what the pushed air itself looks like.  The amplitude is what we perceive as volume the frequency is what translates into pitch.  A highly regular frequency such as the even back and forth motion of these struck tuning forks will be perceived as a very stable pitch. Even the most well designed guitar with the highest quality strings on it when plucked will not be as regular in motion as these tuning forks will, although a string is still very stable and when we hear it struck we perceive it for the most part as a single pitch.

Here is how a bow acts on a string, its not really any different than plucking it is just a reoccuring displacement caused by friction of  the bow catching and releasing over and over on the string…

What I see once the string gets going under the bow is a metronome like motion, it’s this ideal state of periodic motion that we hear as a pitch and classify generally as “musical”.

On a side note there are “natural” phenomena at many orders of magnitude that we could label periodic, on the macro scale the orbit of the Earth and Moon are nearly periodic and some pulsars are known to be regularly periodic within the .001 of a second range…

The saying goes that “music is math”, although this little aphorism is a heated philosophical debate waiting to happen it is important to understand that in many early cultures math and music often fertilized each others growth. The use of math as a tool pervades civilization almost completely, all science, technology, architecture ect. are beholden to math and much of the earlier writings about math involved experiments with simple musical instruments.  In part two will will look the natural overtones of the string and we will do so using a simple one string instrument model much like what was done in ancient Greece by Pythagoras himself.

Luke W.


Welcome to Accord: My blogspace

I am musician, I have created this space to share my idea’s on the value, significance and practice of music.

DISCLAIMER: I have never attempted to maintain a blog; I’m just now learning the conventions both stylistically and technically. I apologize in advance for any rookie errors/omissions and I’m completely open to counsel:)

I am 33 years old, an expatriate Northern Californian (b. SF, CA 1979) currently residing in Brooklyn NY (2009 -present). I moved to the East Coast to pursue career ambitions of being a performing artist. I never liked the idea that a person needed their surroundings to be some extreme of stimulation or depravation in order to evolve, however in these last 3+ years I have been exposed to things both musically and otherwise that have undoubtably altered me.  I seem to need this place for the time being although my world view and my primary musical instincts were formed at home.  Really what New York confronts a developing musician with is sheer numbers of dedicated and ambitious people trying their damndest to climb that same precarious internal ladder of perfection they are. That’s the allure and for now that’s why I stay. Since I’m here in musical Mecca I might as well report. I’ll dedicate some of this blog to biographical updates and impressions of New York (or at least the creative scenes I run in).

I may also indulge myself and talk about historical musical figures and (here I go…) what role culture plays in generating musical language.

Really though, I set out writing this blog to share my idea’s on the practice of music.

My hope is to create a dialogue that will encompass a spectrum from philosophy to physical technique (and the debatable stuff in between). I consider myself a well trained and well informed student of music. I’ve put certain concepts and exercises to work that I feel have helped me reach my goals as a musician; I am now inclined to document and share them here.


Kindly yours,

Luke W.