Scales in Music – A Tonal System

Acoustics of Music – Part 7

Acoustic Principals – Overtones

Welcome to Part 7 of our article series the Acoustics of Music. The complexities of sound created by musical instruments, is an important topic to review. Within this article we will discover the harmonic divisions along a guitar string to help us understand how complex sound really is.

Prerequisite – Part 7 of Scales in Music – a Tonal System is an extension of the article titled, Basic Characteristics of Sound. Please feel free to visit this article as a prerequisite and to gain a brief overview on the basic study of the principal of overtones in acoustics as presented here.

Pure Tones – The note we hear from a musical instrument is comprised of more than one sound. As mentioned, a pure tone does not have any other sound associated to it. It is an exact frequency rather than a representation of more than one frequency including the overtones produced through musical instruments. Generally, pure tones are produced either by electronic devices or by tuning forks, the idea being that only one frequency is created rather than a collection of frequencies found as produced by musical instruments.

Musical Instruments – Producing Sound

Basically there are several ways that musical instruments produce sound. Most commonly they are produced via any one or more of the various means to which cause an undulation or variation in air pressure, thus creating a sound. To cause the instrument to vibrate one must do such activity as strumming a guitar, plucking a violin using the pizzicato technique, beating a drum with a drum stick or some other percussive technique, blowing through the mouthpiece of a trumpet or through a reed such as in playing the oboe. In all cases the action causes the vibration which in turn produces a sound.

Think of a guitar string for a moment. It is actually a very good example for explaining overtones and harmonics. When a musician picks, plucks or strums the open string it vibrates causing a disturbance in the air which we hear as the sound of the pitch the string helps to create based upon its length and its gauge or diameter. The sound is actually a complex sum or total of all of the sounds produced along its length and the additional sounds produced as the vibrations pass through the wood the guitar is made from.

Further, the vibration of the string is picked up by the instrument itself adding even more vibration and amplitude as it passes through the body of the guitar and finally through its sound hole. What we hear is the fundamental tone of the full length of the string as it vibrates unless we do something to shorten the length of the string such as fret or cut the length of the string using a finger pressing on it at any given fret location along the neck of the guitar. This act causes a different fundamental tone to be heard.

Also, without any fretting, different tones or frequencies are generated along the entire length of the string. The drawing below shows some of the relationships  or harmonic divisions along the length of a guitar string which includes those created based upon the following relationships; 1:1, 1:2, 1:3, 1:4, 1:5 and 1:7 among other harmonic divisions. The same principal applies to all other bowed, plucked or strummed stringed instruments.

This graphic shows the concept very well. It was taken from the Wikipedia about overtones and used here under the Creative Commons Share/Alike License 3.0.

The top figure shows the entire length of the string. The second figure divides the string into two equal parts. Each half produces a harmonic division, a different frequency than the fundamental frequency. Its relationship to the fundamental is 1:2. The additional harmonic frequencies are shown moving down the chart. Each produces its own frequency and yet it remains a part of the whole sound. Again, the fundamental frequency is what we hear “colored” by the harmonic sounds also produced when the string is being played. Our purpose here is to support the idea with this additional information so that you are fully aware that there exists more than one frequency or multiple harmonic divisions, when playing music an instrument. This concept is important to understand especially if you wish to compose formal and advanced music.

For the brass instruments the length and diameter of the tubing used to manufacture the instrument plays a key role as do the valves of the instruments. Likewise for the woodwind instruments however some of them rely on a reed or multiple reeds to assist in generating various sounds from them. For drumming or percussion instruments, sound is produced by rattling, striking, brushing or using some other percussive action to cause the vibration. The use of different devices including using your fingers rather than another object can alter the rate of the vibration.

Irregardless of what device or method is being used to start the vibration process all instruments produce a sound from one or more of these principals. The overtones are fractions of the fundamental tone and collectively they create the complex and dynamic vibrations which produces the unique and beautiful sounds we hear from musical instruments.

The interplay of the acoustic principals and the components of sound are vital to know about. They are the important things to consider when engineering sound and when composing music. Of course, this is all relative as to what you want to do with, of and for the field of music.

Part 8 completes the commentary for the Acoustics in Music series of articles. Please proceed to the conclusion for this section of the overall series included in Scales in Music – A Tonal System.

Please continue to Part 8 of the Acoustics in Music article series. It is simply called Acoustic Principals – Conclusion.

Mini Series Links

To return to the Music Theory – Level 1 directory for the article listings within the series, please proceed to Music Theory Section – Level 1 – Series Introduction – Part 10.

To continue onto Music Theory – Level 2 directory for the article listings within the series, please proceed to Music Theory Section – Level 2 – Series Introduction – Part 20

To proceed to Acoustics of Music directory for the listings within the mini-series, please proceed to Acoustics of Music – Part 1 – Series Introduction.

Valuable References

For additional information and to expand even more your understanding of the concept of overtones, please review these very good resources for college level information about them.

MIT Open Courseware – Walter Lewin – Musical Instruments, Sound Cavities, and Normal Modes.

This video is a part of the full lecture series referenced immediately below. The lecture includes a lot of the information in this article series but from a college level. It includes the mathematics behind the concepts presented here.

Physics III – Vibrations & Waves –  The referenced video series is the complete 23 part lecture series by Professor Walter Lewin of MIT.

Play List – This link will take you to the Academic Earth website where a lot of academically focused material is available to you. Please feel free to visit them as your time permits.

The University of New South Wales in Sidney Australia has a very cool section on their website that can continue your study of the acoustics of sound as related to the guitar. For those interested I would urge that you visit this excellent sight for further insights.