Lesson 16
The Harmonic Series
As I have mentioned before, musical sounds are caused by vibrations of objects or surfaces that vibrate air that, in turn, vibrates your eardrum. The human voice and musical instruments do not create just one vibration when sound is made, they created many harmoneous vibrations. These many vibrations join together to form the unique sound the voice or instrument makes.This set of vibrations made by the voice or instrument is called the harmonic series or overtone series. Each of the different vibrations is called a partial. The partials are numbered beginning with the partial with the lowest vibration frequency, the lowest tone. This is the 1st partial. As many as 16 or more partials can be discussed when discussing musical tones. The first partial is the primary tone of the pitch. The other partials are all colorations for the primary partial. The timbre of an instrument or voice is determined by the pitches and strengths of the partials above the 1st. Low, mellow instruments emphasize the low partials, and high shrilly instruments emphasize the highs. For those involved with sound systems, it is the strength of these partials that are adjusted when using equalizers.
There is an ideal harmonic series that music theorists use as a baseline for discussing harmonic construction. It is called the natural harmonic series. Essentially, the frequencies of the partials of this series are all multiples of the frequency of the first partial. For example, if the frequency of the first partial is 100hz, then the frequencies of the partials above the first are 200hz, 300hz, 400hz, 500hz, 600hz, 700hz, 800hz, etc. The first 8 partials, which we have enumerated here, are the most important partials. We can enumerate this series in terms of note names. This is where the previous lesson on note nomenclature becomes important. If the note we are interested in is C (the first note of the image below), then the partials above it are c, g, c1, e1, g1, bb1 and c2 (note 8 below).
Study this representation of the harmonic series built on C.
Pay particular attention to the first, second, fourth and eighth partials. The frequencies of each succeeding partial in that list is double that of the preceeding one and each of these partials have the same pitch name. As you know, our pitch material is divided up into octaves with the first note of each octave group possessing the same pitch name. This exposes one of the major principles of music. A pitch an octave higher than another has a vibration frequency double that of the lower pitch. Notice that these notes are perceived by the listener as having the same pitch quality only higher or lower respectively. This musical principle is one of the major factors in musical organization.
Study the following chart to learn more about the harmonic series. We will be using this information in our study of two-note intervals in a future course.
| The first eight partials of the harmonic series of Contra-A (AA) with partial name, note name and frequency. | ||
| Partial Name | Note Nomenclature | Frequency (hz) |
| 1st | AA | 110 |
| 2nd | A | 220 |
| 3rd | e | 330 |
| 4th | a | 440 |
| 5th | c#1 | 550 |
| 6th | e1 | 660 |
| 7th | g1 | 770 |
| 8th | a1 | 880 |
These would be the frequencies used if perfect tuning were used for the key of A major. But in order to allow for the use of all major and minor keys simultaneously, perfect tuning is not used. Instead, we use what is called even temperment. Small adjustments are made in the frequencies of certain notes so that they can be used in all keys. For example, in even temperment, C# and Db, have the same frequency. In perfect tuning, Db would have a lower frequency (and would be a lower pitch) than C#.