You will remember from chapter 3 that a musical note is made up of lots of frequencies all sounding at the same time: the fundamental frequency, along with its other harmonics.
At the risk of being accused of scrimping on the illustration budget here, I would like to show you the final illustration from the previous chapter again because it shows us the basic principle behind the production of different timbres.
Harmonics can join together in different mixtures—depending on the instrument and how it is being played—to give different timbres.
Here we see the first five harmonics involved in a note joining together in different mixtures to produce notes with different timbres. There are many more frequencies involved in most real notes so these ripple patterns can become very complex. The reason why instruments have different timbres is because they produce notes which contain different mixes of these harmonics. For example, on a violin, the mixture of harmonics for the note middle C involves lots of fundamental frequency backed up by the second, fourth and eighth harmonics. On a flute, however, the same note involves mostly the second harmonic backed up by the fundamental and the third harmonic. In both cases lots of the other harmonics join in to enrich the sound.
As we saw earlier, the different mixes result in a much more complicated pressure ripple pattern for the violin than for the flute. As far as the physics is concerned, the flute ripple is closer to the shape you would get off a pure “fundamental frequency only” wave and so we could say that the flute produces a “purer” note. The odd thing is that, as listeners, we don’t seem to favor purity over impurity. We enjoy the complicated sounds of the violin and saxophone just as much as the purer timbres of the flute, harp and xylophone. This is also true of our appreciation of singers. We like the purity of sound we get from Charlotte Church singing her version of “Silent Night” just as much as we
appreciate the whiskey and smoke sound of Louis Armstrong singing
“What a Wonderful World.”
As I said earlier, the reason why the instruments produce different mixes of frequencies is because they are different shapes and sizes, and also because they make their sounds in different ways.
Let’s take a closer look at the violin. Whatever note is being played, the sound is being produced by a vibrating wooden box which has a particular shape and size. The size and shape of the box makes it very responsive to certain frequencies and less so to others. Every note played on the instrument is made up of lots of related frequencies and, whatever note is being played, some of the frequencies involved will be among those “favored” by the shape and size of the box. As you might expect, these favored frequencies are produced a little more loudly than the others which make up the note. The technical name for the collection of favored frequencies of an instrument is its formant.
To understand what a formant is, let’s consider a couple of notes played one after another on a pathetically bad cello. A real cello has a formant which favors lots of different frequencies, so that it sounds good for a wide range of notes. But we are going to invent a dreadful instrument which favors only a narrow range of frequencies. We will play the notes A and D on the instrument and assume that, although it vibrates at all frequencies to some extent, it favors only the frequencies close to 440 vibrations per second (440Hz).
When the A is played, we will hear its basic, or fundamental, frequency (110Hz), together with twice that frequency (220Hz) and three times (330Hz) and four times (440Hz), etc. On an instrument which had a uniform, fair response to all frequencies, we would hear an evenly mixed combination of all these vibrations. But, as I say, real instruments are not fair, they have favorites and in this discussion our instrument is entirely unreasonable and only favors frequencies around 440Hz, so the fourth harmonic (440Hz) will have more than its fair share in the sound we hear.
When we change the note to D, the frequencies we will hear will be the
fundamental (146.8Hz), together with twice that frequency (293.6Hz), three times (440.4Hz), four times (587.2Hz), and so on. But the instrument hasn’t changed: it still favors frequencies around 440Hz. So when D is played, our instrument will now favor the third harmonic frequency of 440.4Hz and we will hear that component of the note more prominently than we would from an unbiased instrument.
These more prominent harmonics do not affect the fundamental frequency of the note. They just change the mix of harmonics, which affects the timbre of the note we hear—so these two notes would have different timbres. An instrument like the pathetic cello I have just described would be useless, because it has only one favored frequency, which would dominate any music you played on it. Fortunately, real instruments have lots of favorite frequencies and this ensures that all the notes are produced clearly. However, each instrument type has its own family of favored frequencies and this is one of the reasons that cellos sound different from violins even if they are playing the same note.
It is also interesting to note that, in many cases, the ripple pattern of a note changes during its lifetime. The illustration below shows this very clearly—the ripple traces are from near the beginning, middle and end of a single note played on a harpsichord. These changes are different for each type of instrument and add to our assessment of the timbre of the instrument involved.
These three ripple patterns show how a note changes during its own lifetime. Here we see traces taken from near the beginning, middle and
end of a single note played on a harpsichord. (Source: C. Taylor, Exploring Music, Taylor & Francis, 1992).
Now that we understand the basics of timbre, it’s a good time to compare the ways in which various instruments produce the sounds they make. The following chapter investigates the musical personalities of some of our favorite instruments, from violins to synthesizers.