Mason Blake
Complex periodic sounds are a combination of sine waves (Fourier's theorem) and are not pure tones. A pure tone consists of only a single frequency and has a wave form that is a pure sine wave. Conversely, a complex tone is not a pure sine wave, but it is periodic, meaning it has an underlying pattern that repeats. Complex tones consist of multiple frequencies, with the fundamental frequency being the lowest frequency of repetition. The relative amplitude of the different harmonics in a complex tone determines the tone quality or timbre.
| Characteristics | Values |
|---|---|
| Complex periodic sound | A combination of sine waves (Fourier's theorem) |
| Spectrum | Looks like a comb with tines at the frequency components of the sound |
| Real-world spectrum | A mathematical approximation, so the spectrum is a fuzzy-looking comb |
| Fundamental frequency | The lowest frequency of repetition of the sound |
| Harmonics | Integer multiples of the fundamental frequency |
| Pure tone | A single frequency |
| Waveform | A pure sine wave |
| Complex tone | Not a pure sine wave but it is periodic |
| Period | Time for the periodic pattern to repeat |
| Pitch | The same even though there is almost no 200 Hz in the complex tone |
| Timbre | Different as the mix of harmonics is different |
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What You'll Learn
Pure tones are sine waves with a single frequency
A pure tone is a sound with a sinusoidal waveform, or a sine wave of constant frequency, phase shift, and amplitude. In other words, it is a single-frequency tone. When presented in isolation, and when its frequency pertains to a certain range, pure tones give rise to a single pitch percept, which can be characterized by its frequency.
On the other hand, a complex tone is a sound wave that repeats with a given pattern, but this pattern is not a sine wave. A complex tone consists of not just one frequency sine wave but several different frequency sine waves superimposed on one another. The fundamental frequency of a complex tone is the lowest frequency of repetition of the sound. It is based on the periodicity of the entire complex sound and is not just the frequency of the lowest component of the complex sound.
The nature of all the other frequencies and their relationship to the fundamental periodicity of the wave is crucial to understanding musical acoustics. For instance, the presence of higher harmonics in addition to the fundamental causes variation in the timbre, which is why the same musical pitch played on different instruments sounds different.
In psychoacoustics, a pure tone is a sine wave with a single frequency. It is a sound with a sinusoidal waveform, and it has the unique property among real-valued wave shapes that its wave shape is unchanged by linear time-invariant systems. Only the phase and amplitude change between a pure-tone input and its output.
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Complex tones are a combination of multiple frequencies
The fundamental frequency of a complex periodic sound is the lowest frequency of repetition of the sound. This fundamental frequency is based on the periodicity of the entire complex sound. The fundamental frequency is not just the frequency of the lowest component of the complex sound. For example, a complex sound may consist of a 100-Hz sine wave and a 150-Hz sine wave. The harmonics of a complex periodic sound are the integer multiples of the fundamental frequency.
Musical tones, as produced by instruments, are not pure tones. They consist of a fundamental frequency and harmonics. For example, when one plays an A = 440 Hz on a violin, the violin produces a frequency of 440 Hz, but in addition, it is also producing sound at 880 Hz, 1320 Hz, 1760 Hz, etc. This is referred to as a complex tone. The relative amplitude of the different harmonics determines the tone quality or timbre of the note, but all real tones have some amount of harmonics present.
Complex tones add a layer of richness and variety to auditory experiences. Most of the sounds in natural environments are complex tones, from a harmonizing choir to the rich sounds of a symphony orchestra. These sounds are characterized by their depth and can contain fundamental frequencies along with harmonics and overtones. Any sound from a musical instrument, voice, or even background noise in a bustling city is usually made up of such multiple frequencies.
There are two types of combination tones: sum tones and difference tones. Sum tones are found by adding the frequencies of the real tones, while difference tones are the difference between the frequencies of the real tones. Combination tones are heard when two pure tones, differing in frequency by about 50 cycles per second (Hertz) or more, sound together at sufficient intensity.
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Complex tones have a fundamental frequency and harmonics
Complex tones are a combination of two or more pure tones of different frequencies that are harmonically related. A pure tone, on the other hand, consists of only a single frequency and has a wave form that is a pure sine wave.
The fundamental frequency of most naturally generated periodic sounds, such as the vibrations of tuning forks, guitar strings, or motors, depends on the size of the vibrating item. A larger item will give a lower frequency, while a smaller item will give a higher frequency. In addition to vibrating at the fundamental frequency, these items also vibrate at all integer multiples of the fundamental frequency, with each higher harmonic at a shorter wavelength and higher frequency.
The addition of harmonics to a fundamental frequency changes the tone quality of the note, making it "richer", "brighter", or more "mellow". This is because the resulting wave always has the same period as the fundamental, no matter how many harmonics are added. Thus, the resultant wave always seems to have the same pitch as the fundamental, even though it can sound quite different.
The relative strength of the different harmonics gives an instrument its particular timbre, tone colour, or character. For example, the clarinet and saxophone produce sound through the resonance of air inside a chamber. However, the clarinet's resonator is cylindrical, so the even-numbered harmonics are less present. The saxophone's resonator is conical, which allows the even-numbered harmonics to sound more strongly and thus produces a more complex tone.
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The fundamental frequency is the lowest frequency of repetition
A pure tone consists of only a single frequency and its waveform is a pure sine wave. On the other hand, a complex tone is not a pure sine wave but it is periodic—it has an underlying pattern that repeats. Complex periodic sounds can be described as a combination of sine waves (Fourier's theorem).
In music, the fundamental frequency is the musical pitch of a note that is perceived as the lowest partial present. It is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. The fundamental frequency is often referred to simply as the fundamental and is abbreviated as f0 or f1. The fundamental is also considered a harmonic because it is 1 times itself. The fundamental is the frequency at which the entire wave vibrates. Overtones are other sinusoidal components present at frequencies above the fundamental. All of the frequency components that make up the total waveform, including the fundamental and the overtones, are called partials. Together they form the harmonic series.
The harmonics of an instrument, when played together, sound good. Overtones that are perfect integer multiples of the fundamental are called harmonics. When an overtone is near to being harmonic but not exact, it is sometimes called a harmonic partial, although they are often referred to simply as harmonics. Sometimes overtones are created that are not anywhere near a harmonic, and are just called partials or inharmonic overtones.
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Complex tones can be created by adding harmonics to a pure tone
A pure tone is a simple sine wave with only one frequency. It is produced by a simple harmonic oscillator, which has only one resonant frequency. On the other hand, a complex tone is a sound wave that repeats with a given pattern but is not a sine wave. It consists of multiple frequencies superimposed on one another.
The perception of pitch in a complex tone remains unchanged even with the addition of harmonics. This is because the resulting wave always has the same period as the fundamental frequency, regardless of the number of harmonics added. However, the timbre or tone colour of the complex tone differs due to the mix of harmonics.
The relative strength of the different harmonics in a complex tone influences the musical timbre or tone colour of a steady tone produced by an instrument. The timbre is strongly affected by the relative strength of each harmonic. For example, the clarinet and saxophone produce sound through the resonance of air inside a chamber. The clarinet's cylindrical resonator results in weaker even-numbered harmonics, while the saxophone's conical resonator allows these harmonics to sound more strongly, producing a more complex tone.
In summary, complex tones are created by adding harmonics to a pure tone, which alters the tone quality without changing the pitch. The fundamental frequency and its harmonics contribute to the overall perception of the complex tone, with the relative strength of each harmonic influencing the timbre or tone colour.
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Frequently asked questions
A pure tone is a simple sine wave at a single frequency.
A complex tone is a sound wave that repeats with a given pattern but is not a sine wave. It consists of a number of different frequency sine waves superimposed on top of one another.
A pure tone consists of only a single frequency and has a wave form that is a pure sine wave. A complex tone is not a pure sine wave but it is periodic—it has an underlying pattern that repeats.
The fundamental frequency of a complex tone is the lowest frequency of repetition of the sound. It is based on the periodicity of the entire complex sound and is not just the frequency of the lowest component of the complex sound.
This is because if you add a harmonic to a fundamental, the resulting wave always has the same period as the fundamental, no matter how many harmonics you add. Thus, the resultant wave always seems to have the same pitch as the fundamental, even though it can sound quite different.
