| Like everything else in life, some sounds may be described as simple, some as complex. Being able to distinguish between the simple and complex, both in the kind of difference and in the amount of difference, is a necessary skill for those in audio. In this exercise, we shall examine sounds of varying degrees of complexity, as we come to grips with that most nebulous aspect of sound—sound quality: |
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| In previous lessons, we have called the sine wave an elemental and basic sound. All the energy of this simplest of all sounds is concentrated at a single frequency and, in the case of 1000 Hz, sounds like this: |
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| If we change the sine wave shape to a triangular wave shape, it sounds different. Let’s compare the 1000-Hz sine wave and the 1000-Hz triangular wave. Listen carefully for the differences in sound: |
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| The triangular wave sounds different because of the harmonics it contains. Harmonics are multiples of the 1000-Hz fundamental. The sine wave has only the 1000-Hz fundamental, without any harmonics. The triangular wave has the 1000-Hz fundamental but also a weak third harmonic at 3000 Hz: |
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| A fifth harmonic at 5000 Hz: |
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| A seventh harmonic at 7000 Hz:
And so forth.
These harmonics are whole-number multiples of the fundamental frequency. In the case of the ideal triangular wave, only odd multiples are involved. Taken together, these harmonics account for the difference in sound between a sine wave and a triangular wave. |
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| Let’s refresh our memories on this difference between the 1000-Hz sine wave and the 1000-Hz triangular wave:
Remove the harmonics of the triangular wave and what do we have? For a little experiment, let’s put the 1000-Hz triangular wave through a filter that rejects the harmonics but allows the fundamental to pass through: |
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| The 1000-Hz fundamental of the triangular wave is a simple sine wave! |
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| Now, let’s use a different filter which rejects the fundamental so we can only hear the harmonics: |
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| Even if it is not the most interesting sound in the world, we conclude that the triangular wave certainly has its own distinctive quality. The distinctiveness of its sound is all wrapped up in its harmonic structure. To emphasize this, let’s review a bit. This is the simple 1000-Hz sine wave: |
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| And this is the 1000-Hz triangular wave:
The harmonic content of a signal is the key to its distinctive sound quality. |
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| A 1000-Hz square wave has its own distinctive sound. All of its harmonics occur at the same odd multiples of the fundamental as with the triangular wave, but their magnitudes and time relationships are different. This is the sound of a 1000-Hz square wave: |
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| Here again, by use of filters, we can dissect the square wave. First, the harmonics are rejected, leaving only the sine fundamental: |
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| By filtering out the fundamental, only the low-level harmonics are left: |
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| It is instructive to compare the triangular and square wave shapes and to identify the source of the differences with the harmonics. First, the triangular wave signal and its harmonics: |
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| And now, the square wave signal and its harmonics: |
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| And now, only the harmonic contents of the triangular and square waves are compared: |
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| A violin playing middle C gives a fundamental frequency close to 260 Hz. Compare this violin tone with a pure sine wave at the same frequency from an oscillator: |
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| There is a richness to the violin tone which the sine wave certainly does not have. The violin tone is rich in overtones. As we deal with musical tones, it is fitting that we switch over to the musician’s terminology. Instead of harmonics, the terms overtones or partials should be used. Later we shall see the logic behind this. | |
| The violin tone can also be broken down into fundamental and overtones by means of filters. First, we shall hear the full tone, followed by the fundamental, and then the overtones:
Overtones dominate the violin sound. Its rich tonal quality depends entirely on the overtone pattern. The difference between the tone of a Stradivarius and a cheap violin lies principally in their different overtone patterns. The richer tone of the Stradivarius results from its richer overtone content. |
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| Each instrument of the orchestra has its own overtone pattern, which gives it its characteristic sound. For example, middle C on the violin sounds quite different from the middle C on the piano: | |
| This study of sound quality must place emphasis on the overtone structure. Therefore, let’s compare the fundamentals and overtones of the violin and the piano: | |
| To achieve high quality in the recording and reproduction of sound, it is necessary to preserve all the frequency components of that sound in their original form. Limitation of the frequency band or irregularities in frequency response, among other things, affect sound quality. This point can be demonstrated by going back to the middle C violin tone: | |
| Middle C has a frequency of about 260 Hz. Overtones occur near 520, 780, 1040, and 1300 Hz, and up. If an equalizer peak of 10 dB is introduced at 1000 Hz, the original pattern of harmonics is changed and the overall sound is changed: |
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| Also, if the higher frequency overtones of the violin are cut off by limiting the band, the quality of the tone is affected:
Some musical instruments have overtones that are not whole-number multiples of the fundamental and thus cannot be called harmonics. For such instruments, the general word overtones must be used. Piano tones, for example, are not strictly harmonic: |
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| Bells produce a wild mixture of overtones and the fundamental may not even be recognized as such: | |
| The overtones of drums are also not harmonically related to the fundamental, but they are responsible for the unique, rich drum sound: | |
| Summarizing, we have learned that preserving the integrity of the fundamental and overtone pattern of our signal preserves the quality of the signal, and this is what high fidelity is all about. | |
