How is tone created in sound?

Acoustics

The essentials in brief...

In acoustics, an audio signal with exactly one frequency is called a (pure) sound
From tone to sound

Sounds consist of more than one frequency. It contains fundamental frequencies and overtones, with the overtones being an integral multiple of the fundamental frequency.
Sound components

Audio signals can be represented in different ways. With the Fourier transformation, an oscillogram can be translated into a frequency spectrum.
Forms of representation of audio signals in acoustics

We hear in frequency ratios (tone intervals) and not in frequency differences!
Tone intervals

Sounds contain many different frequencies with no particular frequency ratio. Dominant frequencies determine the character of a sound.
Sounds

Noise makes communication difficult. A distinction is made between different types of noise in technical signal processing and acoustics.
White noise and pink noise

From tone to sound

So far we have dealt with sound waves whose sound pressure curve can be described with a sine curve. This type of sound consists of exactly one frequency and is known as pure tone, simple tone or sine tone. The concert pitch a ', which is used all over the world for tuning musical instruments, is such a pure tone with a frequency of 440 Hz. The orchestra is tuned after the oboe (possibly organ, piano or harpsichord). Pure tones can practically only be generated electronically.

A sound is defined as a fundamental tone on which other tones with integral multiples of the fundamental frequency are superimposed. These tones are known as overtones or harmonics.

Source: "Akustiklehre per Computer", Mediacoustic

Visualization with audio examples of individual pure tones and together as a harmonic sound. The fundamental oscillation shown comprises three wavelengths.


In the case of periodic sound processes, the frequency of the fundamental tone determines the pitch of the sound. The different volume levels of the overtones make up the so-called timbre. Sounds are produced by musical instruments, among other things.

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Sound components

Names of the sound components in acoustics.

Multiples of
Base frequency

Harmonics

Overtones

Partials or partials

11st harmonic or
Fundamental wave
Keynote1st partial
22nd harmonic1st overtone2nd partial
33rd harmonic2nd overtone3rd partial
4etc.etc.etc.
Source: http://www.dasp.uni-wuppertal.de/ ars_auditus / akustik / akustik3.htm

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Forms of representation of audio signals in acoustics

In acoustics, there are various ways of representing a sound event. The oscillogram and the frequency spectrum are common. The oscillogram shows the course of the sound pressure over time. As a result, a pure tone has a sinusoidal shape, which clearly shows that sound is a wave. If a sound is represented in the oscillogram, it is no longer a nice sine curve, but a superposition of several sine curves of the fundamental and the overtones, which together result in a new, more varied curve. What remains in common with tone and sound is the periodicity of the pattern, which is repeated after the duration of a fundamental oscillation.

Source: Werner Stalder, (2000). "Education and training course on noise protection", p. 2.7

Oscillogram and frequency spectrum of a pure tone and sound. The pitch a 'is played both times. If you play a "note" with a musical instrument, the overtones are automatically created in addition to the basic note - you unintentionally produce a "sound". Only electronic instruments can produce pure tones. But they sound a bit dull, which is why the automatic creation of the overtones is actually an enrichment.


From the oscillogram, something can be learned about the purity of a sound and the repetition of certain parts of the sound. The more the curve resembles a sine, the purer the sound. You can also see volume changes due to amplitude fluctuations.
If you want to know which frequencies occur in an audio signal, then the representation of the frequency spectrum is helpful. In the spectrum, the sound frequencies are shown on the "x-axis". The corresponding sound level is on the "y-axis". If you spectrally analyze a pure tone, you only see a sound level at one frequency that is greater than zero. The other frequencies do not occur at all. In a sound, however, several frequencies are represented, namely that of the fundamental and that of the overtones. In the spectrum you can see immediately which frequencies these are and that they are each an integral multiple of the basic frequency. In contrast to the oscillogram, it is therefore possible to read directly which frequencies are represented and how strongly, but there is no information about the signal over time.

Nowadays an oscillogram can easily be created with any computer. For this purpose, an audio signal is recorded with a microphone - or an existing music file can be used. With suitable software (audio editor) the audio or music file can be displayed as an oscillogram. In order to obtain the frequency spectrum from an oscillogram, a so-called Fourier analysis is carried out. With this method developed by Fourier (French mathematician 1768 - 1830) every periodic signal can be composed of a superposition of pure sinusoidal oscillations. These functions are already available in some CD burning programs, otherwise there are free programs for editing, editing and displaying audio signals at www.freeware.de, for example.

If you want to give a sound a different "timbre", you can use electronic means to filter out individual overtones or change their level.

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Tone intervals

Pythagoras recognized that pleasant sounds are created when you strike strings whose lengths are in integer ratios. The more complicated the relationship between the string lengths, the more dissonant (jarring) the interval sounds. So it is the frequency relationships that determine whether a tone interval sounds harmonious, not the absolute frequencies.

relationshipdescriptionAudio sample
1:2Okatave
2:3Fifth
3:4Fourth
4:5Size third
5:6Kl. Third
8:9Size Second
15:16Kl. Second
The fundamental tone of the examples is a '(440 Hz)
Source: The Granger Collection, New York City; SuvaPro AUDIO DEMO 3

Frequency relationships and harmony or dissonance. The tones in this example were generated with a computer. The base frequency is 440 Hz. A tone one octave higher has a frequency of 880 Hz.


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One octave corresponds to a doubling of the frequency, regardless of whether the base frequency is 200 Hz or 3390 Hz. We hear in frequency ratios, not in absolute frequencies! For this reason, neighboring frequencies in acoustics are often grouped into classes with the width of an octave or a major third. These classes are called octave bands resp. Third octave bands. As a result, the third octave band with frequencies from 89.1 Hz to 112 Hz and the center frequency 100 Hz has the same weight as the third octave band from 4467 Hz to 5623 Hz and the center frequency of 5000 Hz. In absolute numbers, however, the second third octave band contains 50 times more frequencies than the 100 Hz band! You can find out more about our hearing properties in the hearing module.

Sounds

Noises contain very many different frequencies and therefore not just whole-number multiples of a basic frequency. The frequency relationships are chaotic. Since the sonic process of a noise usually does not have any repetitive parts, the noise also lacks a clear pitch.

Everything we hear is always slightly "noisy". So there are always frequencies that do not belong to a sound. The reason for this are background noises from other sound sources, from reflections and through refractions of sound waves in the environment and finally through processing in the ear. in the measuring device. Since some frequencies are often more strongly represented in an audio signal than others, they give a sound its special character and enable us to distinguish so many different noises. If a signal contains a large number of frequencies that make it difficult to understand - for example, if the reception on the telephone is poor - it is referred to as a noisy signal.

Source: Werner Stalder, (2000). "Education and training course on noise protection", p. 2.8

Oscillogram and 1/3-octave band spectrum of two noises. The oscillogram shows that a noise no longer has much to do with a pure sine wave. There are many different frequencies represented, some with clear level differences. Instead of a pure frequency spectrum, neighboring frequencies are grouped into classes in the right half of the image, the so-called third octave bands.


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White noise - pink noise

If all audible frequencies are represented in an acoustic signal with random, constantly changing, but on average equally high sound pressure levels, the signal does not contain any information. In analogy to visible light, such a signal is called "white noise". The energy content of the different frequency bands is the same (e.g. there is just as much power in the range from 100 Hz to 200 Hz as in the range from 2000 Hz to 2100 Hz). "Pink noise" means a signal in which the power is the same in every octave: the range from 100 Hz to 200 Hz contains just as much power as that from 2000 Hz to 4000 Hz. That is why it sounds white noise is brighter and more cutting than pink noise. With pink noise, the sound pressure level of one octave decreases by 3 dB compared to the previous octave.



White noise and pink noise are used especially in sound engineering for adjusting and adjusting devices, the so-called calibration.

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