Why are musical timbres compared to colors? Expressive means of music: Timbre

Timbre

The most difficult subjectively felt parameter is timbre. With the definition of this term, difficulties arise, comparable to the definition of the concept “life”: everyone understands what it is, but science has been struggling with a scientific definition for several centuries. Similarly with the term “timbre”: everyone understands what we are talking about when they say “beautiful timbre of a voice”, “dull timbre of an instrument”, etc., but... You cannot say “more or less”, “higher or lower” about timbre ", dozens of words are used to describe it: dry, sonorous, soft, sharp, bright, etc. (We’ll talk about terms for describing timbre separately).

Timbre(timbre-French) means “tone quality”, “tone color” (tone quality).

Timbre and acoustic characteristics of sound
Modern computer technologies make it possible to perform detailed analysis the temporal structure of any musical signal - this can be done by almost any music editor, for example, Sound Forge, Wave Lab, SpectroLab, etc. Examples of the temporal structure (oscillograms) of sounds of the same height (note "C" of the first octave) created by various instruments (organ, violin).
As can be seen from the presented wave forms (i.e., the dependence of the change in sound pressure on time), three phases can be distinguished in each of these sounds: the attack of sound (the establishing process), the stationary part, and the decay process. In different instruments, depending on the methods of sound production used in them, the time intervals of these phases are different - this can be seen in the figure.

The drums and plucked instruments, for example guitars, a short time period of the stationary phase and attack and a long time period of the decay phase. In the sound organ pipe one can see a fairly long segment of the stationary phase and short period attenuation, etc. If you imagine a segment of the stationary part of the sound more extended in time, you can clearly see the periodic structure of the sound. This periodicity is fundamentally important for determining musical pitch, since the auditory system can determine the pitch only for periodic signals, and non-periodic signals are perceived by it as noise.

According to the classical theory, developed starting with Helmholtz for almost the next hundred years, the perception of timbre depends on the spectral structure of sound, that is, on the composition of overtones and the ratio of their amplitudes. Let me remind you that overtones are all components of the spectrum above the fundamental frequency, and overtones whose frequencies are in integer ratios with the fundamental tone are called harmonics.
As is known, in order to obtain the amplitude and phase spectrum, it is necessary to perform a Fourier transform on the time function (t), i.e., the dependence of sound pressure p on time t.
Using the Fourier transform, any time signal can be represented as a sum (or integral) of its constituent simple harmonic (sinusoidal) signals, and the amplitudes and phases of these components form the amplitude and phase spectra, respectively.

Using digital Fast Fourier Transform (FFT) algorithms created over the past decades, the operation of determining spectra can also be performed in almost any audio processing program. For example, the SpectroLab program is generally a digital analyzer that allows you to construct the amplitude and phase spectrum of a musical signal in various forms. The forms of spectrum presentation can be different, although they represent the same calculation results.

The figure shows the amplitude spectra of various musical instruments (the oscillograms of which were shown in the figure earlier) in the form of frequency response. The frequency response here represents the dependence of the amplitudes of the overtones in the form of sound pressure level in dB on frequencies.

Sometimes the spectrum is represented as a discrete set of overtones with different amplitudes. Spectra can be presented in the form of spectrograms, where the vertical axis is frequency, the horizontal axis is time, and the amplitude is represented by color intensity.

In addition, there is a form of representation in the form of a three-dimensional (cumulative) spectrum, which will be discussed below.
To construct the spectra indicated in the previous figure, a certain time interval is selected in the stationary part of the oscillogram, and the average spectrum over this interval is calculated. The larger this segment, the more accurate the frequency resolution is, but at the same time, individual details of the temporal structure of the signal may be lost (smoothed out). Such stationary spectra have individual traits, characteristic of each musical instrument, and depend on the mechanism of sound formation in it.

For example, a flute uses a pipe that is open at both ends as a resonator, and therefore contains all even and odd harmonics in the spectrum. In this case, the level (amplitude) of harmonics quickly decreases with frequency. The clarinet uses a pipe as a resonator, closed at one end, so the spectrum mainly contains odd harmonics. The pipe has many high-frequency harmonics in its spectrum. Accordingly, the sound timbres of all these instruments are completely different: the flute is soft, gentle, the clarinet is dull, dull, and the trumpet is bright, sharp.

Hundreds of works have been devoted to the study of the influence of the spectral composition of overtones on timbre, since this problem is extremely important both for the design of musical instruments and high-quality acoustic equipment, especially in connection with the development of Hi-Fi and High-End equipment, and for the auditory evaluation of phonograms and other tasks. standing in front of the sound engineer. The accumulated vast auditory experience of our wonderful sound engineers - P.K. Kondrashina, V.G. Dinova, E.V. Nikulsky, S.G. Shugal and others - could provide invaluable information on this problem (especially if they wrote about him in their books, which I would like to wish them).

Since there is an extremely large amount of this information and it is often contradictory, we will present only some of it.
Analysis of the general structure of the spectra of various instruments shown in Figure 5 allows us to draw the following conclusions:
- in the absence or lack of overtones, especially in the lower register, the timbre of the sound becomes boring, empty - an example is a sinusoidal signal from a generator;
- the presence in the spectrum of the first five to seven harmonics with a sufficiently large amplitude gives the timbre fullness and richness;
- weakening of the first harmonics and strengthening of the higher harmonics (from the sixth-seventh and above) gives timbre

Analysis of the amplitude spectrum envelope for various musical instruments made it possible to establish (Kuznetsov “Acoustics of Musical Instruments”):
- a smooth rise in the envelope (increasing the amplitudes of a certain group of overtones) in the region of 200...700 Hz allows you to obtain shades of richness and depth;
- a rise in the 2.5…3 kHz region gives the timbre a flighty, sonorous quality;
- a rise in the 3…4.5 kHz region gives the timbre sharpness, shrillness, etc.

One of the many attempts to classify timbre qualities depending on the spectral composition of sound is shown in the figure.

Numerous experiments assessing the sound quality (and, consequently, timbre) of acoustic systems made it possible to establish the influence of various peaks and dips in the frequency response on the noticeability of changes in timbre. In particular, it is shown that noticeability depends on the amplitude, location on the frequency scale and quality factor of the peaks and dips on the spectrum envelope (i.e., on the frequency response). IN middle region frequencies, the thresholds for the noticeability of peaks, i.e. deviations from the average level, are 2...3 dB, and the noticeability of timbre changes at peaks is greater than at troughs. Narrow-width gaps (less than 1/3 of an octave) are almost invisible to the ear - apparently, this is explained by the fact that it is precisely such narrow gaps that the room introduces into the frequency response of various sound sources, and the ear is accustomed to them.

The grouping of overtones into formant groups has a significant effect, especially in the region of maximum hearing sensitivity. Since it is the location of the format areas that serves as the main criterion for the distinguishability of speech sounds, the presence of formant frequency ranges (i.e., emphasized overtones) significantly affects the perception of the timbre of musical instruments and the singing voice: for example, the formant group in the region of 2 ... 3 kHz gives flight, sonority to the singing voice. voice and violin sounds. This third formant is especially pronounced in the spectra of Stradivarius violins.

Thus, the statement of the classical theory is certainly true that the perceived timbre of a sound depends on its spectral composition, that is, the location of overtones on the frequency scale and the ratio of their amplitudes. This is confirmed by numerous practices of working with sound in different fields. Modern musical programms make it easy to check this simple examples. For example, in Sound Forge, using the built-in generator, you can synthesize variants of sounds with different spectral compositions, and listen to how the timbre of their sound changes.

Two more very important conclusions follow from this:
- the timbre of music and speech changes depending on changes in volume and transposition in height.

When you change the volume, the perception of timbre changes. Firstly, with an increase in the amplitude of vibrations of the vibrators of various musical instruments (strings, membranes, soundboards, etc.), nonlinear effects begin to appear in them, and this leads to the enrichment of the spectrum with additional overtones. The figure shows the spectrum of a piano at different strengths impact, where the dash marks the noise part of the spectrum.

Secondly, as the volume level increases, the sensitivity of the auditory system to the perception of low and high frequencies changes (equal loudness curves were written about in previous articles). Therefore, when the volume increases (to a reasonable limit of 90...92 dB), the timbre becomes fuller, richer than with quiet sounds. With a further increase in volume, strong distortions begin to affect the sound sources and the auditory system, which leads to a deterioration in timbre.

Transposing the melody in pitch also changes the perceived timbre. Firstly, the spectrum is depleted, since some of the overtones fall into the inaudible range above 15...20 kHz; secondly, in the high-frequency region, hearing thresholds are much higher, and high-frequency overtones become inaudible. In low-register sounds (for example, in an organ), overtones are enhanced due to increased sensitivity of hearing to mid-frequencies, so low-register sounds sound richer than mid-register sounds, where there is no such increase in overtones. It should be noted that since the curves of equal loudness, as well as the loss of hearing sensitivity to high frequencies, are largely individual, the change in the perception of timbre with changes in volume and pitch also varies greatly among different people.
However, the experimental data accumulated to date have made it possible to reveal a certain invariance (stability) of timbre under a number of conditions. For example, when transposing a melody along a frequency scale, the shades of timbre, of course, change, but in general the timbre of an instrument or voice is easily recognized: when listening, for example, to a saxophone or other instrument through a transistor radio, you can recognize its timbre, although its spectrum has been significantly distorted. When listening to the same instrument at different points in the hall, its timbre also changes, but the fundamental properties of the timbre inherent in this instrument remain.

Some of these contradictions were partially explained within the framework of the classical spectral theory of timbre. For example, it has been shown that in order to preserve the basic characteristics of timbre during transposition (transfer along the frequency scale), it is fundamentally important to preserve the shape of the amplitude spectrum envelope (i.e., its formant structure). For example, the figure shows that when the spectrum is transferred by an octave in the case where the structure of the envelope is preserved (option “a”), the timbre variations are less significant than when the spectrum is transferred while maintaining the amplitude ratio (option “b”).

This explains the fact that speech sounds (vowels, consonants) can be recognized regardless of the pitch (frequency of the fundamental tone) they are pronounced, if the location of their formant regions relative to each other is preserved.

Thus, summing up the results obtained by the classical theory of timbre, taking into account the results of recent years, we can say that timbre, of course, significantly depends on the average spectral composition of sound: the number of overtones, their relative location on the frequency scale, on the ratio of their amplitudes, that is, the shape spectral envelope (AFC), or more precisely, on the spectral distribution of energy over frequency.
However, when the first experiments in synthesizing the sounds of musical instruments began in the 60s, attempts to recreate the sound, in particular, of a trumpet, known composition its average spectrum turned out to be unsuccessful - the timbre was completely different from the sound of brass instruments. The same applies to the first attempts at voice synthesis. It was during this period that, relying on the possibilities provided by computer technology, the development of another direction began - establishing a connection between the perception of timbre and the temporal structure of the signal.
Before moving on to the results obtained in this direction, the following must be said.
First. It is quite widely believed that when working with audio signals, it is enough to obtain information about their spectral composition, since you can always go to their temporal form using the Fourier transform, and vice versa. However, an unambiguous connection between the temporal and spectral representations of the signal exists only in linear systems, and the auditory system is a fundamentally nonlinear system, both at high and low signal levels. Therefore, information processing in the auditory system occurs in parallel in both the spectral and temporal domains.

Developers of high-quality acoustic equipment constantly face this problem, when the distortion of the frequency response of the acoustic system (that is, the unevenness of the spectral envelope) is brought almost to auditory thresholds (unevenness 2 dB, bandwidth 20 Hz...20 kHz, etc.), and experts or sound engineers they say: “the violin sounds cold” or “the voice is metallic,” etc. Thus, information obtained from the spectral region is not enough for the auditory system; information about the temporal structure is needed. It is not surprising that the methods of measuring and evaluating acoustic equipment have changed significantly in recent years - a new digital metrology has appeared, which makes it possible to determine up to 30 parameters, both in the time and spectral domains.
Consequently, the auditory system must receive information about the timbre of a musical and speech signal from both the temporal and spectral structure of the signal.
Second. All the results obtained above in the classical theory of timbre (Helmholtz theory) are based on the analysis of stationary spectra obtained from the stationary part of the signal with a certain averaging, but the fact that in real music and speech signals there are practically no constant, stationary parts is fundamentally important. Live music- this is continuous dynamics, constant change, and this is associated with the deep properties of the auditory system.

Studies of the physiology of hearing have established that in the auditory system, especially in its higher sections, there are many so-called “novelty” or “recognition” neurons, i.e. neurons that turn on and begin to conduct electrical discharges only if there is a change in the signal (turn on, turn off, change volume level, pitch, etc.). If the signal is stationary, then these neurons are not turned on, and the signal is controlled by a limited number of neurons. This phenomenon is widely known from everyday life: if the signal does not change, then often it is simply stopped being noticed.
For musical performance any monotony and constancy are destructive: the listener’s neurons of novelty are switched off and he stops perceiving information (aesthetic, emotional, semantic, etc.), so in live performance there is always dynamics (musicians and singers widely use various signal modulations - vibrato, tremolo, etc. ).

In addition, each musical instrument, including the voice, has a special sound production system, which dictates its own temporal structure of the signal and its dynamics of change. A comparison of the temporal structure of sound shows fundamental differences: in particular, the durations of all three parts - attack, stationary part and decay - differ in duration and form for all instruments. Percussion instruments have a very short stationary part, attack time 0.5...3 ms and decay time 0.2...1 s; for bowed instruments, the attack time is 30...120 ms, the decay time is 0.15...0.5 s; the organ has an attack of 50...1000 ms and a decay of 0.2...2 s. In addition, the shape of the time envelope is fundamentally different.
Experiments have shown that if you remove part of the temporal structure corresponding to the attack of the sound, or swap the attack and decay (play in the opposite direction), or replace the attack from one instrument with the attack from another, then identifying the timbre of a given instrument becomes almost impossible. Consequently, for timbre recognition, not only the stationary part (the average spectrum of which serves as the basis of the classical theory of timbre), but also the period of formation of the temporary structure, as well as the period of attenuation (decay) are vital elements.

Indeed, when listening in any room, the first reflections arrive at the auditory system after the attack and the initial part of the stationary part have already been heard. At the same time, the decay of the sound from the instrument is superimposed by the reverberation process of the room, which significantly masks the sound and, naturally, leads to a modification in the perception of its timbre. Hearing has a certain inertia, and short sounds are perceived as clicks. Therefore, the duration of the sound must be more than 60 ms in order to recognize the pitch, and, accordingly, the timbre. Apparently the constants should be close.
Nevertheless, the time between the beginning of the arrival of direct sound and the moments of arrival of the first reflections is enough to recognize the timbre of the sound of an individual instrument - obviously, this circumstance determines the invariance (stability) of timbre recognition different instruments V different conditions listening. Modern computer technologies make it possible to analyze in sufficient detail the processes of establishing the sound of different instruments, and to highlight the most significant acoustic features that are most important for determining timbre.

The structure of its stationary (averaged) spectrum has a significant influence on the perception of the timbre of a musical instrument or voice: the composition of overtones, their location on the frequency scale, their frequency ratios, amplitude distributions and the shape of the spectrum envelope, the presence and shape of formant regions, etc., which fully confirms the provisions of the classical theory of timbre, set forth in the works of Helmholtz.
However, experimental materials obtained over the past decades have shown that an equally significant, and perhaps much more significant role in timbre recognition is played by a non-stationary change in the structure of sound and, accordingly, the process of unfolding its spectrum in time, primarily on the initial stage of sound attack.

The process of changing the spectrum over time can be especially clearly “seen” using spectrograms or three-dimensional spectra (they can be built using most music editors Sound Forge, SpectroLab, Wave Lab, etc.). Their analysis for the sounds of various instruments allows us to identify characteristics processes of "unfolding" of spectra. For example, the figure shows a three-dimensional spectrum of the sound of a bell, where frequency in Hz is plotted along one axis, time in seconds on the other; on the third amplitude in dB. The graph clearly shows how the process of growth, establishment and decay of the spectral envelope occurs over time.

A comparison of the C4 tone attack of various wooden instruments shows that the process of establishing vibrations for each instrument has its own special character:

The clarinet is dominated by odd harmonics 1/3/5, with the third harmonic appearing in the spectrum 30 ms later than the first, then higher harmonics gradually “line up”;
- in the oboe, the establishment of oscillations begins with the second and third harmonics, then the fourth appears, and only after 8 ms the first harmonic begins to appear;
- the first harmonic of the flute appears first, then only after 80 ms all the others gradually enter.

The figure shows the process of establishing oscillations for a group brass instruments: trumpet, trombone, horn and tuba.

The differences are clearly visible:
- the trumpet has a compact appearance of a group of higher harmonics, the trombone has the second harmonic appearing first, then the first, and after 10 ms the second and third. The tuba and horn show a concentration of energy in the first three harmonics; higher harmonics are practically absent.

Analysis of the results obtained shows that the process of sound attack significantly depends on the physical nature of sound production on a given instrument:
- from the use of ear pads or canes, which, in turn, are divided into single or double;
- from various shapes of pipes (straight narrow-bore or conical wide-bore), etc.

This determines the number of harmonics, the time of their appearance, the speed at which their amplitude builds, and, accordingly, the shape of the envelope of the temporal structure of sound. Some instruments, such as flutes,

The envelope during the attack period has a smooth exponential character, and in some, for example, the bassoon, beats are clearly visible, which is one of the reasons for the significant differences in their timbre.

During an attack, higher harmonics sometimes precede the fundamental tone, so fluctuations in the pitch of the tone may occur; periodicity, and therefore the height of the total tone, builds up gradually. Sometimes these changes in periodicity are quasi-random in nature. All these signs help the auditory system to “identify” the timbre of a particular instrument at the initial moment of sound.

To assess the timbre of a sound, it is important not only the moment of its recognition (i.e., the ability to distinguish one instrument from another), but also the ability to assess the change in timbre during the performance. Here, the most important role is played by the dynamics of changes in the spectral envelope over time at all stages of sound: attack, stationary part, decay.
The behavior of each overtone over time also carries vital information about timbre. For example, in the sound of bells, the dynamics of change are especially clearly visible, both in the composition of the spectrum and in the nature of the change in time of the amplitudes of its individual overtones: if at the first moment after striking several dozen spectral components are clearly visible in the spectrum, which creates the noise character of the timbre, then after a few seconds, several basic overtones remain in the spectrum (fundamental tone, octave, duodecima and minor third two octaves apart), the rest fade out, and this creates a special tonally colored sound timbre.

An example of changes in the amplitudes of the main overtones over time for a bell is shown in the figure. It can be seen that it is characterized by a short attack and a long decay period, while the speed of entry and decay of overtones of different orders and the nature of the change in their amplitudes over time are significantly different. The behavior of various overtones over time depends on the type of instrument: in the sound of a piano, organ, guitar, etc., the process of changing the amplitudes of the overtones has a completely different character.

Experience shows that additive computer synthesis of sounds, taking into account the specific development of individual overtones in time, allows one to obtain a much more “lifelike” sound.

The question of the dynamics of changes in which overtones carry information about timbre is related to the existence of critical hearing bands. The basilar membrane in the cochlea acts as a series of bandpass filters, the width of which depends on frequency: above 500 Hz it is approximately 1/3 octave, below 500 Hz it is approximately 100 Hz. The bandwidth of these hearing filters is called the “critical hearing bandwidth” (there is a special unit of measurement, 1 bark, equal to the critical bandwidth across the entire audible frequency range).
Within the critical band, hearing integrates incoming sound information, which also plays an important role in the processes of auditory masking. If you analyze the signals at the output of auditory filters, you can see that the first five to seven harmonics in the sound spectrum of any instrument usually fall into their own critical band, since they are quite far apart from each other; in such cases they say that the harmonics “unfold” the auditory system. The discharges of neurons at the output of such filters are synchronized with the period of each harmonic.

Harmonics above the seventh are usually quite close to each other on the frequency scale, and are not “swept” by the auditory system; several harmonics fall inside one critical band, and a complex signal is obtained at the output of the auditory filters. The discharges of neurons in this case are synchronized with the frequency of the envelope, i.e. fundamental tone.

Accordingly, the mechanism for processing information by the auditory system for expanded and non-expanded harmonics is somewhat different: in the first case, information is used “in time”, in the second “in place”.

A significant role in pitch recognition, as shown in previous articles, is played by the first fifteen to eighteen harmonics. Experiments using computer additive synthesis of sounds show that the behavior of these particular harmonics also has the most significant impact on the change in timbre.
Therefore, in a number of studies it was proposed to consider the timbre dimension equal to fifteen to eighteen, and assessing its change on this number of scales is one of fundamental differences timbre from such characteristics of auditory perception as pitch or loudness, which can be scaled according to two or three parameters (for example, loudness), depending mainly on the intensity, frequency and duration of the signal.

It is quite well known that if the signal spectrum contains quite a lot of harmonics with numbers from 7th to 15...18th, with sufficiently large amplitudes, for example, in a trumpet, violin, reed pipes of an organ, etc., then the timbre is perceived as bright, sonorous, sharp, etc. If the spectrum contains mainly lower harmonics, for example, tuba, horn, trombone, then the timbre is characterized as dark, dull, etc. Clarinet, in which odd harmonics dominate the spectrum , has a somewhat “nasal” timbre, etc.
In accordance with modern views, the most important role for the perception of timbre is the change in the dynamics of the distribution of maximum energy between the overtones of the spectrum.

To evaluate this parameter, the concept of “spectrum centroid” was introduced, which is defined as the midpoint of the distribution of the spectral energy of sound; it is sometimes defined as the “balance point” of the spectrum. The way to determine it is to calculate the value of a certain average frequency:

Where Ai is the amplitude of the spectrum components, fi is their frequency.
For the example shown in the figure, this centroid value is 200 Hz.

F =(8 x 100 + 6 x 200 + 4 x 300 + 2 x 400)/(8 + 6 + 4 + 2) = 200.

The shift of the centroid towards high frequencies is felt as an increase in the brightness of the timbre.
The significant influence of the distribution of spectral energy over the frequency range and its change over time on the perception of timbre is probably associated with the experience of recognizing speech sounds by formant characteristics, which carry information about the concentration of energy in various areas spectrum (it is unknown, however, what was primary).
This hearing ability is essential when assessing the timbres of musical instruments, since the presence of formant regions is typical for most musical instruments, for example, for violins in the areas of 800...1000 Hz and 2800...4000 Hz, for clarinets 1400...2000 Hz, etc.
Accordingly, their position and the dynamics of change over time affect the perception of individual timbre characteristics.
It is known what a significant influence the presence of a high singing formant has on the perception of the timbre of a singing voice (in the region of 2100...2500 Hz for basses, 2500...2800 Hz for tenors, 3000...3500 Hz for sopranos). In this area, opera singers concentrate up to 30% of their acoustic energy, which ensures the sonority and flight of their voices. Removing the singing formant from recordings of various voices using filters (these experiments were carried out in the research of Prof. V.P. Morozov) shows that the timbre of the voice becomes dull, dull and sluggish.

A change in timbre when changing the volume of a performance and transposing in pitch is also accompanied by a shift in the centroid due to a change in the number of overtones.
An example of changing the position of the centroid for violin sounds of different heights is shown in the figure (the frequency of the centroid location in the spectrum is plotted along the abscissa axis).
Research has shown that for many musical instruments there is an almost monotonic relationship between an increase in intensity (loudness) and a shift of the centroid to the high-frequency region, due to which the timbre becomes brighter.

Apparently, when synthesizing sounds and creating various computer compositions, the dynamic relationship between intensity and the position of the centroid in the spectrum should be taken into account in order to obtain a more natural timbre.
Finally, the difference in the perception of timbres of real sounds and sounds with “virtual height”, i.e. sounds, the height of which the brain “completes” according to several integer overtones of the spectrum (this is typical, for example, for the sounds of bells), can be explained from the position of the centroid of the spectrum. Since these sounds have a fundamental frequency value, i.e. height may be the same, but the position of the centroid is different due to the different composition of overtones, then, accordingly, the timbre will be perceived differently.
It is interesting to note that more than ten years ago, a new parameter was proposed for measuring acoustic equipment, namely the three-dimensional spectrum of energy distribution in frequency and time, the so-called Wigner distribution, which is quite actively used by various companies to evaluate equipment, because, as experience shows , allows you to establish the best match with its sound quality. Taking into account the above-mentioned property of the auditory system to use the dynamics of changes in energy characteristics sound signal to determine timbre, it can be assumed that this parameter, the Wigner distribution, can also be useful for evaluating musical instruments.

The assessment of the timbres of various instruments is always subjective, but if, when assessing pitch and volume, it is possible, on the basis of subjective assessments, to arrange sounds on a certain scale (and even introduce special units of measurement “son” for loudness and “chalk” for height), then the assessment of timbre significantly more difficult task. Typically, to subjectively assess timbre, listeners are presented with pairs of sounds that are identical in pitch and loudness, and are asked to place these sounds on different scales between various opposing descriptive features: “bright”/“dark”, “voiced”/“dull”, etc. . (We will definitely talk about the choice of various terms to describe timbres and the recommendations of international standards on this issue in the future).
A significant influence on the determination of such sound parameters as pitch, timbre, etc., is exerted by the time behavior of the first five to seven harmonics, as well as a number of “unexpanded” harmonics up to the 15th...17th.
However, as is known from the general laws of psychology, a person’s short-term memory can simultaneously operate with no more than seven to eight symbols. Therefore, it is obvious that when recognizing and assessing timbre, no more than seven or eight essential features are used.
Attempts to establish these characteristics by systematizing and averaging the results of experiments, to find generalized scales by which it would be possible to identify the timbres of sounds of various instruments, and to associate these scales with various time-spectral characteristics of sound have been undertaken for a long time.

One of the most famous is the work of Gray (1977), where a statistical comparison of estimates was carried out various signs timbres of sounds of various string instruments, wooden, percussion, etc. The sounds were synthesized on a computer, which made it possible to change their temporal and spectral characteristics in the required directions. The classification of timbral features was carried out in three-dimensional (orthogonal) space, where the following were chosen as scales by which a comparative assessment of the degree of similarity of timbral features (ranging from 1 to 30) was made:

The first scale is the value of the centroid of the amplitude spectrum (the scale shows the displacement of the centroid, i.e., the maximum of the spectral energy from low to high harmonics);
- second - synchronicity of spectral fluctuations, i.e. the degree of synchronicity in the entry and development of individual overtones of the spectrum;
- third - the degree of presence of low-amplitude non-harmonic high-frequency noise energy during the attack period.

Processing the results obtained using a special software package for cluster analysis made it possible to identify the possibility of a fairly clear classification of instruments by timbre within the proposed three-dimensional space.

An attempt to visualize the timbral difference in the sounds of musical instruments in accordance with the dynamics of changes in their spectrum during the attack period was made in the work of Pollard (1982), the results are shown in the figure.

Three-dimensional space of timbres

The search for methods for multidimensional scaling of timbres and the establishment of their connections with the spectral-temporal characteristics of sounds continues actively. These results are extremely important for the development of computer sound synthesis technologies and for the creation of various electronic musical compositions, for correction and sound processing in sound engineering practice, etc.

It is interesting to note that at the beginning of the century, the great composer of the 20th century Arnold Schoenberg expressed the idea that “... if we consider pitch as one of the dimensions of timbre, and modern music is built on variations of this dimension, then why not try to use other dimensions of timbre for creating compositions." This idea is currently being implemented in the work of composers who create spectral (electroacoustic) music. That is why interest in the problems of timbre perception and its connections with the objective characteristics of sound is so high.

Thus, the results obtained show that if in the first period of studying the perception of timbre (based on the classical theory of Helmholtz) a clear connection was established between the change in timbre and the change in the spectral composition of the stationary part of the sound (composition of overtones, the ratio of their frequencies and amplitudes, etc.), then the second period of these studies (from the beginning of the 60s) made it possible to establish the fundamental importance of spectral-temporal characteristics.

This is a change in the structure of the time envelope at all stages of sound development: attack (which is especially important for recognizing the timbres of various sources), stationary part and decay. This is a dynamic change in time of the spectral envelope, incl. shift of the spectrum centroid, i.e. a shift in the maximum of spectral energy in time, as well as the development in time of the amplitudes of the spectral components, especially the first five to seven “undeveloped” harmonics of the spectrum.

Currently, the third period of studying the problem of timbre has begun, the focus of research has moved towards studying the influence of the phase spectrum, as well as the use of psychophysical criteria in recognizing timbres that underlie the general mechanism of sound image recognition (grouping into streams, assessing synchronicity, etc.).

Timbre and phase spectrum

All the presented results on establishing the connection between the perceived timbre and the acoustic characteristics of the signal related to the amplitude spectrum, more precisely, to the temporary change in the spectral envelope (primarily the displacement energy center amplitude spectrum-centroid) and the time development of individual overtones.

Work has been done in this direction greatest number works and many interesting results were obtained. As already noted, for almost a hundred years in psychoacoustics, Helmholtz's opinion prevailed that our auditory system is not sensitive to changes in the phase relationships between individual overtones. However, experimental evidence was gradually accumulated that the hearing aid is sensitive to phase changes between various signal components (work by Schroeder, Hartman, etc.).

In particular, it was found that the auditory threshold for phase shift in two- and three-component signals in the low and medium frequencies is 10...15 degrees.

In the 1980s, this led to the creation of a number of loudspeaker systems with linear-phase response. As is known from the general theory of systems, for undistorted signal transmission it is necessary that the transfer function modulus be maintained constant, i.e. amplitude-frequency characteristic (envelope of the amplitude spectrum), and linear dependence of the phase spectrum on frequency, i.e. φ(ω) = -ωT.

Indeed, if the amplitude envelope of the spectrum remains constant, then, as mentioned above, distortion of the audio signal should not occur. The requirements for maintaining phase linearity over the entire frequency range, as Blauert’s research has shown, turned out to be excessive. It has been found that hearing responds primarily to the rate of phase change (i.e., its frequency derivative), which is called " group delay time ": τ = dφ(ω)/dω.

As a result of numerous subjective examinations, audibility thresholds for group delay distortion (i.e., the magnitude of the deviation Δτ from its constant value) were constructed for various speech, music and noise signals. These hearing thresholds depend on frequency, and in the region of maximum hearing sensitivity they are 1...1.5 ms. Therefore, in recent years, when creating Hi-Fi acoustic equipment, they have been guided mainly by the above auditory thresholds for group delay distortion.

View of the waveform at different overtone phase ratios; red - all overtones have the same initial phases, blue - the phases are randomly distributed.

Thus, if phase relationships have an audible effect on pitch detection, then they would be expected to have a significant effect on timbre recognition.

For the experiments, we selected sounds with a fundamental tone of 27.5 and 55 Hz and with one hundred overtones, with a uniform amplitude ratio characteristic of piano sounds. At the same time, tones with strictly harmonious overtones and with a certain inharmonicity characteristic of piano sounds, which arises due to the finite rigidity of the strings, their heterogeneity, the presence of longitudinal and torsional vibrations, etc., were studied.

The sound under study was synthesized as the sum of its overtones: X(t)=ΣA(n)sin
For auditory experiments, the following relationships of initial phases were chosen for all overtones:
- A - sinusoidal phase, the initial phase was taken equal to zero for all overtones φ(n,0) = 0;
- B - alternative phase (sinusoidal for even and cosine for odd), initial phase φ(n,0)=π/4[(-1)n+1];
- C - random phase distribution; the initial phases varied randomly in the range from 0 to 2π.

In the first series of experiments, all one hundred overtones had the same amplitudes; only their phases differed (fundamental tone 55 Hz). At the same time, the timbres listened to turned out to be different:
- in the first case (A), a distinct periodicity was heard;
- in the second (B), the timbre was brighter and another pitch was heard an octave higher than the first (though the pitch was not clear);
- in the third (C) - the timbre turned out to be more uniform.

It should be noted that the second pitch was listened to only in headphones; when listening through loudspeakers, all three signals differed only in timbre (reverberation affected).

This phenomenon - a change in pitch when the phase of some components of the spectrum changes - can be explained by the fact that when analytically representing the Fourier transform of a type B signal, it can be represented as the sum of two combinations of overtones: one hundred overtones with a phase of type A, and fifty overtones with a phase different by 3π/4, and with an amplitude greater than √2. The ear assigns a separate pitch to this group of overtones. In addition, when moving from phase A to phase B, the centroid of the spectrum (maximum energy) shifts towards higher frequencies, so the timbre seems brighter.

Similar experiments with phase shifting of individual groups of overtones also lead to the appearance of an additional (less clear) virtual pitch. This property of hearing is due to the fact that the ear compares the sound with a certain sample of musical tone that it has, and if some harmonics fall out of the series typical for a given sample, then the ear identifies them separately and assigns them a separate pitch.

Thus, the results of studies by Galembo, Askenfeld, and others showed that phase changes in the ratios of individual overtones are quite clearly audible as changes in timbre, and in some cases, in pitch.

This is especially evident when listening to real musical tones of a piano, in which the amplitudes of the overtones decrease with increasing their number, there is a special shape of the spectrum envelope (formant structure), and a clearly expressed inharmonicity of the spectrum (i.e., a shift in the frequencies of individual overtones in relation to the harmonic series ).

In the time domain, the presence of inharmonicity leads to dispersion, that is, high-frequency components propagate along the string at a higher speed than low-frequency components, and the waveform of the signal changes. The presence of a small inharmonicity in the sound (0.35%) adds some warmth and vitality to the sound, however, if this inharmonicity becomes large, beats and other distortions become audible in the sound.

Inharmonicity also leads to the fact that if at the initial moment the phases of the overtones were in deterministic ratios, then in its presence the phase relationships become random over time, the peak structure of the wave form is smoothed out, and the timbre becomes more uniform - this depends on the degree of inharmonicity. Therefore, instantaneous measurement of the regularity of the phase relationship between adjacent overtones can serve as an indicator of timbre.

Thus, the effect of phase mixing due to inharmonicity manifests itself in some change in the perception of pitch and timbre. It should be noted that these effects are audible when listening close to the soundboard (in the pianist's position) and when the microphone is close, and the auditory effects differ when listening through headphones and through loudspeakers. In a reverberant environment, a complex sound with a high peak factor (which corresponds to a high degree of regularization of phase relationships) indicates the proximity of the sound source, since as we move away from it, the phase relationships become increasingly random due to reflections in the room. This effect can cause different assessments of the sound by the pianist and the listener, as well as different timbres of the sound recorded by the microphone at the soundboard and at the listener. The closer, the higher the regularization of phases between overtones and the more defined pitch; the further away, the more uniform timbre and less clear pitch.

Work on assessing the influence of phase relationships on the perception of the timbre of a musical sound is now being actively studied in various centers (for example, at IRCAM), and new results can be expected in the near future.

Timbre and general principles of auditory pattern recognition

Timbre is an identifier of the physical mechanism of sound formation based on a number of characteristics; it allows you to identify the source of sound (an instrument or group of instruments) and determine its physical nature.

This reflects the general principles of auditory pattern recognition, which, according to modern psychoacoustics, are based on the principles of Gestalt psychology (geschtalt, “image”), which states that in order to separate and recognize various sound information coming to the auditory system from different sources at the same time (an orchestra playing, a conversation between many interlocutors, etc.), the auditory system (like the visual) uses some general principles:

- segregation- division into sound streams, i.e. subjective identification of a certain group of sound sources, for example, with musical polyphony, the ear can track the development of melody in individual instruments;
- similarity- sounds similar in timbre are grouped together and attributed to the same source, for example, speech sounds with a similar pitch and similar timbre are determined as belonging to the same interlocutor;
- continuity- the auditory system can interpolate sound from a single stream through a masker, for example, if a short piece of noise is inserted into a speech or music stream, the auditory system may not notice it, the sound stream will continue to be perceived as continuous;
- "common destiny"- sounds that start and stop, and also change in amplitude or frequency within certain limits synchronously, are attributed to one source.

Thus, the brain groups incoming sound information both sequentially, determining the time distribution of sound components within one sound stream, and parallelly, highlighting frequency components that are present and changing simultaneously. In addition, the brain constantly compares the incoming sound information with the sound images “recorded” in the learning process in memory. By comparing the incoming combinations of sound streams with the existing images, it either easily identifies them if they coincide with these images, or, in the case of incomplete coincidences, assigns them some special properties (for example, assigns a virtual pitch, as in the sound of bells).

In all these processes, timbre recognition plays a fundamental role, since timbre is a mechanism by which signs that determine sound quality are extracted from physical properties: they are recorded in memory, compared with those already recorded, and then identified in certain areas of the cerebral cortex.

Auditory areas of the brain

Timbre- a multidimensional sensation, depending on many physical characteristics of the signal and the surrounding space. Work has been carried out on scaling timbre in metric space (scales are various spectro-temporal characteristics of the signal, see the second part of the article in the previous issue).

In recent years, however, there has been an understanding that the classification of sounds in subjective space does not correspond to the usual orthogonal metric space, there is a classification in "subspaces" associated with the above principles, which are neither metric nor orthogonal.

By separating sounds into these subspaces, the auditory system determines the "quality of sound", that is, timbre, and decides which category to classify these sounds into. However, it should be noted that the entire set of subspaces in the subjectively perceived sound world is built on the basis of information about two parameters of sound from the external world - intensity and time, and the frequency is determined by the time of arrival of identical intensity values. The fact that hearing divides incoming sound information into several subjective subspaces at once increases the likelihood that it can be recognized in one of them. It is precisely on the identification of these subjective subspaces, in which the recognition of timbres and other characteristics of signals occurs, that the efforts of scientists are currently directed.

Conclusion

To summarize, we can say that the main physical characteristics by which the timbre of an instrument and its change over time are determined are:
- alignment of overtone amplitudes during the attack period;
- changing the phase relationships between overtones from deterministic to random (in particular, due to the inharmonicity of the overtones of real instruments);
- change in the shape of the spectral envelope over time during all periods of sound development: attack, stationary part and decay;
- the presence of irregularities in the spectral envelope and the position of the spectral centroid (maximum

Spectral energy, which is associated with the perception of formants) and their change over time;

General view of spectral envelopes and their change over time

The presence of modulations - amplitude (tremolo) and frequency (vibrato);
- change in the shape of the spectral envelope and the nature of its change over time;
- change in intensity (volume) of sound, i.e. the nature of the nonlinearity of the sound source;
- the presence of additional signs of instrument identification, for example, the characteristic noise of a bow, the knocking of valves, the creaking of screws on a piano, etc.

Of course, all this does not exhaust the list of physical characteristics of a signal that determine its timbre.
Searches in this direction continue.
However, when synthesizing musical sounds All features must be taken into account to create a realistic sound.

Verbal (verbal) description of timbre

If there are appropriate units of measurement for assessing the pitch of sounds: psychophysical (chalks), musical (octaves, tones, semitones, cents); There are units for loudness (sons, backgrounds), but for timbres it is impossible to construct such scales, since this is a multidimensional concept. Therefore, along with the above-described search for a correlation between the perception of timbre and objective parameters of sound, to characterize the timbres of musical instruments, verbal descriptions are used, selected according to the characteristics of the opposite: bright - dull, sharp - soft, etc.

In the scientific literature there is a large number of concepts related to the assessment of sound timbres. For example, an analysis of terms adopted in modern technical literature has revealed the most frequently occurring terms shown in the table. Attempts were made to identify the most significant among them, and to scale the timbre according to opposite characteristics, as well as to connect the verbal description of timbres with some acoustic parameters.

Basic subjective terms for describing timbre used in modern international technical literature ( statistical analysis 30 books and magazines).

Acidlike - sour
forceful - strengthened
muffled - muffled
sober - sober (reasonable)
antique - ancient
frosty - frosty
muhy - porous
soft - soft
arching - convex
full - full
mysterious - mysterious
solemn - solemn
articulate - legible
fuzzy - fluffy
nasal - nasal
solid - solid
austere - harsh
gauzy - thin
neat - neat
somber - gloomy
bite, biting - biting
gentle - gentle
neutral - neutral
sonorous - sonorous
bland - insinuating
ghostlike - ghostly
noble - noble
steely - steel
blaring - roaring
glassy - glassy
nondescript - indescribable
strained - tense
bleating - bleating
glittering - brilliant
nostalgic - nostalgic
strident - creaky
breathy - breathing
gloomy - sad
ominous - ominous
stringent - constrained
bright - bright
grainy - grainy
ordinary - ordinary
strong - strong
brilliant - brilliant
grating - squeaky
pale - pale
stuffy - stuffy
brittle - mobile
grave - serious
passionate - passionate
subdued - softened
buzzy - buzzing
growly - growling penetrating - penetrating
sultry - sultry
calm - calm
hard - hard
piercing - piercing
sweet - sweet
carrying - flying
harsh - rude
pinched - limited
tangy - confused
centered - concentrated
haunting - haunting
placid - serene
tart - sour
clangorous - ringing
hazy - vague
plaintive - mournful
tearing - frantic
clear, clarity - clear
hearty - sincere
ponderous - weighty
tender - tender
cloudy - foggy
heavy - heavy
powerful - powerful
tense - intense
coarse - rude
heroic - heroic
prominent - outstanding
thick - thick
cold - cold
hoarse - hoarse
pungent - caustic
thin - thin
colorful - colorful
hollow - empty
pure - pure
threatening - threatening
colorless - colorless
honking - buzzing (car horn)
radiant - shining
throaty - hoarse
cool - cool
hooty - buzzing
raspy - rattling
tragic - tragic
crackling - crackling
husky - hoarse
rattling - rattling
tranquil - calming
crashing - broken
incandescence - incandescent
reedy - shrill
transparent - transparent
creamy - creamy
incisive - sharp
refined - refined
triumphant - triumphant
crystalline - crystalline
inexpressive - inexpressive
remote - remote
tubby - barrel-shaped
cutting - sharp
intense - intense
rich - rich
turbid - muddy
dark - dark
introspective - in-depth
ringing - ringing
turgid - pompous
deep - deep
joyous - joyful
robust - rough
unfocused - unfocused
delicate - delicate
languishing - sad
rough - tart
unobtrsuive - modest
dense - dense
light - light
rounded - round
veiled - veiled
diffuse - scattered
limpid - transparent
sandy - sandy
velvety - velvety
dismal - distant
liquid - watery
savage - wild
vibrant - vibrating
distant - distinct
loud - loud
screamy - screaming
vital - vital
dreamy - dreamy
luminous - brilliant
sere - dry voluptuous - lush (luxurious)
dry - dry
lush (luscious) - juicy
serene, serenity - calm
wan - dim
dull - boring
lyrical - lyrical
shadowy - shaded
warm - warm
earnest - serious
massive - massive
sharp - sharp
watery - watery
ecstatic - ecstatic
meditative - contemplative
shimmer - trembling
weak - weak
ethereal - ethereal
melancholy - melancholy
shouting - shouting
weighty - heavy
exotic - exotic
mellow - soft
shrill - shrill
white - white
expressive - expressive
melodious - melodic
silky - silky
windy - windy
fat - fat
menacing - threatening
silvery - silvery
wispy - thin
fierce - hard
metallic - metallic
singing - melodious
woody - wooden
flabby - flabby
misty - unclear
sinister - sinister
yearning - sad
focused - focused
mournful - mournful
slack - slack
forboding - repulsive
muddy - dirty
smooth - smooth

However, the main problem is that there is no clear understanding of the various subjective terms that describe timbre. The translation given above does not always correspond to the technical meaning that is put into each word when describing various aspects of timbre assessment.

In our literature, there used to be a standard for basic terms, but now things are quite sad, since no work is being done to create the appropriate Russian-language terminology, and many terms are used in different, sometimes directly opposite, meanings.
In this regard, AES, when developing a series of standards for subjective assessments of the quality of audio equipment, sound recording systems, etc., began to provide definitions of subjective terms in appendices to the standards, and since standards are created in working groups that include leading experts from different countries, this is a very important procedure leads to a consistent understanding of the basic terms for describing timbres.
As an example, I will cite the AES-20-96 standard - “Recommendations for the Subjective Evaluation of Loudspeakers” - which provides an agreed upon definition of such terms as “openness”, “transparency”, “clarity”, “tension”, “sharpness”, etc.
If this work continues systematically, then perhaps the basic terms for verbal description The timbres of sounds of various instruments and other sound sources will have agreed upon definitions, and will be unambiguously or fairly closely understood by specialists from different countries.