Tembre

The most difficult subittively sensible parameter is the timbre. With the definition of this term, difficulties are comparable to the definition of the concept of "life": everyone understands what it is, however, several centuries have been fighting on the scientific definition of science. Similarly, with the term "timbre": it is clear to everyone, what are we talking about when they say "the beautiful voice timbre", "deaf tool timbre", etc., but ... about Tembre it is impossible to say "more or less", "above "For its description, dozens of words are used: dry, ringing, soft, sharp, bright, etc. (about terms for describing the tone Talk separately).

Timbre (Timbre-Fr.) means "tone quality", "Tone color" (Tone Quality).

Timbre and acoustic sound characteristics
Modern computer technologies allow you to perform a detailed analysis of the temporary structure of any music signal - it can almost any music editor, for example, Sound Forge, Wave Lab, Spectrolab, and others. Examples of the time structure (oscillograms) of the sounds of one height (note "to" the first octave) created by various tools (organ, violin).
As can be seen from the presented waveforms (i.e., the dependence of the change in time from time), in each of these sounds, three phases can be selected: the sound attack (the installation process), the stationary part, the recess process. In various tools, depending on the methods of sound formation used in them, the time intervals of these phases are different - this is visible in the figure.

At shock and tweezing tools, such as guitars, a short time segment of the stationary phase and attack and a long time - the plug phase. In the sound of the organ pipe, it is possible to see a sufficiently long segment of the stationary phase and a short period of attenuation, etc. If you represent the segment of the stationary part of the sound more stretched over time, then it is possible to clearly see the periodic structure of the sound. This frequency is fundamentally important for determining the musical height of the tone, since the hearing system only for periodic signals can determine the height, and non-periodic signals are perceived as noise.

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

With the help of the Fourier Fast Conversion (BPF or FFT) created over the past decades or FFT), you can also perform an operation to determine the spectra almost in any sound processing program. For example, the Spectrolab program is generally a digital analyzer that allows you to construct an amplitude and phase spectrum of a musical signal in a different form. The form of the presentation of the spectrum may be different, although they represent the same results of calculations.

The figure shows in the form of ACH amplitude spectra of various musical instruments (the oscillograms of which were shown in the figure earlier). The ACH represents the dependence of the amplitude of overtones in the form of sound pressure level in dB, from frequencies.

Sometimes the spectrum is represented as a discrete kit of overtones with different amplitudes. The spectra can be represented as a spectrogram, where the frequency is postponed along the vertical axis, by horizontal - time, and the amplitude is represented by the color intensity.

In addition, there is a form of representation in the form of a three-dimensional (cumulative) spectrum, which will be mentioned below.
To construct the spectra specified on the previous figure, in the stationary part of the oscillogram there is some time segment, and the average spectrum is calculated on this segment. The more this segment, the more precisely the resolution of the frequency is obtained, but it can be lost (smoothed) separate parts of the time structure of the signal. Such stationary spectra possess individual features characteristic of each musical instrument, and depend on the sound forming mechanism in it.

For example, the flute uses the pipe open from two ends as a resonator, and therefore contains all even and odd harmonics in the spectrum. At the same time, the level (amplitude) harmonic is rapidly decreasing with the frequency. The clarinet is used as a resonator a pipe closed from one end, so in the spectrum, mostly contains odd harmonics. The pipe in the spectrum has many high-frequency harmonics. Accordingly, the timbres of the sound in all of these tools are completely different: the flute - soft, gentle, in clarinet - matte, deaf, in the pipe - bright, sharp.

Hundreds of works are devoted to the effects of the spectral composition of overtones on the timbre of the 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 equipment and high-end, and for the hearing assessment of phonograms and others. Tasks Freshing in front of the sound engineer. Accumulated huge hearing experience of our wonderful sound engineers - PK Kondrashin, V.G. Dinaova, 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 these information is extremely much and often contradictory, we only give some of them.
Analysis of the general structure of the spectra of various tools shown in Figure 5 allows you to draw the following conclusions:
- in the absence or disadvantage of overtones, especially in the lower case, the voice timbre becomes a boring, an empty example serves a sinusoidal signal from the generator;
- the presence of the first five-seven harmonics in the spectrum with a sufficiently large amplitude gives timbre fullness and juiciness;
- the weakening of the first harmonics and the strengthening of higher harmonics (from the sixth seventh and above) gives timbre

An analysis of the envelope of the amplitude spectrum for various musical instruments allowed to establish (Kuznetsov "Acoustics of musical instruments"):
- I smelted under the envelope (increasing the amplitudes of a certain group of overtones) in the region of 200 ... 700 Hz allows you to obtain shades of juits, depth;
- subsidence in the region of 2.5 ... 3 kHz gives timbre flight, beability;
- Substitute in the region of 3 ... 4.5 kHz gives the timbre sharpness, piercing, etc.

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

Numerous experiments with an assessment of the quality of sound (and, consequently, the timbre) of acoustic systems have made it possible to establish the effect of various respiration peaks response to the visor's change. In particular, it was shown that the visibility depends on the amplitude, the location according to the frequency scale and the quality of the peaks on the envelope of the spectrum (i.e., on acc). In the middle region of the frequencies of the peaks of peaks, i.e. deviations from the mean level, are 2 ... 3 dB, and the noticeability of changes in the peaks is greater than on the failures. Narrow in the width of the failures (less than 1/3 of the octave) is almost not noticeable by ear - apparently, it is explained by the fact that it is such narrow failures that makes a room in response of various sound sources, and the rumor is used to them.

Significant influence has a grouping of overtones into formation groups, especially in the field of maximum hearing sensitivity. Since it is the location of format areas that serves as the main criterion of the distinguishability of speech sounds, the presence of formate frequency ranges (i.e., underlined overtones) significantly affects the perception of the timbre of musical instruments and the singing voice: for example, the formative group in the region 2 ... 3 kHz gives the flight, the bellier Voice and violin sounds. This third formant is especially expressed in the spectra of Stradivari violin.

Thus, it is certainly fairly approved by the classical theory that the perceived voice timbre depends on its spectral composition, that is, the location of the overtones on the frequency scale and the ratio of their amplitudes. This is confirmed by the numerous practice of working with sound in different fields. Modern musical programs make it easy to check it on simple examples. For example, it is possible to synthesize with a built-in generator with a built-in generator. Sounds with different spectral compositions, and listen to how the timbre of their sound changes.

From this there are two more very important outputs:
- The timbre of the sound of music and speech varies depending on the volume of volume and from transpose height.

When the volume changes, the perception of the tone is changing. First, with an increase in the amplitude of vibrator vibrators of various musical instruments (strings, membranes, Dec, etc.), nonlinear effects begin to appear in them, and this leads to the enrichment of the spectrum by additional obverseons. The figure shows the piano spectrum with different impact strength, where the noise part of the spectrum is noted the stroke.

Secondly, with an increase in the volume level, the sensitivity of the hearing system to the perception of low and high frequencies changes (about the curves of equal volume was written in previous articles). Therefore, when increasing the volume (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 are beginning to affect the sources of sound and the auditory system, which leads to a deterioration in the tone.

Transposition of height melodies also changes the perceived timbre. First, the spectrum is imposed, because part of the overtones falls into the inadvertible range above 15 ... 20 kHz; Secondly, in the field of high frequencies of hearing thresholds are much higher, and high-frequency overtones become not heard. In the sounds of a low register (for example, in the organ), overtones are enhanced due to increased hearing sensitivity to medium frequencies, so the low register sounds are suitable more than the sounds of the average register, where there is no such strengthening of overtones. It should be noted that since the curves of equal volume, as well as the loss of hearing sensitivity to high frequencies, is largely individual, then the change in the perception of the timbre when changing the volume and height is also very different from different people.
However, the experimental data accumulated to date have revealed a certain invariance (stability) of the tone with a number of conditions. For example, when transposing a ringtone on the frequency scale, the timbre shades, of course, change, but in general the timbre of a tool or voice is easily recognized: when listening, for example, a saxophone or other tool through a transistor radio can be identified by its timbre, although its spectrum has been significantly distorted. When listening to the same tool at different points of the hall, its timbre also changes, but the fundamental properties of the tone inherent in this tool remain.

Some of these contradictions managed to partially explain within the framework of the classical spectral theory of the tone. For example, it was shown that in order to maintain the main signs of the timbre during transposition (transposher on the frequency scale), it is initially important to maintain the shape of the envelope of the amplitude spectrum (i.e. its formation structure). For example, the figure shows that when transferring the spectrum to octave when the structure of the envelope is maintained (option "A"), the timbre variations are less significant than when the spectrum is transferred while the ratio of amplitudes (B "variant).

This is explained by the fact that the sounds of speech (vowels, consonants) can be recognized regardless of which, with which height (frequency of the fundamental tone) they are pronounced if the location of their formation regions is preserved relative to each other.

Thus, summing up the results obtained by the classical theory of the tone, taking into account the results of recent years, it can be said that the timbre is definitely significantly dependent on the averaged spectral composition of the sound: the number of overtones, their relative location on the frequency scale, from the ratio of their amplitudes, that is, forms spectral envelope (ACH), or rather, on the spectral distribution of energy in frequency.
However, when the first experiences of the synthesis of sound musical instruments began in the 60s, attempts to recreate the sound, in particular, the pipes on the well-known composition of its averaged spectrum were unsuccessful - the timbre was completely out of the sound of copper brass instruments. The same applies to the first attempts to the synthesis of voting. It is in this period that, based on the possibilities that computer technology provided, the development of another direction began - the establishment of a communications to the timbre with the time structure of the signal.
Before moving to the results obtained in this direction, I must say the following.
First. The view is quite widespread that when working with sound signals, it is enough to obtain information about their spectral composition, since it is always possible to switch to their time form using Fourier transform, and vice versa. However, the unambiguous communication between the time and spectral representations of the signal exists only in linear systems, and the auditory system is a fundamentally non-linear system, both at large and at low levels of the signal. Therefore, the processing of information in the hearing system occurs in parallel both in the spectral and in the time domain.

The developers of high-quality acoustic equipment are confronted with this problem constantly when the distortions of the response acoustic system (that is, the uneven spectral envelope) was brought to almost the hearing thresholds (non-uniformity of 2 dB, the bandwidth of 20 Hz ... 20 kHz, etc.), and experts or sound engineers They say: "The violin sounds cold" or "voice with metal", etc. Thus, the information obtained from the spectral region is not enough for the auditory system, information on the temporary structure is needed. It is not surprising that the methods of measurements and evaluation of acoustic equipment have changed significantly in recent years - a new digital metrology has appeared, which allows to determine up to 30 parameters, both in the temporal and spectral regions.
Consequently, the information about the tech of the musical and speech signal The auditory system should receive both from the temporal and from the spectral signal structure.
Second. All results obtained in the classical theory of the timbre (theory of the Helmholtz) are based on the analysis of stationary spectra obtained from the stationary part of the signal with a certain averaging, but it is fundamentally important that in real musical and speech signals there are practically no permanent, stationary parts. Live music is a continuous dynamics, a constant change, and this is due to the depth properties of the auditory system.

Hearing physiology studies have made it possible to establish that in the auditory system, especially in its highest sections, there are many so-called "novelty" or "identification" neurons, i.e. neurons that turn on and begin to carry out electrical discharges only if there are changes in the signal (Enable, turn off, change the volume level, height, etc.). If the stationary signal, then these neurons do not turn on, and control over the signal carries out a limited number of neurons. This phenomenon is widely known from everyday life: if the signal does not change, then often it is simply no longer noticed.
For musical performance, all sorts of monotony and constancy are destructive: the listener disconnects neurons novelty and it ceases to perceive information (aesthetic, emotional, semantic, etc.), therefore there are always dynamics in live performance (musicians and singers are widely used by various modulation of the signal - Vibrato, Tremolo etc.).

In addition, every musical instrument, including a voice, has a special sound formation system, which dictates its time signal structure and its change dynamics. Comparison of the temporal structure of sound shows fundamental differences: in particular, the duration of all three parts - attacks, stationary part and recession - all tools differ in duration and in form. At the percussion instruments, a very short stationary part, the attack time is 0.5 ... 3 ms and the recession time 0.2 ... 1 s; At the bottom of the time attack 30 ... 120 ms, the recession time is 0.15 ... 0,5 s; At the attack authority - 50 ... 1000 ms and a decline of 0.2 ... 2 s. In addition, a form of temporary envelope is fundamentally different.
Experiments have shown that if you remove part of the temporary structure corresponding to the audio attack, or change the attack and recession places (play in the opposite direction), or the attack from one tool is replaced with an attack from another, then identify the timbre of this tool becomes almost impossible. Therefore, for the recognition of the timbre not only the stationary part (the average spectrum of which serves as the basis of the classical theory of the timbre), but also the period of formation of a temporary structure, as well as the attenuation period (recession) are vital elements.

Indeed, when listening to any room, the first reflections come to the auditory system after the attack and the initial part of the stationary part were already heard. At the same time, the reverb process of the room is superimposed on the sound of sound from the tool, which significantly masks the sound, and, of course, leads to a modification of the perception of its timbre. The rumor has a certain inertia, and short sounds are perceived as clicks. Therefore, the duration of sound should be more than 60 ms so that the height can be recognized, and, accordingly, the timbre. Apparently, constant should be close.
Nevertheless, the time between the beginning of the arrival of direct sound and the moments of receipt of the first reflections turns out to be enough to recognize the timbre of the sound of a separate tool - obviously, this circumstance is determined by the invariance (stability) of the timbres of different tools in different limiting conditions. Modern computer technologies allow enough to analyze the processes of establishing sound from different tools, and allocate the most essential acoustic signs most important to determine the timbre.

The structure of its stationary (averaged) spectrum is a significant impact on the perception of the timbre of a musical instrument: the composition of the overtones, their location on the frequency scale, their frequency ratios, the distribution of amplitudes and the shape of the envelope spectrum, the presence and form of formation regions, etc., which Fully confirms the provisions of the classical theory of the tone set out in the writings of the Helmholtz.
However, the experimental materials obtained over the past decades have shown that no less significant, and maybe a much more significant role in the timbre recognition plays a non-stationary change in the structure of sound and, accordingly, the process of deployment in the time of its spectrum, first of all, The initial stage of the audio attack.

The process of changing the spectrum in time is particularly clearly visualized can be "see" using spectrograms or three-dimensional spectra (they can be built using most Sound Forge, Spectrolb, Wave Lab and other music editors. Their analysis for sounds of various tools allows you to identify the characteristic features of the processes of the "deployment" of the spectra. For example, the 3D spectrum of the sound of the bell is a three-dimensional spectrum of the bell, where the frequency in Hz is postponed by one axis, at another time in seconds; According to the third amplitude in dB. The graph is clearly seen how the process of increasing, establishing and recession in time of spectral envelope occurs.

Comparison of the Tone C4 attack at various wooden tools shows that the process of establishing oscillations for each tool has its own special character:

The clarinet is dominated by odd harmonics 1/3/5, and the third harmonic appears in the spectrum by 30 ms later, then gradually "lined up" higher harmonics;
- Goboy establishing oscillations begins with the second and third harmonics, then the fourth and only after 8 ms begins to appear the first harmonic;
- The flute first appears the first harmonic, then only after 80 ms all the others are gradually entering.

The figure shows the process of establishing oscillations for a group of copper tools: pipes, trombones, horn and tubes.

Differences are clearly visible:
- The pipe has a compact appearance of the group of higher harmonics, the first harmonic of Trombone appears, then the first, and after 10 ms the second and third. The tube and horsavers are visible to the concentration of energy in the first three harmonics, the higher harmonics are practically absent.

Analysis of the results shows that the sound attack process significantly depends on the physical nature of sound recovery on this instrument:
- from the use of incubuser or canes, which, in turn, are divided into single or double;
- from various forms of pipes (straight uncommon or cones and cones), etc.

This determines the amount of harmonics, the time of their appearance, the rate of building their amplitude, and, accordingly, the shape of the envelope of the time structure of the sound. Some tools, such as flutes

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

During the attack, the highest harmonics are sometimes ahead of the main tone, therefore, fluctuations of the tone height can occur, which means that the height of the total tone can be built up gradually. Sometimes these changes of the frequency are quasistless. All these signs help the hearing system "identify" the timbre of a tool in the initial moment of sound.

Not only the moment of recognition of it is important to assess the voice of the sound (i.e. the ability to distinguish one tool from the other), but also the ability to estimate the change in the timbre in the execution process. Here the most important role is played by the dynamics of changes in spectral envelope in time at all stages of sound: attacks, stationary part, recession.
The nature of the behavior of each obhrothon in time also bears the most important information about the tech. For example, the sound of the bells is particularly clearly visible to the dynamics of the change, both in the composition of the spectrum and in the nature of the time of the amplitude of its individual overtones: if at the first moment after the strike in the spectrum is clearly visible several dozens of spectral components, which creates the noise of the tone, After a few seconds, several main overtones remain in the spectrum (basic tone, octave, duodetsis and minor tone through two octaves), the rest are faded, and it creates a special tonal painted voice timbre.

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

Experience shows that the additive computer synthesis of sounds, taking into account the specifics of the deployment of individual overtones in time, allows you to get significantly more "life" sound.

The question of whether the dynamics of changes in which obchtonov carries information about the debron, is associated with the existence of critical hearing bands. The basilar membrane in the snail acts as a line of strip filters, the width of the strip of which depends on the frequency: above 500 Hz it is approximately 1/3 octaves, below 500 Hz it is approximately 100 Hz. The width of the strip of these hearing filters is called a "critical hearing strip" (there is a special unit of measurement 1 Bark, equal to the width of the critical strip in the entire range of audible frequencies).
Inside the critical strip, the hearing is integrated by the audible information, which also plays an important role in the hearing disguise processes. If you analyze signals at the outlet of the auditory filters, you can see that the first five to seven harmonics in the spectrum of the sound of any tool usually fall each into your critical strip, as they are far enough away from each other in such cases they say that the harmonics are "deployed" the auditory system. The discharge of neurons at the exit of such filters is synchronized with a period of each harmonic.

Harmonics Above the seventh are usually located close enough to each other on the frequency scale, and several harmonics fall into the auditory system inside the same critical band, and a complex signal is obtained at the outlet of the auditory filters. The discharges of neurons in this case are synchronized with the frequency of the envelope, i.e. Basic tone.

Accordingly, the information processing mechanism of the auditory system for deployed and uniform harmonics is somewhat different in the first case, information "in time" is used, in the second "on the place".

A significant role in recognizing the tone height was shown in previous articles, the first fifteen-eighteen harmonics play. Experiments with the help of computer additive synthesis of sounds show that the behavior of these harmonics also has the most significant impact on changing the timbre.
Therefore, in a number of studies, the size of the timbre was proposed to be considered to be equal to fifteen-eighteen, and evaluate its change on this amount of scales this is one of the fundamental differences in the tone from such characteristics of the hearing perception, as the height or volume that can be scaled in two or three parameters (for example, Volume) depending mainly from the intensity, frequency and duration of the signal.

It is well known that if there is a lot of harmonics with numbers from the 7th up to15 ... 18th, with quite large amplitudes, for example, in a pipe, violin, organ pipes, etc., the timbre is perceived as Bright, ringing, sharp, etc. If there are mainly lower harmonics in the spectrum, for example, in tubre, horn, trombone, then the timbre is characterized as dark, deaf, etc .. Clarinet, in which odd harmonics dominate the spectrum , has several "nasal" timbers, etc.
In accordance with modern views, the most important role for the perception of the timbre has a change in the dynamics of the distribution of the maximum energy between the range of spectrum.

To evaluate this parameter, the concept of the "Spectrum" concept was introduced, which is defined as the average distribution point of the spectral sound energy, it is sometimes defined as the "Balance point" of the spectrum. The method of determining it is that the value of a certain average frequency is calculated:

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

F \u003d (8 x 100 + 6 x 200 + 4 x 300 + 2 x 400) / (8 + 6 + 4 + 2) \u003d 200.

The offset of the centeride towards the high frequencies is felt as an increase in the brightness of the tone.
The significant effect of the distribution of spectral energy in the frequency range and its changes in time to the perception of the timbre is probably due to the experience of recognizing speech sounds on formant signs, which are informed about the concentration of energy in various fields of the spectrum (it is unknown, the truth that was primary).
This hearing ability is essential when evaluating the timbres of musical instruments, since the presence of formation areas is characteristic of most musical instruments, for example, in violins in areas 800 ... 1000 Hz and 2,200 ... 4000 Hz, 700 Hz, and so on.
Accordingly, their position and dynamics of time changes affect the perception of individual characteristics of the voice.
It is known what a significant impact on the perception of the timbre of a singing voice is having a high singing formant (in the region of 2100 ... 2500 Hz at Basov, 2500 ... 2800 Hz in tenors, 3000 ... 3500 Hz in soprano). In this area, opera singers focuses to 30% acoustic energy, which ensures the bellier and affordability of the voice. Removing with filters of singing formants from recordings of various votes (these experiments were performed in studies prof. V.P. Morozova) shows that the voice of the voice becomes dim, deaf and sluggish.

Changing the timbre when changing the volume of execution and transpose in height is also accompanied by a shift of the centroid at the expense of the amount of overtones.
An example of a change in the position of the centroid for the sounds of violin of different height is shown in the figure (the frequency of the centroid position in the spectrum is postponed along the abscissa axis).
Studies have shown that many musical instruments have an almost monotonic connection between an increase in the intensity (volume) and the centroid shift to the high-frequency area, due to which the timbre becomes brighter.

Apparently, in the synthesis of sounds and creating various computer compositions, a dynamic connection between the 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 the timbres of real sounds and sounds with the "virtual height", i.e. Sounds whose height "completes" in several integer oracleons of the spectrum (this is characteristic, for example, for the sounds of bells), can be explained from the position of the position of the spectrum center. Since these sounds have the value of the main tone frequency, i.e. Heights may be the same, and 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 even more than ten years ago, a new parameter was proposed for measuring the acoustic equipment, namely the three-dimensional spectrum of energy distribution in terms of frequency and time, the so-called distribution of the Wigner, which is quite actively used by various firms to evaluate the equipment, as the experience shows It allows you to establish the best match with its sound quality. Considering the above property of the auditory system to use the dynamics of changes in the energy signs of the audio signal to determine the timbre, it can be assumed that this parameter of the Wigner distribution may be useful for assessing musical instruments.

Evaluation of the timbres of various tools is always subjective in nature, but if, when assessing the height and volume, it is possible on the basis of subjective assessments to arrange sounds on a specific scale (and even enter special units of measurement "sleep" for volume and "chalk" for height), then the timbre assessment is significantly A more difficult task. Usually, a pair of sounds are presented to the listeners to the students of the auditors, the same in height and volume, and they are asked to arrange these sounds on different scales between different opposite descriptive features: "bright" / "dark", "ringing" / "deaf", etc. . (On the choice of various terms for describing the timbres and on the recommendations of international standards on this issue we will definitely talk in the future).
A significant impact on the determination of such sound parameters as height, timbre, etc., has a behavior in the time of the first five-seven harmonics, as well as a number of "non-verminated" harmonics up to 15 ... 17th.
However, as is known from the general laws of psychology, a man's short-term memory can simultaneously operate no more than seven-eight characters. Therefore, it is obvious that at the recognition and evaluation of the tone, not more than seven eight significant signs are used.
Attempts to establish these signs by systematizing and averaging the results of experiments, find generalized scales for which you could identify the timbres of the sounds of various tools, link these scales with different temporal spectral characteristics of sound, have been made for a long time.

One of the most famous is the work of Gray (1977), where a statistical comparison of estimates on various signs of sounds of sounds of various tools of strings, wooden, percussion, and other sounds were synthesized on a computer, which allowed them to change their temporal and spectral directions in the required directions. characteristics. The classification of the colors was performed in a three-dimensional (orthogonal) space, where as a scale for which a comparative assessment of the degree of similarity of the timbreless signs (ranging from 1 to 30) was selected:

The first scale is the value of the centroid amplitude spectrum (the discharge of the center of the centroid, i.e. the maximum of spectral energy from low to high harmonics);
- The second is the synchronization of spectral fluctuations, i.e. The degree of synchronization of the entry and development of individual spectrum overtones;
- The third is 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 sufficiently clear classification of tools on the timbres inside the proposed three-dimensional space.

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

Three-dimensional Tembra space

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

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

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

This is a change in the structure of the temporary envelope at all stages of sound development: attacks (which is especially important for the recognition of the timbres of various sources), stationary part and recession. This is a dynamic change in time spectral envelope, incl. Displacement of the spectrum center, i.e. The displacement of the maximum spectral energy over time, as well as the development of the amplitudes of spectral components, especially the first five-seven "non-verminated" spectrum harmonics.

Currently, the third period of studying the problem of the Time of the Center of Studies has begun towards studying the influence of the phase spectrum, as well as to the use of psychophysical criteria in the timbre of the timbre underlying the overall mechanism of sound image recognition (grouping in streams, synchronization estimation, etc.).

Timbre and phase spectrum

All outlined results on the establishment of a perceived timbre with the acoustic characteristics of the signal were treated with an amplitude spectrum, more precisely, to a temporary change in the spectral envelope (primarily the displacement of the energy center of the amplitude spectrum-centroid) and the deployment of separate overtones.

In this direction, the largest number of works were done and many interesting results were obtained. As already noted, for almost a hundred years in psychoacoustics, the opinion of the Helmholtz was prevailing that our hearing system is not sensitive to changes in phase relations between individual obverseons. However, experimental data were gradually accumulated on the fact that the auditory apparatus is sensitive to phase changes between different signal components (Schroedher, Hartman, etc.).

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

In the 1980s, this led to the creation of a number of acoustic systems with a linear phase characteristic. As is known from the general theory of systems, for undischarged signal transmission, it is necessary that the constancy of the transfer function module is respected, i.e. The amplitude-frequency characteristic (envelope of the amplitude spectrum), and the linear dependence of the phase spectrum on the frequency, i.e. φ (ω) \u003d -ωt.

Indeed, if the amplitude envelope spectrum is saved constant, then, as mentioned above, the distortion of the sound signal should not occur. The requirements for maintaining the linearity of the phase in the entire frequency range, as showed by the research of the Bluerta, turned out to be redundant. It was found that the hearing reacts primarily on the rate of phase change (i.e. its frequency derivative), which is called " group time delaying GVZ ": τ \u003d dφ (ω) / dω.

As a result of numerous subjective examinations, thresholds were constructed by the hearing of Distortion of GVZ (i.e., the deviations of Δτ from its constant value) for various speech, musical and noise signals. These hearing thresholds depend on the frequency, and in the region of the maximum sensitivity of the hearing are 1 ... 1.5 ms. Therefore, in recent years, when creating acoustic equipment, Hi-Fi is focused mainly on the above hearing thresholds for the distortion of GVZ.

View of the waveform with different ratios of the phases of overtones; Red - all overtones have the same initial phases, blue - phases are distributed randomly.

Thus, if the phase ratios have an audit effect on determining the height of the tone, then we can expect that they will have a significant impact on the timbre recognition.

For experiments, sounds were selected with the main tone of 27.5 and 55 Hz and from one hundred oraches, with a uniform ratio of amplitudes characteristic of piano sounds. At the same time, tones were studied with strictly harmonious overtones, and with a non-charity characteristic of the sounds, which arises due to the ultimate rigidity of the strings, their heterogeneity, the presence of longitudinal and tweezing oscillations, etc.

The sound under study was synthesized as the sum of its overtones: x (t) \u003d σa (n) sin
For auditory experiments, the following ratios of initial phases for all overtones were selected:
- A - the sinusoidal phase, the initial phase was taken equal to zero for all overtones φ (n, 0) \u003d 0;
- B - alternative phase (sinusoidal for even and cosine for odd), the initial phase φ (n, 0) \u003d π / 4 [(- 1) n + 1];
- C - random phase distribution; The initial phases have changed randomly in the range from 0 to 2π.

In the first series of experiments, all one hundred obchtonov had the same amplitudes, only their phases were distinguished (the main tone of 55 Hz). At the same time, the listened timbres turned out to be different:
- in the first case (a), there was a distinct frequency;
- second (b), the timbre was brighter and listened to another height of the tone to octave above the first (altitude was not a clear);
- In the third (c) - the timbre turned out to be more uniform.

It should be noted - the second height was listening only in the headphones, while listening through the loudspeakers, all three signals differed only by the timbre (reverb was affected).

This phenomenon - change in the height of the tone when the phase changes of some components of the spectrum - can be explained by the fact that with the analytical representation of the Fourier transformation of the type b signal, it can be represented as the sum of two combinations of overtones: one hundred overtones with a phase type A, and fifty overtones with a phase, and fifty overtones with a phase that is different 3π / 4, and amplitude more in √2. This group of overtones is assigned a separate tone height. In addition, in the transition from the ratio of phases A to the type of phases, the center of the spectrum (maximum energy) is shifted towards high frequencies, so the timbre seems brighter.

Similar experiments with a phase shift of individual overtone groups also lead to an additional (less clear) virtual tone height. This property of hearing is due to the fact that the rumor compares the sound with a sample-specific music tone, and if some harmonics fall out of a series typical of this sample, then the rumor allocates them separately, and prescribed a separate height.

Thus, the results of the research of Gablebo, Askenefeld, etc. showed that phase changes in the ratios of individual overtones are quite clearly audible as changes in the timbre, and in some cases - the height of the tone.

This is especially manifested when listening to the real musical tones of the piano, in which the amplitudes of the overtones decrease with an increase in their number, there are a special form of the envelope spectrum (forman structure), and a clearly pronounced non-harmonicity of the spectrum (i.e., the frequency shift of individual overtones relative to the harmonic row ).

In the time domain, the presence of non-harmonicity leads to dispersion, that is, high-frequency components spread over a string with a greater speed than low-frequency, and the waveform of the signal changes. The presence of a small non-harmonicity in sound (0.35%) adds some warmth, the vitality of the sound, however, if this non-harmonicity becomes large, there are beyonds and other distortions in the sound.

Nearmonicity also leads to the fact that if at the initial moment of the OPERTON Phase were in deterministic ratios, if it was presented with the ratio of phases, it becomes random, the peak structure of the waveform is smoothed, and the timbre becomes more uniform - it depends on the degree of non-harmonicity. Therefore, the instantaneous measurement of the regularity of the phase ratio between adjacent overtones can be a tone indicator.

Thus, the effect of phase mixing due to non-harmonicity is manifested in some change in the perception of the height of the tone and the timbre. It should be noted that these effects are heard when listening at close range from decks (in the position of the pianist) and with the close position of the microphone, and the auditory effects differ when listening to headphones and through loudspeakers. In a reverb surrounding, a complex sound with a high peak factor (which corresponds to a high degree of regularization of phase ratios) indicates the proximity of the sound source, since, as phase ratios are removed from it, it is becoming increasingly random due to reflections in the room. This effect may cause various spectacle estimates with a pianist and a listener, as well as different voice timbre recorded by the microphone at the deck and the listener. The closer, the higher the regularization of the phases between the overtones and the more defined tone height, the further, the more uniform the timbre and the less clear height.

Works on the assessment of the influence of phase ratios on the perception of the timber of musical sound are now actively studied in various centers (for example, in Irkama), and can be expected in the near future new results.

Tambre and general principles of auditory recognition

The timbre is the identifier of the physical sound formation mechanism for a number of features, it allows you to select the sound source (tool or group of tools), and determine its physical nature.

This reflects the general principles of recognition of auditory images, which, according to, considers modern psychoacience, are the principles of gestalt psychology (Geschtalt, it is "image"), which claims that for separation and recognition of various sound information coming to the hearing system from Of different sources at the same time (the game of the orchestra, the conversation of many interlocutors, etc.) the auditory system (as well as visual) uses some general principles:

- segregation - separation on sound streams, i.e. The subjective allocation of a certain group of sound sources, for example, with a musical polyphony of hearing can monitor the development of the melody from individual tools;
- similarity - Sounds, similar on Tembre, are grouped together and are attributed to one source, for example, speech sounds with close base tone height and similar rates are defined as belonging to one interlocutor;
- continuity - the auditory system can interpolate sound from a single stream through a masker, for example, if in a speech or musical stream insert a short noise cut, the auditory system may not notice it, the sound stream will continue to be perceived as continuous;
- "Total Fate" - The sounds that start and stop, and also change over the amplitude or frequency in certain limits synchronously, are attributed to one source.

Thus, the brain produces a grouping of the received audio information as a serial, determining the time distribution of the sound component within a single audio stream and parallel, highlighting the frequency components present and varying simultaneously. In addition, the brain all the time compares the audio information with the "recorded" in the process of learning in memory with sound images. Circling received combinations of sound streams with existing images, it or easily, they identifies them if they coincide with these images, or, in case of incomplete The coincidences attributes to them some special properties (for example, assigns a virtual tone height, as in the sound of bells).

In all these processes, the timbre recognition plays a fundamental role, since the timbre is a mechanism with which is extracting from physical properties. Symptoms that determine sound quality: they are recorded in memory, compared with already recorded, and then identifies in certain zones of the cerebral cortex.

Hearing zones of the brain

Timbre - Sensation is multidimensional, depending on many physical characteristics of the signal and the surrounding space. Works were carried out on the scaling of the timbre in the metric space (scale are various spectral time characteristics of the signal, see the second part of the article in the previous issue).

In recent years, however, an understanding has appeared that the classification of sounds in a subjectively perceived space does not correspond to the usual orthogonal metric space, there is a classification for "subzzines", associated with the above principles, which are not metric, and not orthogonal.

Sharing sounds on these subversias, the auditory system determines the "sound quality", that is, the timbre, and decides which category to take these sounds. However, it should be noted that all sets of subspaces in the subjectively perceived sound world are built on the basis of information on two parameters of the sound from the outside world - intensity and time, and the frequency is determined by the time of the arrival of the same intensity values. The fact that the ear shares the received audio information immediately in several subjective subversias, increases the likelihood that in some of them it can be recognized. It is that the allocation of these subjective subspaces, which occurs the timbres and other signs of signals, and the efforts of scientists are currently directed.

Conclusion

Summing up, we can say that the main physical signs for which the timbre of the tool is determined, and its change in time is:
- building the amplitudes of overtones during the attack period;
- change of phase relations between obhrtons from deterministic to random (in particular, due to the non-harmonicity of overtones of real instruments);
- change in the shape of the spectral envelope in time in all periods of sound development: attacks, stationary part and recession;
- the presence of irregular spectral envelope and the position of the spectral center (maximum

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

General view of spectral envelopes and their change in time

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

Of course, all this does not exhaust the list of physical signs of the signal defining its timbre.
Searches in this direction continue.
However, with the synthesis of musical sounds, it is necessary to take into account all the signs for creating realistic sound.

Verbal (verbal) description

If there are appropriate units for assessing the height of sounds: psychophysical (chalk), musical (octaves, tones, halftone, cents); There are units for volume (sons, backgrounds), then for the timbres, such scales cannot be built, since this concept is multidimensional. Therefore, along with the search described above, the correlation of the perception of the tone with the objective parameters of the sound, to characterize the timbres of musical instruments, use verbal descriptions, selected on the signs of opposites: bright - dim, sharp - soft, etc.

The scientific literature has a large number of concepts related to the evaluation of sound timbres. For example, the analysis of terms adopted in modern technical literature made it possible to identify the most common terms shown in the table. Attempts to identify the most significant among them, and to scale the timbre on the opposite features, as well as to link the verbal description of the timbres with some acoustic parameters.

The main subjective terms for the description of the timbre used in modern international technical literature (statistical analysis of 30 books and magazines).

Acidlike - sour
Forceful - reinforced
Muffled - shuffle
Sober - sober (judgling)
Antique - old
Frosty - Frosty
Mushy - porous
Soft - soft
Arching - convex
Full - Full
Mysterious - Mysterious
Solemn - Gala
ARTICULATE - RIGHT
Fuzzy - Fluffy
NASAL - nose
Solid - hard
Austere - Stern
Gauzy - Slim
Neat - neat
Somber - gloomy
Bite, biting - biting
Gentle - Gentle
Neutral - neutral
Sonorous - sonorous
Blond - patterned
Ghostlike - Ghost
Noble - noble
Stely - Steel
Blaring - roaring
Glassy - Glass
Nondescript - indescribable
Strained - stretched
Bleating - bleach
Glittering - Brilliant
Nostalgic - nostalgic
Strident - Squeaky
Breathy - respiratory
Gloomy - Sad
Ominous - ominous
Stringent - crammed
Bright - Bright
Grainy - grains
Ordinary - ordinary
Strong - Strong
Brilliant - Brilliant
Grating - Squeaky
Pale - pale
Stuffy - Fools
Brittle - Movable
Grave - serious
Passionate - passionate
Subdued - Softening
Buzzy - buzzing
Growly - lying penetrating - penetrating
Sultry - Rooms
Calm - calm
Hard - hard
Piercing - Piercing
Sweet - Sweet
Carrying - Flight
Harsh - rude
Pinched - limited
Tangy - confused
Centered - concentrated
Haunting - pursuing
Placid - Ceremony
Tart - sour
Clangorous - ringing
Hazy - Vituly
PlainTIVE - SUNNYY
Tearing - Few
Clear, Clarity - Clear
Hearty - sincere
Ponderous - weighty
Tender - gentle
Cloudy - Foggy
Heavy - Heavy
Powerful - powerful
Tense - stressful
Coarse - Rough
Heroic - heroic
Prominent - Outstanding
Thick - fat
Cold - Cold
Hoarse - hoarse
Pungent - caustic
Thin - Slim
Colorful - colorful
Hollow - empty
Pure - clean
Thretening - Threatening
Colorless - colorless
Honking - buzzing (car beep)
Radiant - shining
Throaty - hoarse
Cool - Cool
Hooty - Guedy
Raspy - rattling
TRAGIC - tragic
Crackling - Cracked
Husky - Siploma
Rattling - Gorching
Tranquil - Soothing
Crashing - broken
Incandescence - heated
Reedy - Piercing
Transparent - proxy
Creamy - creamy
Incisive - sharp
Refined - refined
Triumphant - triumphant
Crystalline - crystal
INEXPRESSIVE - Increased
Remote - Remote
Tubby - Bocho-shaped
Cutting - sharp
Intense - intense
Rich - rich
Turbid - muddy
Dark - Dark
Introspective - in-depth
Ringing - ringing
Turgid - High Flight
Deep - deep
Joyous - joyful
Robust - Rough
Unfocussed - 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 - remote
Liquid - watery
Savage - wild
Vibrant - Vibrating
Distant - distinct
Loud - Loud
Screamy - screaming
Vital - life
Dreamy - Dreamy
Luminous - Brilliant
SREE - Dry Voluptuous - Lush (Luxurious)
Dry - Sukhoi
Lush (Luscious) - juicy
Serene, Serenity - calm
WAN - dim
Dull - boring
Lyrical - Lyrian
Shadowy - Shaded
Warm - warm
Earnest - serious
Massive - Massive
Sharp - sharp
Watery - watery
Ecstatic - Ecstatic
MEDITATIVE - contemplative
Shimmer - trembling
Weak - weak
Ethereal - Essential
Melancholy - Melancholic
Shouting - screaming
Weighty - Heavyweight
Exotic - exotic
Mellow - soft
Shrill - Piercing
White - White
Expressive - expressive
Melodious - melodic
Silky - silky
Windy - Windmate
Fat - fat
Menacing - threatening
Silvery - silver
WISPY - Slim
Fierce - Hard
Metallic - metallic
Singing - Pevichy
Woody - wooden
Flabby - Diryaboy
MISTY - unclear
Sinister is ominous
Yearning - Smeal
Focussed - focused
Mournful - Mourning
Slack - Ducklown
Forboding - repulsive
Muddy - dirty
Smooth - smooth

However, the main problem is that there is no unambiguous understanding of various subjective terms describing the timbre. The translation given before the translation is not always consistent with that technical sense, which is invested in each word when describing various aspects of the scorer.

In our literature, there was a standard for the basic terms, but now things are very sad, because it does not work on creating relevant Russian-speaking terminology, and many terms are used in different, sometimes directly opposite, values.
In this regard, AES in developing a series of standards on subjective assessments of the quality of audio equipment, recording systems, etc. began to set identifying subjective terms in annexes to standards, and since standards are created in working groups, including leading specialists from different countries, then this very important procedure leads to a consistent understanding of the main terms for the description of the timbre.
As an example, I will give the AES-20-96 standard - "recommendations for subjective assessment of loudspeakers," where the agreed definition of such terms as "openness", "transparency", "clarity", "tension", "sharpness", etc.
If this work is systematically continued, then, possibly, the main terms for the verbal description of the timbres of the sounds of various tools and other sound sources will have consistent definitions, and will be unambiguously or fairly understood by specialists from different countries.