Sound (bell)
When a bell is struck, a characteristic sound is created . This consists of
- a number of real, measurable, almost sine- shaped partials , occasionally beeps , called and
- mostly a virtual , non- measurable strike note .
The tones of a bell are not referred to as the fundamental and overtones , because the higher partials here are only very rarely harmonics of the 1st partial.
Although the bell is a musical instrument as an idiophone , the terms tone and sound are used differently in bell science than is generally used in music.
Each cast bell is unique and therefore has an individual sound based on its geometric shape - the rib - and the metal used .
Vibrations
Waveforms
Upon excitation of a bell by a shock formed - similarly to the vibration of a plate - standing waves .
The bell swings in different modes at the same time . Each mode has a characteristic pattern of nodal lines, at which the amplitude becomes zero, and a natural frequency that can be measured and audibly perceived as the partial tone of the bell . The nodal lines either lie vertically in a sectional plane through the bell, in which their axis of symmetry lies (then the nodal lines are also called node meridians ), or horizontally in a circle around the bell ( node circles) . Compare with the spherical surface functions .
The oscillation pattern can be identified by a pair of numbers (m, n), in which the first number m indicates the number of vertical node lines and the second number n the number of horizontal node lines. If there is only one horizontal knot line, a dash 'in the number indicates that the knot line is not at the level of the flank, but much lower. For example, the lowest partial of a bell has the pattern (2.0), the fifth the pattern (3.1 ').
If one imagines the adjacent figure of a standing circular wave as a plan view of the bell, the node lines go from the edge of the bell up to its apex and on the opposite side down to the edge, so that there are 8 vertical node lines.
Measurement
The natural frequencies of a bell can be determined both actively and passively:
- During the active measurement, the bell is excited with a tuning fork or with the probe of an audio frequency generator. The frequency is then changed until resonance occurs and a partial tone is found.
- with the passive method, the stationary bell is struck and its sound is recorded . The recording is then subjected to a spectral analysis, which provides the spectrum of the sound in which the partials are recognizable as peaks .
The measured values from active and passive measurement differ slightly because the bell vibrates undamped with active measurement, but dampened with passive measurement .
Before the tunable tuning fork was invented around 1900, the partials were determined with the help of tunable clinking whistles .
Sound system
scale
In order to musically represent the natural frequencies of the bell, the 12-step chromatic scale common in music is used in equal tuning .
In the German-speaking world, the old tuning tone a 1 = 435 Hz, which was valid from 1885 to 1939, is still used as the basis for bells today , while abroad the more recent definition of 440 Hz is mostly used.
Because the frequency resolution is too low for purposes of bell science when dividing into semitone steps , the semitone steps are divided into sixteenths, so that 192 different tones can be represented in one octave . So the frequency ratio of a semitone sixteenth is . A semitone sixteenth corresponds to 6.25 cents . In written representation, the sixteenth notes are written after the tone designation. For example, 333 Hz is equivalent to e 1 +6 or 959 Hz to h 2 −5 (base 435 Hz).
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Because the sixteenth deviations can be applied both positively and negatively, it would also be possible to specify e 1 +6 as f 1 −10 . Which spelling is to be preferred depends in each individual case on the position of the striking note, which in turn is also indicated with semitone sixteenth.
Chime
The striking tone is the nominal tone of a bell, because it is a subjectively perceived tone that creates the perception of the pitch of the bell. At the same time, it serves as a reference tone for naming the partials in the form of intervals . The strike sound is not a real sound, but a residual sound . Therefore it does not appear in the sound spectrum, nor can its frequency be measured directly.
There are bells that do not have a strike tone, not even as a residual tone; among them are mainly beehive bells , bowl-shaped bells and low-height bell bells.
Partials
The partials of a bell are named by the intervals that they normally form with the striking note. Because these interval designations ultimately characterize oscillation patterns, they can even be used if there is no striking note at all (not even a virtual one) or the interval is a different one (e.g. sixth instead of fifth). In the latter case, one speaks of a representative (the sixth is the fifth representative).
In a certain analogy to registers of the organ the first 5 partials principal tones called and the higher partials Mixturtöne . With the exception of the duodecime, the mixed tones have weak amplitudes and fade away very quickly; nevertheless they are also essential for the sound of a bell.
| group | Partial tone | Interval by which the partial is above the striking note |
Oscillation pattern (vertex lines vertical, horizontal) |
properties |
|---|---|---|---|---|
| Mixed tones | Triple octave | (9.1) | ||
| Double octave | (6.1) | is often slightly increased and is therefore only sometimes used as a beat tone generator. | ||
| Duodecime | (5.1) | often the strongest mix tone and a beat tone maker. | ||
| Undezime | (3.2) | should not be too strong, because as a fourth 4 'it can be a side note tone generator . |
||
| Decime | (4.1 ') | is a major decime, although the third is a minor third. It contributes significantly to the timbre . |
||
| Principal tones | 5th partial | octave | (4.1) | strong, but mostly not as strong as the first three partials. The octave is significantly involved in the formation of the strike tone, so it is counted among the strike tone creators. |
| 4th partial | Fifth | (3.1 ') | has a weak amplitude and fades away quickly, so tonal inaccuracies are not a problem. The fifth often follows the undertone, so a high undertone can go hand in hand with a high fifth (up to the seventh ). |
|
| The first three partials usually have stronger amplitudes and longer decay times than all other partials, so they are sonically fundamental. | ||||
| 3rd partial | third | (3.1) | Depending on the third one divides Oktavglocken in minor - and major -Oktavglocken . The third is a minor third in the Gothic rib . In the 1980s it was possible for the first time to construct ribs with clean major thirds. |
|
| 2nd partial | Prime | (2.1) | The pitch can coincide with the strike note, but it can also be slightly above or below it. |
|
| 1st partial tone (undertone) |
Sixth ... None below the strike note, depending on the geometric proportions of the bell |
(2, 0) | According to the undertone, a bell is called | |
example
Musical dates of two arbitrarily selected bronze bells from 1546 and from 1955:
| volume | 1546 | 1955 |
|---|---|---|
| Chime | e 1 −4 | e 1 +1 |
| undertone | ice 0 −1 | e 0 −2 |
| Prime | d 1 −12 | e 1 +1 |
| third | g 1 −3 | g 1 +1 |
| Fifth | h 1 ± 0 | h 1 +2 |
| octave | e 2 −4 | e 2 +1 |
| Decime | g sharp 2 −1 | g sharp 2 +3 |
| Duodecime | h 2 −10 | h 2 +1 |
| Double octave | e 3 −5 | e 3 +9 |
Thousands of other examples can be found in the bell books of the dioceses of Cologne, Aachen and Essen.
Pure intervals
If one considers the totality of the partials of a bell from a musical point of view, one speaks of its internal harmony .
It would be a fallacy to believe that a bell whose partials are, for example, d 0 +2, d 1 +2, f 1 +2, a 1 +2, d 2 +2, f sharp 2 +2, has a particularly clean interior harmony would have. In the equally tempered tuning, all the intervals are in principle unclean compared to the pure intervals . The slight narrowing or spreading of the fifths and fourths is not critical, but with thirds and sixths the "detuning" is clearly perceptible to a trained ear:
- the major third has the frequency ratio in pure tuning , but in equal tuning , so that the equal major third is perceived around 14 cents = 2.2 semitone sixteenth too high;
- the equal minor third , on the other hand, appears around 16 cents = 2.5 semitone sixteenth too deep.
Therefore the bell in the above example with d 0 +2, d 1 +2, f 1 +4 , a 1 +2, d 2 +2, f sharp 2 ± 0 would have a purer internal harmony.
Sound ideal
The pitch and interior harmony of the beehive bells cast in the Romanesque era, like those of the later sugar loaf bells, were purely coincidental.
Over the centuries, the foundrymen succeeded in developing their art by changing the bell ribs in such a way that ultimately not only did the chimes of several bells stand at clean intervals, but the interior harmonies were also improved.
At the end of the 15th century, the medieval art of bell casting was at its peak in terms of quality, both in terms of craftsmanship and casting technology, as well as the sound of the bells. The Gothic minor triad rib , also called the minor octave bell in the Gothic rib , developed at the time, has an excellent sound that is still considered the ideal sound, so that even modern bells are almost exclusively cast with ribs of this type.
But there are also voices that contradict a stipulation of this sound ideal in the sense of standardization , because a tonal variety such as existed in the High Middle Ages is prevented today.
Sound corrections
By turning or grinding you can edit a bell in order to correct the frequency of individual partials. However, such corrections are only possible within narrow limits.
Glockenspiel bells usually have to be reworked because of the increased demands on the precise position of the notes.
In monumental bells editing is strictly prohibited.
Many foundries , especially those who work in the German-speaking area, have mastered their art so perfectly that their bells do not need any post-processing to correct the sound.
Regulations
In the Limburg guidelines of 1951, an agreement between the Advisory Committee for the German Bell System and the Association of German Bell Founders , the following maximum permissible deviations of the partials are specified for new bells:
- Sub-octave: + 3 / −10 semitone sixteenth
- Prime: + 3 / −6 semitone sixteenth
- Third: + 4 / −4 semitone sixteenth.
In addition, the octave interval between sub-octave and prime must not be narrowed.
Not prescribed by the guidelines, but it is common practice to limit the deviation of the fifth to + 16 / −16 semitone sixteenth, i.e. to +/- a semitone.
additional
Amplitudes
Each partial tone has a certain strength, which can be measured as an amplitude . With a good bell sound, the amplitudes of the partials are in a balanced relationship to one another. In many bells, the third is the strongest partial, followed by the prime, undertone, and octave. The strength of the individual partials is mainly determined by the respective bell rib . A scientific investigation of the sonically optimal amplitude relationships of the partials has not yet been carried out.
Excitement from attack
The clapper also has an influence on the sound of the bell. If the clapper or a hammer hits the brass knuckles, it is a partially elastic impact . The clapper and brass knuckles touch each other for a very short time. The amplitudes of the partials and thus the heights of the peaks in the spectrum change depending on the duration of contact. A heavy ball of the clapper leads to a longer contact time and to a strong excitation of the principal tones, which is associated with weaker mixed tones. A light ball weaker excites the principal notes and gives the mixtures more strength. Because of the very short contact time when a steel clapper hits a steel bell, the sound is sharp. Therefore, in this case the bobbins are equipped with gunmetal or bronze buffers.
Bell experts disagree with the extent to which the surface hardness of the ball of the clapper influences the sound of a bell.
Cooldown
The sound of a bell excited by impact experiences a loss of energy as a result of sound radiation, external and internal friction, whereby the sound becomes weaker and the vibrations of the bell are therefore subject to damping . Earlier because the measurement capabilities were quite limited, the amount of attenuation is not as damping ratio or decrement specified, but rather a decay time (unfounded in older literature reverberation called). The internal damping of the bell is largely based on the porosity of the metal and to a small extent also on the composition of the alloy . The higher the cooldown, the better the bell. The rule of thumb used to be that a good bell had to have a decay time in seconds at least equal to its diameter in centimeters. The gloriosa (11450 kg, 256 cm) in Erfurt Cathedral has a decay time of over 6 minutes after welding in 2004.
Each partial tone of a bell has its own value of the decay time, whereby the values usually decrease with increasing partial tone frequency. Because mixed tones already have weak amplitudes, they fade away quickly. The strong principal tones, on the other hand, linger for a long time. For new bells, the Limburg guidelines stipulate minimum values for the decay time of undertone, prime and third.
The measurement of the decay time can in principle not be an objective measurement, because the decay time depends on the strength of the attack, the distance between the listener and the bell and the abilities of his hearing.
Beats
It happens that a partial tone is split, so that two peaks are very close to each other in the spectrum, which leads to an audible beat . With principal tones, beats are more noticeable than with mixed tones. Whether a beat is perceived as disturbing or not depends on the amplitude of the partial tone, but above all on the beat frequency. Slow beats (below 5 Hz) do not sound unpleasant, but faster beats lead to a rough, stuttering sound that rattles with mixed tones. Split partials with their beats can be caused by two causes: On the one hand, the bell can be out of round, so that its lower edge or horizontal sections are not circular but rather slightly elliptical; on the other hand, an ornament (thick relief) applied to the flank of the bell can be caused. lead to local differences in mass distribution and bending stiffness. A prominent example of the latter case were the bells cast in 2002 for the Dresden Frauenkirche .
Structure-borne noise
When a bell hangs on a steel yoke in a steel chair, both the sound of the bell and the noise that occurs when the clapper is struck are transmitted to the bell cage and emitted by it. The sound can also be entered into the floor of the bell chamber and the adjacent masonry. Bells mounted in this way sound harder than bells that hang on wooden yokes in wooden chairs, so that today yokes and bell stalls made of wood are preferred.
Doppler effect
A vibrating bell is subject to the Doppler effect , so the pitch fluctuates depending on the speed of the bell. Therefore, the higher the ringing angle and the greater the distance between the yoke axis and the lower edge of the bell, the stronger the Doppler effect. Because this distance is significantly smaller with a cranked yoke than with suspension on a straight yoke, the Doppler effect has only a weak effect with cranked suspension. The Doppler effect is a desirable effect on bells because it brings the sound to life. That is why the cranked suspension of bells is avoided as much as possible nowadays.
Bell chamber
If the belfry is in a room, the bell house , the properties of this room also contribute to the sound of the bells . The bell chamber can amplify some partials through resonance through room modes . In addition, the properties of the surfaces delimiting the room (plastered or unplastered masonry, concrete, wood, glass) lead to reflections and attenuation of the sound, i.e. to a short reverberation and a slight low-pass effect. The fact that the pitch fluctuates due to the Doppler effect results in a further effect due to the sound reflections and delay times, which corresponds to the chorus effect known in sound engineering . The sound boards and lamellas possibly arranged in the sound outlet openings of the bell chamber hardly influence the sound due to the diffraction of the sound waves, but their respective design determines in which areas outside the bell chamber the direct sound emanating from the bells hits, so that the sound impression depends on Position of the listener can vary.
The synthetic sound of a bell shown here was generated purely by software. Amplitude fluctuations, Doppler and chorus effects were applied.
literature
- A. Weissenbäck, J. Pfundner: Tönendes Erz . Böhlau, Graz / Cologne 1961.
Individual evidence
- ↑ Gerhard Hoffs: Bell books of the Archdiocese of Cologne ( Memento of the original from May 10, 2013 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , Bell books of the Diocese of Aachen ( Memento of the original from May 17, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. , Bell books of the Diocese of Essen ( Memento of the original from May 17, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
- ↑ Jörg Wernisch: Investigations on church bells . Dissertation, Vienna 2004. ( online ; PDF; 14.0 MB)
- ↑ J. Bauer, L. Schmidt, B. Kotterba: Influence of the bell decorations on the sound of church bells . Karlsruhe 2004. ( online ; PDF; 1.3 MB) ( page no longer available , search in web archives )
- Advisory committee for the German bell system (Hrsg.): Contributions to bell technology . [Heidelberg] 1970.
- ↑ Walter Leib: The standard tuning tone and the bell measurement .
- ↑ Theo Fehn : The structure of the tone structure in its meaning for the sound quality of the bell .
- ↑ Hans Rolli : About the retuning of bells .
- ↑ Theo Fehn: Läute-Klang and Läute-Technik .
- Kurt Kramer, Advisory Committee for the German Bell System (Hrsg.): Bells in past and present . Contributions to bells, volume 1. Badenia, Karlsruhe 1986, ISBN 3-7617-0237-X / ISBN 3-7617-0238-8 .
- ↑ Johannes Schlick: The auditory assessment of the bell sound .
- ↑ Gerhard D. Wagner: Standardized poverty of the ringing sound .
- ^ Limburg guidelines .
- ↑ Theo Fehn, Volker Müller: The importance of clapper and intonation for the sound effect of the bell .
- ↑ Carl-Rainer Schad: Influences of materials on the sound properties of bells .
- ↑ Kurt Kramer : Basic concepts of tower room acoustics and sound radiation .
- Kurt Kramer, Advisory Committee for the German Bell System (Hrsg.): Bells in past and present . Contributions to the bells, volume 2. Badenia, Karlsruhe 1997, ISBN 3-7617-0341-4 .
- ^ Jobst Peter Fricke : Forms of oscillation of the bell .
- ^ Kurt Kramer, Wolfram Menschick , Gerhard Wagner: For naming the bell tones .
- ↑ Kurt Kramer: The prerequisites for a good sound development of the peal .