# Bell rib

The bell rib is the vertical section (longitudinal section) of a bell that shows the course of the wall from the lowest edge ( sharpness ) to the hood . Since bells rotating body (except some Far Eastern bells), extends the half cut in order to determine the shape of the bell. This is given by rotating the rib around the vertical central axis of the bell. This is used in bell casting to produce the mold using a rotating template of the rib.

The rib determines the sound behavior of the bell. The structure of the partial tone in particular only depends on the rib, while its pitch ( strike tone ) and the decay time of the strike and partials are influenced by the material of the bell. Every bell foundry therefore has one or more rib shapes of its own, which are kept as a trade secret.

## Structure of the bell rib

The rib includes the following sections:

• The brass knuckles are the lowest part of the bell, where it has its greatest wall thickness, which is called the strike . When the bell rings, the clapper must strike right here. The lower edge of the bell is called sharpness . This is where the bell has its largest diameter.
• The mantle begins above the brass knuckles with the inwardly curving Wolm , which merges upwards into the almost vertical flank . The shoulder is the uppermost part of the coat at the transition to the hood.
• The hood is the uppermost part of the bell and consists of the flat top plate and the slightly inclined lower plate .

The crown of the bell is not part of the rib. It sits on the top plate and is used to hang the bell. The crown has no significant influence on the sound behavior of the bell.

On the underside of the top plate is the suspension for the clapper .

The following dimensions are essential for the construction of the bell rib:

• The lower diameter or sharpness diameter at the sharpness of the bell. Since this is the largest diameter of the bell, it is also simply called the diameter .
• The height of the bell to the hood, i.e. without the crown.
• The oblique height measured from the sharpness to the shoulder.
• The brass knuckle thickness , i.e. the wall thickness of the bell at the thickest point, the brass knuckle.
• The neck diameter , usually measured as the inside dimension below the shoulder.

The knuckle thickness is also used as a unit for relative dimensions and is then referred to as the impact . For example, the sharpness diameter of a bell can be 14 beat or the inclined height 10 beat.

## Rib shapes

Lullus bell (1038) in beehive shape
Elfuhr bell (1221) of the parish church of Ober-Mockstadt in the shape of a sugar loaf
Gothic Salvator bell (1505) by Gerhard van Wou in the Utrecht Cathedral
Woman of twelve (1752) of the parish church in Tulln in a typical baroque rib
The Peter Bell (1923)
The Pummerin (1951)

### Historical development of the bell ribs

Today's bell rib has only developed gradually over the centuries. The most important development steps for bell casting in Europe are the following forms:

#### Beehive bells

Beehive bells represent the oldest rib shape, which was in use between the 8th and 12th centuries. It is characterized by a compact bell body, a weak knuckle-box, slight curvature and a rounded hood. The top diameter at the shoulder is relatively large. These bells are usually very thin-walled and the wall thickness for all parts of the rib is almost the same, only in younger specimens the brass knuckles are somewhat thickened. As a rule, beehive bells do not have a clear strike tone due to their inharmonious partial tone structure .

Significant examples: Canino's bell in Italy from the 9th century with a diameter of 390 mm is the oldest known beehive bell. It is on display in the Vatican Museums . The Haithabu bell (around 950) is the oldest completely preserved chime north of the Alps. It was discovered in 1978 and is now in the Viking Museum in Haithabu. The Lullus bell in the Bad Hersfeld monastery ruins was cast in 1038. The Kunigunden bell in Bamberg Cathedral (cast around 1185) is the largest preserved beehive bell weighing around 3450 kg. Only the latter two are still rung regularly.

#### Sugar loaf bells

Sugar loaf bells originated in the 12th century and were in use in Central Europe until the beginning of the 14th century, and longer in southwestern Europe. It is characterized by an extremely elongated, slim, conical bell body with a domed hood and a sweeping brass knuckles. The height of the bell is significantly larger than its diameter, the upper diameter at the shoulder is relatively small. These bells are often quite thick-walled. The strike tone is usually only weakly pronounced and can be split into 2 tones, the partial tone structure shows deepened undertones and primes. Significant examples include the Arnoldus bell from Gilching (cast around 1180), the death bell in Konstanz Minster (cast around 1200), or the storm bell in Limburg an der Lahn Cathedral (cast around 1225).

#### Transitional forms

From the late 12th century onwards, various further developments of existing forms emerged: compact transitional forms from the beehive bells, elongated transitional forms from the sugar loaf bells. These transitional forms are usually thicker-walled and more curved than their predecessors and have a more pronounced brass knuckles. In terms of sound, they are better than the older forms and usually have a clearly pronounced strike tone . The Clinsa in Merseburg Cathedral (cast around 1180) is an example of the compact, the Hosanna in Freiburg Minster (cast in 1258) is an example of the elongated transitional form.

#### Gothic rib

The Gothic rib was created around 1200, largely replaced all older forms in the 13th century, and was used until the 16th century. In the 20th century it served - especially the famous Erfurt Gloriosa by Gerhard van Wou (1497) - as a model for modern bell ribs of the present. The well-proportioned, moderately curved, flowing shape without edges on brass knuckles and shoulders is characteristic. The brass knuckles are low but massive, the hood is slightly arched. The upper diameter at the shoulder is a little more than half the lower, the height without the crown a little less than the diameter. Historical bells in Gothic ribs are usually very thick-walled ( heavy ribs ), with the rib thickness decreasing over time. In terms of sound, a fundamental change took place with the Gothic rib, because for the first time the bell now had a clear strike tone and the partial tone structure of lower octave (sometimes deepened), prime, minor third, fifth, octave etc., which is still required today , bells in Gothic rib sound usually soft and full. The oldest known example of such a minor octave bell is the St. Martin's Peace Bell in the parish church of St. Martin am Ybbsfelde , cast in 1200 by an unknown master. Many famous bells are cast in Gothic ribs, e.g. B. Le Bourdon in Strasbourg Cathedral (cast in 1427), Pretiosa (1448) and Speciosa (1449) in Cologne Cathedral , the Gloriosa in Erfurt Cathedral (cast in 1497), the Sigismund Bell in Wawel Cathedral in Warsaw (cast in 1520) Etc.

#### Secondary ribs

From the 16th century various secondary ribs developed from the Gothic rib, all of which are still similar to the medieval shape, but differ from it in certain details. Artistic reasons seem to have caused this development, because the tonal differences to the Gothic rib are slight. Depending on the cultural area , a distinction is made between French , English and Dutch ribs , which are still in use today, as well as the Mannerist rib in the German cultural area , which was only in use for a short time.

#### French rib

Bells in French rib were made by traveling founders, e.g. B. from Lorraine , widespread in a large part of Central Europe in the 17th century. The traveling founders moved from place to place in search of orders and often cast bells for several neighboring places in simple circumstances, especially after losses in the Thirty Years' War . Antonius Paris , for example, worked predominantly in Germany , while Claudius, Alexander and Nikolaus Arnold as well as Stefen Bruncler and Johannes Arnolt poured bells in southern Hesse , Bavaria , especially Baden-Württemberg and occasionally in Austria and Switzerland . The partial tone structure of the French rib can come very close to the Gothic rib, but light ribs with a modified, often increased prime are typical.

#### Baroque rib

The baroque rib is only found in the German cultural area, where it replaced the Mannerist rib in the 16th century, and was used until the 20th century. Characteristic is the compact bell body with strong curves and the high, massive brass knuckles accentuated by a kink. Compared to the Gothic and Mannerist ribs, baroque bells are usually constructed a little lower, the rib thickness is usually in the middle. The sound is usually very powerful and full, sometimes a bit tart or tinny. In the partial tone structure , the undertone is usually too high ( seventh type or also sixth type ), the prime often too low. Significant examples include the complete bells of Melk Abbey (cast in 1739) and of the Weimar City Palace (cast in 1712), as well as the bell canopy of Salem (cast 1754-58), which today is only partially located in the Salem Minster ( the large Herrgottsbell, for example, was sold to the Reformed Church in Herisau ).

#### Modern ribs

Modern ribs emerged from around 1850 as new developments or modifications of existing ribs in order to achieve an optimal sound. They are mainly used in the German cultural area, while they are rare in those countries where secondary ribs are still predominant. The Gothic rib was often used as a model, mostly the Erfurt Gloriosa . Baroque ribs were also modified in such a way that the optimal partial tone structure ( octave bell ) was achieved, while the powerful sound of a baroque bell is retained, for example by Andreas Hamm . A French rib was used by Rincker until the late 19th century . Famous examples, both based on the Erfurt Gloriosa , are the Gloriosa in Frankfurt Cathedral (cast in 1878) and the second largest free-swinging church bell in the world, the Petersglocke in Cologne Cathedral (cast in 1923). The Pummerin in St. Stephen's Cathedral in Vienna, on the other hand, has a modified baroque rib.

### Bell type

Bells and their ribs are divided into different types based on the partial structure . The interval between the striking sound and the undertone of the bell is used for this. The third also plays a role in the classification.

#### Octave bells

The undertone is an octave below the strike note . Another distinction is made depending on the position of the partial third

• Minor Oktavglocken : the partial tone third is a small third above the percussive
• Major Oktavglocken : the partial tone third is a large third above the percussive

This type of bell is required by modern bells. Mostly minor octave bells are cast, major octave bells only for special tonal situations. Bells in a Gothic rib are usually also minor octave bells.

#### Nongbells

The undertone is a ninth below the strike note . This type of bell occurs more frequently , especially with bells with a Gothic rib .

#### Septim bells

The undertone is a major or minor seventh below the strike note . This type of bell occurs more frequently , especially with bells in baroque ribs .

#### Sixth bells

The undertone is a major or minor sixth below the strike note . Steel bells mostly belong to this type, but it also occurs in bells with a baroque rib .

### Rib thickness

The rib thickness is a measure of the thickness of the rib, i.e. the relative wall thickness of the bell, based on its diameter. It can be determined using the following formula from the diameter (in cm), the strike frequency (in Hz) and a material-dependent correction factor : ${\ displaystyle dm}$ ${\ displaystyle f}$${\ displaystyle I}$

${\ displaystyle RS = {\ frac {dm \ cdot f \ cdot I} {387 {,} 5}} - 100}$

The correction factor for bells made of tin bronze is 1, for special bronze 0.95 and for cast steel 0.65. Based on this RS value, the following classification can be made: ${\ displaystyle I}$

• Very light rib: RS under −6
• Slight rib: RS in the range −6 to 0
• Middle rib: RS in the range 0 to 6
• Heavy rib: RS in the 6 to 12 area
• Very heavy rib: RS over 12

The Limburg guidelines from 1951, an agreement between the Advisory Committee for the German Bell System and the Association of German Bell Founders , define the rib thickness via the bell weight. There, the following minimum weights are defined to delimit the individual rib designations for a c 1 bell made of tin bronze:

• Heavy rib: at least 2,600 kg
• Medium weight rib: at least 2,100 kg
• Light rib: at least 1,700 kg

The minimum weights for bells with other pitches can be determined using the law of proportionality . However, this classification according to bell weight has the disadvantage compared to the RS classification that factors that influence the weight of the bell but are irrelevant for the rib thickness falsify the result (e.g. height of the bell, design of the crown). Bells in baroque ribs, for example, tend to be classified as having too light ribs, as their height and thus their weight are lower than other ribs with the same wall thickness. In general, the Limburg guidelines are only intended for the evaluation of newly cast bells, so their application to older bell types is questionable.

### Ribs for steel bells

The partial tone structure of a bell is only determined by its rib, not by the material. Steel bells would therefore have the same sound pattern as bronze bells in the same rib - but about a fifth higher. The reason for this is that the speed of sound in cast steel with 5,150 m / s is around half higher than that in bronze with 3,350 m / s. Therefore ribs for steel bells were developed, which are much thinner-walled than those for bronze bells, as this lowers the pitch. Even so, steel bells are usually slightly larger than bronze bells at the same pitch.

## Influence of the rib on the pitch

### Influencing factors

The pitch of a bell depends on 2 factors, which are determined by the bell rib: diameter and rib thickness , as the wall thickness of the bell rib is called.

• A bell sounds the deeper the larger its diameter.
• With the same diameter, the lower the rib thickness, the deeper the bell sounds.

With the same tone, heavy-ribbed bells have a larger diameter than light-ribbed bells.

The material of the bell also affects the pitch. For example, steel bells with the same rib would need about one and a half times the diameter of bronze bells of the same pitch. Therefore, special ribs for steel bells were developed, which are much thinner-walled than ribs for bronze bells, in order to lower the pitch.

### Law of proportionality

Bells of different sizes have the same rib if all dimensions are in the same proportion to each other at any point on the two bells. So scaling up or down does not change the rib, it is only determined by its shape.

Bells of different sizes, which are cast in the same rib and made of the same material, have the same sound image (with very different pitches, however, the auditory impression may differ slightly due to the different sensitivity of the hearing for different frequencies).

The law of proportionality describes the relationship between diameter and pitch for bells of the same rib and material:

The frequency of a bell is inversely proportional to its diameter.

The frequency ratio of two bells 1 and 2 is therefore dependent on their diameter

${\ displaystyle {\ frac {f_ {1}} {f_ {2}}} = {\ frac {dm_ {2}} {dm_ {1}}}}$

The weight, or more precisely the mass, increases with the volume of the bell. Since the proportions are the same in all three dimensions with the same rib, the mass can be described as follows for the same material:

The mass of a bell is proportional to the cube of its diameter, or inversely proportional to the cube of its frequency.

The mass ratio of two bells 1 and 2 is therefore:

${\ displaystyle {\ frac {m_ {1}} {m_ {2}}} = \ left ({\ frac {dm_ {1}} {dm_ {2}}} \ right) ^ {3} = \ left ( {\ frac {f_ {2}} {f_ {1}}} \ right) ^ {3}}$

With the help of the law of proportionality, it is possible for the bell founder to calculate the required size of a bell for a certain pitch in advance and to coordinate several bells in a targeted manner.

The following table shows the size and mass ratios according to the law of proportionality for some intervals :

 interval Frequency ratio (lower: upper tone) Size ratio (diameter and all other dimensions) Mass / weight ratio pure octave ${\ displaystyle 1: 2}$ ${\ displaystyle 2: 1}$ ${\ displaystyle 8: 1}$ perfect fifth ${\ displaystyle 2: 3}$ ${\ displaystyle 3: 2 = 1 {,} 5}$ ${\ displaystyle 27: 8 = 3 {,} 375}$ Semitone ( equal tuning ) ${\ displaystyle 1: {\ sqrt [{12}] {2}}}$ ${\ displaystyle {\ sqrt [{12}] {2}}: 1 \ approx 1 {,} 0595}$ ${\ displaystyle {\ sqrt [{4}] {2}}: 1 \ approx 1 {,} 189}$ Whole tone ( equal tuning ) ${\ displaystyle 1: {\ sqrt [{6}] {2}}}$ ${\ displaystyle {\ sqrt [{6}] {2}}: 1 \ approx 1 {,} 1225}$ ${\ displaystyle {\ sqrt {2}}: 1 \ approx 1 {,} 4142}$

## Influence of the rib on the sound

### Influence on the bell type

The influence of the bell rib on the partial tone structure and thus the bell type is based on two essential factors: the curvature of the wolf and the proportions of the bell shape (lower diameter on the brass knuckles , upper diameter on the shoulder, height without crown). The following fundamental principles can be determined, which were also checked using the finite element method :

• The undertone is all the higher:
• the more the wolm is curved inwards with the same upper and lower diameter and the same height,
• the greater the height without the crown compared to the diameter, and
• the smaller the upper diameter is compared to the lower diameter.
• The prime is influenced by the same factors, but behaves in exactly the opposite way: if the undertone rises, the prime falls.

Strongly curved bells such as B. Baroque bells are therefore mostly septum bells and have recessed primes.

Other partials are also influenced by the rib, for example by the inclination and strength of the striking ring.

### Influence on the sound quality

Together with the material, the rib affects the sound quality of the bell. The main influencing factors of the rib are:

• The decay time of the strike tone increases with the strength of the ribs as well as with a relative increase in the upper diameter of the shoulder. However, not all partials of the bell are affected to the same extent by these factors, because there are no effects for the undertone, prime and third (these three partials are not involved in the formation of the strike). In addition to the rib, a good material quality is essential for a long decay time.
• More flowing ribs, low brass knuckles and heavy ribs favor a soft and fundamental sound.
• The volume of the bell increases with its size and rib thickness .

## Voices of bells

Bells can be tuned by changing their ribs again after casting. This is done by grinding the bell in certain areas in a rotationally symmetrical manner around the bell casing, for example using a special lathe . Most of the time, the inner wall is sanded down so as not to affect the decorations on the outer wall.

For reasons of monument protection, historical bells should not be retuned or changed in sound.

### Tuning the pitch

Tune the striking tone lower by grinding the inside of the striking ring and is possible to the extent of a whole tone and more. Tuning up is done by grinding the sharpness and is only possible to a minimal extent. Together with the strike note, the octave part also changes . Since the structure of the partial tone altogether changes when the pitch is tuned, this must also be corrected.

### Tuning the partials

When tuning the partial tone structure , the intervals for the partial tones undertone , prime , third and fifth are tuned in relation to the strike note. For each of these partials one can localize a certain area of ​​the bell. If you grind the bell in this area, then the partial tone changes the most, but other partial tones are usually also affected. Tuning the partials is only possible to a small extent.