Church Bells

A bell being tested with tuning forks and a stop watch

Bells have existed for thousands of years, but the profile of bells made in the western world did not evolve until the early 14th century. The tradition of "change-ringing" in Britain began in the 17th century, whilst in the rest of europe, small numbers of bells were hung for swinging, and in the low countries, sets of bells hung stationary for tune playing became popular, and is still as popular today. A chime of bells may consist of a set of 8 bells in the diatonic scale (having no accidentals or chromatic semitones), or a chime may consist of say 21 bells with several chromatic semitones. A carillon consists of not less than 2 full chromatic octaves (23 bells). Some carillons have over 5 octaves, Wellington, N.Z., New York and Chicago have carillons of 6 octaves. Bells hung for change-ringing are nearly always tuned in the major diatonic scale, and additional semitone bells are comparitively rare, except in the case of rings of 12, the majority having at least 1 additional semitone, in order that a lighter diatonic octave may be rung. This is particularly useful if the bells are heavy; many rings of 12 have tenor bells of over 1.5 tonnes. If the tenor is in the key of "C", a sharp 2nd bell (F#) enables a lighter octve in the major scale to be rung, with a tenor of just over 0.5 tonnes.

Until the invention of the calibrated tuning fork and vertical boring lathe (tuning machine), it was totally impracticable to tune the harmonic tones of a bell accurately. Unlike almost all other musical instruments, bells do not produce natural pure harmonics (or "partials"), as these are a direct function of profile and thickness. The availability of the two above named inventions enabled the process of tuning the strike note to be carried out neatly and accurately. Hitherto, the process of flattening the strike note had entailed chipping the inside of the bell around its soundbow, employing a chipping hammer or a hammer and chisel. If the strike note was flat, the lip of the bell was chipped away in order to raise it. Whilst the other harmonics were known of and even had names, there was no means of recording them or controlling their relationship. The exception was the Dutch bell foundry of Francois and Pierre Hemony, which in the 17th century developed a profile that produced an octave hum note and octave fundamental. They had a treadle lathe for turning small bells, and a capstan lathe for machining large bells. This foundry understood the principles of correct partial tones, and did in fact often achieve them. The bells were tuned to chime bars, and perhaps some of the relationships were based on tuning bells to the partial tones of other bells within the set.

Unfortunately, when the Hemony brothers died, their skill died also. It was not until the 1890’s that musical “experts” in England began to pressurise the bell foundries to perfect harmonic tuning, on the basis that Victorian bells were generally, poorer than English bells cast two centuries earlier.

Until the 17th century, few churches had more than four bells. These rarely formed a scale; this was of little consequence as each bell was used for a specific purpose, such as the curfew, sanctus, or tolling for the dead. Little, if any attempt was made to tune additional bells to sound in tune with existing ones. In the mid-17th century, English change-ringing was beginning to develop, and with it the demand for greater numbers of bells in a set. For change-ringing to make any sense, clearly the bells must form a recognisable scale. Bells were added to existing rings, and often, badly out of tune bells were recast or tuned. But, how were bells tuned? It is generally considered that when musical diatonic intervals are tuned by ear, the natural tendancy is towards just intervals. However, if we are familiar with a given temperament, our ears become accustomed to that tuning, and this must influence the way in which we perceive musical intervals as being in or out of tune. For instance, let us say that all the music we listened to was in 1/3rd comma mean tone, although this is an extreme form of tempering, if we listened to this tuning all the time, our ears would soon become used to its mainly flat intervals. If we were to attempt to tune a diatonic scale purely by ear, we would naturally aim for these intervals, because they would sound in tune to us.

Bellfounders would ideally cast a bell or ring of bells in tune. Unfortunately, there are several variables which affect the cast pitch of a bell: metal temperature; alloy; accuracy in closing the two halves of the mould together. All these can and do affect the pitch of a bell. A moulding gauge or "profile" can be used repeatedly to produce the moulds, but each casting will have small differences in pitch, and if the outer mould is positioned incorrectly to the inner mould, the resultant bell can be eccentric, with one side thicker than the other; or the casting as a whole may be thicker and therefore sharper; or thinner and therefore flatter. When a bellfounder cast a new ring of bells, after the bells had been extracted from their moulds and cleaned, they would be inverted and sounded. The founder/tuner would establish which bell or bells were the flattest. If two or more bells sounded reasonably in tune when rung together, they would be left as cast and were called: "maidens". The bells that were sharp of the untuned bells were flattened by chipping metal away from the section where the clapper strikes, called the soundbow. Removing metal from this area of the bell flattens the nominal or "tap note", and consequently the perceived strike note, which corresponds to one half the frequency of the nominal. If the bell sounded flat, its nominal could be raised, or sharpened by chipping away metal from the rim or lip. On the continent, some of the carillon builders such as the Hemony brothers, used tuned bars with which they could align the nominal, octave hum and 2nd partial with reasonable accuracy. In England, it is unlikely that the bellfounders of the 17th and 18th centuries used bars or simple tuning forks: they almost certainly relied solely on the accuracy of their ears.

Most "old style" rings were cast when the majority of church organs were tuned to 1/4 or 1/5th comma mean tone. In Britain, the "well-tempered" tunings began to supercede mean tone tunings in the concert hall, and in the music rooms of the wealthy, during the 1730's. Unless a bellfounder was wealthy, or circulated amongst high society, it is unlikely that he would have heard well-tempered tuning: he would have been familiar with mean tone tuning; this would have influenced his ears, and consequently, his perception of what constituted an acceptable interval. However, tuning by hand was a crude, laborious and inexact task. With only their ears to guide them, the bellfounders would carry out the absolute minimum of hand chipping in order to produce a tolerable diatonic scale. Often, they succeeded inspite of the odds.

How the pitches of a bell and a ring of bells are determined

The main partial tones of a modern bell are the hum note; 2nd partial or fundamental; minor 3rd (tierce); 5th (quint); nominal. The hum note is the lowest note (unlike other instruments where the fundamental is the lowest); the 2nd partial is an octave above the hum note. Above the 2nd partial are the 3rd and 5th, with the nominal an octave above the 2nd partial. The strike note of a bell is an aural perception, and not a measurable partial, although the "strike note" corresponds to 1/2 the nominal frequency. As an example, let us consider the tuning of a new ring of eight in the key of "A". If we are using international standard pitch, the basis is on A=440 cycles per second or A+0 cents. As the tenor is note A, the strike note (1/2 the nominal) will be 440 c.p.s.. The calculated "tune to" figures for the tenor will be:

Hum note 220 c.p.s. A+0 cents
2nd partial Hum X2=440 A+0
Minor 3rd Nom/10X6=528 C+16 ( calculation ratio varies depending on temperament)
5th Hum X3=660 G+2 (but varies with temperament)
Nominal Hum X4=880 A+0

Typically, a modern bell sounding "A" above middle C will be 35-36 inches (889-914 m.m.) in diameter, and will weigh 8 to 9 hundredweights (406 to 457 kgs). Once we have determined the size and pitch of the tenor bell, we can calculate the sizes, weights and pitches of the other seven bells. If the tenor is 35" diameter, the scale of thickness (the ratio of the thickness at the soundbow to the diameter) will be approximately 1/15th. The smallest bell will sound one octave higher, so that the hum note of the treble will be 440 c.p.s. and the strike note 880 c.p.s.. If we were to make the treble to the same proportions as the tenor, the diameter of the treble will be 17 1/2 inches diameter and weigh just over 1 hundredweight (444 m.m., 52 kgs). The treble would sound rather weak and thin, even if used within a chime where the bells are hung stationary and struck by hammers. For a change-ringing peal, the treble would be wholly inadequate, as its sound would be overpowered by the larger bells, and it would turn very much faster than the larger bells, thus making it difficult to ring accurately. For a chime, the proportions of the smaller bells have to be scaled up so that the treble is around 19-20 inches and weighs 1.5-1.75 cwts. (483-508 m.m., 76-89 kgs). For a change-ringing bell, the proportions have to be scaled up significantly; typically to around 23 inches and weighing just over 3 cwts (584 m.m., 155 kgs.). The sizes and weights for a typical modern ring of 8 bells would be as follows:

Tenor 35" 889m.m.A 8-0-0 406kgs.
7th 32" 813m.m.B 6-1-0 317.6kgs.
6th 29" 737m.m. C# 4-3-0 241.4kgs
5th 27 1/2" 698m.m. D 4-0-0 203.3kgs
4th 26" 660m.m. E 3-2-21 184.4kgs
3rd 24 1/2" 622m.m. F# 3-1-21 174.7kgs
2nd 23 1/2" 597m.m. G# 3-0-21 162kgs
Treble 23" 584m.m. A 3-0-0 152.5kgs

Having determined the sizes and weights of the ring, and also the tuning figures of the tenor and treble, it then remains to calculate the figures for the other bells. You could use equal temperament, in which case the tones will each be 200 cents apart and the semitones 100 cents. An octave consists of 1200 cents, and the 12 chromatic notes of the equally tempered scale are all 100 cent values. If equal temperament is used, the cent values and strike note frequencies would be:

Tenor A+0 (0 cents) 440.0c.p.s.
7th B+0 (200) 493.9
6th C#+0 (400) 554.4
5th D+0 (500) 587.3
4th E+0 (700) 659.26
3rd F#+0 (900) 740.0
2nd G#+0 (1100) 830.6
Treble A+0 (1200) 880.0

The disadvantage of using equal temperament for rings of bells is that it produces a pure but rather "bland" key character, and for what is usually a single key instrument, the intervals are unneccesarily compromised. The system works well enough in rounds (descending the scale from smallest to largest), except that the semitone intervals sound and are narrower than they need be. The treble in rings of 6 tuned in equal temperament is and sounds rather sharp. The most noticeable differences in the intervals becomes apparent when the bells are rung in changes. The obvious intervals are those relating to the tenor bell which is the key note. There are a number of more subtle internal intervals which also affect the overall character. There are many other options for how to calculate the intervals to produce a more satisfying sound. If we were to use a well-tempered tuning, for example Kirnberger III, the cents and strike note frequencies would be:

Tenor A+0 (0 cents) 440.0c.p.s.
7th B-7 (193) 491.9
6th C#-14 (386) 550
5th D-2 (498) 586.7
4th E-3.5 (696.5) 658
3rd F#-10.5 (889.5) 735.6
2nd G#-12 (1088) 825
Treble A+0 (1200) 880.0

A diatonic ring of 8 contains 3 minor and 3 major 3rd intervals; 4 fifths; and 2 major and 1 minor sixth. The following table shows the interval values for intervals encountered whilst ringing changes on a ring of 8. The values are shown as the number of cents between the strike notes of the paired bells using 4 well known temperaments. A pure minor 3rd is 316 cents; a pure major 3rd 386; a pure (perfect) 5th is 702; a minor 6th is 814 and a major 6th is 884.

IntervalEqual Temp.Just IntonationKirnberger IIKirnberger III
Tenor-6th (Maj 3rd)400386386386
5-3 (maj 3rd)400386397391.5
4-2 (maj 3rd)400386386391.5
7-5 (min 3rd)300294294305
6-4 (min 3rd)300316316310.5
3-Treble (min 3rd)300316305310.5
8-4 (5th)700702702696.5
7-3 (5th)700691702696.5
6-2 (5th)700702702702
5-Treble (5th)700702702702
Tenor-3 (maj 6th)900884895889.5
7-2 (maj 6th)900884884895
6-Treble (min 6th)800814814814

Example of the partial tones in an old style bell

Hum note139.5Hz C#+11
2nd partial268.4 C+44
Minor 3rd322.7 E-37

The following table gives the intervals of a number of rings of eight cast in the 18th, 19th, and early 20th centuries. With one exception, all the rings are "stretched": the trebles being well sharp of the octave. There is clearly a tendancy for the intervals to become progressively sharper as the scale ascends. Examples 4, 5 and 6 are rings cast in the latter half of the 18th century. Example 5 shows relatively well aligned nominals, apart from the 6th and treble. The 6th in this example is not the original, having been recast in 1902 by Bond of Burford. He left this bell well sharp, and aurally, it was unsatisfactory. What is readily apparent is that the tuning in the 18th century is no less accurate than in the late 19th.

Examples of intervals from 18th and 19th century rings of eight before tuning

Intervals in cents
Ex No.Tenor7th6th5th4th3rd 2ndTreble
Just Scale0204386498702884 10881200
1D-46(0)204399515710907 11071223
2D+14(0)228418539719920 11481247
3D+42(0)201402508710918 11001249
4Eb+13(0)230407497712908 11211223
5E+10(0)190428503691885 10971243
6E+33(0)197400502733938 11271235
7F#-35(0)178378479680881 10611179
8F#-30(0)204390515711936 11231237
9F#-19(0)208415516734931 11401230
10G-27(0)222441562742913 11491230
11G-6(0)193384500736884 11261244

Until bell founders began to aquire calibrated tuning forks, the reliance of tuning accuracy was placed almost entirely on the ear. Bells were not cast to specific pitches, although the more intelligent bell founders probably considered the relative inaccuracies within the strike notes in commas and parts of a comma.

The old bellfounders were aware of the harmonic tones that bells produced, but were unable to control them. The tuning machine enabled tuning to be carried out neatly, and at the Whitechapel Bellfoundry, individual sets of tuning forks were used to tune a set of bells. The practice was to cast a new ring of bells, invert them so that they could be sounded; listen carefully to establish which bell (or bells) were the flattest; make up a set of forks, to tune the bells which required tuning, leaving the flattest bell(s) untuned. This is how things were to remain until the company aquired a set of calibrated tuning forks, which at a stroke, enabled the strike notes to be aligned accurately, and for the harmonics of the bell to be also recorded. This in turn led to experimental cutting, and the subsequent development of a new profile, enabling bells to be tuned harmonically.

The following table shows the values of the partial tones of a ring of eight bells, before and after tuning. This ring consists of 17th, 18th and 19th century castings. The values are relative to a modern bell with an octave hum note (0) and octave 2nd partial(0). The minor 3rds are related to +10.5 (e.g. if the nominal is E-27 the 3rd should be G-16.5). Note that the tenor bell had a very sharp hum note; the hum notes of the other larger bells were not flattened to octaves, in order to maintain a reasonable balance.

Intervals in cents
Bell No.
Hum2nd Par.3rd5thNominal Nom. in centsNom. error
TenorReceived+245+20+49-51E-2 0Datum

Tuned+74+3+22-30E-27 0Datum
7thRcd.+76-36+30-79 F#+16218+25

Tnd.+65+1.5+35.5-64F#-34 1930
6thRcd.+54-36-4-16 G#-4398+12

Tnd.+58.5+1.5+5-22G#-41.5 385.5-0.5
5thRcd.+124-83+30-79 A+9511+13

Tnd.+87.5-30.5+36.5-39A-29.5 497.5-0.5
4thRcd.+142-28+27-31B-9 693-3.5

Tnd.+100.5-4+27-33.5B-31.5 695.5-1
3rdRcd.+159-145+2+22C#+19 921+31

Tnd.+93-109-10.5+9.5C#-39 888-2
2ndRcd.+88-91+10+17Eb+29 1131+43

Tnd.+80-17.5+10.5+2.5Eb-39.5 1087.5-0.5
TrebleRcd.+43-230-28+28E+15 1217+17

Tnd.+86-159-9.5-4.5E-27 12000

The partials of a modern harmonically tuned bell, to some extent follow the natural harmonic series: the main difference being that bells produce a minor rather than a major 3rd . The five principle harmonic tones are, assuming a bell with a strike note of middle C, tuned "just", and to the pitch standard of A=440 Hz.

Hum note130.8Hz C+0
2nd partial261.6 C+0
Minor 3rd313.92 Eb+16

The company of John Taylor and co. in Loughborough were the first to perfect harmonic tuning; obtaining new vertical boring machines (tuning machines) and calibrated tuning forks, they began to experiment with profiles and cutting different areas within the inner profile to establish how the partial tones could be adjusted. By 1896, they were supplying complete rings of bells tuned on the harmonic principle. The calculations were based on just values, although in practice, the minor 3rds(tierces) and 5ths(quints) varied in accuracy. Gillett and Johnston of Croydon perfected harmonic tuning in 1907. John Warner and Son of London, Charles Carr and Co. of Smethwick (who also made tuning forks) and Llewellin’s and James of Bristol also attempted to tune bells on the harmonic principle, with varying degrees of success. All however worked to just values.

Initially, Taylor’s used Just Intonation but appear to have adopted an unequal temperament tuning before adopting equal temperament prior to the First World War. However, the remaining companies, including, The Whitechapel Bell foundry (which began to produce harmonically tuned bells in the 1920’s), continued using just intonation. With the demise of Warner’s and Carr’s, this left Gillett and Johnston, Taylor’s and Whitechapel as the principle British bell foundries. Gillett and Johnston built a large number of carillons, using equal temperament strike notes, but employing just values for the harmonics. Unlike Taylor and Whitechapel bells which have basically equal temperament 3rds, the bells cast and tuned at Croydon have just 3rds. They also produced a number of bells with the 3rds slightly flat of a major 3rd. However, they ceased using the profiles that produced these bells circa 1924. Only where there were additional semitones, did they use equal temperament for change ringing peals, except for a period in the late 1920's and early 30's when they adopted equal temperament as a standard tuning.

Whitechapel continued to use just values for ringing peals until 1969. The advent of the 12 disc chromatic stroboscopic tuner, which gives readings in notes and cents, coupled with the fact that equal temperament was in general use, both for pop and classical music, and therefore the public had become familiar with its sharp intervals, resulted, after some years of consideration, in the adoption of equal temperament. This was applied to old bells sent to the foundry for tuning, and new bells. Like Gillett and Johnston and Taylor’s, Whitechapel had employed equal tuning for chromatic chimes and carillons, since adopting harmonic tuning. An interesting exception to this is at Fenham, near Newcastle; Whitechapel supplied a ring of 8 in 1930 tuned just. A year later an order was placed for additional chiming bell trebles and semitones, also tuned just.

Most rings of bells are single key instruments, although there are a number of rings of 12, which have additional semitone bell(s). Commonly used is the flat 6th or sharp 2nd. If for example, we have a ring in the key of C, the flat 6th is Bb and enables a diatonic ring of 8 to be used in the key of F (the 9th being the tenor); a #2nd (note F#) enables a ring of 8 in the key of G to be used. If the ring is tuned to just intervals, these key changes result in the 3rd of the ring of 8 in F (4th of 12) being 22 cents sharp; the ring in the key of G has one bell 22 cents flat: the 7th (also 7th of 12), which is a minor tone 10/9. However, these errors are not severe and the overall perceived result is satisfactory. The intonation for the rest of the intervals is perfect in both cases. Indeed, such rings do exist: examples being Great Yarmouth, Croydon and Halifax; all having flat 6th’s. By using unequal temperament, "middle" and "front" eights do not sound out of tune, but will differ in key character from the back eight.

At Whitechapel, equal temperament is still used for the tuning of musical handbells, unless a customer specifies a different temperament. Kirnberger III has become the standard tuning for new rings of tower bells, and this tuning is sometimes used for the tuning of old rings of bells, other tunings: Werckmeister III, Bach, 1/4c. mean tone, and occasionally Young or Vallotti are also used.