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Church Bells
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:
Bell | Diameter | Note | Weight |
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.
Interval | Equal Temp. | Just Intonation | Kirnberger II | Kirnberger III |
Tenor-6th (Maj 3rd) | 400 | 386 | 386 | 386 |
5-3 (maj 3rd) | 400 | 386 | 397 | 391.5 |
4-2 (maj 3rd) | 400 | 386 | 386 | 391.5 |
7-5 (min 3rd) | 300 | 294 | 294 | 305 |
6-4 (min 3rd) | 300 | 316 | 316 | 310.5 |
3-Treble (min 3rd) | 300 | 316 | 305 | 310.5 |
8-4 (5th) | 700 | 702 | 702 | 696.5 |
7-3 (5th) | 700 | 691 | 702 | 696.5 |
6-2 (5th) | 700 | 702 | 702 | 702 |
5-Treble (5th) | 700 | 702 | 702 | 702 |
Tenor-3 (maj 6th) | 900 | 884 | 895 | 889.5 |
7-2 (maj 6th) | 900 | 884 | 884 | 895 |
6-Treble (min 6th) | 800 | 814 | 814 | 814 |
Example of the partial tones in an old style bell
Hum note | 139.5Hz | C#+11 |
2nd partial | 268.4 | C+44 |
Minor 3rd | 322.7 | E-37 |
5th | 411.6 | G#-15.5 |
Nominal | 537 | C+45 |
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. | Tenor | 7th | 6th | 5th | 4th | 3rd |
2nd | Treble |
Just Scale | 0 | 204 | 386 | 498 | 702 | 884
| 1088 | 1200 |
1 | D-46(0) | 204 | 399 | 515 | 710 | 907
| 1107 | 1223 |
2 | D+14(0) | 228 | 418 | 539 | 719 | 920
| 1148 | 1247 |
3 | D+42(0) | 201 | 402 | 508 | 710 | 918
| 1100 | 1249 |
4 | Eb+13(0) | 230 | 407 | 497 | 712 | 908
| 1121 | 1223 |
5 | E+10(0) | 190 | 428 | 503 | 691 | 885
| 1097 | 1243 |
6 | E+33(0) | 197 | 400 | 502 | 733 | 938
| 1127 | 1235 |
7 | F#-35(0) | 178 | 378 | 479 | 680 | 881
| 1061 | 1179 |
8 | F#-30(0) | 204 | 390 | 515 | 711 | 936
| 1123 | 1237 |
9 | F#-19(0) | 208 | 415 | 516 | 734 | 931
| 1140 | 1230 |
10 | G-27(0) | 222 | 441 | 562 | 742 | 913
| 1149 | 1230 |
11 | G-6(0) | 193 | 384 | 500 | 736 | 884
| 1126 | 1244 |
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. |
| Hum | 2nd Par. | 3rd | 5th | Nominal |
Nom. in cents | Nom. error |
Tenor | Received | +245 | +20 | +49 | -51 | E-2
| 0 | Datum |
| Tuned | +74 | +3 | +22 | -30 | E-27
| 0 | Datum |
7th | Rcd. | +76 | -36 | +30 | -79
| F#+16 | 218 | +25 |
| Tnd. | +65 | +1.5 | +35.5 | -64 | F#-34
| 193 | 0 |
6th | Rcd. | +54 | -36 | -4 | -16
| G#-4 | 398 | +12 |
| Tnd. | +58.5 | +1.5 | +5 | -22 | G#-41.5
| 385.5 | -0.5 |
5th | Rcd. | +124 | -83 | +30 | -79
| A+9 | 511 | +13 |
| Tnd. | +87.5 | -30.5 | +36.5 | -39 | A-29.5
| 497.5 | -0.5 |
4th | Rcd. | +142 | -28 | +27 | -31 | B-9
| 693 | -3.5 |
| Tnd. | +100.5 | -4 | +27 | -33.5 | B-31.5
| 695.5 | -1 |
3rd | Rcd. | +159 | -145 | +2 | +22 | C#+19
| 921 | +31 |
| Tnd. | +93 | -109 | -10.5 | +9.5 | C#-39
| 888 | -2 |
2nd | Rcd. | +88 | -91 | +10 | +17 | Eb+29
| 1131 | +43 |
| Tnd. | +80 | -17.5 | +10.5 | +2.5 | Eb-39.5
| 1087.5 | -0.5 |
Treble | Rcd. | +43 | -230 | -28 | +28 | E+15
| 1217 | +17 |
| Tnd. | +86 | -159 | -9.5 | -4.5 | E-27
| 1200 | 0 |
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 note | 130.8Hz | C+0 |
2nd partial | 261.6 | C+0 |
Minor 3rd | 313.92 | Eb+16 |
5th | 392.4 | G+2 |
Nominal | 523.2 | C+0 |
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.
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