Long-waisted bells

From time to time I analyse the partials of long-waisted bells. In the UK, bells with this shape are typically from the 12th century or earlier. Their partials have a different relationship to those of bells with normal, more recent shape, and Wavanal does not detect them automatically. Prompted by a visit to St Botolph’s, Hardham, Sussex where the older bell may be pre-conquest, I have looked afresh at the partials of a number of long-waisted bells. The insights gained may help others who investigate recordings of such bells.

The bells are as follows:

Leighton BuzzardLeighton Buzzard sanctus, date around 1250, weight around 80kg, diameter 0.48m. Youtube recording by George Vant.Myndtown, ShropshireMyndtown, Shropshire, date around 1150, diameter 0.37m. Recording provided by George Dawson.
HardhamHardham, dated by George Elphick to 1050, diameter 0.41m. Section taken from Elphick’s Church Bells of Sussex page 6. Recording by me.Auckland CastleAuckland Castle, dated 1180, diameter 0.71m. Photo courtesy of Taylor’s Bellfoundry. Recording provided by George Dawson.
HarescombeHarescombe, Gloucestershire, dated circa 1199, weight 50kg, diameter 0.45m. Photograph taken from page 359 of Bliss and Sharpe’s Church Bells of Gloucestershire. Youtube recording by Ringer Mikey.HognastonHognaston, Derbyshire, date unknown, diameter 0.38m. Photograph taken from page 141 of Church Bells of Derbyshire, recording from Nick Bowden.
LlanelieuLlanelieu, Powys, date around 1300, diameter 0.43m. Photograph page 60 of John Eisel’s Church Bells of Breconshire, recording from Andrew Deamer. There is also an older bell in this church, but no recording of it.RibbesfordRibbesford, Worcestershire, date circa 1150, diameter circa 0.5m (the bell is not circular). Recording and picture from Chris Pickford. The picture is upside down, the bell was ‘up’ when it was taken.
WarminghurstWarminghurst, Sussex, dated circa 1200, diameter 0.46m. Section taken from Elphick’s Church Bells of Sussex page 6. Recording by me.CoombesCoombes, Sussex, dated circa 1150, diameter 0.40m. Section taken from Elphick’s Church Bells of Sussex page 6. Recording by me.

The partial frequencies of these bells are as follows:

Harescombe420.0-2727757.5-17061174.0-947  2029.52985.06684041.51193
Hognaston *450.0-28981034.0-14581210.4-11851800.0-4982400.038688265300.01372
Leighton Buzzard460.5-2653898.5-14961224.0-961  2132.03191.56984345.51233
Ribbesford *353.0-2746789.0-1354897.5-11311027.5-8961724.52608.07163795.01366

The intervals in cents of all the partials in this table are given relative to the nominal of the bell. The recordings for the bells marked * (Hognaston and Ribbesford) are poor and the identification of the partials a little uncertain. Some partial frequencies for the Harescombe bell are given on page 360 of Church Bells of Gloucestershire but I do not think they are correct.

A bell with a modern profile would have hum, prime and tierce intervals to the nominal broadly as hum: -2400 cents, prime: -1200 cents and tierce: -900 cents. So the effect of the long waist is to significantly lower these partials relative to the nominal. The superquint and octave nominal, on the other hand, are not exceptional. The interval of the superquint and octave nominal relative to the nominal is dominated by the shape and thickness of the rim or soundbow. As these bells have a thickened soundbow, the upper partials have the normal relationship with the nominal. This relationship was used when analysing these bells to confirm that the nominal was identified correctly.

As a practical guide to the difficulty in assigning names to the partials of bells like these, here are spectra of two bells:

The partials are named in each case with their initial letter. In the spectrum of the Leighton Buzzard bell, it would be tempting to assign the partial immediately above the quint as the nominal. However this gives no reasonable candidates for the superquint, octave nominal and higher frequency rim partials. With the nominal finally chosen, the spacing of the rim partials is conventional which is plausible given the well-developed soundbows in these bells. There are three partials between the quint and the partial selected as nominal. In a bell of normal profile, these three partials are generated in the waist, not the rim, and would be higher in frequency and appear between nominal and superquint. In these bells, it is plausible that the long waist has lowered the frequency of the partials.

The bell at Coombes is muffled (with cloth wrapped round the clapper) and even ringing the bell energetically didn’t stimulate the upper rim partials significantly. With this bell, it would be tempting to assign the partial at around 2000Hz as the nominal, but comparing the spectrum with that of Leighton Buzzard, again there are three partials between the quint and the partial I assigned as the nominal. With this choice of nominal, there are candidates for the superquint and octave nominal which give conventional spacing, but they are very quiet because of the muffling.

Because these bells are small with high frequency partials, the pitch is set by the hum, not the nominal, so it is not possible to use an estimation of pitch (as was done for tubular bells) to identify the nominal.

It was illuminating to compare the partial frequencies of these bells. Bells like these have been difficult to analyse, but once the common pattern of the lower partials became clear, it became obvious how to assign the partials for each. Final confirmation of the assignment of partials would require physical access to a long waisted bell to allow counting of nodes and antinodes around the rim for each partial. The nominal is the rim partial with 8 nodes and antinodes around the circumference of the bell.