The Sound of Bells

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What determines the quality of a peal of bells?

This section of the site considers the effect of bells rung together in a peal rather than singly, in English changes - with each bell striking a fixed interval, usually 200 to 250 mS, after the previous one. Peals of bells can sound very different in character, and the effect is influenced by many factors; the frequency and amplitude of the bells' partials, considered individually and as a group; how they are clappered; and rather critically, the building in which they are being rung. This section has been completely updated to reflect recent work.

Caution is warranted in this analysis for several reasons. First, the aesthetic effect of a peal of bells inside and outside the tower can depend as much on the tower construction and materials, layout of floors etc. as on characteristics of the bells themselves. Second, the appreciation of many ringers for a peal of bells can depend as much on their 'go' as their tuning. A peal of bells that lacks something in the tuning but which are mechanically in top condition and installed in an acoustically generous tower will be deservedly popular with ringers.

Quality in the sound of a peal of bells is to some extent a matter of taste. It is not possible to establish absolute standards, i.e. to say that all listeners will judge one peal of bells to be better than another. I used to think it was - but years of asking people of their opinion of particular peals of bells has convinced me otherwise. However, what is possible is to link particular types of sound to objective measurements. To do this requires listening to and analysing many peals of bells. Modern bells are produced to a formula, involving both bell profile and tuning, where each bell has hum, prime and nominal in perfect octaves. However, this does not always give a result which is generally liked, and there are many peals of bells not profiled and tuned in this way which are generally recognised as being worthy of recognition.

There is very much more to the sound of a bell than the frequencies of its partials. The sequence of events whereby the sound reaches the ear involves at least the following steps:

The very short period of time for which one bell sounds in changes before the next strikes is a big factor in our perception of bell quality, for two reasons:

There are a number of criteria related to the bells only which determine the quality of a peal of bells. They include:

If the above terms are not familiar and you need some background in bell tuning, I suggest you read the 'Sound of Bells' article on the Keltek Trust website, and How bells make their sound and some of the classic papers on this site.

To give examples of the various effects, on a later page is a set of recordings demonstrating many different tunings, for individual bells.

The test of quality of a peal of bells is the effect they create in the ear of the listener. Any judgments made from measurements of partial frequency and intensity are provisional until the various psycho-acoustic effects are taken into account. Here is a brief summary of the effects.

Pitch

Pitch - the note heard - is a very important attribute of a bell, because it determines whether it is in tune with its neighbours. The pitch of a bell is roughly half its nominal frequency, but the partials above the nominal affect the pitch as well. If they are sharper, the pitch is sharper, and vice versa. In special cases variations in pitch of up to 30 cents are possible because of this effect.

Pitch can be perceived in different ways. A casual listener hearing a bell for a brief instant (for example, in changes) will hear the virtual pitch influenced by several partials. A musically trained listener hearing a bell for an extended time (for example, chimed alone) may focus on a single partial - so called analytical hearing - and give it a different pitch.

Fletcher-Munson effects

The ear is differently sensitive to different frequencies. The plot below shows a typical equal-loudness curve, it shows the intensity required of a sound to appear equally loud at different frequencies. The vertical axis is logarithmic, and an increase of 3 decibels (dB) implies a doubling of intensity. A sound has to be 15 dB or 30 times more intense at 100 Hz as at 460 Hz to sound equally loud. The effect is to reduce considerably the effect on the ear of partials below 200 Hz, and accentuate those between 1500 and 5000 Hz.

Fletcher-Munson equal loudness curve

This affects our perception of a bell's pitch. Small bells are pitched by the hum, not nominal and upper partials, because these are too high to hear well. Big bells are pitched by partials higher than the nominal, the so-called secondary strike effect, often giving a pitch a third or fourth above the nominal, because the lower partials are hard to hear.

Ability to discriminate frequencies

The ear gets progressively poorer at discriminating frequencies as they get lower. This makes it difficult to identify the tuning of hums of bigger bells. The plot below are a typical set of 'just noticeable differences' - the interval between two tones which can just be recognised. The figures are an average, there are wide differences for different listeners.

Just-noticeable difference curve

At frequencies above a few hundred Herz, the typical listener can detect differences of 10 cents. This justifies the tuning tolerance used by the founders. At lower frequencies, it becomes increasing difficult to decide if an interval is in tune. The curve above shows the ability of an average listener to distinguish two tones close in frequency; if asked whether the low hum of a big bell is a pure octave, listeners are likely to be more tolerant even than the plot would suggest.

(The chart above was derived from figures originally published by Roederer.)

Quality of intervals

There is a large body of practice concerning the tuning of keyboard instruments - tuning in temperaments - which depends on the fact that strings and organ pipes have near-harmonic partials. This practice is not directly applicable to bell tuning because many of the key partials in a bell are inharmonic; differences in temperament are much less important in change ringing bells.

With this as background, each of the criteria listed above is discussed in more detail on the following pages:

Bell pitch

Prime tuning

Doublets

Hums, tierces and other partials

Relative partial intensity


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Last updated May 1, 2004. Site created by Bill Hibbert, Great Bookham, Surrey