The Sound of Bells

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Temperaments and nominal tuning – results of the experiment

Below are the results of an experiment conducted to investigate the audible effect of tuning peals of bells in different temperaments. Eight bell recordings were provided, four peals of twelve, and four peals of six. The four peals in each case were tuned in three different temperaments, with one repeated as a control. Ringers were asked (on various bell-ringing internet chat-groups and by email) to listen to the recordings and to attempt to distinguish between them. Two carilloneurs also responded. Details of the experiment and the recordings are available on another page.

Response to the experiments

So far, 25 people have responded to the experiment. The selection of people was of course not random; those who responded I assume had some interest in the subject and hoped that they would be able to distinguish the tunings. People were more successful in general in differentiating the sixes than the twelves, and more than one person commented that the twelve bell ringing was too quick for them to hear the differences clearly. The 12 bell ringing was at a peal speed of 3h30m, and with the benefit of hindsight a slightly more relaxed speed might have been better. I am very grateful to the respondents and thank them for participating.

Identifying the sound of a peal of bells as being in a particular temperament is not easy – it requires knowledge of and familiarity with the various tuning styles. Although I was interested in attempts to identify the temperaments, I was equally if not more interested in results from people who could tell the various tunings apart, but not necessarily ascribe a name to the tuning style, or who could not hear a difference. Several of the respondents expressed likes or dislikes between the various tunings – even if they could not identify them by name. With the benefit of hindsight all respondents should have been asked for their preference. After all, whatever the theory, bells are musical instruments, and people’s likes or dislikes are the ultimate decider.

The results to date are as follows:

. Twelves Sixes Total
Could hear no difference111021
Attempted to name the tuning styles6612
Correctly identified all tuning styles134
Spotted which peal was equal6511
Spotted which peals were the same6814
Preferred equal246
Preferred just10.51.5
Preferred meantone31.54.5
Disliked equal1.512.5
Disliked just235
Disliked meantone1.523.5

Fractional scores arise because some people expressed equal preferences for two tuning styles, or expressed a preference for one of a pair of recordings both tuned the same. Not all people attempted to identify both the twelves and the sixes, so the total of each column is not meaningful.

Tuning of the peals

The actual tuning of each peal was as follows:

The recordings were loosely based on a set of recordings of Worcester Cathedral originally taken by David Bagley.

Interpretation of results

Very few people were able to correctly identify all the tunings, and even people I know to have good knowledge had trouble with this. Only one person successfully identified all the twelves. However, a higher number of people were able to spot which peal was tuned equal, or identify which of the two peals was tuned the same for both the twelves and the sixes. So, for the twelves, 6 people (about a quarter of the total respondents) and for the sixes, 8 people (about a third of the respondents) could hear sufficient difference between the tunings to make some correct differentiation, even if they did not know which tuning was which.

The last six results are quite illuminating. Some, but by no means all, the respondents expressed preferences between the various bells. I have counted these likes and dislikes against the actual tuning, because often those expressing preferences wrongly identified the tunings! One respondent expressed distinct likes and dislikes between just, equal and meantone but appeared not to be able to distinguish the tunings in practice and I have discounted his results. There is a marginal leaning towards equal temperament, more in the sixes (where the differences were easier to hear) than the twelves. The aggregated likes and dislikes for the twelves and sixes are:

Tuning Prefer Dislike Difference
Equal62.53.5
Meantone4.53.51.0
Just1.55-3.5

The number of participants is low, and it would be a mistake to assign too much statistical significance to the figures. There was quite a difference in opinion between different respondents as to the qualities of the various tunings. However, there is an indication that equal temperament was preferred to just, with feelings about meantone being evenly divided.

Conclusions

The respondents to this experiment were self-selected, and were likely to be people who expected or hoped to hear differences between the tunings. Even in this population people struggled to identify the differences. One can surmise that in the total population of ringers, and in the general public, many or most people would fail to detect differences between the various tunings, and that differences in temperament in nominal tuning are not a major issue in people’s opinions as to the quality of a peal of bells.

In a keyboard instrument, the different tunings have different ‘colours’ or aural effects when played in different keys. These different effects are caused by interaction between the overtones of the notes (giving rise to differing degrees of beats) and by the wideness of various intervals. There is a considerable body of theory supporting and explaining the differences which are heard, relying to a very great extent on the fact that almost all non-percussion instruments have harmonic upper partials.

None of this theory is applicable to bells, because they have quite inharmonic upper partials, even if the lower partials are tuned ‘true-harmonic’. Also, the compromises needed in keyboard tuning (which give rise to the requirement for temperaments) are driven by the need to play in different keys, which is not an issue in change-ringing.

Rather than try to explain the observations (in particular the slight preference for equal temperament) from the theoretical basis used to justify this tuning in keyboard instruments, I think it is more likely that people were responding to the various interval widths based on pitch memory. We live in an equal-tempered world (some would say, more’s the pity!), and people’s pitch memory, the capability which allows them to say that individual notes in a melody are ‘in’ or ‘out’ of tune, is something they have learned from repeated exposure to music in equal temperament. Many of the people who participated in the experiment, who were able to differentiate between the tunings, did so by listening to the different interval widths at the various points in the scale and relating them to their knowledge of the various tunings.

The assertion that pitch memory and familiarity with equal temperament dominates many people’s reactions to the various tunings ought to be verified with more experiments on a bigger sample of experimentees. But I think most ringers would echo Mrs Munt and say, "Of course I do not go in for being musical. But still I will say this for myself - I do know when I like a thing and when I don't". And for most of them, temperament is not a critical issue.


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Last updated September 19, 2002. Site created by Bill Hibbert, Great Bookham, Surrey