Bells

Bells have been put to much microtonal use over the years.

Bronze Age Chinese bell chimes

In Bronze Age China, bells were arranged into chimes (tuned sets of bells) and used to play ceremonial music. Bell chimes were often buried in tombs and are typically well preserved, so accurate tone measurements can be made on them today.

Figure 1: Histogram of A–B tone intervals in Bronze Age Chinese bells

The bells were made with an asymmetrical shape so that two notes could be produced by striking the bell at two different points – call these the A and B tones. The interval between the A and B tones is determined by the construction of the bell. It varied from anything between around a major second to around a perfect fourth. Figure 1 shows a histogram of the A–B tone intervals from a number of bells, adapted from Table 13 in Suspended Music.

The use of the A and B tones of multiple bells gives rise to a range of interesting scales for the full chime. For example, for the chime of three bells given as Zhuangbai Chime no. V in Suspended Music, we get the following six-note scale:

Bell	Tone	Pitch (cents)
1	A	0
1	B	303
2	A	484
2	B	820
3	A	861
3	B	1224

In this case the interval between the A and B tones is 303 cents for bell 1, 336 cents for bell 2, and 363 cents for bell 3.

By the end of the Bronze Age, bell chimes and use of the two-tone phenomenon had fallen out of use.

Bell tuning

Let us turn now to symmetrical Western bells. The spectrum of a bell is inharmonic. The following table, adapted from Bill Hibbert's Building a bell sound talk, gives the names for each partial along with their frequencies measured for a particular bell:

Name	Frequency (Hz)	Relationship to strike pitch
Hum	270.0	Octave below
Prime	540.0	Close to strike pitch
Tierce	649.5	Minor third above
Quint	805.0	Fifth above
Nominal	1078.5	Octave above

The strike pitch is the perceived fundamental pitch of the bell sound; it does not necessarily coincide with one of the partials, and varies from person to person, but is typically around an octave below the partial called the nominal.

The frequencies of the bell partials depend on the shape and profile of the bell. By design and subsequent adjustment by removing metal, the individual partials can be tuned. The technique of tuning the partials was discovered by the Hemony brothers and Jacob van Eyck in the 17th century, lost, and rediscovered in the 19th century by Taylors bell foundry and Canon Arthur Simpson (to shorten a long story).

While the tierce usually lies about a minor third above the prime, bells can be designed with other intervals for this partial. A carillon with neutral third partials was made in 1955 for the town hall of Zeist, in the Netherlands – a video of this carillon is available on YouTube. And at Deinze in Belgium there is a carillon of major third bells, which appears on the CD Landscapes: The Major-Third Carillon Of Deinze.

Australian Bell have made bells with a range of just intervals between their lower partials. You can see pictures and hear sound samples on the Australian Bell website.

Carillons

A carillon is a tuned set of bells played with a keyboard. Easley Blackwood wrote a Chaconne for carillon, a video of which is available on YouTube.

Until the 20th century, carillons were tuned in meantone temperament; they later used equal temperament. You can hear sound examples of a meantone carillon from Ghent, Belgium at Arranging for carillon, where there is also a nice interactive spectrogram.

Other temperaments were discussed and tried. In 1952 a carillon tuned to a 17-note scale was built for the city of Nieuwpoort, Belgium. There was also a tuning in which the minor third partial was tuned to the fundamental of the bell a minor third higher.

Modern developments

Harry Partch's Cloud-Chamber Bowls are, effectively, glass bells. More recently Meara O'Reilly has designed and used a set of 18 microtonal glass bells. There are some recordings of O'Reilly's bells available online.

Jonathan Harvey's 1980 Mortuos Plango, Vivos Voco is based on the partials of a bell at Winchester Cathedral, UK. There is a recording available on Bandcamp.

The Federation Bells are an installation of 39 inverted bells in Birrarung Marr, Melbourne, Australia. They are tuned to a 12-note 7-limit just scale. You can hear pieces played on the bells on SoundCloud. You can also submit pieces to be played on the bells.

Dongryul Lee has developed virtual bells with partials related by various just intervals approximated in 96TET.

The Phexioenesystems track Stepping stones (Hexany 1-3-9-13) (Pomonte, Italy) uses a field recording of church bells retuned to a hexany – it is available on Bandcamp.

Further reading

• Bianzhong (Wikipedia article)
• Video about the Wang Sungao bianzhong (YouTube)
• Percival Price, Bells and Man. Oxford University Press, 1983
• Luc Rombouts, Singing Bronze: A History of Carillon Music. Lipsius Leuven, 2014