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← Older revision		Revision as of 17:23, 21 June 2026
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	intervals approximated in 96TET.<ref name="lee2020thousand" />		intervals approximated in 96TET.<ref name="lee2020thousand" />

	The Phexioenesystems track ''Stepping stones (Hexany 1-3-9-13) (Pomonte,		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
	Italy)'' uses a field recording of church bells retuned to a [[hexany]] — it is
	[https://citiesandmemory.bandcamp.com/track/stepping-stones-hexany-1-3-9-13-pomonte-italy available on Bandcamp].		[https://citiesandmemory.bandcamp.com/track/stepping-stones-hexany-1-3-9-13-pomonte-italy available on Bandcamp].

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'''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.<ref name="vonfalkenhausen1993suspended" /> Bell
chimes were often buried in tombs and are typically well preserved, so accurate
tone measurements can be made on them today.

[[File:Bell-a-b-tone-histogram.svg|thumb|600px|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.<ref name="rossing1989acoustics" /> 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''.<ref name="vonfalkenhausen1993suspended" />

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:

{| class="wikitable"
! 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 ''[https://www.hibberts.co.uk/building-a-bell-sound/ Building a bell sound]''
talk, gives the names for each partial along with their frequencies measured
for a particular bell:<ref name="hibbert2021building" />

{| class="wikitable"
! 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
doesn't 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.<ref name="hibbert2008quantification" />

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).<ref name="hibbert2021building" />

While the tierce usually lies about a minor third above the prime, bells can be
designed with other intervals for this partial.<ref name="lehr1987designing" />
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
[https://www.youtube.com/watch?v=GAOPW57fqsk available on YouTube].
And at Deinze in Belgium there is a carillon of major third bells, which
appears on the CD
[https://www.discogs.com/release/11365394-Aimé-Lombaert-Symphonic-Band-Of-The-Belgian-Guides-François-De-Ridder-Landscapes-The-Major-Third-C 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
[https://www.ausbell.com.au/polytone.html 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
[https://www.youtube.com/watch?v=aufLDe1fWNk available on YouTube].

Until the 20th century, carillons were tuned in meantone temperament; they
later used equal temperament.<ref name="swager1993history" /> You can hear
sound examples of a meantone carillon from Ghent, Belgium at
[https://arrangingforcarillon.com/lessons/carillon/sound/ Arranging for carillon],
where there is also a nice
[https://arrangingforcarillon.com/spectrogram/ 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.<ref name="swager1993history" />
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.<ref name="oreillybells" />
There are some [https://mearaoreilly.com/Glass-Bell-Music 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
[https://icstzurich.bandcamp.com/track/jonathan-harvey-mortuos-plango-vivos-voco-1980 available on Bandcamp].

The Federation Bells are an installation of 39 inverted bells in Birrarung
Marr, Melbourne, Australia.<ref name="federationbells" /> They are tuned to a
12-note 7-limit just scale. You can hear pieces played on the bells
[https://soundcloud.com/fedbells on SoundCloud]. You can also
[https://www.melbourne.vic.gov.au/composing-bells submit pieces] to be played
on the bells.

Dongryul Lee has developed virtual bells with partials related by various just
intervals approximated in 96TET.<ref name="lee2020thousand" />

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
[https://citiesandmemory.bandcamp.com/track/stepping-stones-hexany-1-3-9-13-pomonte-italy available on Bandcamp].

== References ==
<references>
<ref name="vonfalkenhausen1993suspended">
Lothar Von Falkenhausen, ''Suspended Music: Chime-Bells in the Culture of Bronze Age China''. Univ of California Press, 1993.
</ref>
<ref name="rossing1989acoustics">
Thomas D. Rossing, [https://www.jstage.jst.go.jp/article/ast1980/10/5/10_5_241/_pdf Acoustics of Eastern and Western bells, old and new]. Journal of the Acoustical Society of Japan (E) 10.5 (1989): 241-252.
</ref>
<ref name="hibbert2021building">
Bill Hibbert, [https://www.hibberts.co.uk/building-a-bell-sound/ Building a bell sound], 2021
</ref>
<ref name="hibbert2008quantification">
William A. Hibbert, [https://www.hibberts.co.uk/wp-content/uploads/2021/12/wah_thesis_18_4_08.pdf The Quantification of Strike Pitch and Pitch Shifts in Church Bells]. The Open University, 2008.
</ref>
<ref name="lehr1987designing">
André Lehr, [https://campaners.com/pdf/pdf2572.pdf The designing of swinging bells and carillon bells in the past and present], Athanasius Kircher Foundation, 1987
</ref>
<ref name="swager1993history">
Brian Swager, [https://www.allegrofuoco.com/media/SWAGER.I.U.Document.1993.pdf A history of the carillon: Its origins, development, and evolution as a musical instrument]. Indiana University, 1993.
</ref>
<ref name="oreillybells">
Meara O’Reilly, [https://mearaoreilly.com/Glass-Bells Glass Bells].
</ref>
<ref name="lee2020thousand">
Dongryul Lee, [https://www.ideals.illinois.edu/items/116053 A Thousand Bells: Acoustical implementation of bell spectra using the finite element method and its compositional realization], University of Illinois at Urbana-Champaign, 2020
</ref>
<ref name="federationbells">
Australian Bell, [https://www.ausbell.com.au/federation_bells.html Federation Bells]
</ref>
</references>

== Further reading ==
* [https://en.wikipedia.org/wiki/Bianzhong Bianzhong] (Wikipedia)
* [https://www.youtube.com/watch?v=l-pXu3Ly-TU Video about the Wang Sungao bianzhong] (YouTube)
* Percival Price, [https://archive.org/details/bellsman00pric/ Bells and Man]. Oxford University Press, 1983
* Luc Rombouts, [https://www.bruna.nl/images/active/InkijkPDF/eboekhuis/9789461661814.pdf Singing Bronze: A History of Carillon Music]. Lipsius Leuven, 2014

[[Category:Instruments]]

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