In Situ Acoustic Analysis of Two Twentieth-Century Heritage Carillons
Orr Herit Sci (2021) 9:16 https://doi.org/10.1186/s40494-021-00482-8
RESEARCH ARTICLE Open Access In situ acoustic analysis of two twentieth‑century heritage carillons Scott Allan Orr*
Abstract Carillons are a diverse and global form of musical and civic heritage: musical instruments comprised of a series of 23 or more bells, typically hung in a tower-like structure, tuned chromatically and played from a touch-sensitive manual and pedal console using an elaborate mechanical action. Carillon bells have a distinct series of musical overtones which should be accurately tuned to one another and with other bells they sound alongside. Although these over- tones have been previously studied ex situ, this study assesses the acoustic characteristics of two early-twentieth century carillons in Toronto, Canada as a combination of structure, bells, and mechanical action. Thus, the instrument and its context are considered holistically, more accurately refecting the musical sensitivity of a carillonist. Spectral analysis of audio samples of each bell at diferent musical dynamic levels enabled the analysis of the acoustic qualities of the bells and the mechanical action of the instruments. The tuning of bells in the instruments varied; most impor- tantly, there was a signifcant diference between the audial intensity of the bell tones produced by the instruments, demonstrating the importance of the mechanical action as part of the ‘carillon system’. This was represented with a resistive power-law model, that represents the sensitivity of intensity to carillonist musical dynamic level. A discussion of the implications for artistic and heritage practice follows. Understanding the in situ physical acoustics of the carillon as a holistic instrument in its context informs performers, arrangers, and composers of how they can best embrace the instrument’s unique qualities to improve artistic pursuits and support the appreciation of carillons as heritage instruments and function as civic voices. Keywords: Musical heritage, Bells, Bell tuning, Historic instruments
Introduction Many carillons are important heritage landmarks and A carillon (derived from the French; Dutch: beiaard; are an integral part of local community identity and German: glokenspiel) is “a series of at least 23 tuned culture. In the Low Countries where the instrument bells, played from a keyboard that allows expressiveness originated, 56 belfries of Belgium and France have been through variation in touch” [1] that may be transposed. collectively inscribed as a World Heritage Site since 1999 A standard carillon generally includes four chromatic (expanded in 2005) [2]. Teir outstanding universal value octaves (about 49 bells), which vary in weight from many is derived from their representation of the winning of tonnes to a few kilograms. Te bells are operated from a civic liberties and testimony to a range of architectural console comprised of a series of wooden keys (‘batons’), styles prevalent from the eleventh to seventeenth cen- arranged over two rows in a typical keyboard confgu- turies. Te instruments and their towers have become ration, and a pedalboard that doubles up the control of a strong component of regional cultural identity. More some of the largest bells (typically one and half to two recently, under the Convention for the Safeguarding octaves). of the Intangible Cultural Heritage [3] there has been a programme to safeguard the carillon culture that exists *Correspondence: [email protected] in seventy-six cities and villages of Belgium and in thirty Institute for Sustainable Heritage, University College London, 14 Upper countries worldwide [4]. In the twenty-frst century, Woburn Pl, London WC1H 0NN, UK
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carillons have become strong voices for fostering equal- Gerken provides excellent examples of thinning out ity, diversity, and inclusion in communities [5]. texture while retaining harmonic structure [18] for While the structures in which the instruments are arrangement and transcription purposes. On the whole, housed present complex challenges to heritage manage- these guides are based on experiential practice of play- ment, additional challenges are posed by the nature of ing the carillon and composing and arranging music for carillons as mechanical instruments. Although no robust the instrument. study has been undertaken, formal and informal protec- Tis lack of literature is—in part—due to a lack of sci- tion is generally given to the bells within the instrument. entifc documentation on in situ acoustics of carillon Due to this, many carillons dating from the seventeenth bells. Te authoritative texts on carillon bell acoustics to twentieth centuries are still comprised of several of were undertaken in isolated conditions and utilise stand- the bells originally installed in the instruments. Over the ardised mechanical strikes to initiate sound [19–21]. Tis course of the twentieth century several technical inno- is strikingly diferent to the informed touch of the experi- vations improved the control a carillonist had over the enced carillonist, who adapts the input force depending musical capabilities of the instruments. Tese were pri- on the response from the weight of a clapper to produce marily improvements in the mechanical action and fab- a balanced sound landscape. Tus, the perceivable acous- rication techniques for bells that expanded the typical tic character of bells in the instrument is diferent in situ range of the instruments compared to their historical than in controlled experimental conditions. One excep- precedents during earlier centuries. Due to this, mechan- tion is [22], who characterise modal frequency, exponen- ical actions of carillon instruments have frequently been tial decay rate, and initial complex amplitude from audio upgraded and replaced with little care of their potential samples taken in situ; it is notable that the decay rates are heritage value. Research on preserving original integrity analysed in the context of the non-neglible ambient noise and material of carillons is typically limited to the bells of the campus environment. However, these samples do themselves [6]. Tus, material value is ascribed to only not represent the dynamic musical input of a carillonist. part of the instrument. Instead, emphasis is placed on Although bellfounding has incorporated technolo- the intangible heritage value and role of the carillon as gies as they have become available (such as 3D scan- an instrument with a civic voice, which necessitates the ning [23]), it still incorporates elements of a traditional technical improvements of the instrument to enable a craft. Each carillon bell cast—especially those fabricated modern standard of artistic performance. While the pres- prior to electronic frequency analysers—possesses a ervation of material authenticity has been discussed in unique sound colour based on the balance of the frequen- depth by restorers of other instruments (e.g. organs [7]), cies produced and their relative intensities. In contrast to and many challenges have been identifed for heritage the landmark work published by Lehr in 1951 [24] that instruments more broadly [8], discussion about the con- focuses on seventeenth-century instruments, this study servation and restoration of heritage carillons has been analyses twentieth-century instruments founded with very limited. modern techniques. Notably, these instruments were Composing and arranging musical compositions for tuned with a mechanical lathe but without electronic the carillon is complicated by: analysis. Tis study investigates the physical attributes of two • a lack of damping mechanisms, heritage carillons in Toronto, Canada, and subsequently • extended, but varied sound decay periods, applies spectral analysis to analyse the in situ frequency • the complex, prominent overtones associated with and sound intensity of the fve primary overtones at dif- each bell. ferent musical dynamic levels. Testing the acoustic char- acteristics of the bells in situ means that the transmission Many introductory guides have been published to system (the mechanical action) is considered as an inte- encourage and aid composers interested in the instru- gral component of the instrument, which can greatly ment [9–12] and more recently [13], although these impact its musical capabilities. Tis study identifes focus on the physical limitations of the player and the characteristics that are relevant to carillon performance mechanism and do not provide detailed information on and composition by analysing the sounds produced by the overtones (referred to as partials) and sound decay the bells from within the belfry. In contrast with estab- rates/periods. Tose that do mention partials [14, 15] lished methods in the feld that remove the bells from the do not elaborate beyond the prominent minor third, tower structures and analyse them in acoustic isolation, except for the video component of the former and this method thus employs an innovative approach by one that discusses the frst 7 partials [16]. Tere have analysing the carillon as a composite musical instrument also been unpublished lectures on the topic (e.g. [17]). comprised of its structure, a set of bells, and mechanical Orr Herit Sci (2021) 9:16 Page 3 of 15
action, in the context of its common role as both tangible clapper δ1 and the bell δ2 , the clapper parameters: radius, heritage and civic voice. r, mass m, and impact velocity v. 3/5 1/2 6/5 Carillon characteristics m r v F ≈ 0.44 sin(πt/τH ) (1) Mechanism δ1 + δ2 Te carillon console is comprised of a single manual of where δi = f (Ei, µi) , and τH is the contact time wooden batons [25] with pedals located at foot-level of = f (δ1,2, m, r, v). the console, which approximately double the lowest two Separating the amplitude and temporal components of octaves of the manuals. Te manuals are generally played this relationship, at the point of maximum bell defection by striking the baton with a closed fst. Te consider- able weight of the larger clappers (the size of which vary m3/5r1/2v6/5 Fmax ≈ 0.44 (2) according to the size of the respective bell) means agile δ1 + δ2 playing within this part of the instrument is executed more easily with the pedals rather than the manual, due for any given bell in a carillon with known dimensions to the increase in available inertia from the weight of the (and assuming negligible changes in m, r, and δi due to leg. Clapper weights, relative to the mass of the associ- the efects of weather or oxidation), we can then directly ated bells, difer greatly between sources—most likely relate the force and the overall sound decay ( sin(πt/τH ) ) due to foundry practices and instrument variations ([26], to the velocity of the strike force with a constant propor- p. 112) ([27], p. 46) [28]. tionality coefcient, ie. Te transmission wires extend through the foor and m3/5r1/2 ceiling of the playing cabin or space. A common type F ∝ F ≈ 0.44 v6/5 player max δ + δ (3) of connection between the transmission lines and the 1 2 clapper wires in twentieth-century instruments is a Tis means that, for each bell, the force exerted by strik- transmission bar ([27], p. 81–83): a long metal cylinder ing of the clapper is only dependent on the velocity of the that rotates axially that can pull a clapper wire located baton strike by the player. in a remote horizontal position of the belfry. Depress- ing a baton puts this system into action, which bring Acoustic characteristics of bells the clapper into contact with the interior rim of the bell. When struck by its clapper, a bell is distorted and then Crucially, the dimensions of connections between the vibrates in a complex manner [31]. Te vibration can be console can vary for sets of bells, or for each bell indi- described as the combination of several ‘modes’ of vibra- vidually. Each clapper is also equipped with a sensitive tion around a number of stationary lines around the adjuster that modifes the wire length between baton and circumference of the bell (‘nodal meridians’) and along clapper to accommodate for changes in the dimensions the length of the body (‘nodal circles’). Te observed of the metal components due to changes in temperature. frequencies (also referred to as partials) are normally To control the force with which the clapper comes into grouped into families based on similar properties. Te contact with the bell, carillonists develop a technique to relative prominence of a partial is dependent on the loca- ‘prepare’ a note: sufcient force is applied to depress the tion and other details of the clapper strike. Te most key to a certain depth such that the the clapper does not important families of partials are those with an antinode make contact with the bell. From this position the per- (places where the bell wall vibrates at a maximum) near- former determines the volume of the bell strike by vary- est to the clapper strike [32]. Te frst fve modes of a bell ing a torque-like fick of the wrist or ankle. Depressing are often referred to by descriptive/colloquial names, and the respective appendage results in a very dull, soft tone, fall within two families: while a quick action transmits greater speed and force to the clapper to produce louder dynamics. • those in Group 1 (the hum, the tierce, and the nomi- Te time-dependent force exerted by the clapper on nal) with an antinode near to the sound bow, and the bell can be represented by a sphere impacting a very • those in Group 2 (the fundamental and the quint) massive plate [29, 30]. Te force gradient is dependent on 1 2 with an antinode near the waist of the bell as a result the Poisson’s ratios ( µ ) and Young’s moduli (E) of the of the entire bell’s vibration.
1 Te ratio of transverse contraction strain to longitudinal extension strain in Te number and location of these modes for the frst fve the direction of stretching force. partials of a tuned European bell are presented in Table 1. 2 Measure of the stifness of an elastic material; obtainable from the slope of the linear portion of a stress-strain curve. Orr Herit Sci (2021) 9:16 Page 4 of 15
Table 1 Characteristics of the modes of the primary with a volume comparable to mid-range bells of larger partials within a well-tuned European bell [33] size. Te following formula can be used to relate various Name Number of nodal Number dimensions of a bell [37]: meridians and position 4 of nodal M = cfD (4) circles
Hum 4 0 where the mass M in kg (without a canon or any attach- ment pieces) is dependent on a profle constant c in kg s Fundamental 4 1 (between −4 the rim and m , the fundamental frequency f in Hz, and the external the waist) diameter D in m. A higher constant indicates a heavier Tierce 6 1 (in waist) profle. Quint 6 1 (near rim) Due to the aforementioned inversely proportional Nominal 8 1 (in waist) relationship between the dimensions of similar-shaped bodies (e.g. bells with typical European profles) and fre- quencies produced, another parameter used to discuss −1 the proportions of bells is the fD value in m s [38, 39]: the product of fundamental frequency and diameter, an indicator of wall thickness. A higher fD value indicators a thicker wall.
Methods Analysed carillons Te two carillons studied are located in Toronto, Canada Fig. 1 Comparison of overtone series. The tuned carillon bell would be notated by the fundamental tone, C 4 . a The natural harmonic and are carillons typical of the musical range and weight series, b a tuned carillon bell, c an untuned bell for North American instruments incorporating twentieth century bells and mechanical actions.
Soldiers’ Tower Memorial Carillon, University of Toronto A comparison of these partials in a tuned and untuned Soldiers’ Tower was constructed in the 1920s as a memo- bell to the natural harmonic series is presented in Fig. 1. rial to the members of the University of Toronto com- Unlike those of many instruments which are integer munity who fought and gave their lives in the First World multiples of the fundamental tone, the most prominent War. Te original instrument incorporated 23 original overtones (‘partials’) of a well-tuned bell in equal tem- bells from the English frm Gillett & Johnston (G&J) in perament are 1:2:2.378:2.997:4 [34] (although most com- 1927 ([40], p. 271). Te carillon was dedicated at a cer- monly rounded to 1:2:2.4:3:4 [35, 36]). Carillon bells are emony coinciding with the University’s centenary ([41], musically notated by their fundamental. p. 20). An additional nineteen bells cast by the American foundry Van Bergen were purchased in the 1950s, but the Physical proportions tuning of these newer bells did not match the original For similar-shaped bodies (i.e. bells with similar pro- English bells, and were sold of to interested alumni. 28 fles) made of the same material, the frequencies of cor- replacement bells were later ordered from the Dutch frm responding modes of vibration are inversely proportional Petit & Fritsen (P&F), and the composite 51-bell carillon to the dimensions. A bell with twice the diameter of was rededicated in 1976. Since its an inauguration, the another should produce tones at half the frequencies (a carillon has been an integral component of signifcant musical octave below) of those produced by the smaller events in the University’s academic calendar, including bell, while weighing eight times as much. Tis relation- the annual Remembrance Day Memorial service and con- ship was defned as the ‘Line of Absolute Musical Propor- vocation (graduation) ceremonies. tion’ [19]. What was observed in the work of the Hemony Te tower was designed in a neo-gothic style and rises brothers (whose instruments were the pinnacle of bell- to a height of 142 feet. Te belfry is enclosed on all four founding in the seventeenth century) was a deviation sides by thick stone walls, with screened openings repre- from the linear trend in the high treble bells: this was a senting approximately 35% of the total vertical surface of compensation technique for weak audibility of smaller the enclosure (Fig. 2a). bells within the instrument. By increasing the wall thick- ness of the bell, decreasing height and diameter, and care- fully tuning, a bell could produce the desired frequency Orr Herit Sci (2021) 9:16 Page 5 of 15
Fig. 2 External façades of the two carillon towers investigated. a Soldiers’ Tower that houses the carillon, as seen from Hart House Circle. “Soldiers’ Tower 2007” by V. Samarin is licensed under CC BY 3.0 (https://commons.wikimedia.org/wiki/File:Soldiers_Tower_2007.jpg). b The carillon tower of Metropolitan United Church, as seen from Queen St E
Massey/Drury Memorial Carillon, Metropolitan United unconventional system is thought to be less sensitive Church than the transmission bar confguration more com- Te tower of the Metropolitan United Church housed monly employed in modern instruments, such as in the frst instrument of bells installed in North America Soldiers’ Tower. that adhered to the modern-day defnition of a carillon: 23 Gillett & Johnston bells were purchased by Chester D. Sampling Massey and installed in 1922, although the tower dates Recordings were taken on weekend afternoons to mini- back to 1872 [42]. Tese bells were tuned to A432, a ref- mise the efect of urban noise pollution caused by higher erence frequency that Gillett & Johnston employed for weekday vehicle trafc. Tis issue was most evident at the ‘heavy’ carillons; lighter instruments were tuned higher Metropolitan site, where the tower is located approxi- than A440 [43]. Te initial expansion added 12 bells mately 100 m from a major intersection with high rates founded by Petit & Fritsen that chromatically extended up from the highest original bell; these bells used A435 as a reference frequency. Te fnal addition were 19 bells extending in a similar fashion cast by the French frm Paccard in 1971 that were tuned to match the reference tone of the original 23 bells, to form the 54-bell instru- ment currently housed in the tower. Te instrument transposes down 3 semitones. Te tower is constructed of large stone masonry units, and includes an entrance hall for the church at ground level, a playing cabin beneath the belfry, and access to the latter elements. At 36%, the belfry has a similar per- centage of open space to that of Soldiers’ Tower, but the panels are covered by wooden louvers, which are slats intended to keep the elements out and direct sound downwards to ground level (Fig. 2b). At the time of data collection, the pedals were con- Fig. 3 The pedal board of the carillon at the Metropolitan United Church, which has an irregular connection of guiding roller wheels to nected to the manuals with a non-traditional tensile connect the pedals to the keyboard batons string-based mechanism, guided by rollers (Fig. 3). Tis Orr Herit Sci (2021) 9:16 Page 6 of 15
of vehicle trafc, in addition to streetcars that contribute Audio signal analysis signifcant noise pollution. Soldiers’ Tower is much more Te recorded samples varied in duration from approxi- isolated and less susceptible to interference from vehicle mately 3 to 28 s. A Discrete Fourier Transform was trafc. applied over the duration of each sample, resulting in frequency resolutions from 0.0359 to 0.3139 Hz for the Player input largest and smallest bells, respectively. Tis approach enabled a high sensitivity for partials with especially Te carillonist was instructed to adapt their style of play- low frequencies (prevalent in larger bells that were ing to the instruments, based on their experience with recorded for longer durations) while minimising the the varying weights and bells of each carillon. Tree potential impact of ambient noise and other interfer- dynamic levels were tested on each bell: pp, mf, and f. ence on the spectra of smaller bells with more rapid Tese dynamics should be played at a force appropriate sound decay. for the weight and frequency of each bell, based on expe- A two-stage peak detection algorithm was rience and personal preference that ensures evenness of implemented: input across all instruments. Bells below E 4 (4 semitones above ‘middle C’) were played with the pedals, as is com- • Stage 1: Identifying peaks within the practical range mon practice in carillon performance technique. of the instrument. 3000 frequency peaks between 0 and 12 kHz; this upper bound was truncated from Recording the detectable range (22.05 kHz) based on the high- Te pre-amp (485B36, PCB Piezoronics; Depew, NY), est expected partial with an allowance for upper was connected to a personal laptop computer which deviation. accepted the microphone input via a 2.5 mm to 3.5 mm • Stage 2: Identifying the frst fve partials for each stereo jack adaptor. Te microphone (377B02, PCB Pie- bell. Selecting the most intense peak within zoronics; Depew, NY) was suspended from a boomstand ± 200 cents (¢) of the theoretical frequencies for at a height of 1 m above the foor at a fxed point within each partial, equivalent to a frequency ratio (F.R.) the belfry, and angled down slightly. Although these range ± 0.122, or 2 musical semitones in equal measurements were taken in the belfry, a fxed meas- temperament. urement point is more closely aligned with the auditory experience of a listener at a fxed point further away. Te Te measured frequency of each partial was compared sound meter was elevated slightly of a fat surface as to a reference frequency determined by the theoretical proximal to the microphone as possible. frequency ratios within a well-tuned bell with a typical Te microphone was operated with a foam ball wind- European profle (see "Acoustic characteristics of bells" screen, to minimise clipping efects from increased wind section). Tis was determined using the appropriate speeds. Te laptop soundcard had a sampling frequency reference note (e.g. A435) based on foundry tuning log- of 44.1 kHz at 16-bit resolution. Te microphone had a books and assuming equal temperament. frequency range of 3.15 to 20000 Hz ± 2 dB. Te raw audio samples were not altered or modifed. Te bells were recorded from lowest to highest in Although noise reduction was considered, it was rejected terms of musical note, and from softest to loudest primarily over concerns that lower-intensity partials that musical dynamic marking. Te samples from larger neared ambient background levels would be excluded bells were recorded for up to 28 s, and repeated if nec- from analysis. It was decided that, in order to truly refect essary to reduce any signifcant external sound sources, accurate carillon performance, the in situ analysis should such as vehicle engines, in the frst 7–10 s. Tis sam- consider partials within the context of urban ambient pling time was gradually decreased to a minimum of 3 s noise—a partial that is undetectable in the context of for bells with shorter decay times, as determined by the ambient noise levels indicates a performance and compo- carillonist’s judgement by ear, for the sake of efciency. sition contribution signifcantly less important than par- Te audio input was patched through to Audacity tials with much greater intensities. [44] and saved as bulk fles per sampling session. Bell tones were rerecorded when necessary to ensure that Representing sensitivity to carillonist musical dynamic the carillonist was satisfed with the dynamic level and levels major contributions of background noise were avoided. Te sensitivity of summative intensity to changes in Each sample was exported individually to a .WAV fle fundamental frequency (i.e. bell size) is analysed by for analysis. creating resistive power-law models. It should be noted that these intensities are derived from the spectral Orr Herit Sci (2021) 9:16 Page 7 of 15
analysis over the entire sample duration, and therefore 230 Soldiers' Tower 3.90 do not represent decay times. Tis analysis ftted the intensities across the frequency range of each instru- 220 3.55 ment for the three dynamic levels, according to: 210 3.20 − 1 k A = af (5) 200 2.85 −4 where A is the amplitude, or resultant intensity of the −1 190 2.50 230 Metropolitan 3.90 /m s
sample, a is a power-law coefcient, f is the fundamental /kg s m c fD frequency, and k is a so-called resistive coefcient. Tese 220 3.55 relationships were derived by using log–log plots of fre- quency versus intensity, which, if accurately modelled 210 3.20 with a power-law relationship, yielded linearity. Te slope −1 200 2.85 of this relationship is equivalent to k , from which the resistive coefcient can be calculated. 190 2.50
1 C3 C4 C5 log(A) = − log(f ) + log(a) k (6) Note Fig. 4 Two indicators of proportion for the Gillett & Johnston bells within the Metropolitan and Soldiers’ Tower carillons: fD (in black) and In this resistive power-law model, the coefcient k is the profle constant c (in grey) indicative of how signifcantly changes in fundamental frequency afect the intensity; they are only applicable for the instrument frequency ranges and detected inten- diferent proportions (Fig. 4). fD is an indicator of wall sities. As k →∞ there is little to no change in intensity thickness, while c is a profle constant used to relate sensitivity with changing frequency. In contrast, as k → 1 mass, fundamental frequency, and diameter. On aver- there is infnitely strong sensitivity to diferent funda- age, the G&J bells in Soldiers’ Tower have thicker walls mental frequencies. Tis is used to evaluate how signif- fD = 214 ± 6.84 (1 S.D.) than those in the Metropoli- cantly the sound intensity levels change with decreasing tan carillon fD = 202 ± 5.04 (1 S.D.). However, the bell size, and to enable comparison between musical Metropolitan carillon has a higher (heavier) profle dynamic levels. constant ( c = 2.99 ± 0.24 , 1 S.D.) than Soldiers’ Tower ( c = 2.91 ± 0.08 , 1 S.D.). Both of these constants are c = 2.8 Results and discussion greater than that Lehr recommends for general use. It has been proposed that G&J based their early for- Te bells were analysed with respect to their physical ays into founding well-tuned bells on on observations proportions, frequency deviations (tuning) from theo- and designs of 19th century bells, which would be infu- retical relationships, total and partial intensity (volume enced by Grimthorpe’s advocacy for bells with very thick or audibility) and sensitivity to carillonist input. walls and heavy profles [45]. It is proposed that the higher variability of the fD value Bell dimensions and c between individual bells within the Metropolitan carillon is, in part, likely related to these bells represent- An investigation of the dimensions of bells provided ing G&J’s frst foray into producing bells for a carillon. insight into design and production processes with Te F♯ 4 bell is particularly of note for its unusually low implications for interpreting the acoustic measure- fD value and high c constant. It is possible that this bell ments of the bells. Suitable data was available for the was originally cast for another purpose and appropriated bottom two octaves of both instruments (founded by for inclusion within this instrument, which was common Gillett & Johnston in 1922 and 1927, respectively) and G&J practice in the 1920s [46]. the upper bells of Soldiers’ Tower, founded by Petit & Te profle constant for Soldiers’ Tower is more con- Fritsen in 1976. Data for the remaining portions of the sistent (as represented by a smaller standard deviation) Metropolitan instrument were unavailable. than that of the Metropolitan carillon, which suggests it Although the instruments have similar musical might have been part of the design process. Within Sol- ranges, their bells reveal foundry-specifc variation in diers’ Tower, the fD value is very consistent in the bottom proportions. octave (up to C 4 ) before sharply increasing. Te causes Despite being founded only a few years apart, the two sets of Gillett & Johnston bells have signifcantly Orr Herit Sci (2021) 9:16 Page 8 of 15
the theoretical frequency). Te same trend is seen to a Soldiers' Tower less degree for the quint. Tis increasing proportionality 450 3.75 represents a phenomenon knows as stretch tuning, a sys- 400 3.52 tem in which notes are tuned increasingly sharp toward −4
−1 the the upper end of a keyboard instrument. Although 350 3.29
/m s typically applied to string percussion instruments such /kg s m
fD 300 3.06 c as pianos [47], Gillett & Johnston were also known to apply this approach in their early carillons [48]. How- 250 2.83 ever, for the tierce the opposite behaviour is observed; 200 2.60 that is, the diference between the measured partial fre- quency and the theoretical frequency changes from being C5 C6 C7 positive to being negative. Te trend is stronger in the Note Metropolitan G&J bells. In the Metropolitan carillon, it Fig. 5 Two indicators of proportion for the Petit & Fritsen bells within is possible that Paccard was aware of this characteristic the Soldiers’ Tower carillon: fD (in black) and the profle constant c (in grey) and implemented a similar method into their expansion of the instrument, to provide historical continuity to the instrument as a whole. However, this would require fur- ther investigation. In contrast, the Petit & Fritsen exten- of these changes are uncertain, and require further sion of the Soldiers’ Tower carillon did not incorporate investigation. this characteristic, instead opting for a ‘neutral’ approach Twentieth-century carillon bells were not typically cast in which the bells are tuned to a constant reference pitch in direct proportion as is typical practice for swinging without incorporating stretch tuning. bells: the smaller bells have thicker walls and profles to Te measured frequencies of the humtone and the compensate for their smaller size in sound intensity and −1 fundamental deviated between − 20 and + 10 ¢ from duration (fD from 214 to 439 m s ). To this end, a sin- theoretical frequencies: this represents a level of con- gle profle constant would not be suitable for the Petit sistency in tuning (in terms of variability relative to the & Fritsen bells within the Soldiers’ Tower carillon. Tis other overtones) across the instruments. Tere is a sig- is exhibited by the linear trends in Fig. 5. Tis suggests nifcant negative deviation present in the bass bells (bell that the use of fD and related parameters were part of a notes lower than C 5 ) in both instruments. Above this, systematic intentional design practice and is line with the humtone and the fundamental within the Soldiers’ bellfounding practice toward the end of the twentieth Tower bells hovered a few cents below expected (theo- century [39]. Of additional note is the peak in c constants retical) frequencies, while the bells in the top octave of at E 6 followed by a consistent decrease for the highest the Metropolitan carillon were measured to be higher octave of the instrument. While this could also be related than theoretical frequencies, with increasing deviations to manufacturing practice, this would require further from theoretical frequencies up to the smallest bell in the investigation. instrument. Te measured nominal exhibit similar trends to those discussed in the humtone and fundamental, except that Frequency it was not detected in the audio samples for bell notes Frequency deviations (bell tuning) greater than G 6 (except for a few bells in Soldiers’ Tower). Te results of the frequency analysis of all 5 partials in Te quint exhibited the least apparent trend with funda- both instruments is presented in Fig. 6. In general, the mental frequency but is generally below theoretical fre- tuning of the Soldiers’ Tower carillon is more consistent quencies. Although the partials are physically present in than its counterpart at Metropolitan: the deviations from the bell, the quint was not detected in situ for bells in the theoretical frequency are smaller, and variation between top octave. It is proposed that these partials are absent measured and theoretical frequency are more gradual from the analysis as they could be not detected above and consistent with decreasing bell size. ambient noise levels. However, it is also possible that the With decreasing bell size (i.e. with rising musical note), clapper impact position on these bells is in the vicinity of for the humtone, fundamental and nominal the diference the corresponding normal mode node. between the measured partial frequency and the theo- Te tierce has the most extreme behavior across both retical frequency changes from being negative (meas- instruments: measured frequencies deviated from ured frequency fatter than the theoretical frequency) to theoretical frequencies by ± 50 ¢, and, in general, pro- being positive (measured frequency being sharper than portional to bell size (smaller bells have measured Orr Herit Sci (2021) 9:16 Page 9 of 15
Soldiers' Tower Metropolitan 20
10
Humtone 0
10
20 20
10
Fundamental 0
10
20 60 40 20
Tierce 0 viation/¢
De 20 40 20 10 0 * * 10 Quint 20 30 40 50 20
10
Nominal 0 * *
10
20
G&J C3 C4 C5 C6 C7 C3 C4 C5 C6 C7 P&F * undetected Paccard Note Fig. 6 Frequency deviations for the fve primary overtones in the Metropolitan and Soldiers’ Tower instruments. It is noteworthy that in both sets of bells the quint and the nominal were not detected for roughly the highest half and full octave of bells, respectively. The red line indicates a moving average ( n = 10 ), indicating the general trend with decreasing bell size frequencies closer to theoretical frequencies). Te most bells produced by Petit & Fristen have tierces consistently signifcant tuning deviations from theoretical frequen- tuned to theoretical frequencies while those produced by cies are observed in the largest bells of both instruments G&J are more varied. (+ 25/+ 50 ¢ from theoretical frequencies), especially in Te location of nodal meridians (tuning points) for the Metropolitan carillon. Te erratic behavior (and gen- each partial may cause some to be more susceptible to erally positive deviations) of the tierce in both carillons weathering and corrosion. For instance, the tierce merid- is similar to characteristics observed in other Gillett & ian is located mid-way up the bell’s waist, where the Johnston instruments in which they aimed to tune inter- wall is quite thin. In contrast, the quint is located at one nal minor thirds to the interval of a perfect third [48] of the thickest points on the bell’s wall, near the mouth (despite the potential clash of this with other bells within (and clapper strike point). It is proposed that, because of the instrument). Tis is demonstrated by the contrast in these locations, the efects of weathering and corrosion consistency of tierce tuning between the upper and lower may afect some partials more strongly than others, when portions of the Soldiers’ Tower carillon, in which the their vibrational modes are located at thin portions of the Orr Herit Sci (2021) 9:16 Page 10 of 15
between the three dynamic playing levels. Te bells 100 Soldiers' Tower within the Soldiers’ Tower carillon show a consistent 80 decrease proportional to bell size, while the Metropoli- 60 tan carillon has a smaller and less distinct dynamic range.
40 ff Also of note is the coupled mf and f intensities for the mf p upper range of the Metropolitan carillon. Tis implies 20 that the carillonist is limited by the mechanism to create 100 Metropolitan * a contrast between mf and f dynamic levels. Intensity/d B 80 Te resistive power models are presented in Fig. 8. A 2 60 highly linear ft (represented by high R values) implies a consistent decrease in intensity with decreasing bell 40 ff mf p size produced by the carillonist input. Te carillon of Sol- 20 diers’ Tower exhibits much more consistent behaviour 2 C3 C4 C5 C6 C7 for all three dynamic levels, as represented by R > 0.69 . Note * coupled mf and ff In contrast, only the f playing level of the Metropolitan Fig. 7 The summative intensive of the frst fve partials of bells followed a power-law relationship with a commensurate 2 2 within the Soldiers’ Tower and Metropolitan carillons at three musical R = 0.67 ; the other two dynamic levels had very low R dynamic levels values so these models were discarded. Put another way, it is impossible to discuss the k coefcients as the rela- tionship was not sufciently consistent across the instru- bell wall. Te two previous examples support this claim: ment range. In general, a louder dynamic input level the measured tierces demonstrate the most variability yielded a narrower range of resultant intensities, i.e. the while the quint is relatively stable in both instruments carillonist had less control of the output sound intensity relative to theoretical frequencies. from the carillon action. Te frequency deviations across the sets of Gillett & k (in this case, the slope of the ftted line in red in Fig. 8) Johnston bells provides evidence for a characteristic that is indicative of the sensitivity of intensity to changes in has hitherto been discussed anecdotally. Te tuning forks fundamental frequency. From the values of k in Fig. 8, it that the frm used to tune their instruments were fawed: can be seen for the Soldiers’ Tower carillon that the sensi- they were generally fat (especially within the middle of tivity to carillonist input decreases with playing dynamic; octaves C-C). Te outcome of this is that musical tones put another way, intensities at a pp vary more in inten- within these sets of bells close to C will generally be tuned sity than at mf and f levels. In contrast, the Metropolitan more closely to theoretical frequencies, but there is an carillon at a f dynamic level is less sensitive than the Sol- oscillating trend toward the middle of octaves in which diers’ Tower carillon at any musical dynamic level, while the middle of octaves (C-C) are more prominently tuned the other levels did not sufciently-consistent relation- below theoretical frequencies. Tis is especially promi- ships to discuss k coefcients. nent in the upper-right panel of Fig. 6. So, although the tuning books reported the Soldiers’ Tower carillon and Relative partial intensity the Metropolitan carillon to be tuned to references notes Te partials, in general, followed an established order A435 and A432 respectively, in practice both instruments of audial prominence, relative to one another: the are tuned closer to A432 and A430, respectively. humtone, the tierce, the fundamental, the nominal, and the quint. Although the tierce is quite prominent, Intensity its intensity is ofset by the combined tonality of the Summative intensity humtone, fundamental and nominal—which stresses Te summative intensities of the fve primary partials the importance that these octave overtones must be in ranged from 25 to 100 dB for the Soldiers’ Tower bells, accordance with one another in the internal tuning of while the Metropolitan bells had a smaller dynamic range each bell. Figure 9 shows the intensity of each partial is of 45–95 dB (Fig. 7). Te lower maximum for Metropoli- compared to the intensity of its respective fundamental tan is likely due to the thinner profles used in the Met- frequency, so that their relative prominence across the ropolitan carillon (see "Bell dimensions" section), despite instrument ranges can be discussed. its lower transposition compared to Soldiers’ Tower. Te humtone hovers around the same intensity as Te samples taken of bells provided by Gillett & John- the fundamental frequency until ≈ D ♯5 , at which point ston (23 lowest-sounding bells in both instruments, bell it increases prominence to 10–20 dB greater than the notes approximately below C5 ) have distinct separation fundamental frequency. Orr Herit Sci (2021) 9:16 Page 11 of 15
Soldiers' Tower Metropolitan 2.0
1.9
1.8
ff 1.7
1.6
1.5 R 2 = 0.88 R 2 = 0.67 1.4 k = 7.1 k = 12 2.0
) 1.9
1.8
mf 1.7
1.6
log(Intensity)/log(dB 1.5 R 2 = 0.83 R 2 = 0.04 1.4 k = 6.7 k = 59 2.0
1.9
1.8
pp 1.7
1.6
1.5 R 2 = 0.69 R 2 = 0.05 1.4 k = 4.6 k = 53 Founder G&J C3 C4 C5 C6 C7 C3 C4 C5 C6 C7 P&F Note Paccard Fig. 8 Summative bell intensity (total of the fve main partials) log–log plots for Soldiers’ Tower and Metropolitan bells at pp, mf, and f musical dynamic levels
Te tierce is more stable than the humtone, remain- kHz), it is not surprising that these partials do not make ing equally prominent to the fundamental over the a signifcant contribution to the bell’s overall tone qual- instruments’ entire frequency ranges. Te only excep- ity, as they approach the limit of human detection. tion to this is a noticeable increase in the Metropoli- Te relative intensity of a partial is partly dependent tan Paccard bells (upper range), which peak at + 20 dB on the clapper impact position. However, this was not intensity relative to the fundamental frequency. studied due to access limitations. Te quint is very weak and inconsistent as compared to the other partials. It can best be described as a loose Partial sensitivity cluster centered around − 20 dB relative to the funda- Resistance power-law models were applied to the fve mental frequency. primary partials, which produced better-ftting resis- 2 = Te nominal is also quite strong in the lower fre- tive models (Rav 0.64 ) for the Soldiers’ Tower caril- 2 = quencies ranges, before tapering of to levels between lon as compared to Metropolitan (Rav 0.33 ). Tese 2 − 10 and − 20 dB relative to the fundamental. Given R av values demonstrate that the prominence of the the extreme frequency ranges of these overtones (7–10 overtones within the Soldier’s Tower carillon are more Orr Herit Sci (2021) 9:16 Page 12 of 15
Soldiers' Tower Metropolitan 30 20 10
Humtone 0 −10 −20 −30 30 20 10
Tierce 0 −10 −20 −30
to fundamental/dB 30 20 10 * * Quint 0 −10
Intensity relati ve −20 −30 30 20 10
Nominal 0 * * −10 −20 −30 Founder G&J C3 C4 C5 C6 C7 C3 C4 C5 C6 C7 P&F Paccard * undetected Note Fig. 9 Partial intensities relative to the fundamental (F.R. 2.000) overtone for Soldiers’ Tower and Metropolitan bells. The intensity deviations were = averaged across all three dynamic levels consistently related to carillonist input across the range Tower samples, demonstrating similar consistency of the instrument than those in the Metropolitan caril- across the range of the instrument. lon (Fig. 10). Te tierce and the quint of the bells within the Sol- Te intensity (or prominence) of the Metropolitan diers’ Tower carillon exhibit the smallest variation in humtone behaves inversely to the fundamental fre- resistive coefcients: regardless of musical dynamic quency (as represented by k values < 0 ). Tis means level, the change in prominence across the instruments that bells of smaller size are producing a more intense range is very similar. Te nominal has the lowest aver- partial than the larger bells in the set. One possi- age resistive coefcient, demonstrating that its intensity ble explanation is the production techniques of P&F is the most sensitive across the range of the instrument. and Paccard in the upper portions of the instrument that may contrast those of the original G&J bells. One Discussion exception to the overall behaviour of the Metropoli- Although the greatest heritage importance is typically tan is the fundamental partial, which exhibits simi- placed on the bells in a carillon, the results presented lar power-law behaviour and k values to the Soldiers’ herein demonstrate the importance of the mechanical Orr Herit Sci (2021) 9:16 Page 13 of 15
Soldiers' Tower Metropolitan producing a more even intensity output. However, it is unclear to the extent to which this result would apply to k 20 other carillons by the same founder or diferent eras of construction. ecient 10 Te original bells of the Metropolitan carillon are mounted directly above the playing cabin, while the sec- e coff 0 ond set of bells was placed above these. Te tower is quite narrow, and there is little room to manoeuvre around the −10 Resistiv bell frame. To facilitate access for maintenance, the 1971 Paccard bells were installed in the space around the origi- ff mf nal base bells. Te decreased length of parts involved
p Quint Quint Tierce Tierce with playing these bells increases dynamic sensitivity, but Nominal Nominal Humtone Humtone the proximity to the playing cabin is quite uncommon
Fundamental Partial Fundamental for bells in this range. To this end, the carillonist hears Fig. 10 Resistive coefcients (k) for Soldiers’ Tower and Metropolitan a dynamic bias towards these bells, that is not repre- bells. As represented by k values closer to 1 than its Metropolitan sentative of the sound at exterior ground level. Tis likely counterpart, the transmission system of the Soldiers’ Tower allows for exacerbates the player’s ability to gauge diferent musical a greater range of dynamic response across the instruments range dynamic levels at their close proximity to the upper bells and higher contrast between dynamic levels in the playing chamber. Tis demonstrates an important point: the proper- ties of carillon installations of bellfounding frms have action as part of the holistic system of the carillon as a changed signifcantly over time. Tis is most prominently musical instrument. Te mechanical action is an impor- seen in the contrast of the Petit & Fritsen sections of the tant control on the sensitivity and regularity of the sound instruments. Te mid-section of the Metropolitan caril- intensity produced by the input from the carillonist. Tis lon shows more strongly deviating measured frequencies has implications for how carillon music is arranged and from theoretical frequencies (Fig. 6) than the correspond- composed. Figure 7 shows that, due to the mechanical ing range of Soldiers’ Tower. While it is possible that part action of the Metropolitan carillon, there is no discern- of this is due to the application of stretch tuning, it seems ible diference in the audio intensity produced at the mf unlikely that this technique would have been applied in and f dynamic levels. Te practical result of this is that, the Metropolitan carillon for an extension of only one if written music is prepared to be suitable for a wide octave (13 bells) within that particular range of musical range of instruments, the variability of age, consistency, notes. While that installation was in 1960, by 1976 when and quality of the mechanical action should be consid- Petit & Fritsen installed the upper-half of the instru- ered. So, if a distinguishable musical level is required for ment in Soldiers’ Tower, the partials show more consist- artistic efect, a sharper contrast of musical levels (such ent variation in measured frequencies from theoretical as f and pp) should be used to produce this efect. A rel- frequencies (especially the humtone and tierce); there evant example would be the use of ‘terraced dynamics’ is no evidence of stretch tuning to match the technique [49] in baroque music, in which repetition is employed employed by Gillett & Johnston in their early installations with distinct musical dynamic levels to produce an ‘echo- of four musical octaves or greater. Further investigation like’ efect. Further, diferent phases of work on the caril- is required to produce a more rigorous understanding of lon manifest as variations in the musical sensitivity of the the development of founding and installation practices of instrument. For example, Figs. 7 and 8 show that within twentieth-century bellfounding frms. the Metropolitan carillon there are distinct trends of rela- From heritage and artistic perspectives, there are sev- tive partial intensity depending on the bellfounder (which eral considerations of what makes a ‘good’ carillon. While correspond to diferent phases of renovation work on the there is a broad consensus that bells sounded with other carillon). While both the Gillett & Johnston lower and bells (such as in carillons) need to be ‘well-tuned’ [50], Paccard upper sections of the instrument show weakly what is ‘good enough’ is yet to be determined. While decreasing variations of summative bell intensity across the aforementioned range of typical human detection their ranges, the Petit & Fritsen middle section is rela- might be used as an upper limit of acceptable tuning tively constant across it’s range. Whether intentional or constraints, there are other arguments to be made for not, the mechanical action employed by Petit & Fritsen wider variation. For example, when Mechelen (the cen- in this instrument has reduced the natural decrease of tre of revitalised carillon culture in the twentieth cen- the audio intensity in the middle range of the instrument, tury) installed a new carillon in the tower to complement Orr Herit Sci (2021) 9:16 Page 14 of 15
the historic instrument, there was mixed public opinion Conclusion about whether the new instrument was preferable [51]. Various aspects of two twentieth-century carillon bells Although the new carillon was an incredible feat of engi- and transmission systems were compared, with an neering with precisely-tuned bells, many residents found emphasis on identifying in situ characteristics. Audio the change of soundscape resulted in a loss of nostalgia. samples of each bell were taken at three musical dynamic Tus, although the instrument aforded a higher level levels (pp, mf, f). Spectral analysis demonstrated the of artistic potential, the public opinion varied from that great variation between sensitivity to player input and of a well-trained musician. Te early twentieth-century partial intensity. Resistive-power law models represented ‘authoritative’ expert opinion was that the partials of a how the sensitivity to a carillonist’s musical dynamic level bell should be tuned to within 1 cycle per second (1 Hz) is variable over the range of the instruments and depends and that the use of tuning forks, representing mechani- on the characteristics of the bells and the installation. cal precision used to determine the quality of bell tuning, Tis study demonstrates the complex attributes of the mattered more than human perception of the quality of carillon, including: a bell (see, for example, the case of the Coventry Cathe- dral bells in 1926 [52]). Te contribution of this study to • variation of foundry production techniques, as well defning a ‘good’ carillon have implications for the grow- as how these change over time; ing interest in more accurate and precise digital synthe- • the acoustics of bells within the context of musical sis of bell tones [53, 54], which is becoming increasingly dynamics and carillonist perception; and prevalent in multimedia music experiences [55]. Further • the importance of considering the carillon as a holis- investigation is needed of public perception of varia- tic musical system. tions in bell tuning, as well as an exploration of material authenticity in carillon restoration projects. Te discussion that follows explored the important rami- Te irregular pedal mechanism in the Metropolitan fcations of these results for carillonists, composers, and carillon has not signifcantly impacted the sensitivity to arrangers of music for carillon. Developing the under- the carillonist’s musical dynamic level. Tis was likely standing of in situ carillon acoustics and physical attrib- mitigated by the substantial diferences in sound inten- utes supports the ongoing development of the musical sity produced by larger bells as a result of their changing and technical capabilities of the carillon, as well as deeper proportions, so the mechanism in this range is of second- understanding of carillons as heritage that informs their ary importance. conservation and management. A limitation of this study is the method of audio sam- ple collection. As all recordings were taken from a loca- Abbreviations tion within the belfry, they do not accurately represent G&J: Gillett & Johnston Bellfoundry; P&F: Petit & Fritsen Bellfoundry; FR: the experience of a listener from ground level. Typically, Frequency ratio. it is recommended to listen to carillons from distances of Acknowledgements at least 50 to 100 m, depending on the instrument and The author is personally grateful to Roy Lee for ofering his services as the site context. However, obtaining consistent audio sam- performing carillonist for these experiments; and to Willy Wong, Brian Wang ples at a location near to the carillon is made difcult by and Jennifer Tsang of the University of Toronto’s Institute of Biomaterials & Biomedical Engineering and Edward S Rogers Sr. Department of Electrical and several factors, such as varying wind direction (impact- Computer Engineering for providing instrumentation and logistical support. ing how the sound travels) and interference from other The manuscript was also improved by early feedback provided by Bert Augus- noise sources. One mitigation technique is to take sam- tus and Luc Rombouts. ples during the nighttime, when interference is mitigated, Authors’ contributions although further logistical and administrative barriers All contributions were from the sole author. The author read and approved the might present themselves with this approach. As well, fnal manuscript. the impact of local context (such as adjacent buildings, Funding especially large open façades and corners), can signif- There is no funding associated with this publication. cantly impact the audial experience. Further work should Availability of data and materials consider carillons in a complex local setting, and evaluate The data and materials for this publication are unavailable. acoustic properties of the instrument in several locations to explore this efect. Tere may also be the opportunity Competing interests The authors declare that they have no competing interests. for advanced techniques such as acoustic modelling to evaluate this [56] that would build on existing modelling Received: 4 September 2020 Accepted: 7 January 2021 that has studied the relationship between bells and their urban context in a historical perspective [57]. Orr Herit Sci (2021) 9:16 Page 15 of 15
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