Handbells use the same pitch scale notation used by other musical instruments. Namely, the octaves are numbered from lowest bass, notated as octave one (1) to highest treble, commonly notated as octave eight (8). (There are handbells from Malmark even higher pitched in the ninth octave.)
Handbell pitches are commonly notated from G1 to C8, although Malmark makes them up to C9, and has made a one-of-a-kind A0 in bronze.)
Like most bells, the common bronze HandBells have a rich set of vibration modes/overtones/harmonics. The overtones/harmonics are different from stringed instruments. That is because strings vibrate largely in 2 dimensions, i.e., in a plane, and are constrained, i.e., attached at each end. In contrast, a bell’s ringing is created via a flexing of the bell material in 3 dimensions, without any boundary constraints.
In the so‐called English tuning of bronze HandBells, which is followed by most HandBell makers in England and the United States, the principal modes are the [2,0] mode and the [3,0] mode. (Pitit & Fritsen refers to mode 1 as the "hum-tone".) The strike tone of a HandBell is determined by tuning of the fundamental [2,0] mode, or what is called the prime.(1) The fundamental (2,0) mode radiates a rather strong second harmonic partial. So the sound spectrum has prominent partials at the first three harmonics. Additionally, English tuning tunes the (3,0) mode to three times the frequency of the (2,0) mode. The difference of these two principal modes in a bronze bell is exactly a perfect twelfth (one octave and a perfect fifth).
Pitit & Fritsen of Holland/Netherlands instead uses a different tuning, where the (3.0) mode is tuned either as a minor or major 10th overtone (an octave and a minor or a major third, respectively) above fundamental. The Petit & Fritsen website refers to there being five partials they focus on in their bronze bells. They give the example of a C2 bell, whose five tones for those partials are: C1 (hum-tone); C2 Prime/fundamental; C3 Nominal; E#2 (tierce); and G2 (quint).2
HandBells are roughly scaled in size so that the diameter (d ) is inversely proportional to the square root of frequency, except in the smallest bells. In that case it varies inversely with the cube root of frequency. The thickness of the HandBell (t) is then adjusted so that t/d *2 is nearly proportional to the frequency. The fundamental is largely determined by the mouth diameter and wall thickness, while other partials are controlled by the profile.
For economies, foundries commonly provide a limited number of bell size castings that are used by the manufacturers, who make two (or more) consecutive pitched bells from the same casting size. The pitch tuning of the bells by the manufacturer is done principally by removing metal from the inside, i.e., the parameter t (thickness) of the bell is decreased while the outside d (diameter) is kept the same (invariant.)
Starting from a particular size casting, the manufacturer tunes the bells by removing the approporiate amount of material from the inside of the bell. The higher pitched bell made from the same bell casting have more material left inside the bell.(3) As a result, the lower pitched bell made from the same bell casting size will have a thinner wall and less weight than the higher pitched bell(s) made from the same cast size. As a result, a lower pitched bell can be lighter than the higher pitched bell made from the same size bell casting. Without knowing why that occurs, that would seem to violate the intuitive “principle” that “lower bells are heavier.”(1)
FYI - Both Malmark (Plumsteadville, PA 18949) and Schulmerich (Hatfield, PA 19440) use the same foundary (Bridesburg Foundry, Whitehall, PA 18052) to cast their bells for them, which they then manufacture to create their finished products. All three businesses are located in southeastern PA.
Bridesbury Foundry does casting for a number of industies in addition to HandBells.(4)
Another feature of bells is that their physics allows them to be scaled. For example, HandBells are scaled down from significantly larger church bells, but can sound the same fundamental pitches. The same concept of scaling is also applied in making very low pitches of bass handbells, which otherwise would become even larger and heavier than they are.
For example, all the Malmark Handbells with decreasing pitches below F#2 (or Gb2) in bronze have almost exactly the same outside diameter, but have decreasing or about the same weight. Similar is true for aluminum, but their diameter is larger than the bronze bass handbells. The aluminum bass handbells have less harmonic overtones, and thus a purer tone than the bass bronze handbells.
For those who may be interested, the theories of acoustic physics for bells is fairly well developed. A mathmatical overview of those theories can be reviewed in chapter two of Michael Jedamzik's book.(1)
Below the pitch of F#2 (or in common handbell notation Gb2), the bass bells of both Bronze and Aluminum have been scaled to avoid increasing weight. However, the aluminum bells are considerably larger in diameter than those made of bronze.(5) (An aluminum HandBell is approximately 124% larger than a bronze bell with the same fundamental frequency.)(1) Another trade off with aluminum is that in addition to being much larger than a comparable bronze bell, aluminum is also a more fragile material.
The accuracy of pitch perception by the average human at the extreme low frequencies in octave 0 is vague. Piano composers have usually only used such very low notes near A0 for tonal colors and special effects. That is because due to the incapability of most humans' hearing to clearly distinguish between the notes at very low frequencies, it is not possible to make a consistent harmonic and melodic use out of such low notes. Such notes tend to be heard as something approaching noise. Although they may be different in pitch, in practice, one very low pitch sounds similar to the next. That same limitation of accuracy of note perception for very low note HandBells is also certainly true, and the "muddiness," especially of the bronze bells significant overtones, makes it more so.
[FYI - The highest pitch on a standard full piano is matched by the C8 HandBell. Malmark makes bells that go an octave higher than that, i.e., up to C9.]
Dominant harmonics for English tuned bronze bells are:
Dominant harmonics for aluminum bells are quite different:
In low bass bronze bells, the multiple significant overtones can be perceived by listeners as producing a more “muddy” sound. In contrast, in the higher pitched bells the additional overtones of bronze bells are perceived as producing a more mellow sound.
Another factor contributing to this “muddiness of sound” at very low pitches is that large bass bronze bells radiate sound waves inefficiently. This is because the frequency of the vibrating bell in bending waves considerably slower than the speed of sound in air, a condition known as “being below the coincidence frequency.” (5,7)
An example of a very low frequency bronze HandBell can be seen and heard of Mr. Sue ringing the bronze G0 [G zero, i.e., octave 0, (fundamental frequency of 24.5 Hz)] at Malmark. Click here to see and hear the G0 on YouTube Hear the G0 HandBell.
Mr. Sue referred to the sound of that bell in the following way –
You probably noticed that the bronze G0 had a rather muddy sound due to the mess of its overtones.(8)
The bronze G0 is an example of several one-of-a-kind very large low pitch bells produced by Malmark that are somewhere between research tools (for testing the harmonics of really large, low pitched bronze bells) and a “because we could do it” demo. A couple other such very large research bronze bells made by Malmark include an A0, and B0.(8)
The physics of a HandBell’s ringing characteristics are also influenced by the material the bell is made from. Metals other than bronze have different ringing properties for various reasons, including different masses and stiffness. Aluminum is an example of another metal that has noticelably different HandBell harmonics, and sound radiation efficiency.
In order to take advantage of aluminum's higher sound radiation efficiency and less overtone harmonics, which enhances the perceived pitch of the handbell at very low bass handbell pitches, in 1991 the Malmark Company created a new bell design using aluminum.9
As noted above, the feature of aluminum bells that contrasts with bronze is the very different harmonics aluminum bells have. They do not have as many harmonic overtones as bronze. Their dominate harmonics are limited to:
This means ringing of aluminum bells produces much less complex overtone harmonics than produced by bronze bells. As a result, bass aluminum handbells are perceived to have a much purer fundamental pitch.
A result of the simpler harmonics and the greater radiation efficiency, is the sound of low bass aluminum handbells cut through the sound of even a huge number of bronze bells. For example, the Bay View Week of HandBells can balance the sound between ten bronze choirs versus only a double set of aluminum octave 2s, plus G1-B1.(8)
In addition to having lower coincidence frequencies that lead to more efficient radiation of bass notes, aluminum bells are considerably lighter in weight, and thus more easily handled by bell ringers, who even with the scaling of bronze bells, have to deal with increasingly heavier bass bronze bells as the pitch goes lower, down to about F#2.
Currently the lowest pitch bass aluminum bell in Malmark’s production range is G1, and the highest pitch production aluminum bell is F#3.
Mr. Sue said: Just speculating, but they (Malmark) might attempt to make aluminum bells in octave 1 below G1 someday. But if they do, they’ll be really expensive; I’d guess $7,500-$10,000 each.(8)
Reasons they don’t make aluminum bells for pitches higher than F#3 likely include:(8)
- The lack of the multiple overtone harmonics in aluminum bells means the perceived timbre or mellowness of the bell is perceived to become weaker as the pitch increases. Malmark has chosen not to produce aluminum bells above the F#3 pitch, 4 steps below C4 (middle C).
Note. Handchimes are made from aluminum, and they are made in pitches all the way up through octave one (1).
- Also, the physical advantage of having a lighter aluminum bell above F#3 becomes physically less important. The next bell up from F#3 is G3, which in bronze weighs approximately 4.25 pounds. A reasonably fit person can play such bells for an entire rehearsal or concert without too much strain.
- An examination of the weights of the F#3 shows the bronze bell is about a pound heavier than the aluminum bell at 6.15 pounds.The bronze G3 at 4.25 pounds is almost two pounds lighter than the bronze F#3. The G3 is clearly manufactured from a smaller foundary bell casting than the F#3.
- Additionally, aluminum is a softer metal than bronze, and so manufacture and durability are also possibly important considerations.
In the above photo, Mr. Sue is holding a nine and a half pound aluminum C2 HandBell manufactured by Malmark from a bell cast by the Bridesburg foundry. [C2 is in the second octave from the bottom - or to the left on a standard piano keyboard. On a piano middle C is a C4.] (A bronze C2 bell weighs just over 50% more than an aluminum C2 at a bit over fourteen pounds, but the bronze bell is only about half as large in diameter.) Another advantage of an aluminum bell is slightly cheaper price. An aluminum C2 bell is about $5,000.00, while a bronze C2 bell is about $6,400.00.
1 Handbell_Compendium-1, Michael Jedamzik, p.32. (This can be read online or saved as a pdf.) http://www.handglockenchor-wiedensahl.de/wp-content/uploads/2017/03/Handbell_Compendium-1.pdf
2 The tuning of a bell, Bellfoundry Petit & Fritsen, http://www.petit-fritsen.nl/en/producten.php
3 Bridesbury Foundry, https://bridesburg.com/
4 Craftsmanship, https://www.malmark.com/about-us/craftsmanship/
5Bass Handbells of Aluminum, Thomas D. Rossing, Deepak Gangadharan, Edward R. Mansell and Jacob H. Malta, Published online by Cambridge University Press: 29 November 2013, https://www.cambridge.org/core/journals/mrs-bulletin/article/bass-handbells-of-aluminum/A359EAC77D300AD5C274D9B6A33BA091.
6 Why is the lowest note on the piano an A?, Music: Practice & Theory Stack Exchange, Feb., 10, 2015, https://music.stackexchange.com/questions/29675/why-is-the-lowest-note-on-the-piano-an-a
7 From C to Shining C: The Unboxing, a discussion of the differences between Bronze and Aluminim handbells, https://danielreck.com/blog/brains/video-from-c-to-shining-c-the-unboxing
8 Email from Mr. Sue, 4/18/2020.
9 To date, only Malmark produces aluminum HandBells. Whether that might be associated with a copyright or not is unknown to the author.
10 Handbell, Wikipedia, https://en.wikipedia.org/wiki/Handbell#Music
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