Acoustics of handchimes versus handbells

[Wendy Cheng]

Hi everyone - 

  

So this past weekend, my small nonprofit had a retreat for adult musicians with hearing loss in central Virginia.  (You can find more information about the nonprofit here -https://www.musicianswithhearingloss.org/wp/)

We did a handbell workshop where I showed them my bells and we tried to play some simple songs.

I bought my handbells, but not handchimes for this go around.

2 of the participants could hear and ring the bells although it was their first time ringing.  A third participant did not enjoy hearing the handbells.    All three participants are cochlear implant users like me.  This third person remarked that our last retreat featured handchimes and she was fine with that, but she didn't like the sound of handbells.   My guess is it has something to do with the amount of "overtones" one finds in handbells, while handchimes have less "overtones" and a more pure sound.  

I am wondering if anyone here can expand on the acoustics of handchimes versus handbells so I can explain it to her and myself.  I'm not even sure how "overtones" differs from "harmonics".  When I play my viola, I know what a "harmonic" sounds like.  But are "harmonics" the same thing as an "overtone"?  What does an overtone sound like when you ring handbells?

For future musical retreats I'm bringing both handbells and handchimes!

  

Thank you in advance!

Wendy

Wendy Cheng

Director, FDA Ringers

Silver Spring, MD

[Judith Treisback]

I've always felt that overtones and harmonics are the same. You have a fundamental pitch, the lowest pitch that you hear, which is pitched by the number of vibrations per minute. 

Sooo if you have a pitch that is 100 vibrations/min. here's how it breaks down:

Fundamental =100bpm (beats/min) or 1 octave higher

1st harm==200bpm or an octave and a perfect 5th higher

2ndharm=300bbpm or one oct and a very flat 7th higher

3rd=400bpm or 2 oct higher

etc...

the relative amplitude of each harmonic is what makes the tamber of the sound you hear plus differences in materials that make up the instrument. A trumpet & a clarinet make different sound when playing in unison. 

String players note that the first harmonic divides the string in half, the second divides string into 3, the 3rd harm divides into four. 

Brass players note that the pedal tune of your note is the fundamental and that all other notes using that fingering/ position in order is your harmonic series for that note.

With handbells, the 2nd harmonic is the most predominant. 

I think that you have it right when you say that it's the harmonics that make it unpleasant. the very high pitches can be jarring even if you're not hard of hearing.

I digressed - hope not too much; I find all of this really interesting.

Judy Treisback

[Lee G. Barrow]

A very good description, but a slight correction: 

After the fundamental, the overtones are an octave above, then an octave and a fifth, then two octaves, 2+a major 3rd, 2+ a fifth, then the flat minor 7th. 

Sent from my iPhone

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[Wendy Cheng]

Thank you to all who wrote in to explain!

Wendy

[TimR]

If I had a chime handy I'd check the overtones.

Obviously there is a different overtone series for chimes than bells, because they sound different.  You would never mistake one for the other. 

I've been told or read somewhere that bells ring mostly at the fundamental and the 12th.  I'm sure I checked that with Audacity at some point but no longer remember.

There is another difference to my ears.  I hear bells as having a more sudden onset to the sound than chimes.  That possibly means there are overtones that decay quickly for bells.   

.

[Michele Sharik]

Every sound - every single sound, no matter what it is - includes ALL
possible overtones. What makes one thing sound like an oboe and another
like a trumpet is the relative volumes of each of the overtones.

Chimes have a very strong fundamental (the "pitch"). Bells have more
audible overtones - the exact ones and their relative volumes depend on
the brand of bell. For example, Malmarks have fewer audible overtones
than Schulmerichs which have fewer audible overtones than Whitechapels.

We call this the "timbre" of the sound.

Sound also has other components, known as the ADSR envelope. ADSR stands
for Attack, Decay, Sustain, Release. Bells and chimes -- in fact, nearly
all percussion instruments - have very little sustain. They start
decaying immediately after the attack. The different surfaces of the
clapper head (or different mallets) change the profile of the attack -
which sometimes translates into a difference in volume, some of which is
subjective, and some of which is objective and depends on how much
energy the "striker" imparted into the instrument (meaning, how much
does it make the instrument vibrate).

There's a lot more to it, of course; this is just a thumbnail sketch &
I've left out some details. People get PhDs in acoustics and acoustical
engineering!

ps. I haven't even touched on direction of sound, or nodes & anti-nodes!

-Michèle <== does not have a PhD in acoustics or acoustical engineering,
but has read up on this stuff a bit and so knows more than the average
bear

[TimR]

On Thursday, October 26, 2017 at 4:52:40 PM UTC-4, Michele Sharik wrote:

Every sound - every single sound, no matter what it is - includes ALL
possible overtones. What makes one thing sound like an oboe and another
like a trumpet is the relative volumes of each of the overtones.

Well, not wanting to get too nitpickey, but................not quite correct.

Driven instruments - meaning an acoustical system that receives a constant periodic input, like a reed vibrating or a lip buzzing or a bow slipsliding on a string - will have a large set of overtones that are integral multiples of the fundamental.  Meaning if the fundamental was A440, you would be able to detect 880, 1320, 1760, etc.  

As you point out the relative strength of the overtones will vary greatly.  But they certainly reduce in strength quickly after the first few.  

Impulse started sounds are totally different, those from instruments that are struck, like percussion instruments, bells, a frying pan dropped on a tile floor, even a violin string plucked instead of bowed.  etc.  They HAVE overtones, but the overtones have no simple mathematical relationship.  Instead, they line up with the natural frequencies of the structure.  Those natural frequencies are determined by the combination of mass and stiffness, and expressed as eigenvectors.  (you do remember your Bessel functions, right?)  These natural frequencies will in general be nowhere near those simple integral multiples.  I took that course in engineering school from a professor working on nuclear fusion, where the reaction is a series of impulses and it would be a very bad thing to have the containment fail.  Really bad.   

[Michele Sharik - TGD]

Ha yes! I did say I was oversimplifying things. ;-)

Bells are shaped the way they are to maximize certain Overtones and reduce others. (Autocorrect capitalizes Overtones - like the guild's journal -  on my phone LOL!)  And the nodes and anti-nodes play a part in all that, too, as well as in some of our techniques (swing, vib, gyro, etc). 

Handchimes are shaped the way they are (with the flanges) to minimize the lines of reduced sound that one gets from a straight up tuning fork. 

Flutes made out of different materials (nickel, silver, gold, platinum, titanium, bamboo, glass, etc) sound different. Ditto for any other instrument (but I'm a flutist so I know those best).

Then there's the acoustical environment in which one hears the sound. 

It's really incredibly complex. And fascinating. 

-Michèle <== I actually included some of this in the Handbell Techniques Certification materials. Because it matters. :-) 

Sent from my iPhone

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[TimR]

On Thursday, October 26, 2017 at 10:41:57 PM UTC-4, Michele Sharik wrote:

Flutes made out of different materials (nickel, silver, gold, platinum, titanium, bamboo, glass, etc) sound different. Ditto for any other instrument (but I'm a flutist so I know those best).

Until you do careful double blind tests and find no difference due to materials.

This has been known for some hundreds of years now.  Any possible variation due to materials is so much smaller than the note to note variation of players that it has been impossible to detect.  The better the experiment design, the stronger the lack of results.   It has been tested extensively on flutes; for some reason a lot of physicists play flute.  But it is also known for other wind instruments, including clarinets, trombones, trumpets, French horns, etc.  Some experiments used concrete bells - no difference from brass.  I own brass trombones, but also a couple of plastic ones. 

Here's me playing lead on a plastic trombone with an indifferent community band:

https://app.box.com/s/5d0254f346c991a7d0fa

Okay, not my finest performance!  But does it sound plastic? 

PS I'm actually considerably better now, having found a good teacher. 

I will admit I do not know a single performing musicians who does not believe that materials determine the sound.  But then, we are a superstitious lot, are we not? 

[Michele Sharik - TGD]

But wait - you said:

"They HAVE overtones, but the overtones have no simple mathematical relationship.  Instead, they line up with the natural frequencies of the structure.  Those natural frequencies are determined by the combination of mass and stiffness, and expressed as eigenvectors."

Which seems to imply that materials (mass and stiffness) do affect the timbre. ???

-Mè

Sent from my iPhone

[TimR]

On Friday, October 27, 2017 at 3:18:07 PM UTC-4, Michele Sharik wrote:

But wait - you said:

"They HAVE overtones, but the overtones have no simple mathematical relationship.  Instead, they line up with the natural frequencies of the structure.  Those natural frequencies are determined by the combination of mass and stiffness, and expressed as eigenvectors."

Which seems to imply that materials (mass and stiffness) do affect the timbre. ???

-Mè

 Oh yes, absolutely.  Divide the stiffness matrix by the mass matrix of any structure and you'll get a set of eigenvectors that describe the various natural vibration frequencies.

Of the structure.

And that will work for any instrument where the structure vibrating produces the sound.  Bells, cymbals, glockenspiels, guitars and violins to an extent, etc.  And of course, other structures besides instruments where vibration is important, like propellers, turbines, bridges.  

You can do that for the trombone or flute too.  Or without calculations, just tap it gently with a mallet and listen to the various frequencies it rings at.

However, the actual sound of wind instruments is produced by the air column inside vibrating.  

The lips drive the air column.  The air column is going to cause the structure to vibrate to some extent, but those vibrations are largely irrelevant to the air column and room sound.  

[Isenbergs]

This is a reply to a very old thread (October 2017), but I was cleaning out my overloaded [HB-L] email folder, and I thought the attached comments would be of interest.

Several years ago, I brought home our Malmark D4 bell to repair it.  The main screw holding it together had broken … again.  (Is anyone surprised?  Maybe the newer models have beefier screws, but in our set it’s an 8-32; too wimpy IMHO.  I know that our [ancient] Schulmerichs use a bigger 10-32 screw for the same bell.  But I digress...)

Anyway, I thought it’d be interesting to record the bell’s sound on a Tascam digital audio recorder that I’d recently purchased.  Then I downloaded the audio file into the Audacity software, which I use for minor audio editing, mainly video soundtracks.

The sound level plot (first attached JPG) from Audacity is quite interesting.  You can easily see the loudness decay over the 14 or so seconds of the recording … no surpise there.  But what I found fascinating is the oscillation in the loudness, sort of a “wah-wah” or tremolo effect that undoubtedly makes the sound of the bell more interesting.

The second plot (second attachment) shows the audio spectrum of the 14-second sound clip.  You can pretty much ignore anything below 200 Hz as background rumble from outdoor traffic, etc.  The first large peak at 294 Hz is the bell’s fundamental frequency, and the overtones or harmonics are clearly visible as additional peaks at higher frequencies.  To simplify things, I took the frequencies and loudness levels of all peaks higher than -48dB, put them into Excel, and “normalized” them (table at lower left).  The frequencies of the first three overtones are kinda what you’d expect: integer multiples of the fundamental, which is the same (neglecting amplitude) as you get from a vibrating string or air column in a tube (organ pipe, or brass or wind instrument).  And the second overtone (A5) is louder than the first (D5), which I suppose we all knew already.  Surprisingly, though, the higher overtones are not integer multiples.  This is undoubtedly is caused by the shape of the bell.

I haven’t done this experiment with the equivalent handchime, but I suspect the higher harmonics would be fewer in number and quieter, since a handchime is basically a tuning fork with a resonant cavity whose length is tuned to match the fork.  I also haven’t had to repair handchimes! 

— John Isenberg (just the husband of the director)

P.S. Yes, I do remember Bessel functions, which show up (for example) in the vibrational modes of a circular membrane (e.g. drum head of tympani), and also in optics (my field).

On Oct 27, 2017, at 5:19 PM, 'TimR' via Handbell-l <handb...@googlegroups.com> wrote:

On Friday, October 27, 2017 at 3:18:07 PM UTC-4, Michele Sharik wrote:

But wait - you said:

"They HAVE overtones, but the overtones have no simple mathematical relationship.  Instead, they line up with the natural frequencies of the structure.  Those natural frequencies are determined by the combination of mass and stiffness, and expressed as eigenvectors."

Which seems to imply that materials (mass and stiffness) do affect the timbre. ???

-Mè

 Oh yes, absolutely.  Divide the stiffness matrix by the mass matrix of any structure and you'll get a set of eigenvectors that describe the various natural vibration frequencies.

Of the structure.

And that will work for any instrument where the structure vibrating produces the sound.  Bells, cymbals, glockenspiels, guitars and violins to an extent, etc  And of course, other structures besides instruments where vibration is important, like propellers, turbines, bridges.  

You can do that for the trombone or flute too.  Or without calculations, just tap it gently with a mallet and listen to the various frequencies it rings at.

However, the actual sound of wind instruments is produced by the air column inside vibrating.  

The lips drive the air column.  The air column is going to cause the structure to vibrate to some extent, but those vibrations are largely irrelevant to the air column and room sound.  

[TimR]

On Monday, May 16, 2022 at 9:18:35 PM UTC-4 isen...@sbcglobal.net wrote:

 The frequencies of the first three overtones are kinda what you’d expect: integer multiples of the fundamental, which is the same (neglecting amplitude) as you get from a vibrating string or air column in a tube (organ pipe, or brass or wind instrument).  And the second overtone (A5) is louder than the first (D5), which I suppose we all knew already.  Surprisingly, though, the higher overtones are not integer multiples.  This is undoubtedly is caused by the shape of the bell.

Sorry I haven't visited in a while.

But no, that's not what I would expect at all.  I am very surprised that you got anything near integer multiples for anything but a vibrating string or air column.   

In all the calculations done in my engineering classes on structures we never had anything near that appear, nor in any analysis of engines, gear trains, etc.  

Here is some discussion on the topic that asserts what I've been told, that bells ring mostly at the fundamental and the 12th.  A key takeaway is that only the fundamental and the 12th are tuned.  

https://www.moz.ac.at/sem/lehre/lib/pd-sounddesign/acoustics.html

Recently I recorded the church organ chimes, because they sound horrendously out of tune to my ear, and did the same Audacity analysis and hamming plots you did, but without any firm conclusion.  Just too much variation across time - and a surprising amount of pitch change with decay.  

An additional complication:  there is a difference between free vibration and driven vibration.  If you tap the bell of a trombone the brass structure will ring, and it will not have integral multiples.  But if you play the trombone you are driving the air column with your input, and it will sound the input frequencies.  Those are integral multiples.  But if you check where the trombone plays at air column intervals, they are not.  Similarly bowed strings are driven, plucked strings are not.  

[TGD Michele Sharik]

Hi Tim & John! (BTW, great pics, John!)

You both might be interested in the papers by Dr. Thomas Rossing concerning the acoutics of handbells. (He writes about different types of bells, too, although he seems to be most interested in "Tuned Handbells”.) The earliest one I could find was published in 1980, but he’s got more throughout the 80s, and even one from 2001. He had synopses published in Overtones a couple of times, too. 

Here’s a list of some of his papers/articles/writings:

Hansen, Uwe J., and Thomas D. Rossing. “Modal Analysis of a Handbell.” The Journal of the Acoustical Society of America, vol. 79, no. S1, 1986, https://doi.org/10.1121/1.2023468.

Rossing, Thomas D. Acoustics of Bells. Van Nostrand Reinhold, 1984. 

Rossing, Thomas E. “Acoustics of Tuned Handbells.” Overtones: The Official Journal of the American Guild of English Handbell Ringers, vol. 27, no. 1, 1981, pp. 4–10, 27. 

Rossing, Thomas D. “Acoustics of Percussion Instruments: Recent Progress.” Acoustical Science and Technology, vol. 22, no. 3, 2001, pp. 177–188., https://doi.org/10.1250/ast.22.177. 

Rossing, Thomas D., and H. John Sathoff. “Modes of Vibration and Sound Radiation from Tuned Handbells.” The Journal of the Acoustical Society of America, vol. 68, no. 6, 1980, pp. 1600–1607., https://doi.org/10.1121/1.385214. 

Rossing, Thomas D. “Tuned Handbells, Church Bells and Carillon Bells: Part One.” Overtones: The Official Journal of the American Guild of English Handbell Ringers, vol. 29, no. 1, 1983, pp. 15, 27–30. 

Rossing, Thomas D. “Tuned Handbells, Church Bells and Carillon Bells: Part Two.” Overtones: The Official Journal of the American Guild of English Handbell Ringers, vol. 29, no. 2, 1983, pp. 27, 29–30.

One other thing I find fascinating is the waveform of a “whomp damp”. (I’ve attached a pic — the amplitude swell at the end is the whomp.) I’ve attempted to contact Dr. Rossing to ask him about it — none of his papers deal with what happens when a tuned handbell is damped — , but that was during the COVID lockdown, so he may have just missed my email. I should try again. I’ve found that touching the bell near the crown before body- or table-damping helps to reduce or even eliminate the whompage, even on the 2s, especially if you roll the bell up from the crown to the lip while damping. I’m not sure I’m explaining that well….

-Michèle  

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