Harmonics of tones and slaps

[djembeweaver]

whenever they play it, it makes perfectly distinct notes, but the overtones sound disharmonic or dirty to me

Typical! Like I said, africans seem to be partial to inharmonics!

That's because a dustbin lid isn't a uniformly elastic membrane, so the whole harmonic series concept goes out the window. A stretched skin is a uniformly elastic membrane (or very nearly so, depending on how tightly I define "uniform").

Yes that makes sense - as a membrane gets stretched it bahaves in an increasingly uniform way, allowing a harmonic series to emerge. Imperfections in the uniformity would alter the way it vibrates (and therefore the harmonics)

No, that's not really it. Western instruments are choc-a-bloc full of harmonics. All the higher-order harmonics are what give an instrument its timbre. Also, an irregularly-shaped resonant body, such as a guitar corpus or the corpus of a grand piano allow different standing waves to survive that are not in a harmonic relationship. However, the notes come from the vibrating strings; the sound character comes from the harmonics. And a string can only vibrate in even multiples of its fundamental.

Yes but the note is still a combination of the harmonic waves within the string. When the strings get old and a bit gunked-up on an acoustic guitar the harmonics get skewed so no matter how you tune it it always sounds slightly out of tune. Doesn't that show that western instruments have been designed to more precisely control the harmonics? Doesn't that also explain why more 'traditional' instruments can sound slightly out of tune to a western ear?

A dustbin lid or a fence post, no. A goatskin, yes. At least for the first few harmonics. These are clearly audible and visible in a spectrum analysis, proving that the skin indeed obeys physics and and vibrates according to the harmonic series. There are other vibrations caused by unevenness of the skin, the rim, etc. They are audible and add to the sound character, but I don't think they make the "notes" we hear in a skilled player's slaps--I think the notes are caused mainly by the harmonic series because other vibrations will peter out very quickly.

OK - you've convinced me that the skin definitely vibrates according to the harmonic series

Tones and slaps are independent of the bass fundamental. The bass is controlled by the size and proportions of the shell. The tones and slaps are controlled by thickness, diameter, and tension of the skin. (Minor point: playing technique also has a little bit to do with it )

You sound as if you know whereof you speak

Actually, it's not that surprising. Think about flageolet technique on a guitar. There, the player dampens the skin at points that are an even fraction of the total length of the skin. That makes it possible to get the skin to vibrate at f1 and f2 instead of f0. It's the same thing for a goatskin. By striking "just so", you can dampen parts of the skin ever so slightly, setting up the higher order vibration that emphasizes a particular harmonic. (Once the harmonic is going, it's self sustaining even with dampening removed, just like flageolet sound on a guitar

Nice explantation. Is this self-sustaining effect why harmonics can seem to build during an echauffement?

Have a look at the diagram at the bottom of this page, which shows the series for a string plucked at 1/3 length. Note how every third harmonic is absent. I am almost certain that the tonpalo (third slap) relies on the 2D-equivalent of the same thing

That makes perfect sense! Presumably someone could model where those points would occur on a perfectly uniform membrane.

Yes, absolutely, and someone already did this

Cool. Wish it was me who thought of it first though!

I'll have a look at the kettle drum stuff when I have some time.

[djembefeeling]

my goodness, Michi, you definetely learned something in all those years on this forum

[michi]

Yes but the note is still a combination of the harmonic waves within the string.

Right. But the string can only vibrate for any length of time at the frequencies in the harmonic series. The other frequencies we hear are parasitic vibrations and the like, because the string isn't a physically perfect oscillator. There will also be resonance effects with the sound corpus, all adding to the timbre.

When the strings get old and a bit gunked-up on an acoustic guitar the harmonics get skewed so no matter how you tune it it always sounds slightly out of tune.

I'm familiar with the old-string effect on guitars. I think the change in sound comes from corrosion on the string, and dirt accumulating in the wire winding. That'll dampen the string more and change its overtone spectrum.

Doesn't that show that western instruments have been designed to more precisely control the harmonics? Doesn't that also explain why more 'traditional' instruments can sound slightly out of tune to a western ear?

I really don't know. The statement seems too broad to me. I'm not sure whether instrument builders think about precisely controlling harmonics. Probably only indirectly so, by knowing which shapes and material create an instrument that sounds "good".

You sound as if you know whereof you speak

The experiments I did about the bass and tone frequency clearly show the spikes in the harmonic series. There are lots of other frequencies there too, of course. But these are way down in level compared to these spikes, to the point where they won't be heard as a note, but only as timbre.

(Once the harmonic is going, it's self sustaining even with dampening removed, just like flageolet sound on a guitar

Nice explantation. Is this self-sustaining effect why harmonics can seem to build during an echauffement?

I have no idea, but it seems possible. If you look at Mamady's "Djembe Kan" video, the solo he played in Seattle in 1998, right at the end, for about the last three minutes, he plays a technique that has the drum just singing. It's almost like a drone that keeps going while he plays solos over the top. If I didn't know better, I'd almost swear there is more than one drum playing. And you can hear those overtones just going and going, making this incredible melody behind it all. (That's some of the best playing ever recorded on video, IMO.)

So, yes, the "building harmonic" idea during a chauff seems to make sense.

Yes, absolutely, and someone already did this

Cool. Wish it was me who thought of it first though!

Yeah. That's a cool piece of work I've been tempted to try this at home, just for kicks. But I don't have a variable oscillator I could use. Need to find someone at a school or some such to borrow one. (Amplifier and speaker are no problem…)

Cheers,

Michi.

[djembeweaver]

That'll dampen the string more and change its overtone spectrum

Isn't that another way of saying that it will change the harmonics (overtone=harmonic or inharmonic partial)

I really don't know. The statement seems too broad to me. I'm not sure whether instrument builders think about precisely controlling harmonics. Probably only indirectly so, by knowing which shapes and material create an instrument that sounds "good".

I have a friend who has just finished making a clarinet as part of his course. He did a whole module on harmonics and it was all quite technical. Given that the physics of a clarinet are perfectly understood (by physicists, not necessarily by me!) they are built to very exacting specifications. That's not to say that every clarinet builder understands the physics, but if they get it even slightly wrong it will either be out of tune, or not have the correct timbre, or both (my friend's worked out pretty well, though it's ever so slightly out of tune on certain fingerings according to him)

So whereas a clarinet is build to precise mathematical specifications a balafon or kora is made by eye and ear. That's why at the end of the Cafe Couleur gig there is one note on the balafon that is badly out of tune with the kora!

So, yes, the "building harmonic" idea during a chauff seems to make sense

Last summer, as part of my practice routine, I was playing 1 hour of pure echauffement as a warm up to my second hour (I've slipped a bit on the practice front since then). After about 15 minutes of playing I could hear this drone-effect, but thought it might just be a kind of auditory hallucination.

Now then, regarding the Albert Prak article:

Firstly, what an awesome piece of work. The most enlightening thing I've read since Polak's paper on isochronous pulse structures. Thanks for the link.

Actually all the answers are right there in the data. Both Mamady and Famoudou have an interval of around a fifth between the tone fundamental (M1) and the first partial (M2). M3 is about an octave and M4 and M5 are a semitone or two above the octave. This fits with our observations that most folas pull out octave slaps or thereabouts. Notice that Famoudou has quite a lot of M2 in his slap compared to his tone, though M3, 4 and 5 are louder still. This (almost) fits with my observation that the first slap harmonic is a fourth. Maybe whether it's nearer a fourth or a fifth depends on the drum.

Lastly, that djole link was awesome. One of the best I've heard. Regarding the third slap (what do you call it again?) at 3 mins in: if you compare those slaps to ones played earlier in the solo you'll see that what has been added is a lower, not a higher slap. Moreover, the lower slap sounds like a fourth, not a fifth, of the tone. I think the soloist has dropped his slaps to the M2 band, then punches out an M3-4-5 slap for emphasis.

Oh, and this might be pedantry, but if the harmonics of a tensioned-membrane are given by the series 1, 2.33, 3.66, 5, 6.33 etc then these are not whole-number multiples of the fundamental. Can we really call it a harmonic series then?

[michi]

That'll dampen the string more and change its overtone spectrum

Isn't that another way of saying that it will change the harmonics (overtone=harmonic or inharmonic partial)

I guess it is!

I have a friend who has just finished making a clarinet as part of his course.
[…]
So whereas a clarinet is build to precise mathematical specifications a balafon or kora is made by eye and ear. That's why at the end of the Cafe Couleur gig there is one note on the balafon that is badly out of tune with the kora!

I didn't know that instrument builders (or at least clarinet builders) got as scientific as that The question is whether the same outcome can't be achieved by trial and error. (I guess that's how early instrument builders must have done it.) Without the scientific background though, repeatability of good results is probably hard to come by.

Maybe that's why excellent djembes are so rare? I have a (slightly heretical) suspicion that modern science could probably help to improve djembes. Make the effort to work out ideal proportions for a particular sound character, and have carvers use templates to replicate the shape. You'd certainly get better repeatability that way…

Last summer, as part of my practice routine, I was playing 1 hour of pure echauffement as a warm up to my second hour (I've slipped a bit on the practice front since then). After about 15 minutes of playing I could hear this drone-effect, but thought it might just be a kind of auditory hallucination.

No, I don't think you were hallucinating at all. These sounds are really there. It's just damn hard to make them.

Firstly, what an awesome piece of work. The most enlightening thing I've read since Polak's paper on isochronous pulse structures. Thanks for the link.

No prob. That's the only piece of work of its kind that I've been able to find.

This (almost) fits with my observation that the first slap harmonic is a fourth. Maybe whether it's nearer a fourth or a fifth depends on the drum.

When you hear a fourth, you are hearing the interval between the 3rd and 4th harmonic. The 3rd harmonic is one octave and one fifth above the fundamental; the 4th harmonic is two octaves above the fundamental. The interval between them is a perfect fourth.

I'm getting stronger suspicions that the tonpalo and the various pitches we hear in the slaps are definitely related to the series, and the way certain bands can drop out, as shown in the link I sent about plucking a string 1/3 along its length.

I recorded bass, tone, and a lot of slaps on my drum today, trying to bring out the different overtones as best as I could, by varying contact time and contact position. I had a brief look at some of the spectra. It's interesting that, for one slap, I see massive spikes in some overtones whereas, on another slap, I see valleys in the same place. In other words, different slaps achieve their different pitches by either emphasizing or eliminating part of the series. I need to look a bit more at this to figure out what's going on. I'll post when I have something to show.

Lastly, that djole link was awesome. One of the best I've heard.

Fode Bangoura is just awesome. "Fakoly 1" is one of my favourite recordings. (I'm still pissed off… I was planning to study with him for two weeks in Conakry. A mate of mine, who is an accomplished player, just spent four weeks at Fode's camp. I heard from him yesterday, and he told me that the lessons with Fode were just out of this world…)

Regarding the third slap (what do you call it again?)

Tonpalo

at 3 mins in: if you compare those slaps to ones played earlier in the solo you'll see that what has been added is a lower, not a higher slap.

Yes. Mamady's third slap also sounds lower than his normal one.

Moreover, the lower slap sounds like a fourth, not a fifth, of the tone. I think the soloist has dropped his slaps to the M2 band, then punches out an M3-4-5 slap for emphasis.

See above. I think what's going on is that, even though the first few harmonics go up octave, fifth, octave, major third, fifth, what we hear is the perfect fourth between the third and fourth harmonic.

Oh, and this might be pedantry, but if the harmonics of a tensioned-membrane are given by the series 1, 2.33, 3.66, 5, 6.33 etc then these are not whole-number multiples of the fundamental. Can we really call it a harmonic series then?

A perfect fourth is five semitones. For each semitone, frequency increases by the twelfth root of two (1.059463). So, the interval is a frequency ratio of 1.334. The 1 and 2.33 figures make sense: the perfect fourth sits an octave above the fundamental.

Cheers,

Michi.

[djembeweaver]

djembeweaver wrote:
That'll dampen the string more and change its overtone spectrum
Isn't that another way of saying that it will change the harmonics (overtone=harmonic or inharmonic partial)
I guess it is!

In which case deviation from perfection will lead to imperfect harmonics which will lead to a slightly out-of-tune sound.

repeatability of good results is probably hard to come by

...leading to more variability in 'traditional' instruments than classical ones.

Maybe that's why excellent djembes are so rare? I have a (slightly heretical) suspicion that modern science could probably help to improve djembes. Make the effort to work out ideal proportions for a particular sound character, and have carvers use templates to replicate the shape. You'd certainly get better repeatability that way…

I agree, but only by modelling the best djembes in order to be able to more accurately replicate them (i.e. not the remo route)

When you hear a fourth, you are hearing the interval between the 3rd and 4th harmonic. The 3rd harmonic is one octave and one fifth above the fundamental; the 4th harmonic is two octaves above the fundamental. The interval between them is a perfect fourth.

Can you translate this into the M1-M5 bandwidths from that article?

I'm getting stronger suspicions that the tonpalo and the various pitches we hear in the slaps are definitely related to the series, and the way certain bands can drop out

I think Albert Prak has demostrated that quite clearly in his analysis.

(I'm still pissed off… I was planning to study with him for two weeks in Conakry. A mate of mine, who is an accomplished player, just spent four weeks at Fode's camp. I heard from him yesterday, and he told me that the lessons with Fode were just out of this world…)

Gutted

Tonpalo

Never heard that before. Where does that come from?

A perfect fourth is five semitones. For each semitone, frequency increases by the twelfth root of two (1.059463). So, the interval is a frequency ratio of 1.334. The 1 and 2.33 figures make sense: the perfect fourth sits an octave above the fundamental

Er...I might have to think about that one!

Cheers,

Jon

[djembefeeling]

Maybe that's why excellent djembes are so rare? I have a (slightly heretical) suspicion that modern science could probably help to improve djembes. Make the effort to work out ideal proportions for a particular sound character, and have carvers use templates to replicate the shape. You'd certainly get better repeatability that way…

David Mühlemann told me he worked on that for many years -- it didn't work. He said he could do it all the same way, the results turned out different anyway. The same with krins.

[e2c]

Well, yes... it's so dependent on the wood, which will never be "perfect" per these sorts of exacting mathematical standards.

You cannot predict the sound of the instrument from looking at a roughed-out block.

[bkidd]

This variation probably stems from the fact that so many factors ultimately go into creating the sound of an instrument. Through mass production and precision engineering, the variation in many of these factors can be greatly reduced, but not completely eliminated. Even in a tightly controlled process such as guitar making, there are fairly noticeable differences from one guitar to the next. Plus, most professionals don't play the mass produced ones, but instead opt for custom built guitars, which always turn out different.

I agree with Michi that modern science could improve djembes. I wonder if it would be most effective at raising the low-end rather than achieving greater consistency in the high end. Maybe we need a double blind test like what was performed on old and new violins:
http://en.wikipedia.org/wiki/Stradivarius#Evaluation_of_sound_quality
Another way to go about this would be to take djembes produced by expert carvers and see how they vary, which could be compared to the average carver, and then to scientifically designed djembes.

In the end though, we all come to prefer particular djembes, and these preferences are based on many factors. What's more is that these preferences often change over time.

Best,
-Brian

[e2c]

Anyone can opt for a plastic saxophone - or at least, that used to be possible. (They were being manufactured back in the 50s and 60s.)

Or a glue and sawdust drum (Remo), or Fiberglass congas (Latin Percussion aka LP) or even the PVC pipe "djembes" that some music stores sell.

You cannot go with anything handmade from natural material and expect consistency... every single drum will have its own tone and timbre, which will likely change over time, unless the wood it's carved from has been aged for a good while.

Which is why custom luthiers will (most likely) always have a clientele. If there really were ways to reproduce what they do via standardized manufacturing processes, they'd have been driven out of business long ago.

[michi]

Tonpalo

Never heard that before. Where does that come from?

Carl and Bubudi both used the term here.

It's also used on this French site. (Nice djembe kan there, BTW!)

I don't know what the origin of the term is. Mamady calls it "Le". You can hear him talk about it in this post.

Michi.