Harmonics of tones and slaps

[djembeweaver]

Michi recently directed me to a spectrum analysis of bass harmonics he did back in March (awesome work be the way).

This has got me pondering harmonics again...

I have long been aware that my favourite djembe folas make the djembe sing insofar as I percieve their slaps and tones as musical notes. I have often heard my Malinke teachers say that the more open style slap produces a sound like a bell, as opposed to the cupped technique which produces more of a crack.

Moreover, as I improve my technique I realise that it is largely a process of reducing the bandwidth of both slaps and tones to make them consistent and distinct (eliminating the slap from the tone and the tone from the slap if you like).

Another observation is that certain folas (like Mamady) seem to be able to control the harmonics to such an extent they can produce two distinctly-pitched slaps.

Now then, when I play a nice tone and slap I can sing the notes. A friend of mine who is a singer generally sings the same notes when she hears me play (not truly scientific I know but it suggests we're both hearing the same harmonics). The thing is though, the interval seems to be pretty consistent. When I first start to play the first interval I find is a fourth (obviously other harmonics are ringing but that one sounds very dominant) but if I continue to play and really focus on technique I start to get the octave. Also when I play and get the fourth I can hear the octave harmonic 'hiding' behind it. This seems comsistent across different drums.

I never hear a diminished fifth or a major seventh interval!

My first question is: do other people hear the same thing or do you think I'm just hearing what I want to hear?

Secondly I wondered if anyone (Michi...) had thought of comparing the interval between the harmonics of tones and slaps (perhaps comparing across different players and different drums)

Might measuring the bandwidth and interval of your slaps and tones be a good indicator of technique?

[djembefeeling]

Hi Weaver,

this is really interesting. I always try to establish a nice interval between my tones and slaps. But I am still not sure what this interval is. It is very close to a forth, I think. Though when I tune my duns, I am not satisfied with a fourth -- I have a preference for something closer to a fifth between the dunun and the sangban, and try to have the octave from the dunun to the kenkeni.
I think to pay attention to the harmonics is a good indicator of technique. I have never met anyone else who cared about the interval, though, and it might be a better advice to try to make the biggest difference between slap and tone you can (I will focus on the octave from now on, thanks to your post!).
At least I can say that I like my sounds to be in harmony. I noticed in some MKs recordings that he paid much attention to the harmonics of the duns and the djembes involved. But listening to Mady Keita or other djembefolas from Bamako I cannot hear my favorite harmonies. I wonder whether they don't pay attention (unlikely) or just favor other kinds of "harmonies", for West-Africans seems be in favour of snare sounds and very different harmonies. For instance, it is hard to keep track of the melody of many of the songs, too, for they often seem crank the lyrics, at least for my western ears.
I also like it when a djembe starts to sing. The Africans here in Hamburg produce very nice harmonies, so they seem to think its important. I wonder how much this is due to our influence on those djembefolas, because, again, in Mali this singing doesn't seem to be typical.

Another observation is that certain folas (like Mamady) seem to be able to control the harmonics to such an extent they can produce two distinctly-pitched slaps.

Famoudou praises himself that he can produce up to or even more than 32 different sounds, I think. There is a higher slap closer to the rim and played right in the middle-line of the skin -- called something like "claire" (don't know how it's spelled) -- that sounds different to usual slaps, not that hard to produce.

btw, shouldn't this show up in the technique section?

[bkidd]

DjembeWeaver wrote:
My first question is: do other people hear the same thing or do you think I'm just hearing what I want to hear?

That's a great question. How good is your ear? I'm assuming you can correctly identify intervals that someone else plays on an instrument. If you listen to another fola play tones and slaps do you hear a fourth or octave or not?

Secondly I wondered if anyone (Michi...) had thought of comparing the interval between the harmonics of tones and slaps (perhaps comparing across different players and different drums)

Might measuring the bandwidth and interval of your slaps and tones be a good indicator of technique?

Neat idea. This could be a very nice method for teaching people how to produce more distinct tones and slaps.

Best,
-Brian

[djembeweaver]

Hi djembefeeling.

So you get a fourth from a tone to a slap too. Maybe the fourth and the octave are the first two natural harmonics for a slap.

One of my current teachers is Iya Sako (from Wassolon). He seems to get an octave fairly consistently and that's the sound I'm aiming for at the moment (ho ho ho...well you can aim can't you)

Search youtube on Iya Sako and let me know what you think - are those the sounds you like?

I'm not sure I agree about Mamady. Listen to live at Cafe Couleur - sounds like his drum is singing to me!

Hi Brian.

Thanks to a classical training my ears are holding up fine and I still know my intervals (the fourth and sixth give the melody to "We Plough the Fields and Scatter"). As I said above I hear a consistent octave from Iya Sako but I'm very aware of how slippery perception can be and how easy it would be to only attend to the harmonics that made sense to you. Check out Iya Sako and let me know what you hear.

[bkidd]

Hi Djembeweaver,

My ear training isn't that good so I'm not great at picking out intervals on the djembe. Inspired by your post though, I went and measured my tones and slaps, and would produce ~750 - 810 Hz for slaps and 398 - 404 Hz for tones. This is pretty close to an octave apart, but what was most interesting to me is that my tones were much more consistent than my slaps. Maybe it's because I've been working harder on those.

Best,
-Brian

[djembefeeling]

Search youtube on Iya Sako and let me know what you think - are those the sounds you like?

Yepp!

I'm not sure I agree about Mamady. Listen to live at Cafe Couleur - sounds like his drum is singing to me!

Of course it does! I didn't suggest otherwise. I compared MK to Malian drummers I know.

This is a bit poor in quality, but here you can listen to Gabriel Daly, my local hero on the djembe. Do you like his sounds?

[djembeweaver]

I went and measured my tones and slaps, and would produce ~750 - 810 Hz for slaps and 398 - 404 Hz for tones

Nice tight tones then I'll bet.

but what was most interesting to me is that my tones were much more consistent than my slaps. Maybe it's because I've been working harder on those.

Or maybe slaps are harder to control because the fingers are slightly looser on a slap.

Of course it does! I didn't suggest otherwise. I compared MK to Malian drummers I know.

Ah I see. I've noticed a lot of Mali players play with more of a cupped shape which i believe produced less of a ring and more of a pop.

Nice vid - which one was Gabriel? Mostly sounds like an octave though the guy with the dreadlocks seems to be getting fourths and octaves.

[djembefeeling]

which one was Gabriel?

the guy with the dreadlocks. it's different to hear him live. the sound here is just poor...

[djembeweaver]

Oh good - he was my favourite. Now I don't have to be disingenuous. I think he might be controlling it. He plays with lovely octaves from 0.39 onwards, then finishes the echauffement off at 1.10 with a flam that's clearly a fourth.

Would be better to hear a better-quality recording though.

I think we're basically after the same slap.

[michi]

I have long been aware that my favourite djembe folas make the djembe sing insofar as I percieve their slaps and tones as musical notes. I have often heard my Malinke teachers say that the more open style slap produces a sound like a bell, as opposed to the cupped technique which produces more of a crack.
[...]
Another observation is that certain folas (like Mamady) seem to be able to control the harmonics to such an extent they can produce two distinctly-pitched slaps.

Yes, or three or four. (Listen to Famoudou's Sofa on "Rhythmen der Malinke".)

The thing is though, the interval seems to be pretty consistent. When I first start to play the first interval I find is a fourth (obviously other harmonics are ringing but that one sounds very dominant) but if I continue to play and really focus on technique I start to get the octave. Also when I play and get the fourth I can hear the octave harmonic 'hiding' behind it. This seems comsistent across different drums.

I never hear a diminished fifth or a major seventh interval!

Right. That's a consequence of physics. The skin vibrates and has natural harmonics that only occur at certain intervals. This is known as the harmonic series.

My first question is: do other people hear the same thing or do you think I'm just hearing what I want to hear?

What you are hearing is real, and other people hear it too

When you play a tone, the skin resonates at its fundamental frequency (f0). (That's not the same f0 frequency as for a bass, which is completely unrelated and determined by the shell.) The slaps are overtones of that fundamental. The harmonic series gives the following for the first few harmonics relative to the fundamental:

• f1: octave
• f2: fifth
• f4: octave
• f5: fifth
• f6: minor seventh
• f7: octave
• f8: major second
• f9: major third

The harmonics get quieter as you go up the series. Note that the first four harmonics are two fifths and two octaves, which explains why slaps are perceived mainly as those two intervals. It's only once you get to the sixth harmonic that you find other intervals. However, by then, the harmonics are so quiet that they tend to disappear. (They are no longer heard as a dominant note, but as timbre. By the time you get to f6, you are typically down -80dB or so.) In essence, this means that, predominantly, slaps can be played only in fifths and octaves of the tones.

When you listen to people like Famoudou, his technique is so good that he can select which of the harmonics he emphasises. On the Sofa track, he is working f1, f2, and f3 selectively to play these little melodies.

Secondly I wondered if anyone (Michi...) had thought of comparing the interval between the harmonics of tones and slaps (perhaps comparing across different players and different drums)

Might measuring the bandwidth and interval of your slaps and tones be a good indicator of technique?

I don't think the size of the interval would indicate better technique. It's more the ability to select which interval to emphasize that distinguishes a very skilled player from a less skilled one.

When people first start out and learn how to play tones and slaps, usually, they don't manage to excite the skin correctly at all, and you don't get clear overtones, meaning muddled slaps. Moreover, they also can't hit clean tones yet, so their tones have a lot of the slap overtone spectrum in them, meaning that tones and slaps sound much the same.

As their technique improves, they learn to remove some overtones from their tones, and emphasize overtones in their slaps. For the harmonic series, the vibrational modes get increasingly harder to achieve as you move up the series. So, beginners, when the slap starts to develop, first produce f1, which is an octave above the tones. But an octave, to the human ear, isn't all that noticeable as an interval. So, the slaps sound better, but not that much different from tones. As technique improves further, they get f2, and suddenly we have a real slap with a distinctly different pitch from the tones.

We've had extensive discussions of the tonpalo (or third slap) previously. It's not clear to me what combination of harmonics produces that. Just looking at the series, I have a suspicion that that f2 and f4 are strongly involved, but I'm not sure. I really need to find some clear recordings of this and run them through analysis. Would be interesting to know how they come about physically…

Cheers,

Michi.

[djembeweaver]

Hi Michi. Thanks for Harmonics 101

The thing is, I seem to get (hear) the fourth as the first harmonic of the slap. Apologies if I threw you because I originally wrote a fifth, then had doubts and went and checked and found it was a fourth.

Quite apart from the fourth/fifth issue though, consideration of the harmonic series as an explanation opens a whole can of worms...

When you bang a dustbin lid you hear many partials (pure tones) but they don't bear any ordered relationship to each other so we perceive the sound as noise.

As I understand it when a set of partials arise that can be descriced as whole-number ratios of a common fundamental then they are called harmonics and we perceive a note.

The problem is that this situation occurs only in highly controlled/contrived circumstances such as a standing wave in a column of air or a precisely-made string vibrating under tension between two fixed points. This is why 'traditional' instruments can sound odd to a western ear: our instruments have been precisely engineered to eliminate all inharmonic partials.

My point is I'd be very surprised if a dustbin lid, or a fence post, or a......goat skin vibrated with a perfect harmonic series.

So I'm wondering if the tones and slaps are really only a function of the skin (and the technique) or if they are actually related to the bass fundamental (and therefore the dimensions of the shell).

Also, assuming for a moment that a harmonic series is being produced how the hell is it possible to control it just by striking the thing that is vibrating. Remember that on a string the individual harmonics are produced by touching a node and notes on a wind instrument are created by changing the volume of the column of air. Amazing anyone gets a coherent sound from a djembe at all really!

One last thought (might be barmey but you never know): if you played notes at the djembe the skin should vibrate sympathetically. Moreover it should do so particularly at certain frequencies. If you sprinkled iron fillings on the skin would you be able to see the harmonic series?

[djembefeeling]

actually, it does. When I get my delivery of djembes, there are always some I like pretty much and others I don't. Of course, the ones I like are picked early by my costumers. But after the drums sit in my classroom for, say, half a year, they start to sound much better, even though nobody played them. I think this is because they resonate all the time we play in the room and thus well-rehearsed ?!

Sounds plausible to me. The skin of the drums not being played will vibrate along with the sound made by all the other drums. (It's easy to notice this--just touch the skin of an unused drum very lightly when there are other drums being played in the same room. You can clearly feel the vibration.)

So, after a while, I imagine the continuous flexing of the skin on those idle drums will soften those skins, and they end up sounding better. Sort of a slow way of playing them in without playing them

Cheers,

Michi.

[djembeweaver]

there is one djembe in particular that doesn't sound that harmonic to me, it sounds "dirty", and it is interesting that the two African teachers giving classes in my room always go straight for exactly that drum

Ha - typical! I do think that africans are....wait for it.....partial to inharmonics (boom boom). Does it just make an unusual interval or or does it actually make a less distinct note?

djembeweaver wrote:
But that is clearly achieved by the different points on the skin you hit and how you hit it, isn't it?

Clearly you can control the tones you produce but that does not necessarily mean you are controlling a harmonic series. If you get a couple of drum sticks and go and play on your cooker you might find a few places that make nice notes. After a while you'd learn where to hit it to start producing a kind of melody. That would not mean that your cooker produced a harmonic series.

But after the drums sit in my classroom for, say, half a year, they start to sound much better, even though nobody played them. I think this is because they resonate all the time we play in the room and thus well-rehearsed ?!

It's possible. Acoustic guitars improve with age for exactly this reason. It could be other factors too though.

[djembefeeling]

Does it just make an unusual interval or or does it actually make a less distinct note?

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

[michi]

Quite apart from the fourth/fifth issue though, consideration of the harmonic series as an explanation opens a whole can of worms...

When you bang a dustbin lid you hear many partials (pure tones) but they don't bear any ordered relationship to each other so we perceive the sound as noise.

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").

The problem is that this situation occurs only in highly controlled/contrived circumstances such as a standing wave in a column of air or a precisely-made string vibrating under tension between two fixed points. This is why 'traditional' instruments can sound odd to a western ear: our instruments have been precisely engineered to eliminate all inharmonic partials.

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.

My point is I'd be very surprised if a dustbin lid, or a fence post, or a......goat skin vibrated with a perfect harmonic series.

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.

So I'm wondering if the tones and slaps are really only a function of the skin (and the technique) or if they are actually related to the bass fundamental (and therefore the dimensions of the shell).

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 )

Also, assuming for a moment that a harmonic series is being produced how the hell is it possible to control it just by striking the thing that is vibrating. Remember that on a string the individual harmonics are produced by touching a node and notes on a wind instrument are created by changing the volume of the column of air. Amazing anyone gets a coherent sound from a djembe at all really!

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.)

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.

One last thought (might be barmey but you never know): if you played notes at the djembe the skin should vibrate sympathetically. Moreover it should do so particularly at certain frequencies. If you sprinkled iron fillings on the skin would you be able to see the harmonic series?

Yes, absolutely, and someone already did this.

Also, I just found a really interesting page that illustrates vibrational modes of a kettle drum with nice animations. I don't know enough physics to decide whether all of these also apply to a djembe or not. (The vastly greater tension on a djembe may make it harder for some of these modes to happen.)

Cheers,

Michi.