Harmonics of tones and slaps

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Re: Harmonics of tones and slaps

Postby djembeweaver » Sun Jul 01, 2012 8:13 pm

Now then, in all of the above slaps the fundamental and first partial (M2) have been successfully suppressed, while the next 3 partials (at around 700, 800 and 1000Hz) have been emphasised (well, I only really managed to emphasise the first of these effectively).

Here’s a graph of a fluffed left-hand slap (I don’t do this too often thankfully):

Fluffed left hand slap high fundamental.jpg
Fluffed left hand slap high fundamental.jpg (26.14 KiB) Viewed 897 times


Oh dear – you can clearly see that the fundamental is the highest peak here. M2 (at around 550Hz for me) comes next at a lower intensity, with M3 and M4 at the same lower intensity. This was more tone than slap in many ways, but the higher partials are clearly audible, though M2 is way too high also. It’s one of those annoying in-between strokes that is a little bit of both tone and slap. Grrrrr.

So are the masters always perfect……er….no. This is a Mamady slap that is far from perfect:

Mamady ok slap.jpg
Mamady ok slap.jpg (32.17 KiB) Viewed 897 times


Here the first biggish peak is the fundamental, a bit high maybe but so far so good. The next, and highest peak, is the M2 partial (500-600Hz or thereabouts) followed by 3 much lower peaks. This still has the classic Mamady triple-peak shape, but he has failed to suppress the M2 partial (I’m sure it’s not deliberate here because I took it from a signal)

Jurgen – do you remember I was talking about that first partial (that I was hearing as a sixth) creating an ok slap, but the octave being the one I really liked? You can clearly see that’s what’s going on in this slap. Too much M2 (an interval of around a fifth or a sixth) and not enough of the higher partials.

Again, for comparison, here’s a graph of a not-so-great slap from Iya Sako.

Iya ok slap.jpg
Iya ok slap.jpg (31.94 KiB) Viewed 897 times


Again you can clearly see the M2 partial is really high (although M4 is slightly higher still).

Neither Mamady nor Iya’s slap is anywhere near as bad as the abortive effort from me: whereas I managed to accidentally emphasise the fundamental, both Mamady and Iya failed to successfully suppress the M2 partial.

That’s it for now. More on tones to come…
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Re: Harmonics of tones and slaps

Postby djembefeeling » Sun Jul 01, 2012 8:45 pm

djembeweaver wrote:Jurgen – do you remember I was talking about that first partial (that I was hearing as a sixth) creating an ok slap, but the octave being the one I really liked? You can clearly see that’s what’s going on in this slap. Too much M2 (an interval of around a fifth or a sixth) and not enough of the higher partials.

Yes, I do. I like your analysis pretty much. I start to understand the shape of a sound much better now. Would love and hate to do this with my own slaps as well. What software do you use for this analysis? I only work with audacity till now, but I guess it won't work for this?
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Re: Harmonics of tones and slaps

Postby djembeweaver » Sun Jul 01, 2012 9:04 pm

Oh yes it will:

Open Audacity and import a file. Then use the zoom function to go down to a level where you can see the individual hits and select the one you want. Then go to the 'Analyze' menu and select 'Plot Spectrum'. When the next window comes up change the resolution from 521 to 1024 or 2048, and change 'Linear Frequency' to 'Log Frequency'.

That's it.

Go for it Jurgen. I think it's really interesting (obviously).
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Re: Harmonics of tones and slaps

Postby michi » Sun Jul 01, 2012 9:10 pm

Another hint: for the source material, use the highest resolution recording you have, preferably PCM. If it's an MP3, there is a good chance that the overtone spectrum has been messed with by the encoding, and many of the quieter harmonics have already been thrown away.

I still haven't had time to do this analysis justice, djembeweaver. But this is fascinating stuff. I want to do a few experiments of my own too. I'm still convinced that the entire "differently pitched" slap thing is exactly what you say it is: selection of particular harmonics.

One question: where did you take Mamady's samples from? Your own recordings or a CD?

Another one: what do you mean by a "fluffed slap"? Just a poor slap, or something closer to a tonpalo (third slap)?

Cheers,

Michi.
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Re: Harmonics of tones and slaps

Postby djembeweaver » Sun Jul 01, 2012 9:24 pm

One question: where did you take Mamady's samples from? Your own recordings or a CD?


An mp3 file ripped off a cd. It is clearly better quality than my recordings on my zoom (I might not have gotten optimal levels) even though it is mp3.

The graphs of my slaps (and those of Iya) were recorded at 96kHz and saved as a WAV file. Yes some partials might have been clipped but the overall shape conforms quite well to Prak's analysis.

Another one: what do you mean by a "fluffed slap"? Just a poor slap, or something closer to a tonpalo (third slap)?


Ha Ha - no, I mean a totally rubbish slap that ends up being half way between a slap and a tone!
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Re: Harmonics of tones and slaps

Postby djembefeeling » Sun Jul 01, 2012 9:31 pm

thanks for those tipps, guys! I hope my digital recorder and a wav. file will do. I don't want to spend money on new equipment for this analysis...
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Re: Harmonics of tones and slaps

Postby michi » Sun Jul 01, 2012 9:34 pm

djembeweaver wrote:
One question: where did you take Mamady's samples from? Your own recordings or a CD?


An mp3 file ripped off a cd. It is clearly better quality than my recordings on my zoom (I might not have gotten optimal levels) even though it is mp3.

OK, that is potentially a little dangerous. I haven't done any experiments, but there is at least a possibility that the MP3 encoding has already removed some harmonics so, by the time you analyse the sound, you analyse something that differs from the original.

Whether this is significant or not is something we won't know without a direct comparison though.

The graphs of my slaps (and those of Iya) were recorded at 96kHz and saved as a WAV file.

That's definitely the best way to get a spectrum that's accurate.

Another one: what do you mean by a "fluffed slap"? Just a poor slap, or something closer to a tonpalo (third slap)?


Ha Ha - no, I mean a totally rubbish slap that ends up being half way between a slap and a tone!

Oops. Yes, I know what they sound like :)

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Re: Harmonics of tones and slaps

Postby djembeweaver » Mon Jul 02, 2012 12:50 pm

Michi - I've done a little experiment to see what difference converting to MP3 makes.

I took the first slap I analysed (one of my decent ones) and converted it from WAV to MP3. Here are the two graphs:

nice slap spectrum.jpg
This is the original WAV file
nice slap spectrum.jpg (21.72 KiB) Viewed 883 times


Nice slap spectrum MP3!!.jpg
This is the same file converted to MP3
Nice slap spectrum MP3!!.jpg (26.5 KiB) Viewed 883 times


What's the difference? Well the MP3 is generally spikier and less rounded. My fundamental peak has split into a double peak; my M2 peak is still about the same intensity as the fundamental; my M3 peak is the highest and my M4 peak a bit weak.

That's exactly the same overall pattern even though the graph looks a bit different at first glance.

Here's something interesting though: If I take the same converted MP3 file but lower the resolution from 2048 to 1024 then I get this:

Nice slap spectrum MP3 1024 res.jpg
Nice slap spectrum MP3 1024 res.jpg (35.88 KiB) Viewed 883 times


Almost identical to the original WAV I think you'll agree.

So I think comparing MP3 to WAV makes like-to-like comparison difficult but doesn't change the overall characteristics of the spectrum.
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Re: Harmonics of tones and slaps

Postby michi » Mon Jul 02, 2012 10:13 pm

Thanks for checking this! Not sure why the MP3 looks different at the different resolutions. Presumably, at 2048, you are sampling at a higher rate than what is present in the MP3, so you end up taking samples of interpolated values.

I agree, the spectrum at 1024 looks close enough to the WAV one. It definitely doesn't differ enough to invalidate the analysis.

Mmm… I've been meaning to come back to this for months to hunt down the elusive tonpalo…

I'm thinking of extracting the soundtrack from Mamady's Djembe Kan DVD and running a spectrum on the tonpalos on that. I don't know though how good the original source material is for the DVD. It may have been recorded at mediocre resolution to start with.

If anyone has suggestions for tonpalo examples on CDs, I'd love to hear them! If we can find a good-quality CD recording of a player playing tonpalos and normal slaps without too much background noise, that might make for a good starting point to figure out what happens with the harmonics for the third slap.

Cheers,

Michi.
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Re: Harmonics of tones and slaps

Postby michi » Mon Jul 02, 2012 10:21 pm

djembeweaver wrote:Secondly Mamady has a double peak at 344 and 413Hz. I think both of these are really the fundamental (what do you think Michi?) as if you go down to a lower resolution they merge into one wider bump (more like mine).

I suspect it's a sampling artefact. It could also be that there are actually two tone pitches side-by-side, due to some imperfection of the skin or due to a shell that isn't perfectly round, not sure.

Then Mamady has a peak at 587Hz (though just as low as the fundamental) and finally a triple peak at 824, 938 and 1047Hz (I think these are probably M3, M4 and M5 on a tight djembe). This triple peak is quite consistent for Mamady’s slaps that I’ve looked at.

So the main difference between my slap and Mamady’s is this: Whereas my highest peak is M3 and I have very little of M4 or M5, Mamady has equal amounts of M3, M4 and M5. Surprise surprise…he is pulling out higher partials than me.

That looks like a key insight to me: working those higher harmonics is what gives the slaps their rich and distinctive sound, and the trick to playing beautiful tones is to suppress those harmonics as much as possible.

There is also an issue around skin thickness here. I've been increasingly getting sick of thin skins. With a thin skin tuned to solo pitch, I can effortlessly play cracking slaps that are very loud. But they sound boring. It's more like a "bang" than a slap, and the slaps sound empty. In contrast, on a thicker skin, my slaps have this beautiful overtone spectrum in them. Each slap sounds more like a chord than a single note.

For some reason, it's much easier to pull the overtones out of thickish skin than a thin one. (With really thin skins, I found that djembes sound almost like a darabuka. Very high slaps with very short sustain, but few overtones.)

Cheers,

Michi.
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Re: Harmonics of tones and slaps

Postby michi » Tue Jul 03, 2012 2:47 am

I found some nice examples of the third slap on Mamady's "Mögöbalu" CD, track 16: "Djembe Kan". I picked out four clear samples of bass, tone, slap, and tonpalo (third slap—Mamady calls it "Le"). Here are the four samples:

Combined.mp3
Bass, tone, tonpalo, slap
(60.36 KiB) Downloaded 173 times

I normalized all the samples, so it's possible to make a direct comparison of the relative loudness of the different harmonics.

Here is the spectrum of a bass:

Bass spectrum.jpg
Bass spectrum
Bass spectrum.jpg (119.65 KiB) Viewed 873 times

The bass fundamental is at 75 Hz, −13 dB (Helmholtz resonance). The spike at 345 Hz is the (0,1) tone fundamental (−32.6 dB).

Note the 19 dB difference between the bass and the tone fundamental. This means that the bass contains 79 times more energy than the tone fundamental.

Here is the spectrum of a tone:

Tone Spectrum.jpg
Tone spectrum
Tone Spectrum.jpg (127.14 KiB) Viewed 873 times

We can still see the 75 Hz Helmholtz resonance (unlabelled). It's at −26.7 dB. There are two smaller spikes to right of that, at 177 Hz (−39.7 dB) and 225 Hz (−37 dB). Note that the bass component of a tone is 13.7 dB quieter than a normal bass. In other words, the bass component of a tone carries around 23.5 times less energy than a bass.

The 177 Hz spike is the (0,2) mode of the Helmholtz resonance. The theoretical value is 172.125 Hz, well within the measurement error. The 225 Hz spike is the (1,2) mode of the Helmholtz resonance (theoretical value 218.7 Hz).

Looking at the remaining harmonics, the first thing that stands out is the double spike for the tone at 343 Hz and 401 Hz. This is an artefact of the sampling algorithm for the spectrum. At 2048 samples (which is the FFT size for the plot), we get a frequency resolution of 21.5 Hz, meaning the the real value of each of these two spikes can vary by as much as 10 Hz up or down. Dropping the FFT size to 1024 samples results in a single spike at 370 Hz, but now with a frequency uncertainty of 43 Hz.

The spike at 567 Hz is the (1,1) mode of the tone fundamental. To the right of that, we can see the (2,1) mode at 811 Hz, the (0,2) mode at 936 Hz, the (3,1) mode at 1024 Hz, the (1,2) mode at 1200 Hz, and what is most likely the (0,3) mode at 1422 Hz.

It's clearly visible that, going up towards higher frequencies, things are still divided into sharp bands. However, the volume of these spikes is way down, and it's not possible to reliably identify the vibrational mode anymore, both due to analysis error and because the modal frequency spacing gets narrower towards higher frequencies.

More about this in the next post. (I'm limited to three attachments per post.)

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Re: Harmonics of tones and slaps

Postby michi » Tue Jul 03, 2012 3:28 am

Here is Mamady's slap:

Slap Spectrum.jpg
Slap spectrum
Slap Spectrum.jpg (124.1 KiB) Viewed 870 times

Compare that with the tone spectrum in the previous post. The tone fundamental is way down, as is the (1,1) mode, but the (2,1), (0,2), and (3,1) modes are way up. So, the difference between a tone and a slap is basically that a tone has seriously loud (0,1) mode, and a slap has seriously loud (2,1), (0,2), and (3,1) modes.

Now here is what happens for the tonpalo (third slap):

Tonpalo Spectrum.jpg
Tonpalo spectrum
Tonpalo Spectrum.jpg (131.16 KiB) Viewed 870 times

Here we have it: the third slap is basically all (1,1) mode, with everything else suppressed (the tone fundamental as well as higher modes are all way down).

I think this makes it pretty clear that it's all about harmonics and selecting which ones should be emphasized.

If you wonder what these modes actually sound like, below is a sound file that starts out with a 400 Hz sine wave fundamental, and then successively adds the (1,1), (2,1), (0,2), and (3,1) frequencies, so you can hear the progression.

Synthetic.mp3
(0,1), (1,1), (2,1), (0,2), and (3,1) modes as sine waves
(208.47 KiB) Downloaded 158 times

If you want to see what the various wave forms look like, check out this series of illustrations. You can click on each diagram to get an animation.

Cheers,

Michi.
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Re: Harmonics of tones and slaps

Postby michi » Tue Jul 03, 2012 3:47 am

Here is an interesting video that uses a real membrane and coloured sand to show where the nodes are at various frequencies:



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Re: Harmonics of tones and slaps

Postby bkidd » Tue Jul 03, 2012 5:34 am

Nice explanation Michi. It's always nice to see spectrum plots, and even better when they're applied to analyzing djembe sounds. Fun!
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Re: Harmonics of tones and slaps

Postby djembefeeling » Tue Jul 03, 2012 6:49 pm

did some recordings and analysed my slaps with audacity. but when i try to export the graph, I can do so as a text only. how did you change it into a jpeg? however, perhaps it's for the better i can't manage to do so, cause my slaps have almost uniformly higher M2s than M3s, with some rare exceptions... :oops:
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