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uguntde

Frequency analysis violas

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I am trying to understand some frequency analysis of instruments, and wonder whether some of the experts here could give me some hints. Number 1 is a spectrum generated using Audacity with strings muted, by knocking on the bridge. Major frequencies are:862200803_Screenshot2018-12-23at13_34_53.thumb.png.c45e48df2873196435bacfb630adb388.png

231Hz – largest/ widest peak overall

Shoulders at 203 and 259Hz

321 Hz
374/385Hz
453Hz – as large at 231Hz – about 2*231Hz
489Hz
534Hz (with shoulder to the left)

566Hz - 591Hz - 636Hz - 665Hz - 713Hz - 781Hz - 817Hz - 873Hz - 945Hz - 977Hz

Could someone help me assign what is what? This is a 402 body length viola, nicely resonant, very good C string, well balanced sound with an interesting edge to it.

 

Here another instrument:

1429988021_Screenshot2018-12-23at13_48_51.thumb.png.032e4e2b8c9e91eb28e127d92a8e6da5.png

210Hz
Shoulder at 245Hz

342Hz

417Hz/447HZ 480Hz
592Hz - 567Hz - 594Hz - 636Hz - 661Hz - 714Hz - 781Hz - 821/ 851/ 867Hz - 941Hz

This is a 41.6cm body length viola, very strong dark sound, extremely resonant on the C string, very large powerful sound. The better of the two, but the first one is also very new.

I am trying to learn and hope some of you have the patience to look at this:
What is B1, B1+, what are the other frequencies? Which sould would you predict from this analysis? Can provide a sound sample should someone be interested.

I can later add some simpler Chinese instrument.

 

 

 

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Above 1400 it is mainly noise. But I can post it tomorrow. The dynamic range of my setup is limited. I used a Zoom USB mic and switched off all autoscaling etc.

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1 hour ago, uguntde said:

Above 1400 it is mainly noise.

I suggest you take one of the recordings of you playing an instrument and put it through a low pass filter at 1400 Hz.

Trying to think about the sound of a stringed instrument but excluding everything above 1400 Hz is like discussing paint colours with all the samples in black and white.

There's not much point employing "scientific method" if you start out by utterly skewing your dataset ...

Or to be less confrontational, the fact that amplitude above 1400 Hz seems weak on a graph doesn't mean it's irrelevant. Quite the opposite - every musical impulse contains huge amounts of fundamental, but it's the high harmonics that really characterise the sound.

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For the viola, I believe one typically see two peaks between the open G and open D string frequencies (196hz to 293hz). The lower is a body mode sometimes called B0 and the higher is the air mode A0. These can be very close to each other. If you increase the sample points for the response analysis, your first peak may split into two.

From the open D to open A frequencies (293hz to 440hz) one would typically see two more prominent peaks. The lower would be the B1 mode and the higher the air A1 mode.

Prominent peaks beyond the open A string frequency would be various other body modes.

The part of the spectrum that you did not display is not actually noise. Since your frequency scale is logarithmic, you get real modes squished over shorter distances which gives the appearance of noise. Some people look for a hill defined by a cluster of modes, followed by a rapid roll off of the mode amplitudes at some characteristic frequency.

What any of this means in terms of quality of sound is subject to lots of conjecture.

 

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Usually for violins only frequencies below 600Hz seem to be considered for A0, B0, B1, B1+

http://www.catgutacoustical.org/research/articles/modetune/modechrt.html

Schleske looks into the noise at higher frequencies but then one needs a more dampening window function. He also reads a lot out of some noise:

http://www.schleske.de/en/research/introduction-violin-acoustics/sound-analysis.html

One should average these signals, this is what we do in my field, NMR spectroscopy. We ust average equal signals until S/N is stronger. The type of frequency analysis is similar (except that you can't get a complex signal, i.e. two orthogonal signals, from a violin).

Schleske also plots the x-axis chromatically, which I assume means log2 scale, as any double frequency is an octave. Audacity can't do this, but I can use matlab if I can figure out how to fft a signal that is not complex (i.e. of two rectangular channels). Maybe a HIlbert transform and then a power calculation?

All this has been figured out before but is not well dcumented anywhere. At least I can't find it.

My fundamental question is which resonances should be strongest for a good sounding viola.

 

 

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For the first one, it is fairly clear to me:  231= A0,  321=CBR,  374/385=B1-, and 453=B1+.  Although we commonly just talk about these modes as if they are the only things there, quite often there are bumps and blips around them that can muddy the picture.  I wouldn't worry about trying to identify all the other higher peaks, as they vary a lot from instrument to instrument.

For the second one, 210=A0, and 342=B1-, or perhaps a combination of B1- and the CBR.  The B1+ is surprisingly weak, but I"m sure it's there in the 400 - 440 range.

FWIW, this is my VSA tone award winning viola (40 cm), analyzed with impact and bowed semitone scale.  The A0 and B modes are rather obvious, although I expect the bowed result shows a combination of B1- and CBR.  In my  experience, the CBR shows up much more strongly under bowing than it does for impact.  The bowed scale is also shown at lower resolution, to avoid the granularity of the single notes.

11032440_Viola29.jpg.a1f76082b8376c80e523dfb841c4586b.jpg

 

I agree with other posters that above 1400 Hz is definitely not "noise", although it is so chaotic you'd be tempted to ignore it.  Trying to analyze it to determine what it sounds like, or if it's good or bad, is a pretty impossible task... but the same thing can be said about any part of the response spectrum. 

About the only thing you might be able to tell from the first two instruments is that the second one has lower resonances, and more power down low, so is likely to have a deeper sound.  You could probably say the same thing by just looking at the size difference.  Good or bad is far more difficult to determine, likely involves a lot of what is going on at the higher frequencies, and in the end is personal anyway.  About the only thing I can say is that huge gaps in the response are probably not a good thing, as well as excessively high peaks.  But then, trying to figure out what to DO about it is another impossible task.

 

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10 hours ago, martin swan said:

 

Or to be less confrontational, the fact that amplitude above 1400 Hz seems weak on a graph doesn't mean it's irrelevant. Quite the opposite - every musical impulse contains huge amounts of fundamental, but it's the high harmonics that really characterise the sound.

Agreed, and I also think that these higher frequencies can contribute a great deal to the perception of a strong bottom end, and "depth" to the sound.

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34 minutes ago, David Burgess said:

Agreed, and I also think that these higher frequencies can contribute a great deal to the perception of a strong bottom end, and "depth" to the sound.

I had a very interesting discussion along these lines with an old friend of mine the other day, who is a successful and well-respected hi-fi loudspeaker designer. He has found that tweeter choice has a significant effect on perceived bass quality. 

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11 hours ago, Don Noon said:

For the first one, it is fairly clear to me:  231= A0,  321=CBR,  374/385=B1-, and 453=B1+.  Although we commonly just talk about these modes as if they are the only things there, quite often there are bumps and blips around them that can muddy the picture.  I wouldn't worry about trying to identify all the other higher peaks, as they vary a lot from instrument to instrument.

For the second one, 210=A0, and 342=B1-, or perhaps a combination of B1- and the CBR.  The B1+ is surprisingly weak, but I"m sure it's there in the 400 - 440 range.

FWIW, this is my VSA tone award winning viola (40 cm), analyzed with impact and bowed semitone scale.  The A0 and B modes are rather obvious, although I expect the bowed result shows a combination of B1- and CBR.  In my  experience, the CBR shows up much more strongly under bowing than it does for impact.  The bowed scale is also shown at lower resolution, to avoid the granularity of the single notes.

11032440_Viola29.jpg.a1f76082b8376c80e523dfb841c4586b.jpg

 

I agree with other posters that above 1400 Hz is definitely not "noise", although it is so chaotic you'd be tempted to ignore it.  Trying to analyze it to determine what it sounds like, or if it's good or bad, is a pretty impossible task... but the same thing can be said about any part of the response spectrum. 

About the only thing you might be able to tell from the first two instruments is that the second one has lower resonances, and more power down low, so is likely to have a deeper sound.  You could probably say the same thing by just looking at the size difference.  Good or bad is far more difficult to determine, likely involves a lot of what is going on at the higher frequencies, and in the end is personal anyway.  About the only thing I can say is that huge gaps in the response are probably not a good thing, as well as excessively high peaks.  But then, trying to figure out what to DO about it is another impossible task.

 

Thanks for this detailed response.

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3 hours ago, MANFIO said:

Is it possible making this with a recorded solo viola?

You can certainly make a FFT response plot of a recording... but what you get depends on the specifics of what piece is played and the recording.  It is usually possible to see the A0 as long as the range of notes played is wide enough, and sometimes you can see B modes as well.

Below is a comparison of the bowed semitone scale vs. a clip by Annelle Gregory playing the same viola, here.  The major modes are sotof there, although likely distorted by the distribution of notes played in the clip.  The recording conditions were also completely different... computer microphone vs. iPhone, different distance, location, and of course, the player.

1457900631_29recordingvsscale.jpg.f9c4d0834cca8e588c4ae33ec62765d3.jpg

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On 12/24/2018 at 8:45 PM, MANFIO said:

Thanks Don! Would love if someone could do this with this record, one of my 40.7 cms. viola, solo playing by Esther Apituley.

https://www.challengerecords.com/products/14557966537288

I can give it a go, but probably Don knows better how to do it right.

Nice to see Esther plays one of your violas, she is probably the most famous player here in Holland. Did she order direct from you? She is quite a character!

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This is a graph from the first 10 seconds of the adagio.

Looks a bit different than the ones above, so i wont comment on whats what :D

manfio1.thumb.jpg.64bc4ee3ba9289310a7365ccfb4d09f1.jpg

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1 hour ago, Emilg said:

I can give it a go, but probably Don knows better how to do it right.

Nice to see Esther plays one of your violas, she is probably the most famous player here in Holland. Did she order direct from you? She is quite a character!

Hi Emilg! Yes, she is quite famous in Holland indeed! She came here to a festival and asked to see my violas, I had two 40.7 ones.  She took both on trial and chose one after a one day trial. The other went to the principal viola of the Korean Chamber Orchestra a month later. And, yes, she is quite a character!

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36 minutes ago, MANFIO said:

Emilg said "Looks a bit different than the ones above, so i wont comment on whats what". 

Oh, I have no idea, I just can't interpret that.

I think we are seeing the played notes rather than the body modes, and maybe the room acoustics play a part too. A played semi-tone scale would probably give a better picture.

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10 seconds is too short for taking a bowed response plot.  You don't have that many notes in that time frame, so the notes will dominate over the body acoustics.  Also, using 4096 "size" is too high of a resolution for bowed response plots, and will make individual notes stand out.  I use 2048 for bowed, and 4096 for impact.  My plots look different as well because I crop the screenshot down, and cut-and-paste the scale at the bottom.

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13 hours ago, Emilg said:

Ok i will redo a graph with longer recording and lower resolution today..maybe a piece with more notes too.

It will still highly depend on which notes were played.

When I want to do a "played" response graph, I mostly use glissandi, in an attempt to play all frenquecies equally.

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6 hours ago, David Burgess said:

It will still highly depend on which notes were played.

When I want to do a "played" response graph, I mostly use glissandi, in an attempt to play all frenquecies equally.

I did some more tests, but indeed still mainly see the played notes. Now why didn't that Bach guy use more glissandi ;) I will try to post a better result today.

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Hopefully this one makes more sense - 30 sec recording (Chaconne), 2048 resolution, axes cropped:

manfio2.jpg.2d5dc3f220a0554a030d0e81e84f1c39.jpg

 

so possibly:  228 = A0, 296 = CBR, 385 = B1-, 442 = B1+

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16 minutes ago, Emilg said:

so possibly:  228 = A0, 296 = CBR, 385 = B1-, 442 = B1+

That would be my best guess as well.  It seems that the CBR mode on violas is quite a good sound producer when bowed, but not when looking at impact response.  I have seen that as well on violins, but moreso on violas.

Academically interesting, for those so inclined such as myself, but it's hard to see how this could translate into a useful tool for actually making better instruments, and could become more of a distraction.

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