Reed physics - harmonics

[Little John]

3 minutes ago, Don Taylor said:

In that case shouldn't I see a second set of harmonics starting at A5?

 

 

Yes, though it might be low amplitude. However, the harmonic series overlaps so much with that of A4 it would be difficult to spot it.

 

5 minutes ago, Don Taylor said:

... our brains are doing some tricks here.

 

Indeed. I am convinced that we perceive the fundamental from the harmonics. How else could you distinguish a man from a woman on the telephone? In the UK, the telephone system operates only between 300Hz and 3000Hz. How else can you "hear" a bass on a smartphone speaker?

[Don Taylor]

2 hours ago, Little John said:

Yes, though it might be low amplitude..

It would have to be a really low amplitude - I cannot see anything in Transcribe! that is not part of the fundamental's harmonic sequence, or:

 

2 hours ago, Little John said:

However, the harmonic series overlaps so much with that of A4 it would be difficult to spot it.

Is the harmonic series for a note that is exactly 1 octave higher than another (A5 over A4, say) a proper subset of the lower note's series?

 

If so, then that would explain why I cannot see any distinct overtones for the higher note.  If not, then I would expect to see a few distinct overtones - and I do not.

 

(Transcribe! has a feature that lets me mark the harmonic series for a selected note so it is possible to figure out if a sound is potentially an overtone of a lower note or if it is a distinct  sound).

 

Added later:  A quick visual comparison of two such harmonic series seems to show that the higher fundamental's series is a proper subset of the lower note's series.  So, that would explain why a higher sounding note is simply not heard or seen on a display like mine - it just adds to the amplitude of some of the harmonics of the lower note.

 

I guess that this is why a perfect octave sounds perfect.

 

 

Edited October 21, 2020 by Don Taylor

[Little John]

28 minutes ago, Don Taylor said:

Is the harmonic series for a note that is exactly 1 octave higher than another (A5 over A4, say) a proper subset of the lower note's series?

 

Yes. A fundamental of 100 Hz has harmonics at 

 

200, 300, 400, 500, 600, 700, 800, ...

 

The octave above, 200 Hz, has harmonics at

 

400, 600, 800, ...

[David Barnert]

43 minutes ago, Don Taylor said:

I guess that this is why a perfect octave sounds perfect.

 

Indeed, as it’s true that a harmonic series built on ANY harmonic of a given fundamental will be a subset of the harmonic series of that fundamental, the interval between any two notes whose frequencies are in a ratio of small whole numbers will sound nice (there is great agreement between their overtones). This is what we forfeit when we tune to equal temperament, where nothing but the octaves are in rational number ratios.

[Little John]

13 minutes ago, David Barnert said:

This is what we forfeit when we tune to equal temperament, where nothing but the octaves are in rational number ratios.

 

Indeed! I was interested to observe that the fourth harmonic was strong in both Don's and Alex's examples. The fourth harmonic is the major third, which in equal temperament is 14 cents sharp. This explains why 1/4 comma mean tone tuning makes such an improvement on the concertina - it brings the major third exactly in line with the fourth harmonic of the fundamental.

[David Barnert]

20 hours ago, Little John said:

The fourth harmonic is the major third

 

Most people would call that the 5th harmonic, counting the fundamental as the 1st harmonic. That way, the harmonic number is equal to the ratio of frequencies between the harmonic and the fundamental. See the figures here:

 

https://en.wikipedia.org/wiki/Harmonic_series_(music)#Frequencies,_wavelengths,_and_musical_intervals_in_example_systems

[Little John]

4 hours ago, David Barnert said:

Most people would call that the 5th harmonic, counting the fundamental as the 1st harmonic.

 

I think scientists tend to do that, while musicians tend to use "fundamental" with the octave as the first harmonic. In other words, musicians treat "harmonic" as synonymous with "overtone", as in this definition of "harmonic" (the first to come up on a google search):

1. 1. 

   MUSIC

   an overtone accompanying a fundamental tone at a fixed interval, produced by vibration of a string, column of air, etc. in an exact fraction of its length.

 

[Richard Mellish]

21 hours ago, Little John said:

 

I think scientists tend to do that, while musicians tend to use "fundamental" with the octave as the first harmonic. In other words, musicians treat "harmonic" as synonymous with "overtone", as in this definition of "harmonic" (the first to come up on a google search):

1. 1. 

   MUSIC

   an overtone accompanying a fundamental tone at a fixed interval, produced by vibration of a string, column of air, etc. in an exact fraction of its length.

 

I'm both a scientist (Physics PhD) and a musician (obviously a concertina player: that's why I'm here). I might agree about calling 2f the first overtone, but not the first harmonic. But this is thread drift from the original subject of what harmonics there are and how they arise from the air flow over the vibrating reed.

 

I was recently contemplating the respective virtues of alternative temperaments for a new concertina, prompted by one particular equal temperament major third on one of my present concertinas sounding very harsh. But I eventually realised that other major thirds on the same instrument are much less harsh. That suggests that the harshness is due to the strengths of the various harmonics of the particular two notes; but I haven't got around to looking at their spectra.

[David Barnert]

16 hours ago, Richard Mellish said:

...

prompted by one particular equal temperament major third on one of my present concertinas sounding very harsh. But I eventually realised that other major thirds on the same instrument are much less harsh. That suggests that the harshness is due to the strengths of the various harmonics of the particular two notes...

 

Or (more likely, I would think), one of the reeds is a little out-of-tune.

[Richard Mellish]

12 hours ago, David Barnert said:

 

Or (more likely, I would think), one of the reeds is a little out-of-tune.

No, they're in equal temperament and therefore well away from "just" tuning, where the fundamentals are in perfect small-number ratios. And the particular third that sounds rough continued to do so after the instrument had a service including tuning.

[DaveM]

I made a go at grabbing the waveform from my concertina (a brass reeded Lachenal) -- I was focused on the recording, so I hit D5 instead of A4, but this looks a bit different from the earlier post.   I'd say this is much more like a triangle wave + some extra modulation; you can see this in the power spectrum in that the even harmonics are down quite a bit relative to the odd ones.

Edited October 25, 2020 by DaveM

[ttonon]

A picture is worth much speculation and many posts.

The attached plot shows the pressure upstream of a vibrating free reed, with time on the Abscissa.  The reference is:

"Aerodynamic excitation and sound production of blown-closed free reeds without acoustic coupling: The example of the accordion reed"
Denis Ricot, Laboratoire de Me´canique des Fluides et d’Acoustique, UMR CNRS 5509, Ecole Centrale de Lyon, France; Rene´ Causse´ and Nicolas Misdariis
Institut de Recherche et Coordination Acoustique/Musique, UMR CNRS 9912,
1 place Igor Stravinsky 75004 Paris, France

 

The dotted line denotes the time the tongue opens, passing flush to the top of the reed plate as it moves away from the plate, and the dashed line denotes the time the tongue comes back down, closing the slot. 

You may notice that there are two pressure pulses, though they are very different in magnitude and shape.  As some have mentioned here, the ear/brain system is extremely sophisticated and has no trouble interpreting these pulses as different; i.e., there is only one periodic time associated with this wave form. 

I'm delighted by the interest shown here on free reed physics, and this thread is an illustration that all we humans need to each learn individually everything that other humans have likewise learned.  Although it's true that a very large number of such topics have been discussed on Concertina.net, and I presume the record is there for the searching, I understand that the thrill of such discussions of discovery through live discussion is irresistible.  In particular, Dana, Chris, Richard Morse, myself, and others participated in discussions of these topics in great detail, going back at least 17 years.  Not all of it is accurate, since just like here, it takes a while before correct understanding can be achieved, but there's much knowledge to be gleaned from those discussions. 

I can't hope to present all the information available in the scientific papers to this thread, because of it's wide range of concepts.  I will mention one detail that has not been discussed here, and that is the fact that, although the vibrating tongue vibrates mainly in it's first bending mode, the second mode vibration can often be measured, and more importantly, this first mode vibration itself involves overtones that are whole number ratios; aka harmonics.  Said in another way, the first bending mode, which consists of a node at the anchor point, with maximum amplitude at the tip, also contains harmonics that are unique to the tongue material and other parameters of the system.  This harmonic spectrum causes the tongue to move - as a whole - in a jerky motion in time, all the while maintaining the same x-dependency of the first mode transverse cantilever vibration.  Mathematically, that's because the x-dependency (tongue shape) and the time dependency (harmonics) are separable.  It's my hunch that these harmonics in tongue vibration contain the clue to why a tongue of one material, say steel, will produce a different sound than a tongue of say brass.  If not for these harmonics, why would the sound be any different?

Regards,
Tom
www.bluesbox.biz

[alex_holden]

3 hours ago, ttonon said:

The dotted line denotes the time the tongue opens, passing flush to the top of the reed plate as it moves away from the plate, and the dashed line denotes the time the tongue comes back down, closing the slot. 
 

 

Hi Tom, thanks for your input. Is this measuring the pressure across the reed plate? What would the static pressure be if the reed was blocked off? I'm not totally sure I understand why it goes negative for part of the cycle.

[ttonon]

Hi Alex, if that confuses you, let me confuse you further by a similar plot made by a different investigator, James Cottingham, one of the pioneers in experimental investigation of free reed physics.  The figure caption explains the set up and notice the similarity between Ricot's measurement for pressure above the reed and this one: two humps roughly in the same place, with one hump significantly larger than the other.  Notice also the complex pressure waveform in the cavity below the reed. 

That's all I want to point out here.  In my view, the Western free reed can rank as the most difficult to understand musical instrument sound source, at least from a physical point of view.  As usual, this doesn't stop some from holding convictions on unscientific pet theories about how it works.  All this can only stir up lively discussion, which is good, but there's also a cautionary note there for one to be not so certain about his or her suppositions until hard scientific data becomes available. 

Regards,
Tom

[David Barnert]

23 hours ago, Richard Mellish said:

No, they're in equal temperament and therefore well away from "just" tuning, where the fundamentals are in perfect small-number ratios. And the particular third that sounds rough continued to do so after the instrument had a service including tuning.

 

I have difficulty understanding why all the other 3rds don’t sound just as bad. After all, isn’t that what “equal temperament” means?

[Richard Mellish]

1 hour ago, David Barnert said:

 

I have difficulty understanding why all the other 3rds don’t sound just as bad. After all, isn’t that what “equal temperament” means?

It surprised me when I realised how different they are. I surmise that the harmonic content is significantly different between reeds, such that one pair of reeds an ET major third apart (so well sharp of a perfect major third) happen to have clashing harmonics that are especially strong, and another pair, also an ET major third apart, have those harmonics weaker. I suppose I ought to make some more measurements.

[David Barnert]

3 hours ago, Richard Mellish said:

I ought to make some more measurements.

 

Is it an Anglo concertina? If not (ie., if it plays the same note on both the push and the pull, using different reeds), does the problem happen in both directions? The first thing I would measure is the intonation of the reeds. There are many inexpensive or free apps that will turn you smartphone into a sophisticated tuner. It would be nice to think that because it was tuned recently it can’t be out of tune, but I still think that is the most likely explanation.

[Richard Mellish]

It is an Anglo. I do have such an app on my phone. That particular third has sounded rough consistently, regardless of when the instrument was last tuned. I have a lot of other things to get on with at present but I do intend to make some measurements sooner or later because I would like to understand exactly what is going on.