Subharmonics; an 'impossible' violin note

[Third Eye Open]

This (http://www.noiseaddicts.com/?p=16#more-16) violinist, Mari Kimura, is apparently able to make notes on a violin that are too low to be played. A team of Norwegian scientists are trying to figure out how she does it with no luck so far.


Mari Kimura is a New York composer and virtuoso violinist whose music includes haunting low notes on the violin called “subharmonics.” …Problem is, these sounds aren’t supposed to be possible.

The tones she playes are in the register of a cello, and usually cannot be made from a violin. Even she is stumped about how it works. “I don’t really know what it is I do,” she said, because she learned it by “trial and error.”

A team of scientists in Norway, is the latest to take a crack at the puzzle. Kimura has said that she has been making these sounds for more than ten years. She demonstrated her ability to top scientists in the US, but they gave up trying to find out how the effect happens.

Any violinists out there have an idea how she does it? Some people have said that it is the bow vibrating, but I don't know enough about violin to tell if it sounds like that is happening. You can follow the links to a sample of the supposed 'impossible' sounds.

[FramerDave]

As usual, the comments are always more interesting than the article itself. She's obviously hollow.

[DrRocket]

I cannot tell you precisely how she does it, and I am not a good musician. But I can tell you that there is more vibrating with the violin or any musical instrument than just the strings. That is one reason that different instruments, though similar, can produce different and complex sounds. It could be the bow, it could be something in the structure of the violin itself. It could be a complex interaction among the components. It is always perilous to say that something like this is "impossible".

My daughter was once learning the violin. I can tell you that I heard some sounds that seemed "impossible" at the time -- and wished that they really were impossible.

[Thing]

This press release from the Norwegian University where she's being studied:

http://www.physorg.com/news70722951.html

certainly makes the lead investigator sound like a pompous ass.

Scientists from Stanford, Columbia and Tokyo University are amongst those who found the phenomenon interesting. However they did not have the necessary combination of competence within physics, as well as interest in music, to be able to work exhaustingly on figuring out Kimura’s subharmonic violin pitch. In Tromsø however Kimura found the right kind of scientists that can measure and explain the phenomenon.

"We have definitely what it takes to solve this mystery. We have worked with strange and exotic sound systems earlier, and we have the ability to make good measurements, correct theoretical modelling and of course the necessary musical insight and interest", says the physics professor Alfred Hanssen.


This source suggests the technique has been independently discovered by others even if it hasn't been fully explained.

http://michaelvincent.ca/Design/Assets/Writing/contemporary%20violin%20tech.pdf

These techniques utilize the use of extreme pressure to the bow stroke and careful placement across the string(s), which creates a variety of pitches sounding below the fundamental of an open string. For example, by bowing the G string precisely at the point where the octave is divided equally (midpoint of string) and applying overpressure to the bow stroke, the resulting sound will be a G one octave lower than the G string. If one bows the G string on a string divided at the 1/3 point, the result will produce a low D (a twelfth below the open G). This will be consistently produced at any harmonic node when overpressure is applied.

The first literary examples of subharmonics are found in the string quartet Black Angels composed by American composer George Crumb (b. 1929). He calls them pedal tones in the score, and then proceeds to explain to the performer how to produce the subharmonic tones. The following example shows the sounding pitches on the bottom staff, and the played pitches above. Crumb does not elaborate on the exact placement of the bow, leaving this at the performer’s discretion.

[The Mad Hatter]

I managed to get subharmonics on my cello pretty easily, though it's not exactly nice to listen to, and pretty unstable. It's certainly not the horsehair on the bow oscillating, because the fundamental note stops completely (or I guess it just becomes a quiet overtone).

If I had to guess, I'd say that the bow is "artificially" controlling the frequency, somewhat like if you were to actually grab a pendulum and swing it with your hand rather than let it swing at its own pace. The frequency of the subharmonic is largely dependent on the bow speed, and regular notes and harmonics aren't. But the frequencies don't bend; they just jump from one interval to another suddenly.

[robinson]

This (http://www.noiseaddicts.com/?p=16#more-16) violinist, Mari Kimura, is apparently able to make notes on a violin that are too low to be played. A team of Norwegian scientists are trying to figure out how she does it with no luck so far.

She seems quite capable of explaining (as well as showing) how she does it. Maybe the scientist aren't musicians.

http://www.angelfire.com/music2/davidbundler/kimura.html
David Bundler = DB
Mari Kimura = MK
How I discovered Subharmonics

DB: Let’s take the jump to subharmonics. First of all, what is a subharmonic?

MK: Okay. It is a very complicated phenomenon that happens on the string. The result is that I can now play the notes on the violin -- Normally, the open G string is the lowest note on the violin. But then with this technique, which is an extended bowing technique, I can play the notes below the open G without changing the tuning.

DB: What’s the lowest note that you can achieve?

MK: Well, the notes that I can play with a good amount of control as a musical element would be one octave below the open G, which resides in the cello range.

DB: Do you have to play near the bridge to do that?

MK: It’s a very good question. It really depends on what note you are playing, actually. This production of subharmonics has a lot to do with changing the bow pressure and speed combined with precise placement of the bow on the string. And when you’re playing harmonics, like natural harmonics on the string, the left finger is just slightly touching the string instead of pressing down.

DB: Right. Creating intermediate nodes in the string.

MK: Right. Instead of pressing down against the fingerboard. But playing subharmonics, unlike harmonics, the left finger should be pressed down to the fingerboard normally like you’re playing normal notes. The bow arm creates subharmonics by applying a little extra pressure on the string.

DB: So you can pretty much create any degree between, say, the open G and an octave below. Is that right?

MK: Yes, I have lots of different ways. It gets very complicated, but since I have found that I can play subharmonics, which are one octave below. So when I play open G, I get the G below. So when I play middle C on the G string, then you get the viola open C.
http://www.marikimura.com/bundler_interview.html

[Piscivore]

Does this have anything to do with the brown noise?

[bruto]

Just off the top of my head, would not a beat frequency produce a subharmonic? It's pretty easy to get beats from slightly differing tones (that is, after all, how you tune a piano), and I would surmise that you could get beat frequencies on a fiddle, either from adjacent strings or from the resonances of the instrument.

[shadron]

Yes, you would, but according to what is being said the primary tones simply stop and the subharmonic is the only tone present. If the oscillograph shown is representative of what is really being heard, there is the subharmonic and some rather high harmonics (mainly 3-4th order?) that add the non-symmetrical, funny shape to the wave. If it were a beat, you'd see the primary sines amplitude modulating to form the subharmonic beat. Something in the instrument (probably the biggest, strongest piece - the backboard) is being driven in a forced fashion way below it's normal resonance.

[The Man]

Yes, you would, but according to what is being said the primary tones simply stop and the subharmonic is the only tone present. If the oscillograph shown is representative of what is really being heard, there is the subharmonic and some rather high harmonics (mainly 3-4th order?) that add the non-symmetrical, funny shape to the wave. If it were a beat, you'd see the primary sines amplitude modulating to form the subharmonic beat. Something in the instrument (probably the biggest, strongest piece - the backboard) is being driven in a forced fashion way below it's normal resonance.


Well, I think you have hit the nail on the head, as other posters did (if you will pardon the pun). Sub harmonics are by that definition below the normally considered base (or fundamental) harmonic of the instrument. As such, must be forced or result from a deflection of instrumental elements beyond the normal or base resonance of said instrumental elements. Thus, the stress and deformation is also increased on those elements. I hope that these tests were preformed with some base violin and not an expensive violin, as forced resonance can result in plastic (or unrecoverable) deformations. As opposed to elastic deformations which result in the normal harmonics of that instrument. Although not a musician by trade, I have been involved in the design and testing of vibration dampers (for power lines), continued forced resonance tests being one of the most destructive tests and used to determine design or material flaws.

[alfaniner]

I remember a segment oh, 25? years ago of a guy playing a mandolin or something on a show like "That's Incredible!" He talked about how he and a friend had got around to trading shots of Galliano, and he pulled out his lute or something, and discovered this other pitch that was, well, Incredible! I still remember how it chilled me to hear it. I might even still have it on a VHS tape somewhere.

Although this was in a high level, not low like a subharmonic. It was something floating above what he was actually playing.

[jj]

Is this MEASURED low frequencies, or PERCIEVED low frequencies.

One can create the perception of a low frequency by creating a bunch of harmonics of that frequency that are all above that frequency.

This is not mysterious, it's done with French Horns, in your TV set if it has 'bass boost' of some varieties, etc.

Now, if it's MEASURED low frequencies, that plus some kind of nonlinearity would suffice.

[The Man]

I remember a segment oh, 25? years ago of a guy playing a mandolin or something on a show like "That's Incredible!" He talked about how he and a friend had got around to trading shots of Galliano, and he pulled out his lute or something, and discovered this other pitch that was, well, Incredible! I still remember how it chilled me to hear it. I might even still have it on a VHS tape somewhere.

Although this was in a high level, not low like a subharmonic. It was something floating above what he was actually playing.

I guess that would be considered “super-harmonics” which might not be that unusual as the interference of lower harmonic tones can result in a higher tone then those tones, but only if they interfere just right. Hopefully someone will correct me if I am wrong.


Is this MEASURED low frequencies, or PERCIEVED low frequencies.

One can create the perception of a low frequency by creating a bunch of harmonics of that frequency that are all above that frequency.

This is not mysterious, it's done with French Horns, in your TV set if it has 'bass boost' of some varieties, etc.

Now, if it's MEASURED low frequencies, that plus some kind of nonlinearity would suffice.

An aspect that I took for granted as I did not read the link, but as shadron referenced the “oscillograph shown” I surmised that some measurements were taken, although, shadron does also remark as to the representation of those measurements.

[Michael C]

Is this MEASURED low frequencies, or PERCIEVED low frequencies.

One can create the perception of a low frequency by creating a bunch of harmonics of that frequency that are all above that frequency.

This is not mysterious, it's done with French Horns, in your TV set if it has 'bass boost' of some varieties, etc.

Now, if it's MEASURED low frequencies, that plus some kind of nonlinearity would suffice.

A quick analysis of the spectrum of the first sound (octave.mp3) shows that there is a measured low frequency. The fundamental frequency is 98 Hz (an octave below the G-string of a violin). All the normal overtones of this frequency (196 Hz, 294 Hz, 392 Hz, 490 Hz, etc.) are present.

It's not the violin itself that is being forced below its normal resonance. A violin will happily resonate at frequencies below that of its usual low G string, without being damaged. It just depend on what strings you put on it, and how tight you span them. In this case, somehow the string itself is being forced to vibrate at half its normal frequency.

Kimura seems to be able to take any note played normally and then produce the note one octave below by changing bow pressure and speed. When a note is played on a bowed string instrument, the bow first drags the string to the side, setting up a Helmholtz motion in the string. When the Helmholtz motion comes towards the end of its cycle, the string slips back under the bow. This is explained in more detail here: Why is the violin so hard to play? (http://plus.maths.org/issue31/features/woodhouse/). That page explains that when there is too much bow pressure, causing the bow to stick too long to the string, a raucous sound is produced (this sound should be familiar to anybody who has learnt to play a string instrument). Somehow Kimura is able to control increased bow pressure in a way that lets her modify the normal cycle and produce a note with half the frequency. I did wonder if she simply manages to suppress every second cycle, but I imagine that it's more complex than that.

[BenBurch]

Maybe the BOW is that which is resonating, and the strings become a sounding board for it?

[Ladewig]

Well, I think you have hit the nail on the head, as other posters did (if you will pardon the pun).

It's early in the morning, so perhaps I'm dense, but I don't see a pun. Would you explain?

[Michael C]

Maybe the BOW is that which is resonating, and the strings become a sounding board for it?

No: if it was the bow vibrating, the pitch would be in relation to the tension and length of the bow. The pitch of the subharmonic is clearly related to the normal sounding pitch of the string: Kimura says she gets a sound one octave below the normal sound, which means that the frequency is half the normal frequency.

It's easy to make a string vibrate at a multiple of its normal frequency: if you want it to vibrate a double the normal frequency, create a node in the middle. For triple frequency, create a node a third of the way along the string. This is how the usual harmonic notes are made: you lightly touch the string with the left hand at the node position. Every string player knows how to do this.

Kimura is able to make a string vibrate at a fraction of its normal frequency. The possible notes are shown in the article that Thing linked to (http://michaelvincent.ca/Design/Assets/Writing/contemporary%20violin%20tech.pdf) in Ex. 4. The technique described there is to place the bow at a node position, so that to produce a subharmonic one octave below, you place the bow in the middle of the string. From Kimura's description I'm not sure if she's doing that. She does say that the location of the bow on the string is important, but she doesn't explain exactly where she places the bow.

[aggle-rithm]

Take this with a grain of salt, because it's from an over hundred-year-old source, but here it is:

Bells have a way of sounding much lower than they actually are, because they lack overtones. The fundamental note, in this case, is heard as one of the overtones, which makes the listener mentally "fill in" a lower fundamental note.

(Bells, reportedly, also have an "undertone", which is a second tone determined by the shape of the bell.)

[Michael C]

Bells are a different thing altogether. Bells don't lack overtones; they just don't have the normal series of harmonic overtones that are produced by a vibrating string. The complex series of overtones produced by a bell can certainly produce aural illusions. Often different listeners will not agree on the fundamental sounding pitch of a certain bell.

In the case of Kimura's subharmonics, there is no aural illusion: the analysis of the spectrum of the low G shows clearly that there is really a fundamental 98 Hz vibration.

[Cuddles]

I don't see why there's all this fuss about this violinist, subharmonics are absolutely standard with string instruments. They're uncommon because they're hard to play, don't sound very nice and the ranges are already covered by other instruments anyway, but she's nothing special and hasn't made any discovery at all. Investigating how they are made is interesting, but why do they have to make it all about this one person and ignore the thousands of people who have been doing exactly the same for the last few centuries?

[Elvis666]

I don't see why there's all this fuss about this violinist, subharmonics are absolutely standard with string instruments. They're uncommon because they're hard to play, don't sound very nice and the ranges are already covered by other instruments anyway, but she's nothing special and hasn't made any discovery at all. Investigating how they are made is interesting, but why do they have to make it all about this one person and ignore the thousands of people who have been doing exactly the same for the last few centuries?

They aren't just standard with strings. I have a degree in music and majored in trombone. It is nothing unusual for a good trombone player to play lower than the fundamental of the instrument. It just takes excellent breath and embouchure control.

[Michael C]

I don't see why there's all this fuss about this violinist, subharmonics are absolutely standard with string instruments. They're uncommon because they're hard to play, don't sound very nice and the ranges are already covered by other instruments anyway, but she's nothing special and hasn't made any discovery at all. Investigating how they are made is interesting, but why do they have to make it all about this one person and ignore the thousands of people who have been doing exactly the same for the last few centuries?

She would seem to be the first person to have developed a technique to reliably control the pitch of the subharmonics, to the point that she regularly uses them in her compositions. I don't think the technique is "absolutely standard": I didn't come across it during my days as a cello student, and I'm not aware of any string-playing colleagues of mine who use it. Certainly Kimura is not the only person to be able to play subharmonics, but it looks like she's the world specialist.

[aggle-rithm]

They aren't just standard with strings. I have a degree in music and majored in trombone. It is nothing unusual for a good trombone player to play lower than the fundamental of the instrument. It just takes excellent breath and embouchure control.

But I thought that note WAS the fundamental...? Isn't it one octave below what is normally the lowest tone? This is normally not playable by brass instruments; the first harmonic is what we usually hear as the "fundamental".

[aggle-rithm]

Bells are a different thing altogether. Bells don't lack overtones; they just don't have the normal series of harmonic overtones that are produced by a vibrating string. The complex series of overtones produced by a bell can certainly produce aural illusions. Often different listeners will not agree on the fundamental sounding pitch of a certain bell.


As I suspected...my source is an old orchestration book written before a lot of sound theory was worked out.

The bells in the University of Texas tower are pretty horrific...if you are close when they start playing a tune, it sounds like parallel tritones.

[ktesibios]

I remember a segment oh, 25? years ago of a guy playing a mandolin or something on a show like "That's Incredible!" He talked about how he and a friend had got around to trading shots of Galliano, and he pulled out his lute or something, and discovered this other pitch that was, well, Incredible! I still remember how it chilled me to hear it. I might even still have it on a VHS tape somewhere.

Although this was in a high level, not low like a subharmonic. It was something floating above what he was actually playing.

I encountered a similar thing engineering records for a cappella doo-wop groups. On some chords, if everyone hit their notes exactly right, I perceived an additional high note. The really weird thing about it was that while I perceived the voices as coming from the monitor speakers in front of me, that extra note appeared to originate inside my ears.

I suspect that it was probably an intermodulation product, with the ear's nonlinearity acting to generate sum and difference frequencies.

Barbershop quartet singers know this phenomenon and even give it a name: "the bird". When the bird sings, it means that your harmonies are perfect.

[aggle-rithm]

I encountered a similar thing engineering records for a cappella doo-wop groups. On some chords, if everyone hit their notes exactly right, I perceived an additional high note. The really weird thing about it was that while I perceived the voices as coming from the monitor speakers in front of me, that extra note appeared to originate inside my ears.

I suspect that it was probably an intermodulation product, with the ear's nonlinearity acting to generate sum and difference frequencies.

Barbershop quartet singers know this phenomenon and even give it a name: "the bird". When the bird sings, it means that your harmonies are perfect.

I have a recording of Mozart's Requiem where Janet Baker's voice, for a moment, sounds an octave higher.

Weird.

[lomiller]

It sounds to me they are simply saying the note is to low for the string length, but I can’t see it being that much difference then using a 1/4 or 1/8 wave antenna. There are nodes below 1 full wavelength where standing waves can develop especially if you play around with termination impedance.

[The Man]

It's early in the morning, so perhaps I'm dense, but I don't see a pun. Would you explain?


The sound made by the nail when struck on the head would be a forced response, as the nail is forced into the wood its resonance frequency changes making that a forced resonance response. Not totally analogues but it did strike me as being similar.

[mactac]

Hi Everyone,

I run noiseaddicts.com , which is the site originally referenced in this thread. I also wrote the blog entry. I've always been a fan of James Randi & have read this forum on & off in the past. I found this entry quite by accident.

It is an interesting phenomenon, and I am currently in contact with Mari and have been accumulating some further information.

I'll post a followup when I have gathered everything & organized what I have found.

Unfortunately, the physicists involved in the 2006 physorg.com article have not had any futher findings (or any that they have communicated to Mari). There are others doing research on this and I am attempting to contact them.

I hope I'll have some answers soon!

[Michael C]

Thanks for that information, mactac, and welcome to the forum!

Maybe you could answer this question: do you know where Mari places the bow on the string to produce this effect? Is it near the normal position, or is it somewhere over the fingerboard?