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Subharmonics

Technique and Practicing: How do you make pleasant notes below the violin's normal range?

From Edward Ferris
Posted May 7, 2007 at 08:27 PM

Does anyone have any advice on creating cleanish subharmonics?

From Peter Ouyang
Posted on May 8, 2007 at 07:58 AM
Subharmonics are very sensitive to bow parameters, so you have to be careful about maintaining the contact point once you've found something that works, and the pressure must be very consistent through the stroke -- often people have a tendency to "ease up" on the pressure at the beginning and end of the stroke, but that doesn't work for subharmonics. I find that it helps to use a fairly strong bow.

It takes some experimentation to find which notes you can get.

There are some articles on the subject by Mari Kimura which you might want to look up; if I remember correctly, she gives some detailed advice in them.

From Latchezar Dimitrov
Posted on June 10, 2007 at 08:44 AM
Do you know the relation between the intonation and the subharmonics sounds ?
I use the name "differential sound" if we talk about the same thing...
But in general nobody must use the "differential sounds" if he want to preserve the good intonation :-)
From Nathan Cole
Posted on June 10, 2007 at 04:14 PM
The basic idea is to use more pressure and less speed, with a contact point toward the fingerboard. It's far easier on the G string than the others.

The pitch produced should be about an octave below the fingered note. A little more or less depending on your violin.

The concept is a little like making a crystal glass "ring" by rubbing your finger along the top rim. If you've done that you know that you use a wet finger (your rosin) and a good deal of pressure to begin. As soon as the glass is vibrating you can back off the pressure. Otherwise you choke the sound completely.

I'll admit it's not easy, but experiment to find the pressure, speed and contact point for each note you want to create. The usual dead end I see is a player trying to do it close to the bridge.

From Rob Schnautz
Posted on June 10, 2007 at 09:42 PM
What's a subharmonic? You can play lower that a G without retuning?
From Nathan Cole
Posted on June 11, 2007 at 07:11 AM
You can! It's not what anyone would call a great sound, but it can be done.
From Nick Gerry-Bullard
Posted on June 11, 2007 at 07:01 PM
What's the basic technique for this? I hadn't heard of it either.

[edit]

Thank you Google. Not that it appears there is a straightforward way of adding this to my toolkit. Does anyone have any insight on the bowing technique required for this?

From Rob Schnautz
Posted on June 11, 2007 at 08:19 PM
Well, Wikipedia doesn't say much. It just says "Violinist Mari Kimura is purported to be able to produce subharmonic notes on the violin," and stops there. Hardly worth mentioning. Besides, the link on Mari Kimura's name is broken, anyway. (Anyone want to contribute to Wikipedia?)

The article did direct me to this page, though: http://www.world-science.net/othernews/060706_violin.htm

I'll continue my search for more information on this later.

EDIT: I found it! Eureka! Read this: http://www.marikimura.com/ASVA.html

From Rob Schnautz
Posted on June 12, 2007 at 06:26 PM
Okay...I went home and tried it. I can't seem to get it to work at all. I'm just hearing an open G, and the occassional high-pitched harmonic. Suggestions?
From Raphael Klayman
Posted on June 13, 2007 at 01:25 PM
I don't know if this is the same thing, but there's something I call "combination tones". They appear when we play double stops well in tune. Sometimes they're very difficult to hear, and even when they are relatively easier to hear it may take some practice to clearly discern. But it yields more fullness and resonance, and better intonation. I find them easiest to hear in major 6ths and minor 3rds in certain registers. For example, put your 3rd (or 1st or 2nd) finger on the first D on the A string. Then play the ist B on the E string. Play this 6th as well in tune as you can...Do you hear the G added to the D and B? It's a complete triad. That G is the same pitch as the G string - but it's not the G ringing in sympathetic vibration (or at least not entirely).It will still work if you cover (put a finger on) the G string. Play that same 6th an octave lower. The combination tone is an octave below the G. it's very faint and hard to hear. But it contributes a pleasent, organ-like 'rumbling' to the sonority. Go back to the original D above the A. Now play the F natural above it together with the D. Do you her the Bb? Etc...
From Daniel Stone
Posted on June 13, 2007 at 06:23 PM
yeah they're not the same thing but i do know what you're talking about - i think its called the "beat phenomenon" when two notes are slightly out of tune the sum of their sine waves is a bigger sine wave and you are able to hear a pulse. if the two notes are perfectly in tune then the beat actually turns into the frequency of a consonant note. i find it easiest to hear with 4ths and 5ths.

i've tried subharmonics a little bit and i got them to work a few times but not very consistantly. i don't know exactly how it works but i think it has something to do with added friction between the bow and the string that doesnt let it vibrate as fast. either way the tone quality of them is pretty bad.

From Tim Dale
Posted on June 14, 2007 at 03:16 AM
buy a viola?
From Rob Schnautz
Posted on June 14, 2007 at 03:31 PM
I was thinking an octocontrabass flute...it can hit even lower notes than a viola. :)
From Daniel Stone
Posted on June 14, 2007 at 03:36 PM
haha my friend got a low b extension on his bass (the lowest b on a piano)...it sounds like an elephant fart
From Rob Schnautz
Posted on June 14, 2007 at 04:02 PM
wow...I'm sure my coworkers got a kick out of that forward lurch I just did as I crashed into the flatscreen reading the above post...funny.
From Mari Kimura
Posted on August 1, 2007 at 06:39 PM
Hi, I'm Mari Kimura, a developer of Subharmonics. You can visit my website: www.marikimura.com to learn and listen to Subharmonics. At this moment I am working on the world premiere of Jean-Claude Risset's Violin Concerto with the Tokyo Symphony on Sept. 5th. It's the first violin concerto, aside of my own, to use subharmonics. I am writing my own cadenza, 'laced' with all kinds of Subharmonic intervals, including octave, 3rd, 2nd below the normal notes. Please send questions to marikimura@mac.com. The Juilliard email worked to register onto this site but it's not my main one. Thanks! Mari
From Ray Randall
Posted on August 2, 2007 at 02:06 PM
Yeee Haaaa! I did it. It didn't take long at all. It's a bit scratchy, but it there and in your face loud. It gave my wife a headache in the next room with her door closed. It sort of sounds like something you might hear coming from a dark, deep cave in Hades. My wife disagrees with it sounding like an elephant passing gas, she said it sounds more like a hippo letting one loose.
From Rob Schnautz
Posted on August 2, 2007 at 04:22 PM
How did you do it? I can't get it to work! I want to get hellish flatulence out of my violin!
From Rob Schnautz
Posted on August 2, 2007 at 04:27 PM
Mari, your "How to Produce Subharmonics" link http://www.swets.nl/jnmr/vol28_2.html is broken.
From Jim W. Miller
Posted on August 2, 2007 at 04:49 PM
Rob, here it is magically resurrected. Bottom of the page. Pays to be a geek.

http://web.archive.org/web/20050410192127/http://www.swets.nl/jnmr/vol28_2.html


From Mari Kimura
Posted on August 2, 2007 at 05:51 PM
Hi Jim,

Thanks for the link! I will update my website. I think that journal changed hands and I hadn't had a chance to track it down.

There is also a more recent article I wrote on STRINGS magazine, 2000 August/Sept issue called "The World Below G", but I don't think it's online...

From Ray Randall
Posted on August 2, 2007 at 05:57 PM
"Hellish flatulence," that's a good one. LOL.
Basically I played near the fingerboard, used fairly decent pressure and not a lot of bow. Lots of scratchy sounds just before it hit. It took just a little fooling around with bow speed and pressure to get it. It physically feels like the G string (got it on the D, too) is vibrating almost out of control when it happens, that the vibrations are very wide. That may be true or not, but that's what it felt like. I may have fun and try this during a soft passage at orchestra rehearsal tonight. Trouble is I can't practice this at home otherwise I won't be able to get back into the house if I'm outside. I know I'll be locked out.
From Albert Justice
Posted on August 2, 2007 at 06:40 PM
How cool--I got one... No not flatulence though there was a resemblance. It only went a half step below, and though I was able to get it on all parts of the stick it works better near the lower half.

Ironically--uh, I guess--it gave me some sort of something when I went back to normal bowing in terms of better hair contact control....

From Bilbo Prattle
Posted on August 2, 2007 at 08:43 PM
Raphael said:
"don't know if this is the same thing, but there's something I call "combination tones". They appear when we play double stops well in tune. Sometimes they're very difficult to hear, and even when they are relatively easier to hear it may take some practice to clearly discern. But it yields more fullness and resonance, and better intonation. I find them easiest to hear in major 6ths and minor 3rds in certain registers. For example, put your 3rd (or 1st or 2nd) finger on the first D on the A string. Then play the ist B on the E string. Play this 6th as well in tune as you can...Do you hear the G added to the D and B? It's a complete triad. That G is the same pitch as the G string"

This is nothing more than the natural sum and difference beat frequencies.

Here's how it works:

Take D as 586.6 Hz which is a 4th above A (at 4/3 just ratio).

Now, B is a major 6th above that which, depending on the temperament, can be anything from 1.66 to 1.7 times the frequency of the lower note (here we'll call it the "tonic").

[In 12 tone equal temperament, the ratio is 1.6818, and in one form of 16-limit just intonation it is 1.6875]

OK, so do a little algebra. (I already know the answer).

The resultant is a G. G is one step below an A, or 8/9th of the frequency in Just Intonation, so that is:

G = 391.11 Hz (586.7 x 9 / 8 = 391.1)

Now solve for the frequency of the B:

X - 586.7 = 391.1
solve X = 977.8

That is using the "difference" frequency.

Now solve the "sum" frequency:

586.7 + x = 4*G = 1564.4 Hz

X = 977.7

So, what we are saying is that you play the following two notes:

586.7 or D
977.8 or B

The sum of these frequencies is 1564.4

The difference is 391.1

When you play a chord, you hear the beat frequencies, which are simply the sums and differences (and their harmonics).

If the chord is in tune, then the sum and difference line up harmonically. Note that:

391.1*4=1564.4.

And, as I showed at the beginning, the 391.1 is the G that is on the D string.

Now, just what sort of "B" did we have to play to achieve this:

We had to play a relatively flat "Just" B with a frequency ratio of 5/3:

1564.4/586.7= 1.666 or 5/3.

The G string is one octave lower, and yet the dominant sound of the G string is actually the second harmonic, or the 391 Hz sound, and so that is part of why you feel that you are making a low G.

Note that if you play "equal temperament" or also if you play "pythagorean" you will not have this sweet settled chord. The sum and differences will not "line up" with eachother.

Here's Equal Temperament:

(A440)

D = 587.3 (yes, a bit higher than Just was above)

B = 987.7

Difference = 400.4
Sum = 1575.

Difference * 4 =1601.6

So the Sum and difference beat against each other at 1601.6 - 1575 = 26.6 Hz.

So you have a very low subaudible waver in there. You also have its 2nd harmonic at 53.2 Hz.

From Ray Randall
Posted on August 2, 2007 at 10:02 PM
That is tough to do counting on your fingers. I'll get back with the answer on my own next month.
From Mari Kimura
Posted on August 3, 2007 at 02:49 AM
Ray,

When I first discovered this technique in the winter of 1992, I was a student at Juilliard and had no life. I lived in a depressing tiny studio apartment next to a very old lady with several cats, who smelled bad and was deaf. So I had all the time and no worry in the world of offending anybody scratching away on my violin. Seriously, it took about two weeks to get rid of transient noises to stablize the low notes. Once my right arm 'remembered' the feeling, then it became very reliable. But then I noticed some new strings doesn't work well (I found out just before a live radio show) and I came to discover TWISTING the string counter-clock-wise helps moving the 'x' point on the string. It's documented in JNMR article. I'm sorry for your wife :)

From Ray Randall
Posted on August 3, 2007 at 03:13 AM
Laughing out loud Mari. Mary read this with me and said to tell you thank you for your thought.
I'll try th twisting while practicing tomorrow while Mary is grocery shopping. I did play one of the subs in the quiet section of the Botticelli Duo for violin and Bass. Literally half the people jumped, a few what the *^%$ was that, and the Concertmaster, who was conducting in the absence of the Conductor on vacation stopped and wanted to know 1. what that was and 2, how to do it.
Thank you for your advice.

Regards,

Ray

From Mari Kimura
Posted on August 3, 2007 at 03:27 AM
Bravo Ray! That's great, sounds like you can produce them now on demand, which is the hardest thing for Subharmonics. Please tell Mary that she can commiserate with my husband. In fact after accompanying me to a tour in Hungary, surviving and sleeping through my practicing in a hotel room, I decided to marry him!
From Emily Grossman
Posted on August 3, 2007 at 04:16 AM
What a fun experiment! I tried some on all four strings. Here are the sounds that resulted:


motor boat
bullfrog
dirt bike in low gear
truck horn
cellar door
nails on chalkboard

Excellent arsenal for future reference.

From Jonathan Yip
Posted on August 3, 2007 at 04:18 AM
I get it too!!
Very interesting sound!!
But it's rather difficult to control. The scratchy sound always comes before the subharmonic.
May I ask will this practice harms the sound quality of my violin? Because my previous teacher told me I always apply too much pressure and that would deteriorate the violin.
From Mari Kimura
Posted on August 3, 2007 at 11:51 AM
Jonathan,

On the contrary, I developed Subharmonics from an old Russian bowing excercise I was taught when I was a child, a variation of 'Son filé', mainly applying to high fortessimo notes on the E string. It is supposed to even out the bow pressure throughout your stroke and improve your tone :) I have been doing this for more than 15 years now and my violin is still fine. Actually it's not too much of a pressure, but to find the right 'scratch' then sustain the same scratch. Funny, isn't it?

From Jonathan Yip
Posted on August 3, 2007 at 12:34 PM
Kimura,

Thank you for discovering such an amazing new violin technique. I hope we can listen to more pieces using this new technique. Next time I will show it to my friends, "You can play artificial harmonics? Cool!! Well, I can play subharmonics."

From Ray Randall
Posted on August 3, 2007 at 02:44 PM
Congratulations Mari. This just proves that we don't know everything there is to know about our chosen profession/avocation. There will always be something new waiting to be discovered.
From Rob Schnautz
Posted on August 3, 2007 at 03:32 PM
It'll be something I'll have to work on next time I'm home alone, which isn't very often. Or maybe I'll work on it at church while I wait for the other quartet people to show up.

I loved reading the interview with David Bundler, by the way. Does touching your nose between Ab's really speed up your arpeggios?

From Mari Kimura
Posted on August 3, 2007 at 06:47 PM
Thanks Ray, and Hi Rob,

Well, that "nose-Aflat" trick is I think mostly psychological. Since the arpeggios range 4+ octaves, in our mind the gap is HUGE. But in fact it is as close as touching your nose from a short distance. So if you can get over the "4+octave" perception, it's easier. I am a believer that most of violin, or instrumental playing isn't mussle, but brain :) And also this---the usual teachers' chanting "lift your violin up", also has a good reason. It's easier for your left arm to pull things down, than lift things up! So if your violin is high, you can COME DOWN to GO UP the arpeggios :) I would also suggest to exhale as you embark on a difficult passage, which I was also proven to me from my child-birth Lamaze class !!! It makes you relaxed and agile when you breath, and if you watch a struggling student, often they are holding their breath when they try to play something difficult... Try to run or dash holding your breath--it doesn't work :):)

From Jesse Irons
Posted on August 5, 2007 at 03:11 PM
Thanks so much for joining the discussion, Mari! I remember reading that Strings article in 2000 and experimenting with sub-harmonics sporadically ever since. Seconds, thirds, and octaves are the most reliable for me.

I was a little bit surprised when I played Crumb's Black Angels and found a passage in what I assumed were sub-harmonics - the "Dies Irae" quotation accompanying the violin solo in the "Devil Music" movement. The pitches are supposed to sound an octave lower than written - C B C A B G A on the G string. Of course, Black Angels was written in 1970.

When you say you discovered sub-harmonics in 1993, do you mean that was when you first learned of them? You have clearly mastered the technique like few others and have expanded its possibilities, but I'm curious if you knew about the Crumb example, and what you know in general about the early history of sub-harmonics.

Thanks again for visiting this discussion!

From Paul Cook
Posted on August 5, 2007 at 07:45 PM
I first noticed subharmonics when I was about 15, which was back in the '60s. I was playing Fall from Vivaldi's seasons, and the opening chords of the third movement, when played just right, supply their own version of the bass line.

The tones are, indeed, the difference tones. In radio theory, they are referred to as heterodyne frequencies, created by the interaction of the incoming radio signal mixing with the local oscillator to create an 'intermediate frequency', which is easier to amplify.

They vanish with the slightest detuning of the double-stop tones. Only a perfectly sustained just-intonation interval will create them.

From Mari Kimura
Posted on August 6, 2007 at 12:59 AM
Hi Jesse, thanks for your note. Actually I had spoken with Crumb several years ago, when the Dark Angels was played by Kronos. I had asked him if he meant the 'octave below' but he only shook his head and shrugged :) since that passage is very difficult to get 'on the spot'. I am largely credited for the development and the systematic execusion method of Subharmonics. There has been a documantation that Paganini was 'practicing' a low notes in his room etc. but I am the first one to write it inside a violin literature systematically.

Paul, I am afraid we are not speaking about the same technique. Indeed the 'Difference tone' would disappear as soon as the intonation shifts, and it is quite faint. Subharmonics is nothing but faint, it is rather loud and in fact, the most difficult, or impossible thing to do is to make is soft! Subharmonics will not disappear, and you can get a fortessimo playing one octave below the open G (and the original note, open G will not be heard).

From Rob Schnautz
Posted on April 2, 2008 at 09:52 PM
I am working on a Wikipedia article on Kimura...anyone care to contribute? Anyone who discovers and explains subharmonics is definitely worth mentioning in the free online encyclopedia. Thanks for any help!

http://en.wikipedia.org/wiki/Mari_Kimura

From Nicole Stacy
Posted on April 2, 2008 at 11:21 PM
Ray, that's hilarious. I would love to see the reaction.
From David Allen
Posted on April 3, 2008 at 08:40 PM
Fascinating! I was always taught that sub-harmonics were not possible. I'll definitely have to look into this.
From Bilbo Prattle
Posted on April 4, 2008 at 01:55 AM
Subharmonics are simply the "scratching" that your teacher taught you not to make. It turns out that with some finesses, you can isolate one of the scratch frequencies and, voila! You are playing at a frequency lower than the fundamental.

Why and how is this possible? Simple: the bow! The bow hairs are alternating between sticking and unsticking. It turns out that you can get this to work at very low frequencies--lower than the natural fundamental note--which is the string vibrating freely.

EDIT: It isn't difficult at all to do this. But, it is not easy to make it sound musical or consistent. I am awed by Mari Kimura's ability yo used them musically!

From Allan Speers
Posted on April 4, 2008 at 12:42 AM
Daniel Stone wrote,

"yeah they're not the same thing but i do know what you're talking about - i think its called the "beat phenomenon" when two notes are slightly out of tune the sum of their sine waves is a bigger sine wave and you are able to hear a pulse. if the two notes are perfectly in tune then the beat actually turns into the frequency of a consonant note. i find it easiest to hear with 4ths and 5ths."

Those are called "Tartini Tones." Sadly, while the result can often be a musical note, it can just as often be distortion. Good recording engineers are aware of this phenomenon & have to deal with it a lot, for instance when two singers sing the same note.

I am not a good enough violinist to have to worry about this (yet) but I'd imagine that you acomplished players have the technique & ears to keep this in the "musical" category, without actually thinking about the physics behind it.

Anyway, it's different from the OP's topic. It MAY have something to do with how the violin produces a loud "G," since this note (and a few more above it) are below the violin bod't ability to vibrate (the Helmholtz frequency.) It's a fascinating topic, and there are several theories about it, but no absolute answer.


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