From Edward Ferris
Posted May 7, 2007 at 08:27 PM
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.
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.
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?
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
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.
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...
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....
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:
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:
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.
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 :)
dirt bike in low gear
nails on chalkboard
Excellent arsenal for future reference.
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?
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."
I loved reading the interview with David Bundler, by the way. Does touching your nose between Ab's really speed up your arpeggios?
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 :):)
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!
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.
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).
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!
"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.
Violinist.com Editor Laurie Niles is in New York to cover the biennial event at The Juilliard School, including classes by Brian Lewis and Sarah Chang.
Please consider supporting Violinist.com by becoming a sponsor, and reaching our dedicated community of violin professionals, students and fans!