September 16, 2011 at 6:22 AM
Don't fret, you can play in tune without a chromatic tuner.
Actually I'm not going to tell you whether or not to use a chromatic tuner to help you, any more than I'm going to tell you whether or not to use a shoulder rest. I'm beginning to suspect, based on a current Violinist.com discussion about chromatic tuners, that V.commies are as passionate about the use or non-use of chromatic tuners as they are about the use or non-use of shoulder rests -- Egads! Here's my advice on both fronts: use anything that ultimately helps you to play better.
Nonetheless, I advise my students to use a chromatic tuner to tune the strings on their instruments, and when it comes to finger placement, I direct them to other references.
So if you have been using a chromatic tuner to help you place your fingers, how do you learn intonation, if you take it away? The advice, "Just use your ear!" -- said with frustration and a sense of moral superiority by a respected teacher -- probably will not help a student who just isn't hearing what's wrong.
Certainly, start by tuning your instrument with the tuner, and frankly, I think you're going to be fine if you tune all four strings with it -- it's certainly going to be better than guessing, before you have developed your sense of pitch. Because yes, there levels and refinements when it comes to hearing pitch. That's what Mendy Smith's blog was about a few days ago: she had realized that she had approached a level where she needed to refine her intonation without the use of a chromatic tuner because she truly was beginning to hear the subtleties of pitch in relation to other tones. You can't tune your violin by hearing a perfect fifth until you can hear a perfect fifth.
A good, basic place to start learning intonation is by becoming sensitive to the ringing tones, also called "resonant notes," on your violin (or viola). What I'd like to do in this blog is to give you an introduction to ringing tones, if you are a student who doesn't yet know about them, or give you some ideas for explaining them, if you are a teacher. I welcome everyone's thoughts on the subject, as well.
The most obvious ringing tones are the strings: E, A, D and G (If you are a violist, A, D, G, and C). As you may have noticed, the open strings ring in a louder, fuller, more obvious way than notes played with a finger placed down on the string. In fact, try playing an open string. Notice that, not only does it sound very full, but also the string vibrates quite a lot -- this is something you can see with your eyes. Notice also that the wood on the body of your fiddle also vibrates, and you can feel this vibration if you put your hand on the back of the violin while playing, or even if you hold the scroll of the violin (yours or someone else's).
Any note on the violin vibrates, but the open strings vibrate the most.
So here's the cool part: What happens when you play an E, A, D or G that is not an open string? For example, try playing the G that is located third finger on the D string. If you play it perfectly in tune -- and only if you play it perfectly in tune -- your violin will have a party and ring with joy. More specifically, the G string will vibrate in sympathy with the G note you are playing on the D string. If you play this note with very good, even tone and perfectly in tune, you can even see the G string vibrating. Certainly it will ring much, much more than an out-of-tune G or than a note such as an E flat, which does not have its own special string to ring with it.
As you can guess, your violin needs to be well-tuned for this to actually work. Where else is there a G on the fiddle? You can try the G that is located on the E string, low second finger. It will not make the earth shake in the same way as the G that was an octave closer, but it definitely will hit a groove when it's perfectly in tune, and the violin will respond by ringing in a very clear way.
You can try this also for all the D's on the fiddle (third finger on A string, third position fourth finger on E, etc.); all the A's (first finger on the G string, third finger on the E, etc.) and all the E's (first finger on the D, etc.) and for the viola, all the C's (third finger on G string, low second on A string, etc.) Yes, and it works if you are playing a fourth finger on the G, the D string will ring in sympathy with the exact same D. Just make sure you aren't touching the string that should be ringing, or it stops the physical vibrating.
Why does this work? It's because all of the A's (and D's and G's and E's) are an octave (or two) away from one another, and an octave is a perfect interval. If your A string is vibrating at 400 hz, the "A" above it -- the third-finger E string A -- is vibrating at twice that, or 800 hz. Their vibrations can mesh very easily, as long as the pitches match.
Guess what else is a perfect interval? A fifth. For example, your A string vibrates three times for every two times that the D string vibrates. The vibrations in those notes also mesh easily, but not quite as easily as octaves which vibrating two to one. Violins are tuned in fifths, therefore each string is a perfect fifth away from the next -- if it is perfectly in tune. This meshing of the fifths is what violinists learn to hear when they are tuning without the help of a chromatic tuner.
But take it a step at a time. Start by listening for the octaves, by really honing in on the natural ringing tones of your instrument. There is a reason why so much violin music -- and especially beginning violin music -- is written in the key of D or the key of A or G. Those keys contain many of the violin's natural ringing tones.
When I hear a student (or anyone!) play and they play slightly out of tune and fail to trigger the resonance of their violin, it makes me cringe. By the way, your violin is cringing, too. The more your violin rings and resonates, the more it "opens up." This is not some mysterious thing that violinists talk about, it's a real phenomenon. The more the wood vibrates, the more pliable it becomes to sound. Make it vibrate a lot by playing in tune, and it will "open up," and so will your ear!
What a wonderful blog - well done, Laurie!
Wow, thanks Laurie, that explains a few things. My violin has begun 'ringing' a lot lately and I thought it was because I finally had the right strings for it. But, as per your explanation, I have been paying a lot more attention to intonation in the last few months, and now I know that this is paying off with the ringing. I will listen more closely in future. One little thing though, I understand what you mean by one string vibrating when playing another in a perfect 5th relationship, but I've noticed when some people tune, they play both open adjacent strings at once. What are they listening for?
Now here is a question I sometimes ponder. Are there any notes on the violin for which this does NOT work AT ALL? Or is there always a resonance to some faraway harmonic on one of the four strings? I'm having trouble finding it for E flat, for example.
Tuning in perfect 5ths requires playing two adjacent strings simultaneously. You then listen for the pure 5th. What are you listening for? Nothing! Yes, thats right, nothing. You want to hear a pure, clean 5th. It is a distinctive single note-like sound, with No Shaking, no Wobbling. As you tune the 5th, you can hear the wobbles and you keep turning the peg until they go away.
Actually the same thing happens with 4ths as well (on a guitar) and even thirds, though thirds are busier to begin with--you can hear their beats as a distinctive sound "flavor."
Here is how the maths works. When you play two pure notes at the same time, our brains here each note, as well as the Sum and the Difference of the frequencies, and the sum and diference of all the harmonic components.
Take note 1 = 150Hz. Take note 2 = 170Hz. Your brain will here a "beat" note at 20Hz, as well as a "sum" note at 320Hz.
Also, the 2nd harmonics will mix as well: that is 300 with 340. This is a difference at 40Hz. Note that this beat frequency is one octave above the beat ofthe fundamentals.
And the 3rd harmonics mix. That is 450hz with 510Hz. This makes a beat of 60Hz. These are getting weaker but they are there.
Why is the 5th special? Because it is, in the end, reinforcing one note! Here is how.
Take ding at 290 cycles per second (also known as Hertz or Hz):
Take the a string at 435 cycles per second.
The beat is 145 Hz,. Note that 145 times 2 = 290. Therefore the pure beat is an octave below the fundamental of the lower note!
The "sum" tone is 290 + 435 = 725Hz.
You are also beating the 2nd harmonics thus:
870 - 580 = 290 = the fundamental again!
Also 870 (harmonic #2 of higher string) is beating against 725 (the sum tone of fundamentals) to produce a difference of 145--once again a subharmonic of the lower note.
Finally and most importantly for 5ths, the 3rd harmonics fall right in line--the 3rd harmonic of the lower string is the same sound as the 2nd harmonic of the upper string:
290 x 3 = 870
435 x 2 = 870!
You will also find some not "clean" harmonic mixing results. But you will find more clean fits than any other beat, save the octave.
What happens when you are a little off? You will hear beating, or thrumming, around 1hz, or 2hz, or 3hz. Very noticable. Here is how that works:
Let's make the "piano" or "equal tempered" 5th.
290.3 = lower; 2nd harmonic = 580.6
435 = upper; 2nd harmonic = 870
difference tones of 1st and 2nd harmonics = 144.67, 289.4
Now, see the difference tone of 289.4? It now beats with the lower string to produce yet another difference tone of 290.3 - 289.4 = 0.9Hz. That is just less than once a second. And there are more of these, as you do more of the sums and differences. But this one is the strongest or nearly so (as oyu go to higher harmonics there is less energy).
And that important relationship between the 3rd harmonic of the lower wth the 2nd harmonic of the upper string also gets a beat:
290.3 X 3 = 870.9
435 x 2 = 870.0
That makes a beat of 0.9Hz--the same as the other beat. So the beats reinforce! And THIS is what you hear when you are tuning a perfect 5th--you hear this beat, and as you get closer and closer to perfect, this beat lengthens (gets slower) and then goes away.
I hope that helps to understand both what you are hearing as well as why!
P.S. in the not so distant past, radio operators used to have to manually tune their transmitters, as well as receivers. They used to do what was called "zero beating" which is the same process--listening for the beats to go away.
Well a fourth is really just a fifth, upside-down. For example, if you have an A, go up a fourth and it's a D. Go down a fifth and it's a D.
yes, that's right--a 4th is an inverted 5th. And yet it doesn't sound like a 5th. It has its own flavor. Why? If you do the harmomic analysis I just did, but with a 4th, you will see some interesting things--reinforcements don't line up quite the same way. Try it--it is fun!
If you want to hear the soundwave beats really beat against each other, just so you can tune into it, try playing a dissonant interval like a second, play your open A with a G (third finger, D).
Paul, certainly there are notes on the violin that are a lot more "dead" than others, and that also depends on the violin. Something like an E flat would qualify, it doesn't have a lot of natural relation, it's pretty distant.
Believe it or not, I understood most of that, though I must admit I was tempted to pull out my old college physics book ;) I was taught the theories of acoustical physics before I knew what it was (my father is a physicist).
When I was first learning how to play, my "tuner" was my fathers oscilloscope. I was fascinated at a very young age by how my viola playing was rendered in green-on-black and would spend hours making those wave forms change on the screen. We didn't have the money to invest in a high-speed video camera to catch the actual oscillations and play them back in slow motion, but I think we would have if we could.
I think part of my challenge is to stop visually analyzing the data, and start doing so with only my ear as my "tool". Needless to say, my ear needs to be sent out to a lab for calibration. It is off by a cent or two under certain conditions ;)
Mendy: I'll see if I can put a sketch up. unfortunately I had puppy chew my scanner DC cord though. Here it is:
Yes, I know it is a real physical phenomenon (we call it the superposition principle) and you see it in everyday life on the water...but with laymen in this context, it is easier to talk about it as perception--because that is what we are getting at--perception. (Maybe Feynman would frown at me but oh well)
As for beating not being correct at far frequencies: I disagree with you! If it is true at close frequencies, it is true far away, too. It is *superposition* plain and simple. Just get out your pencil and sketch a sinewave with a pitch of 2cm and another with a pitch of 3cm. You will see that the constructive interference repeats at 6cm. That is the same as saynig that wen f1=3 X f2/2, then f1-f2=f2/2 (perfect 5th)
take lambda1=2, f1=6
take lambda2 = 3, f2=4
f1-f2 = 6-4 = 2 = f2/2
Mendy, that's pretty funny that you grew up without "enough money" yo buy a high speed camcorder...but you had an oscilloscope! (major bucks back in the day!)
From day one, my teacher has had me to sing. It felt weird at first, but it is a fact that if I can sing it in tune, I caan play it in tune. Also, when i sing in tune with my fiddle under my chin, it will "Sing Along" with me; that is to say it will sympathetically ring with the notes Laurie speaks of. Lastly, Under certain circumstances, the bow seems to "Get Happy" and provide feedback to the right hand by vibrating.
I wasn't "glazing over" at all. I grew up with the theory behind the music and have an engineering background - just not in acoustics.
Back when I was learning to play, camcorders did not exist, and high-speed film cameras were the things of university labs with alot of money or the film industry. My father already had an oscilloscope as part of his trade, I just used it when he wasn't.
Thanks Bill for the thorough explanation, and to everyone who helped to clarify. I do understand and am about to trot off and give it all a try. I suspect I will have to work harder to hear the 'beats' at this stage until I get used to listening for them. It also explains perhaps why I was having trouble playing thirds, they sound dreadful until I move my fingers out of their normal positions, which brings into question the whole tuning and intonation thing again, and perhaps part of the reason we shouldn't be too reliant on chromatic tuners. I guess there's always something to learn!
I have a wonderfully ringing violin and have no trouble with intonation when playing in keys that allow for these sympathetic vibrations. My problem is with four flats. The Dvorak Romance in Fm is killing me. My fingers/ears are always fighting with me as they try to seek out these ringing tones. When I play it along with an accompianiest, my ear hears the accompianiest's notes and my fingers go right to the correct spot, but when practicing the piece alone, I am always struggling against "drifting" toward other keys. In an effort to counteract this, I have been trying to listen for the "intervals", for LACK of ringing, and of course for the occasional ringing of the G natural and any accidental A's, D's or E's. I've had some success with this approach, but it's been limited. I'd like to overcome this problem. Any suggestions for me?
Reading this brought back fond memories of the day my teacher explained harmonics and the phenomenon of sympathetic vibrations...best violin lesson EVER! It was like the whole universe came into focus in that moment of understanding.
I didn't hear ringing tones much at all until I got my current violin a couple of years ago. My teacher often said "find the clarity" and I didn't know what she meant. I could hear it when she played, but not when I played. Out-of-tune notes and in-tune notes tended to sound very similar to me in all aspects except for pitch, and my sense of pitch isn't great. But with my new violin, I've been able to hear resonances and ringing tones much more. That experience has helped me understand why some violins are better than others.
"So if you have been using a chromatic tuner to help you place your fingers, how do you learn intonation, if you take it away? The advice, "Just use your ear!" -- said with frustration and a sense of moral superiority by a respected teacher -- probably will not help a student who just isn't hearing what's wrong."
That advice, especially when offered in that fashion, isn't helpful when said by *anyone*. Thanks for such a genuinely wonderful approach to the topic! I am going to share this blog with friends.
I have really enjoyed this conversation it has really helped. I am a beginner adult 55 years old and just wasn't getting what my young teacher was saying. After reading this I sat down with my scales book and tunner and it clicked. I now have a better understanding of what he was saying. I now know what I should be hearing. I look forward to learning More. Oh and I have a vso. My son knows I have wanted to play since I was 5 so got a cheap one I could afford. Can't wait till I can afford a good one but for now I love playing my cheap violin. I am now a happy person again since I started playing, only been 4months now and I'm playing in the Church band.
I agree with you Laurie................with everything you say.
But if one has no God given ear......................he or she will be stonatto always.
An I have met and heard a few of them in my life............
Yeah, yeah, yeah, Pythagorean tuning is great.....until you play with a piano, and as the late almost great Alexander Schneider used to mutter, playing with well-tempered tuning drove him crazy and he tried to avoid playing piano trios, quartets etc....he may have just been spoofing about having this amazingly discrete sense of hearing....and judging by some of his recordings, he was not immune to producing poor intonation....but it all contributes the the mystery and magic of music.....Playing leading tones high, major 2nd trills high, minor 3rds & 6ths low, and other quirks that establish one's style (Is intonation variation a form of Improv ???) all sort of reduce the flavor of this practice....but for some beginners it is a group of facts that should be known.
Lynn- I suggest learning the "timbre" of your piece. Dvorak Romance is in f minor, so you need to learn what f minor will sound like on your instrument. Here is a place where you can use a chromatic tuner if you don't trust your ability to avoid moving closer to F# or E, or just play very slowly up and down the f minor scale using your ears. The key of f minor does not give the violin a chance to have any opening sympathetic vibrations for a large amount of the piece, since we are looking at Ab, Eb, and Db in the key signature. You need to learn what your violin DOES feel like when it is in tune however.
If you find this difficult, first start by playing the last page of the piece (F Major section). Here, you have A, E, and D natural and it is easier to hear the ring. Then shift to f minor, focusing first on the F, Bb, and C (the 1st, 4th, and 5th scale degrees), which are easy to tune against one another. For instance, play F on the D string and Bb on the A string (first position) and tune the fourth. This allows you to feel the "resonance" of the fourth, even though you aren't on an open string. Once you feel comfortable there, learn the feeling and sound of your violin on the other notes of the scale (G, Ab, Db, Eb).
That is one of the most lucid explanations I have ever read.
Thank you Christina, I'll work in that direction (I have no trouble with that last page btw, lol).
Thanks for the explanation - I'm going to be giving it a lot of thought in the next little while. I just put new strings on my violin - changing from my old standard Dominants to Tonicas - and when I played a 3rd-finger D on the A string my violin rang like I had never heard before. I could see the D string vibrating. A fourth-finger E on the A string started the E string vibrating the same way. I already knew about sympathetic vibration, but this was the most dramatic demonstration I've ever seen. Of course, the instrument went dead as soon as my intonation was even slightly off - good incentive to get it right.
Now it's time to go back and start listening for those fifths...
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