Amateurs and professionals due not play in tune 100 percent of the time (like a keyboard synthesizer). I think variation in pitch creates a tension in the sound that is desirable (the model being the human voice). But you should tune your instrument as accurately as possible to some reference point. That's very important.
Many Decades ago a Japanese computer geek named Tomita recorded a computer playing Bach. Pitch and time were absolutely perfect - it was novel, interesting and downright boring by the second listening. He also tried creating an orchestra with all of the instruments all in perfect tune and time. It was a total bust. The reality of an ensemble is that those slight variations in pitch are what create that ensemble/orchestral sound that has depth and resonance.
Lastly, if you are playing with others, you have to adjust your pitch to each other even if one player is off - if everyone else is in tune relative to each other it will sound ok. Of course, the folks with "perfect pitch" will disagree.
What Tomita proved is that music is more art than science and it is a human expression (Mr. Data's violin playing notwithstanding.)
Recording yourself, and listening for sour notes is a good way too.
There's a realty saying: "location, location, location."
My violin credo and paraphrase is "intonation, intonation, intonation." The problem is, intonation is subjective.
When I was most intensively learning the oboe in 1980, my teacher said, "don't let the oboe intonate for you. If you do, every note can be a few cents off and the audience won't notice, but they'll feel fatigue listening to you. Intonate every note you play on the oboe." You use a combination of lip pressure and diaphragm pressure to control loudness and intonation at the same time. Normal playing, diminuendo, crescendo, vibrato (initially when practising it slowly - when fast you can't help the pitch varying with air pressure, but that's what vibrato should be).
If it's that important on a wind instrument, it's 1000 times more important on the violin.
Tuners & keyboards in Equal Temperament? They are a whole lot better than nothing!! But attentive listening will show us that they are only a useful starting point.
Vibrato? On a bad day it coves our (little) imprecisions; on a good day it keeps our fingers alive enough to make those tiny instantaneous corrections.
In my opinion, intonation must be trained just enough so it doesn't get in the way, but then it's a thousand times more important you musicality, creativity and interpretation of the piece, the how you play and sound, not if you're playing the exact frequency. No professional can play 100% in tune, I guarantee you you take any live piece of the soloist you choose, you analyze just the first 20 seconds and using a computer you can see how almost none of the notes is exactly in tune. It's impossible, besides they will be fluctuating between a range, the same note will give you 440.04 Hz during the first quarter of its duration, then it will go down to 439.8 Hz, etc... A violin does not produce "tuned" notes, it produces ranges of notes. If you pluck one string then it would be a little bit more precise, but again, plucking is also imperfect as it follows a pattern, it will go flatter as the time goes by, of course, you don't notice. I believe the oboe will give you the most steady notes.
So, to sum up. If you are good, you know when you are in tune, and that's enough. If you feel you are in tune, fantastic, stop thinking about intonation and focus on all the other thousand things. If you feel you are out of tune, fix it.
If you are not very good, and can't really tell if you are in tune in "hard" passages, then I suggest the use of a tuner, but that will be only temporary, a violinist can't rely on a tuner in order to know how to be in tune, that's a skill you must honey.
We are never 100% mathematically in tune, but we should strive to have intonation that is good as possible. In other words, intonation that is precise enough not to bother other violinists in the audience. :-)
Why do so many not get this? It doesn't matter if you are mathematically in tune, or matching some tuner. The violin must resonate with itself, and in a pitch-specific way, to sound beautifully in tune.
Playing in tune=playing in timbre
Resonances extend pretty far. G, B, D on the E string, B, D, G on the A string get sympathy from the G string. D, A, F# from the D string, C# from the A string, and so on.
*You work out a JI octave from two tetrachords, but they are "assymetric": add a third tetrachord and there are already some intervals in tune and some not.
Playing in tune in the violin actually means playing in relative tune with others, unless you are playing solo. If you are playing solo, then you can play "mathematically", which is impossible, but in theory you could just hit every note at the exact spot. Change the key of a piece, even for a few moments, and good luck with the new spots you have to hit to perfectly be in tune. It's impossible.
However, when we don't play alone, if we want to play in tune we shouldn't play in perfect tune, we should listen to the others and play accordingly, that is, relative tuning. If you play with a piano, you actually play "out of tune" slightly so you can match the piano keys.
Paul, that's exactly what I was talking about. Not all notes produce the same amount of resonance--every pitch varies, and varies depending on the violin. Obviously, E-flat provokes a different resonance than E. But we have to memorize what that particular dulled resonance should sound like. Some violins are better than others. Many older, fine instruments seem to snap into tonal focus, which may be why people judge them easier to play. Many inexpensive or overly bright violins don't have much timbral variation. They can be difficult to judge and disorienting. It can also be disorienting to use a different tuning because the timber can change.
Anyone who has taught knows what it sounds like when a student plays a leading tone, especially F# or C#, too low (which they often are): you don't have to hear anything else. You don't need to assess it against a tuner or any other relative pitch. It just sounds "sour." Granted, C# and F# don't produce the same resonance as D or G. But they produce a very specific timbre an it can't be too dull (low) or too high (bright).
A fingered E will set the open E vibrating.
An Eb will not excite any open strings, but will resonate in the wood in a way we have have memorised through careful, repeated practice.
Well "nourished" memory. Again.
An interesting phenomenon: After teaching and listening for so long, I can tell when any single note a student plays is out of tune, even when it's just one note by itself, and especially high notes. No context, just timbre. I'll bet most experienced teachers can hear this. I think of it like looking through a camera with a telephoto lens: the image "snaps into focus."
One final "but" - for me "pitch" and "timbre" vary independently of one another so what would I do if the one sounded right and the other not? The perceived pitch isn't just a function of the fundamental frequency, the upper partials also have an influence. A pure sine-wave tone will sound flatter than a tone rich in the higher harmonics. So if you can enrich a tone for example by increasing the bow pressure the pitch will rise.
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