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I get that A is how we define concert pitch, so we tune that first, but then we always tune D-A, G-D, then A-E. Why is that? Is it just convention?
My best conjecture/hypothesis is that it makes it more likely that in an orchestra setting, the violas and cellos won't be as likely to hear E's, but the basses will. Am I close?
Reason I asked this is that one of my young students asked me, and I quickly realized I never learned why myself!
This has been asked on quora, here are the different aspects mentioned:
Michael Hutchison:
The simple answer is E, as the smallest, lightest string, is more susceptible to being pulled back out of tune by the tuning of the other three heavier strings changing the tension on the neck of the violin. By tuning the others first, then tuning E, you avoid needing to retune E.
Basically, the tuning of the lower strings could put the E out of tune, so we end with it.
Graham C Lindsay:
Its to do with comparisons and your ears. The lower strings have lower harmonics and if you start from the bottom to the top with the other strings tuned when you get to the e string it will be easier to tell if the string is in tune.
You could try it the other way but often you will find that it takes longer to tune the instrument as you may have to keep adjusting the other strings.
This is a much better explanation than what I was trying to say. Having lower strings resonate along with the E indicates where really we have to set it.
David Ezell:
We pretend that our tuning system works, but it only almost works. An octave is based on a 2:1 Hz ratio. If open A is 440 cycles per second, then A on the G is 220. A perfect 5th is 3:2, so E on the D is 330. If you start with the lowest note on the piano and double the frequency until you get to the top A on the piano, you will get a certain number. Start with the same low note, and do 3:2 5ths until you get to the top of the piano, and the number will be about a half step sharp. (A half step is 15:16). When tuning in 5ths, to make your music match the rest of the orchestra and/or piano, you will have to “squeeze” the fifths to make things work. Tune to a perfect plain-sounding 5th and then make the fifth a little smaller. This can be more of an issue on the viola and cello. When tuning my viola, I like to tune the A and the C against the piano, and then tune the D and G so that each 5th sounds the same amount off. In a quartet, I check my C against the cello C to make sure we both squeezed the same amount.
This is a bit orthogonal to the question, but it really is important to mention whenever talking about violin tuning.
This is a guess but violinists use fifth interval, which are perfects in the equal temperament to tune their instrument. As you said, one needs to start with the A, for the concert pitch. The D is one fifth apart, so you can easily tune it from the A you now have. Once D is tuned, you can tune the G which is also a fifth apart from the D.
Then you can finish with the E which is a fifth apart from the initial A. Why going first to the D instead of going to the E? Maybe because tuning the D and G strings will probably change the A tuning because of the extra or lower strength applied to the neck. So one can retune slightly the A to the concert pitch before tuning the final string.
This is a wild guess, but seems reasonable to me… Would be happy to see a more motivated one :) !
Another factor not yet mentioned is that having all of the performers in a group tune A, then A-D, then D-G, and then either G-C or E-A, may produce less of a clashing sound than having some performers tune E-A immediately after tuning the A string while others are tuning A-D. For the violas and cellos to all start tuning A-D while the violins are tuning E-A may make things more difficult for everyone than having all of the performers start by tuning A-D.
The tuning order is also meant to equalize tension,to keep the bridge in place by applying comparable amounts of pressure to its legs at all times. Also the neck is prevented from flexing sidewise (in a vertical plane it is supported firmly by a thickened root with a mortise and tennon but is relatively thin sidewise. Beginner instruments and some older instruments are somewhat..flexible- some to a worrying amount,even. So tuning -as explained by all the commenters above- apart from the harmonic and musical considerations, even when performed using an electronic tuner, has to preserve the integrity of instruments. Someone above mentioned briefly the mechanical aspects of tuning- there is uneven tension in each string, and the bridge on a violin is in fact doing a fine balancing act. Some violin top plates are rather thin, and some bridges are prone to breaking with excessive off-plane flexing, especially some of the older or really thin or highly tuned (carved) ones. So succesful tuning has to do all of the following : 1) ensure proper pitch- the approximations are a part of the discussion, along with particularities of each instrument that warrant per-instrument "recommended" variations, supression of wolf notes,and all the complications arising from that (sacrificed intervals,various concessions) 2) ensure the instrument is not damaged from breaking/falling bridge, top plate cracks by extreme tension or uneven aplication thereof, or neck flex and finally 3) be somewhat stable. I am an engineer- the violin is a fine marvel of art and complicated almost magical guesswork and empiric calculation . When you tune your instrument, you accomplish a marvelous and sacred rite of aligning to universal ideals of beauty; when I tune a violin, I see suspension bridges and guy wires, tension, flexion, and overall have the impression of carefully defusing a pressure-sensitive landmine. The way the wood moves under the tension of the strings, the flex in the top plate, efforts in the bridge and bridge legs transferred to the top plate, the way the post is compressed and the way the neck is simultaneously bent and pulled up , the sideways tension and torque in the bridge etc - all of these give me the impression that the violin, for all its beauty, is a tortured little thing, and needs utmost care when defusing..er..tuning.
The strings are tuned in that order because of tension on the bridge in relation to the strings. If you tuned E first, then tuning the lower strings will pull it out of tune.
