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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!

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    I started writing an answer based on my (very limited) knowledge of harmonics and discussions I've had with teachers and other orchestra musicians; I think it has to do with the way lower strings will resonate (or not) so that when we tune the E we get the best pitch possible, but then I realise it does not really make sense, or at least, I really lack any kind of source really. – Félix Gagnon-Grenier Oct 27 '20 at 14:31
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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.

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    It's Ezell's comment that really nails it, I think. It's all about how justly tuned fifths stretch equal temperament, and so starting on the low G would result in a wildly high E string. – Richard Oct 27 '20 at 15:09
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    Hm... I thought about the tension thing when I was writing the question, but then I thought about the violas having A as their top string, so I didn't think that would be a factor. Do violas/cellos find themselves retuning their top strings a lot? The temperament thing definitely makes sense though. – Calculuswhiz Oct 27 '20 at 16:15
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    My personal experience and experimentation is that the idea that tuning in any order on any stringed instrument helps prevent having to make as many tuning passes is an understandable and attractive myth. I haven’t been able to do anything to reduce the number of tuning passes required on violin, guitar, mandolin, banjo, or lute. The closest I’ve come is to predict the tuning drift that will occur and deliberately tune the first strings sharper or flatter than normal, as appropriate, so when I make the next pass it’s closer to being in tune. – Todd Wilcox Oct 27 '20 at 17:03
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    @ToddWilcox I've experienced the same thing on mandolin. I've just come to accept that I'll have to take more than one pass each time, and several when restringing. I try to compensate by over-tuning, but of course I never guess right. I can only imagine what theorbo players must go through! – Calculuswhiz Oct 27 '20 at 20:24
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    @ToddWilcox well I don't know if you tried to experiment with a bass guitar, and you'll notice it's not a complete myth for all instruments: try to tune all the lighter strings with the lower string really off tune, and then tune the lower string, you'll notice all the lighter strings are now clearly out of tune. But I agree that doesn't really change the number of passes, if your bass was really out of tune, you'll need 2 or 3 passes before being right anyway. But it's useless to start with the lighter strings if your lowest is off, they'll all move when tuning your lowest – Kaddath Oct 28 '20 at 8:58
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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 :) !

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  • Maybe I read your first sentence wrong, but it looks like you're saying equal temperament has perfect fifths. Perfect fifths are not the same as fifths in equal temperament; the perfect fifth is just shy of 2 cents too sharp. This is too small a difference to sound out of tune if you just play two strings, but if you tune all four strings a perfect fifth apart it adds up. Especially if you then tune the C string of the viola to a perfect fifth below the G string! It will then be almost 8 cents too low compared to the violin E string. This is definitely audible. – EdvinW Dec 17 '20 at 17:02
  • @EdvinW I agree, and that's maybe also why you do not tune them "in order", so that it does not add up. – Tom Dec 17 '20 at 17:26
  • But it does add up. The order you tune them does not affect this fact: If every string ends up being tuned a perfect fifth away from each of its neighbours, the strings at the ends will be out of tune by about 2*(number of strings - 1) relative to equal temperament. – EdvinW Dec 17 '20 at 17:37
  • @EdvinW ah yeah that's true! But less that if you would do it in order. This way, the "out of tuness" is more balanced: too high on one side, to low on the other if a middle string is tune properly. I agree that i does not change that between the top and the bottom strings will be the same, but it will be more balanced. I wonder, as violins are not fretted, if the player do not compensate as they play. But that would not work for open... – Tom Dec 17 '20 at 18:06
  • @Tom why would it be more balanced? Not only is the difference between the outer strings the same but also with the middle strings. If the pitch difference is two cents per fifth then E is theoretically always 2 cents sharp compared to equal, D 2 cents flat, G 4 cents flat and C 6 cents flat. The order does not matter. – phoog Dec 17 '20 at 18:29
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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.

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  • Right. Though how clashing and counterproductive it is depends on what tuning/temperament is desired. For quarter-comma meantone, it actually makes sense to start by matching the violins' E with the cello and viola C – leftaroundabout Oct 27 '20 at 23:45
  • Well, I did mention it as a guess in my question, but I'm glad some others seem to share the same thought. (Also, don't forget the Bass!) – Calculuswhiz Oct 28 '20 at 3:29
  • If the violinists tune the E last and the violas and cellos tune the C last then they they will have the major third (well, seventeenth or 24th, I guess) to contend with, which should be rather wider than (5-limit) just unless they are playing in some historical temperament. – phoog Dec 17 '20 at 17:47
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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.

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  • Hi Axel Morisson. Welcome to the site. You have some interesting thoughts here, but can you link them to why the violin is tuned in the pitch-order it is? As written, your post doesn't seem to address the original question. – Aaron Oct 28 '20 at 13:51
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    think of it as a way to minimize lateral bending in the said elements : bridge,neck ,top plate.The order mentioned also has the merit of minimizing this. And it is important because some instruments are quite sensible to the bending modes that are not designed to withstand. So it is relevant from a structural point of view.Also it improves stability- that is, minimizing the said bending/warping and avoiding structural collapse. I think I made the points clear(er) now. It is obvious the said tuning order equalizes tension and keeps the bridge in place and evens out lateral forces on the neck. – Axel Morisson Oct 30 '20 at 7:00
  • I see now. You might consider editing your post to clarify. The information is there, but at least for me it was obscured. – Aaron Oct 30 '20 at 7:04
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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.

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