Temperament Tuning: Well or Equal

November 18, 2010 at 02:08 AM ·

For a summary of the differences and technicalities, I suggest looking over the Temperament section of the site; It's very interesting.


We, as violinists, first learn to tune in 5ths listening for that "pure" ringing sound, which is well temperament. The mathematically correct way of tuning, however, is a little bit different. For a 5th, the difference is exactly .0017 in frequency.

When I tune, I find myself tuning in equal temerament (like a tuner) and going slightly above the ringing sound for the D and G and slightly below for E. I think that most recordings are like this as well. Theoretically, equal temperament tuning leads to interval positions to be EXACTLY the same across all four strings as well as being perfectly in tune will an accompaniment.

So, I leave this one to the online violin community.

Replies (11)

November 18, 2010 at 02:35 AM ·

By the way, Well Temperament is not the same as Just or Pythagorean as you are implying. Usually I see people confuse Well tempering with Equal temperament. That "well tempered clavier" piece was not played on an equal tempered instrument. Then there are the earlier 1/4 and 1/6 comma meantones...and the later Viotti... Lots of confusion out there.

What temperament to play? It depends on the setting! Quartets have to find some way to play in tune with them pesky C strings. There are many approaches. There isn't one answer. You should become capable of doing any temperament adjustments as needed.

However, other than the temper of the open strings, the violinist is always going to find a sweet harmony to what is being played and so you will never really play in a strict equal temperament--you can't actually do that as it would require a precision of out of tuneness that is impossible to achieve. In practice, you are simply making the micro-adjustments that you need to, to sound good. It you are in the audience, you can hear this happening if you listen closely!

November 18, 2010 at 02:57 AM ·

If you tune your A to 440 and then tune the other strings in pure (wide) fifths, you're gonna have a problem:  the violins' Es will be way, way out of tune with their Gs, and even more so with the violas' and cellos' open C strings.  All those microtones add up.  This is part of the reason everyone else claims that violinists always play sharp.  (We don't need to discuss the rest of the reason here and now!)  The brutal truth is that the so-called "circle of fifths" we all learned as kids isn't a circle at all.  It's actually a spiral.  This is where the difference between an E# and an F, a Cb and a B come in to play.

No one has developed a universally satisfactory tuning system.  Bach's "well-tempered" clavier was one system, but not the one commonly used now.  Other temperaments have come and gone as well.  So, hold your nose, and tune those 5ths a little narrow.  The violinists will still be sharp, but maybe not as often.

November 18, 2010 at 08:16 PM ·

Agree with Lisa. You have to tune the fifths slightly "tight" otherwise the E is too far out from the G. It's more something you feel i think - you soon notice if the E is too sharp. Since intervals are clearer at higher frequencies, i tend to make the A/E fairly pure and narrow the G/D and D/A to take up most the difference. Anyone else do it this way? Or is this bad? 

November 18, 2010 at 10:07 PM ·

The cure in chamber music is for the viola and cello to raise their C slightly. I think it's a bad idea to tune your 5th narrow.

November 18, 2010 at 11:48 PM ·

Is that right even for ensemble music? - mightn't it be best if everyone takes a little off the C/G, G/D and D/A intervals? if you leave it all up to the viola and cello C string and keep the violin's 5ths spread out to pythagorean intervals you would get some pretty funny sounding open strings and chords, like G major on 4 strings?

November 19, 2010 at 12:16 AM ·

There is only ever one appropriate answer to this sort of question: It depends on the situation.

Western music is an approximation.  2:3 iterated 12 times will NEVER equal 1:2 iterated 7 times.  Period.  The appropriate way to manage this will always be situationally dependent, and the problem will never, ever, ever go away.

November 19, 2010 at 06:07 PM ·

Amen to what Janis said.  There is no neat solution, only approximations.  For those who are interested, this article explains it all.  



November 20, 2010 at 01:37 AM ·

Jefferson you may be correct in thinking that tuning the violin in Equal Temperament may be the best way to achieve good overall pitch.If you play a G scale starting on open G and stop on D1 (E) , this E is going to be considerably lower then the open E string. If you check  this with a tuner the E string will be at +2 cents and the E note on the D string will be around -5 to -10 cents.Tuning in  perfect fifths doesn't make CENTS , equally :) . We have a tendency to hang onto tradition.

November 20, 2010 at 06:01 AM ·

Actually, you can't tune to 12TET, though you can tune Equal Spacing of 5ths, narrow, pure, or wide.

The rest of the notes--the stopped notes--are not going to be ET--they will be tuned by ear and therefore more pure than not on average...which means they will warble about the mean.

Whether it is better to narrow every 5th, or to narrow only one of them, depends on the key of the piece being played. I don't want to do the maths right now but you will find that some keys will work with one arrangement, and others with another. All will work to a compromise of narrow 5ths but that can be difficult to tune up to--unless you have a good pitch reference to tune to.

Really the value of the 12TET narrowed 5th is that it is barely narrowed. It is a luck y coincidence that you can make a base 12 logarithm and that the 5th degree of the scale is almost perfectly mimic'd.

Perhaps an experienced professional chamber player would roll eyes at this discussion. It is, after all, like brushing your teeth or putting on your shoes if you play in string quartets regularly. (For me it is playing with guitars more, and that becomes my "pitch reference" though often, pure 5ths between some strings still work--usually d to a stays pure, the G gets bumped up, and the e down--mainly because the e is easy to tune, and the g is the easiest to peg-tune! Guitarists even mess with pure 5ths as well--sometimes you can get sweeter chords in one key, if you bias just a smidge.)

November 20, 2010 at 11:43 AM ·

How come that all the soloists, chamber music performers, orchestral players et al that I've ever met, just tune up normally from A=440 and tune each 5th for purity?

Have you ever known a soloist come on - take the oboe A and then tune the 5th's out of tune? (i.e. narrow, or wide).

Come on, get real!

November 20, 2010 at 02:36 PM ·

Peter, I believe they/we do tune so that it's more equal tempered. That doesn't mean that you're not tuning using perfect 5ths, it just means your ear makes up for the difference while tuning. It's really not so much of a difference that they are tuning "out of tune."

I'm afraid this discussion I created has gone beyond my high school music theory haha

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