Equal temperament isn't such a bad thing

July 1, 2021, 12:27 PM · I actually tune all my strings using equal temperament, and yes, I can see you shaking your heads in disapproval.

But the thing is, equal temperament doesn't sound bad, and it makes life a lot simpler.

I only have to learn one E on the D string (in first position, naturally). Without equal temperament, there would be an E that sounds nice with an open G and a different E that sounds nice with an open A. Similar problems would show up with every note actually.

There's also the issue of playing with a piano. Because I use equal temperament, I don't have to worry about discrepancies between my violin notes and notes on the piano.

Just intervals sound sweeter, obviously, but I'm willing to wager that most people can't really hear the difference.

Intonation is already complicated. Why complicate it even more?

Replies (34)

Edited: July 1, 2021, 12:58 PM · If it sounds good it's good.
I wish you luck.:)
July 1, 2021, 1:12 PM · So what method do you use to tune your strings, and then how do you play in tune and know whether you are playing in tune or not? How do you check a note to see if it's in tune?
July 1, 2021, 1:27 PM · I use a tuner app on my phone to tune all the strings.
To check if a stopped note is in tune, I compare with an open string. For example, to check that my A on the G string is correct I play it with an open D. If the combination sounds clean, my A is correct.
July 1, 2021, 1:38 PM · It sounds like the OP is tuning the open strings according to equal temperament but using just intonation to tune the fingered notes. Tuning the open strings is just a part of it—all fingered intervals have to be tempered as well. I think the only ways to really play in equal temperament would be to either somehow memorize each exact pitch down to the just noticeable difference or to put markings on the fingerboard after checking each pitch against a tuner.

It’s much easier to simply play two notes against each other and listen for the beats, but that would not be using equal temperament.

Edited: July 1, 2021, 2:01 PM · You could install frets, like a guitar. Viola! Equal temperament.
Edited: July 1, 2021, 2:05 PM · So if you are doing that, then why settle for out of tune open strings? It seems like this is all lose-lose.

Like if your foundation is out of tune 5ths, then why try and build a building on top, when you can level your foundation and build the exact same building on top, but without getting a bunch of cracks in all your walls for being on an uneven foundation?

If you could really have a way to know you were playing equal-tempered (by having perfect pitch, perhaps), then I guess you could mess with the width of your open strings to match the piano, but that seems like a level of sophistication that would be unavailable to people without very special talents, and then I'm not sure if matching the piano tuning would actually sound better, since I'm not the resonance of the violin would play ball.

Has someone run this experiment?

July 1, 2021, 3:21 PM · Now that you guys have said all this, I think my playing probably isn't completely equal-tempered.

To answer your question, Christian, I'm settling because it simplifies things for me.

Following your analogy(I think that's the right word), my foundation is only very slightly uneven. My G and D strings are both only 0.4 Hertz off the mark. But with the E string it's more like 0.7 Hertz.

My point is that my fifths are perfect enough, I guess.

As for the resonance of the violin, whenever I play G, D, A , or E, I actually do hear resonance from the open strings.

I can't believe you suggested frets, Cotton, even in jest. Even I am not that far gone.

July 1, 2021, 5:36 PM · Kennedy,

what do you think of the playing example at the end of this video, after tuning every string of the piano exactly in the spot with the tuner?

Tuning piano

How does it sound to you?

July 1, 2021, 6:02 PM · Equal-tempered fifths only beat around once a second in the middle range of a piano, which I find acceptable: I wonder if my open string bowing is that steady!

Then we decide when to re-adjust our thirds & sixths "on the fly" for sweeter harmony. Is the C# pulling towards D, or is it resting comfortably on an A?

The extremes of the keyboard are "stretched" for both aural and acoustic reasons; and we don't always agree with each other: I believe we have fewer hair-cells per semitone in the cochlea at thes extremes.

July 1, 2021, 6:47 PM · To me it sounded ok, Marco.

Is it not supposed to?

July 2, 2021, 7:49 AM · It hurts my ears...... :)
But if you don't perceive anything wrong, here is explained why you like the violin tuned the way you do.
Nothing against it..... :)
Each one his own.
Edited: July 2, 2021, 9:40 AM · Our ears forgive many things but I don't think they will forgive Mozart string quartets played in equal temperament --- and many other things too. It is the harmonies that "get you." Intonation in melodies can really be "stretched."

I think that as long as you play alone or with a piano, tuning in equal temperament is fine. When I have played with a pianist I have always tuned my lowest string to the piano because there is no other way to play that note but "open string." For violas and cellos that tune A to the piano it really is necessary to tune their lowest string (C) to the piano or the discrepancy can be heard.

Actually, this is quite a fascinating subject. A decade (or so) ago I played in a string quartet formed at the request of a flutist/singer who wanted to become more adept at viola. We hired a professional cellist to coach us (for 4 2-hour sessions) and the insights he provided on tuning our thirds were a revelation. We ended up presenting little concert of Haydn and Mozart quartets. If you go to GOOGLE,COM and search just and equal temperament you will find lots of information.

I am too lazy to do what is necessary to learn what I want - and that is to find in which "keys" are "worst" (i.e., most out of tune) in equal temperament. The information is there, but I think one would have to decide how to define "worst" and then do the math. Alternatively, one could try
1. comparing scales in every key on a piano but I don't think we could really judge it
or
2. transpose various pieces of music into different keys on a piano and judge the failure

July 2, 2021, 9:10 AM · Bartok's string quartets played in ET doesn't bear thinking about.
July 2, 2021, 9:38 AM · Nothing wrong with equal temperament-on keyboards and fretted instruments. A lot is wrong with it, concerning traditional violin playing. The minor convenience is not worth the hassle. Imagine equal temperament does not exist, and work hard on developing your ear. You can do it.
July 2, 2021, 11:00 AM · Equal Temperament is good enough most of the time. Otherwise we would not tolerate the modern piano or the fretted instruments. Most people in the audience and some musicians do not discern the difference. The tempered 5th is only 2 cents, 2/100 of a half-step, shorter than the perfect 5th. The most noticeable, objectionable interval to my ears is the maj 3rd, which is about 12 cents different from the just or Pythagorean maj 3rd.
Tune to the piano when doing chamber music - Yes.
Use neutral, tempered tuning when doing non-tonal modern music- Yes. Use tempered tuning for the two symmetrical chords; augmented, and diminished 7th. Use tempered tuning for the fast chromatic scale and the whole-tone scale.
An idea that I have not tried yet: When doing chamber music with piano, tune to the piano D instead of A. Then the Cello and Viola C will be good enough, only 4 cents lower than the piano C. The Violin E will then be 4 cents higher than the piano E. That's OK, violinists like to play sharp on the top notes anyway.
July 2, 2021, 11:15 AM · As far as I can see the distinction could be important when practising scales and arpeggios and in unaccompanied Bach but not much else! If pianists can play the 48 P&F's without retuning...

My desk partner/concertmaster in a string orchestra had perfect pitch and used to give us the A. Nobody minded which key it was in.

July 2, 2021, 11:22 AM · @Marco Brancalion
Hmm...I'm not sure if this means I am very tolerant to out-of-tune sounds or if it means my musical ear is just bad. Maybe both are the same thing?

Would you mind telling me how badly this hurts your ears?
https://voca.ro/1a6uTR6hnCLs

Your answer might help clarify this for me.

July 2, 2021, 11:26 AM · Considering all that has been said, equal-tempered violin tuning probably isn't my best heretical idea.

I think I'll retune my strings and get those juicy REAL perfect fifths.

July 2, 2021, 12:16 PM · Yes.I also think that equal temperament is not a bad thing
Edited: July 3, 2021, 1:07 AM · If you normally avoid open strings, it's not going to affect matters very much, is it. Ditto for JI (for those who want ET tuning instead)
July 2, 2021, 4:46 PM · I have a friend here in Seattle who tunes his violin to the pitch that it sounds best at. One instruments prefers to be a bit sharp, the other well flat, and he then simply plays in tune with the rest of the orchestra.

Actually blows my mind. I do understand it, being a violin maker I agree with it, but I don't think that I could actually do it.

July 2, 2021, 4:54 PM · @Kennedy Becky:
I hear the Re as sharp.
July 2, 2021, 5:04 PM · Try not to confuse tuning the strings with fingering the strings.

Adjacent open strings tuned to perfect 5ths differ by just 2 cents from ET 5ths. There will always be someone who will claim they can easily hear the difference between the two when open strings are double stopped, but the reality is scientific studies fail to support the claim.

At 4 cents variation from perfect 5ths the distinct beating starts to become easier to detect, but that is equivalent to double stopping an open G to the open A. When was the last time you heard anyone do that?

If you are double stopping adjacent open strings, it does not matter if the strings were tuned to ET 5ths or perfect 5ths.

Just about everything else is fingered, which means you can easily choose them to be the ET scale or anything else your heart desires.

A youtube search will find many master classes where world class soloists and teachers discuss intonation. The reality is great performers will stretch and shrink certain intervals well beyond any standard scale if it suits the music.

Perfect Pitch technically means someone can identify a note on the ET sale when it is within 20cents. Some can go as low as 10 cents. 4 cents seems to be about the limit of human detection in A/B comparisons, or when hearing some reference tone that is burned into their brain, like the open A (440Hz).

July 2, 2021, 5:50 PM · @Marco Brancalion
Thanks for the feedback.

Since those sounds were generated from my very own mouth-hole, and only the Re was sharp, I think my ear must be mostly ok.
*Sigh of relief*

I listened again and the Re sounds fine to me. I wonder why I prefer it sharp.


July 2, 2021, 6:27 PM · Kennedy, tuning your open strings to the tuner may seem easier and more convenient at first. But with a bit of practice you will get the hang of tuning in perfect fifths in no time. It is a great aural training exercise and warm up. Take your time with it and really use your ears. Good luck!
July 3, 2021, 1:06 AM · Play in churches so that what you play now is accompanied by what you played 2 seconds ago, then it won't matter what tuning you use.
Edited: July 3, 2021, 1:21 AM · In orchestras surely others have experienced occasions when the open C of the violas and/or cellos sounds flat? Then half the section performs an emergency tweak. One of the professional string quartets I was coached by (was it the Alberni?) advocated "close fifths" tuning so the open C harmonises with the violins' open E, but I've never known a conductor suggest it.
Edited: July 17, 2021, 4:24 PM · Intereting Fact No73b: Squashing the fifths (ruinously?) so that C & E strings harmonise is "Quarter-comma Meantone" (because D is exactly halfway between C & E, and the "wolf" comma is spread over four fifths). It is only acceptable in the "home key" of the tuning.

Harpsichords, with their many high overtones, sound awful in ET.

ET spreads the comma over all 12 fifths: a sort of "1/12 comma" meantone!

An interesting compromise is 1/5 or 1/6 comma meantone: some thirds are sweeter than others, one can use all 12 keys, and they have subtly different "colours". It is fairly sure that Bach used a version of this in his "Well-Tempered" ( not Equal-Tempered!) 48 Preludes & Fugues.

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July 3, 2021, 5:48 AM · Bach's well tempered clavier would be four equally tempered fifths, a perfect C-E third and all the other thirds progressively worse the further you get away from C major, very symmetrical, and effective for the music. Meantone involves I think 4 perfect thirds, 4 about like equal temp and 4 terrible. I think just tempermant is only one tempered fifth, one terribly out of tune fifth, 11 perfect fifths.
July 3, 2021, 6:03 AM · 11 perfect fifths is Pythgorean tuning.
Just Temperament tries only pure thirds and fifths, but there is immediately a problem: A from F will be a comma lower than A from D from G from C...

We can look up Hermode tuning, a sort of AI imitating what an unaccompanied choir will do (under a good leader!)

Edited: July 3, 2021, 6:44 AM · But Bach's tuning was well tempered, not meantone, it was quite a new invention in the time of Bach, with about 100 years of meantone tuning preceding it, later, after Bach you have tuners like Valotti, that made the tuning even closer to equal temp, by using 6 tempered fifths, and good thirds that were a little worse than Bach's but bad thirds that weren't as bad. True equal temperament didn't really exist on keyboards till he 20th century, owing to how hard it is to tune by ear without testing equipment. Equal temperament was theoretically proposed quite early in the 1700s but there's little evidence anyone put it into practice. Many piano tuners that still tune by ear do not do a true equal temp but rather slightly temper the temperament to favour simpler keys over complex ones. For concerts of piano works, a good tuner will tweak the tuning to favour the keys of the pieces that are to be played, not following equal temperament religiously.
July 3, 2021, 7:50 AM · I read a book on the history of tunings once.
"In this century the following 20 men invented the following 32 tuning systems"
Yep, I'd recommend that book!
Edited: July 3, 2021, 8:01 AM · the Bach tuning I am referring to is Kirnberger III, Kirnberger was a student of Bach's.

Statistical analysis of the thirds used and not used in the WTC appear to indicate either this tuning or something very close to it.

July 4, 2021, 1:33 PM · Here we go again with the equal temperament thing.

You can't just tune four strings in what you think are equal temperament. What about all the other notes?
Playing with a piano is not an issue--just play in tune with yourself. Pianos differ by subtle amounts anyway--big concert grands are not tuned the same as smaller pianos. And even pianos of the same size might differ depending on the scale tension and string design. There are discontinuities between the wound and plain wire strings (the Steinway D, a staple in many teaching studios, exhibits this).

In addition, there's another factor about playing with a piano: How sure are you that the piano in question is perfectly in tune? It's probably not, and it differs depending on the range. For example, I come across many pianos (even those I've tuned frequently) where the bass is slightly sharp, and the high treble has fallen.
Maybe the piano was tuned for a recital, but who knows how well it was tuned? Maybe they put the lights on and the piano falls in pitch. It's a constantly moving target.

Pianos also resonate in different ways that violins do. For example, play a slightly wide major 6th on the violin, and you get an annoying, fast buzzing sound. Play the same interval on the piano and you get a lovely vibrato, although the speed does double with each octave. In the midsection, it's a nice speed.

When a pianist plays a concerto with an orchestra, do you seriously believe everyone in the orchestra attempts to play in equal temperament? Of course not. It's an impossible task. And audiences don't notice. If they do notice something amiss, it will likely be a unison that has drifted under hard pounding.

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