Equal Temperament (Oh No! Not Again!)

[Michael]

I have just been reading , in today’s Sunday Times, a review of a new book called “How Equal Temperament Ruined Harmony: And Why You Should Care” by Ross W Duffin.
I found it difficult enough to follow the review so you can imagine what I would make of the book. As a non-musician who cannot even read music notation, I have always been fascinated by the inner secrets of how music works and have gained a (very) imperfect knowledge of them. Over my years of listening I have come across a curious phenomenon and I think the cause of it comes down once again to equal temperament. If I spend a lengthy time listening to string quartets (which is my favourite music genre) and then switch to solo piano music, I find that, for a time, the piano sounds slightly out of key. I realise that the piano is the instrument that is compromised and that the string quartet is “purer”. However, the effect can be reversed if I switch from piano solo to string quartet. Which is right? And does it matter a damn? Ross W Duffin thinks that music was spoiled in some way but a few minor composers like Bach, Mozart and Beethoven seemed quite happy with the compromise.
I would rather put my trust in Bach and Co. than Mr Duffin, but it is worth mentioning that Tchaikovsky could not bear to listen to string trios because (for him) the piano sounded out of tune with the strings.
However, it didn’t stop him writing three fine piano concertos.
As it is New Year’s Eve, I have forgotten what point I intended to make. I know there was an extensive thread on this subject a few months ago but I got lost in it!
Perhaps Peter could throw some light on this. In piano music are we actually listening to music off-key in certain keys? Or is it just a matter of certain keys sounding dull? Or does it matter?
Anyway, Happy New Year to All!

Michael

[Gurn Blanston]

Here is a link to his website.

http://music.cwru.edu/duffin/JustTuning/index.html

It is not difficult reading, actually.

His premise about equal temperament ruining all later music seems a bit over the top. If you discount works with a keyboard, it really doesn't affect much in modern performance since instruments and voices are quite capable of working in any temperament, with a bit of practice. Of course, his premise does hold true for pre-Romantic works being performed on modern instruments. In Classical and pre-Classical times, D# was not the same as Eb, for example. So if a composer was using an enharmonic key for effect, that effect is lost. Frankly, I doubt that 98% of all listeners would know the difference or appreciate it, and at least one reason for that is that we do not share the same philosophical and aesthetic background as listeners of, say, 1780 for example. So even if the ear detected it, it wouldn't necessarily SAY anything to us.

This is the same, basic, essential reason why "HIP" performance will never be "exactly what the composer heard", because neither the players nor the audience share common ground. That said, I vastly prefer HIP playing, whether I can imagine the milieu or not.

[Chris]

Well...what you are really talking about is comparing equal temperment to just intonation. In equal temperment, an octave is divided into twelve equal parts - the interval bewteen each is exactly the same. That means that the ratio between frequencies of any two adjacent semitones is the twelfth root of 2, which is about 1.05946309.

On the other hand just intonation is where the frequencies of notes are related by whole number ratios. So, no roots here, just fractions. That means the notes are all members of the same harmonic series. So, intervals will sound perfectly in tune here, but the interval between each note will not be the same.

For example, take a root and its major third. In equal temperment the ratio of frequencies of these two notes is 2^(4/12), which is about 1.249921. Now in just intonation, the ratio must be rational. 5/4, say, which is 1.25 exactly. Now, 1.249921 is close to 1.25, but it is not exactly the same. The 1.25 will sound like a perfect interval, as we said, so the 1.249921 is going to sound just slightly off.

If you figure this out for each step in the scale, you will find that the equal temperment intervals are all off by as much as 1% in one way or the other. So yes, you could say that everything is just a little out of tune in equal temperment. But that's the price you pay for the consistency you get with it. You can't have all the notes be part of the same harmonic series and still have different keys available to you without some of them sounding very off.

[Michael]

Thanks Gurn and Chris. I'll re-read your messages when my head clears!

Michael

[atserriotserri]

.... This is the same, basic, essential reason why "HIP" performance will never be "exactly what the composer heard", because neither the players nor the audience share common ground. That said, I vastly prefer HIP playing, whether I can imagine the milieu or not.

You don't have to go that back in time to have conscience that any performance will never be exactly what the composer heard: one of this Christmas' presents I've received (apart from Carlos Kleiber's 5th & 7th, and Gardiner's cycle... sorry Peter it will take some time to arrive to the 9th symphony ) is The Doors' box set "perception" (all The Doors' records remastered, blah, blah... 5.1 blah, blah... outtakes, blah blah... videos...) and the first record, The Doors, has been running slow and almost half-step flat since its issuing as LP and subsequent cassette and cd reissuings... and also '99 remastering which is quite ashaming...

[atserriotserri]

.... This is the same, basic, essential reason why "HIP" performance will never be "exactly what the composer heard", because neither the players nor the audience share common ground. That said, I vastly prefer HIP playing, whether I can imagine the milieu or not.

You don't have to go that back in time to have conscience that any performance will never be exactly what the composer heard: one of this Christmas' presents I've received (apart from Carlos Kleiber's 5th & 7th, and Gardiner's cycle... sorry Peter it will take some time to arrive to the 9th symphony ) is The Doors' box set "perception" (all The Doors' records remastered, blah, blah... 5.1 blah, blah... outtakes, blah blah... videos...) and the first record, The Doors, has been running slow and almost half-step flat since its issuing as LP and subsequent cassette and cd reissuings... and also '99 remastering which is quite ashaming...

[Gurn Blanston]

Atserri,
Nice bunch of Christmas presents there! A Wise Man delivers his myrrh and then buys CDs for himself!

That issue you speak of truly sucks, I'm sorry to hear it. But it isn't exactly what I had in mind. What I was talking about is more in the ability to perceive. This aesthetic is part of our cultural environment, so even if the players manage to achieve just intonation to perfection, the modern audience, who do not share the cultural background of the composer or his contemporary audience, will simply not hear the music the same way. Unfortunately, it is a much easier concept to understand than it is to explain...

[atserriotserri]

Here is a link to his website.

http://music.cwru.edu/duffin/JustTuning/index.html

It is not difficult reading, actually.

His premise about equal temperament ruining all later music seems a bit over the top. If you discount works with a keyboard, it really doesn't affect much in modern performance since instruments and voices are quite capable of working in any temperament, with a bit of practice. Of course, his premise does hold true for pre-Romantic works being performed on modern instruments. In Classical and pre-Classical times, D# was not the same as Eb, for example. So if a composer was using an enharmonic key for effect, that effect is lost. Frankly, I doubt that 98% of all listeners would know the difference or appreciate it, and at least one reason for that is that we do not share the same philosophical and aesthetic background as listeners of, say, 1780 for example. So even if the ear detected it, it wouldn't necessarily SAY anything to us.

This is the same, basic, essential reason why "HIP" performance will never be "exactly what the composer heard", because neither the players nor the audience share common ground. That said, I vastly prefer HIP playing, whether I can imagine the milieu or not.

I agree with you in the sense that most listeners would not appreciate that effect, or understand it, but I think

[Peter]

I have just been reading , in today’s Sunday Times, a review of a new book called “How Equal Temperament Ruined Harmony: And Why You Should Care” by Ross W Duffin.
I found it difficult enough to follow the review so you can imagine what I would make of the book. As a non-musician who cannot even read music notation, I have always been fascinated by the inner secrets of how music works and have gained a (very) imperfect knowledge of them. Over my years of listening I have come across a curious phenomenon and I think the cause of it comes down once again to equal temperament. If I spend a lengthy time listening to string quartets (which is my favourite music genre) and then switch to solo piano music, I find that, for a time, the piano sounds slightly out of key. I realise that the piano is the instrument that is compromised and that the string quartet is “purer”. However, the effect can be reversed if I switch from piano solo to string quartet. Which is right? And does it matter a damn? Ross W Duffin thinks that music was spoiled in some way but a few minor composers like Bach, Mozart and Beethoven seemed quite happy with the compromise.
I would rather put my trust in Bach and Co. than Mr Duffin, but it is worth mentioning that Tchaikovsky could not bear to listen to string trios because (for him) the piano sounded out of tune with the strings.
However, it didn’t stop him writing three fine piano concertos.
As it is New Year’s Eve, I have forgotten what point I intended to make. I know there was an extensive thread on this subject a few months ago but I got lost in it!
Perhaps Peter could throw some light on this. In piano music are we actually listening to music off-key in certain keys? Or is it just a matter of certain keys sounding dull? Or does it matter?
Anyway, Happy New Year to All!

Michael

Equal temperament was not used by Bach, Mozart or Beethoven, in fact it wasn't universally applied until 1917. They had Well Temperament which allowed for variation in semitones and consequently more colour to the individual harmonies. Prinz temperament (or Kimberger III) was published in 1808 and it was a refinement of the earlier well-temperament. To the ear the differences between these tuning systems is very subtle, but it is there none the less. Gurn refers to enharmonics and there is that extraordinary passage in the first movt of the 4th symphony where Beethoven has the timpani playing Bb whilst the strings are playing A# - this was purely practical rather than a desire for different pitch which would surely have been virtually undetectable?