PBDB Book Review Dept.: How Equal Temperament Ruined Harmony (and Why You Should Care)

How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross Duffin
W. W. Norton, paperback

“Don’t even start thinking about this stuff,” said my friend, an excellent musician who does a lot of period performance work. “It’ll ruin your ability to enjoy most music that you hear - anything with piano.” The forbidden topic under discussion: the art and science of temperament and the tuning of the Western 12-note scale. While I can’t say that I’ve had quite the full-on crisis that she warned of, thinking seriously about this topic has led my ear and brain to some unexpected places, and it’s changed a lot about how I hear some music and what I want to do when I’m playing certain music. And the best place for most of us to start to come to grips with this topic is this slim volume by musicologist Ross Duffin. It’s an excellent and highly readable introduction to the (almost) lost history of how we ended up with the scales we have today - scales that we’ve all been conditioned to believe are “correct” but that in fact represent only one of many possible ways to tune the chords and notes that we hear.
I had always been intrigued by the belief, commonly held by composers before 1900, that different keys had “colors” that could be exploited by the composer. Since all the notes in the modern, equally tempered piano scale are the same distance apart, I thought to myself, how they they really sound that different? I figured that this difference must have had something to do with the various systems of tuning that I knew had existed before equal temperament (ET). But I had learned what most music students learned - that these systems also made certain keys sound raw and out-of-tune. I had been told that ET made these problems disappear - that it was the most perfect system and had replaced earlier systems in the way that any superior invention replaced inferior ones.
It turns out that ET was none of these things. It is certainly not perfect, in particular in regards to the intervals of the major and minor third. As a result of forcing the octave into twelve equal semitones, the thirds in an ET scale are pulled far away from where they would be in the harmonic series. The major thirds in particular are stretched far beyond what sounds naturally “in tune” to our ears. Furthermore, ET was not universally loved or adopted by musicians once it was first introduced. Duffin discusses at length the alternate tuning systems used on keyboard instruments, tunings which maintained the purity of most of the major thirds at the expense of the more distant ones. Of even greater interest to myself and other bassists, He points out the many tuning systems that non-keyboard instruments used before the 20th century. The most significant difference in these systems is the true tuning of sharps and flats to make the thirds pure. The result of these systems was that string players and singers were carefully taught to play flat notes HIGHER than their enharmonic sharp equivalents, not lower. Yes, you read that right: flats should be higher than sharps. He reproduces several well-known treatises and manuals of the time showing scale exercises that outline the differences between sharps and flats. Once you begin to wrap your mind around these concepts, and actually hear music played in these temperaments, you start to realize how many varied colors can exist in different harmonies depending on how they are spelled on the page.
An even more intriguing aspect of Duffin’s book is his argument about when and how ET became the dominant system of tuning on keyboard instruments. Most historians allege that ET was the dominant system by around 1850, but he claims that what many at the time claimed was equal temperament was not ET in the way we hear it today, and he demonstrates this by several primary sources and research studies showing that many so-called equally tuned pianos and organs from the late 19th century actually had considerable variation in the sizes of their intervals from note to note - changes that preserved more of the old-style tunings and their purer major and minor thirds.
Duffin is a solid and compelling writer, and he has taken on a challenging task in this book. The book presumes a fairly solid level of musical knowledge, but is not a scholarly work and is clearly aiming for a general audience of musicians and music-lovers. He has a lot of work to do in the book to explain complex principles of overtones and harmony to his audience without boring them or driving them crazy. As a result, he concentrates a lot of information into a very small book. He works hard to keep the tone light and accessible through joking asides, cartoons and illustrations, and biographical sidebars about the various historical figures that he references. He is pretty successful in this effort, a little too much for my taste; I often skipped the biographies and other asides in the book in order to keep my focus on the main arguments of the text.
Yes, my friend wasn’t exactly wrong: reading this book and thinking about these issues can make your brain hurt a bit. As bass players, we are all taught to be constantly worried about “playing in tune.” The idea that the very words “in tune” could in fact have a more complex, and more subjective, meaning than we were first led to believe can feel more than a little scary. But it can also be an incredibly liberating experience to realize that no one has ever had a clear or universally held idea of what being “in tune” is. Western harmony is not some sort of divinely inspired, inerrant system to which we must all surrender. Rather, it is a rickety contraption, full of compromises, tricky adjustments, and just plain wishful thinking - like most human creations. Learning about what those compromises and adjustments are, and what we might be giving up by agreeing to them, is important. Intonation and temperament create the core sound of music, and we all need to try to have some sort of opinion on them.
I recommend this book highly and have been passing it around to many of my colleagues, both in my orchestra and among other teachers and musicians. Take a deep breath and learn the truth about harmony - who knows where it might take you.

Tune That Bass

by JW

I’m often surprised by the lackadaisical and unfocused way that some bassists tune their basses before playing. We all devote enormous amounts of time to training our ears, minds, and bodies so that we can play in tune. If our instrument is not well in tune, we make our task of good intonation much more difficult. Why spend countless hours learning the proper spacing and placement of the left hand when you’re not going to tune the open string to the right pitch?

The bass is more difficult to tune than the other string instruments for a variety of reasons, some technical and some situational.

- The interval of the perfect fourth doesn’t occur in the overtone series. Therefore, it is more difficult to hear on its own than perfect fifths.
- Because of this, we often choose to tune using harmonics. This method assumes that our strings are in good condition, and that the pitches of the harmonics don’t activate any wolf tones on our bass. Often, one or both of these assumptions is mistaken and we need to fix these problems by installing new strings or using wolf eliminators. If we don’t, then our harmonics can be inaccurate and our tuning will be also.
- The bass is not a very loud instrument, and especially in an orchestral context it can be very hard to hear oneself well enough to accurately tune. If we are surrounded by other bassists, it can be even more difficult as we try to pick out our sound amidst all the bass playing around us.
- The way we draw the bow across the string can affect the pitch in subtle ways, especially when we tune with harmonics. If we put a lot of weight into the string as we tune, the bow can bend the string sufficiently to alter the pitch. Try it and see for yourself: Play the “A” harmonic on the D string with a fast light bow and with a slow, heavy, “pressed” bow. This often connects to the issue of our volume; people tuning onstage during orchestra will play their harmonics far too loudly in order to hear themselves, thus distorting the pitch.

For all these reasons, I choose to always check my tuning with an electronic tuner. At the Kennedy Center Concert Hall, we have two high-quality strobe tuners offstage that many NSO members use to check their intonation before going on to rehearse or play a concert. I also have a small tuner like this one that I use whenever I play to check my tuning. They are not expensive, quite accurate, and can also be purchased with a contact microphone that clips to your bass. This can be very useful for tuning in noisy environments (like onstage at an orchestra rehearsal!). They can also be calibrated for different “A’s,” from A435 to A445, so that you can set it precisely to whatever “A” your group uses – the NSO tunes to A442, for example, but when I’m playing with a piano I need to tune to A440.

If I’m in a quiet area, I check each open string with the tuner, drawing a relaxed, mezzo piano sound so as not to distort the pitch of the string. Every member of my bass section in the NSO uses a tuner in this way before we go onstage, and we all agree that it helps our intonation.

When I’m playing with a group that I’m not that familiar with, I often go to the oboe player (or whichever instrument will be giving the “A” at the beginning of rehearsal) and ask them to play the “A” into my tuner so I can see exactly where their pitch center will be. I then set my tuner to that pitch and tune my bass.

After we’ve played awhile, the action of our hands on the string and the vibration of the instrument can cause our strings to go out of tune. I frequently recheck my intonation with the tuner during a practice session.

One final piece of advice regarding tuning: Once I’ve tuned with the tuner, I play all my tuning harmonics, noting if any of them seem false or off pitch. This way, if I don’t have my tuner or need for some reason to tune without it, I can know which harmonics I can trust and which ones I need to “tweak” a bit to get the open string in tune.

Sharps and Flats

by JH

While a student at the Interlochen Arts Academy, I attended a guest master class given by Bernard Linden, then a violist in the New York Philharmonic. His daughter Louise was a student at the Academy. In that class, he inspired a journey for me that continues today, that of understanding tonality and intonation. Mr. Linden demonstrated that he would practice the intonation of a passage by determining an appropriate reference tone for the tonality, and then compare the notes in the passage to this tone.

It was many years later that I started to realize that notes even spelled the same way on the page may need intonation adjustment according to the tonality. Even more recently I became aware of the illustrations of Zarlino in the Groves Dictionary, explaining that not all whole steps are the same size and that not all half steps are the same size. Many errors of intonation involve playing sharps too sharp, and flats too flat.

Try these things, preferably with two or more players:

1. Most important for these activities is that the basses (or other instruments) are tuned accurately. I suggest for two players, agreeing on pitch for the open D string. Then one player finds the D on the G string which they both agree is in tune. The D on the G string is sustained while the other player tunes his or her G string until both are satisfied. After the G strings are settled, one person plays the open D while the other finds the A which is one fifth above, and both agree that it is correct. The A is sustained while the other player adjusts his or her A string. After the A strings are settled, find the E which is a fifth above open A. Sustain this E so the other person’s E string can be tuned. Hopefully the instruments are well in tune now.

2. Have one person play his open A while the other finds the E on the D string. Sustain this E while the first person finds the B on the G string which matches. Silently hold this B while the other person finds the B on the G string which matches the open D. After both B’s are found, compare. Are they the same? Which is higher?

3. One person finds the F# on the G string which matches the open D; the other find the E flat on the D string which matches the open G. Are they in tune with each other?

4. Find a G# which is in tune with the open E; find an A flat which is in tune with the E flat which is in tune with the G string. Are the G# and A flat the same note?

I could go on for a long time with other examples, but it will be more meaningful for you to discover some of this on your own. Good luck.