Thursday, May 03, 2007

Equal Temperament

I bought a book called How Equal Temperament Ruined Harmony (and Why You Should Care) by Ross W. Duffin. This is some sort of joke, right? In the 21st century I am supposed to believe equal temperament is controversial. Boy am I going to trash this, I thought.

So maybe a singer isn't the right person for this task. The average operatic voice has a substantial vibrato that fluctuates in pitch by as much as a semitone or more. An opera singer will sound in tune as long as the listener's imagined pitch is near the middle point of the vibrato. The pitch you hear is all in your mind. So we are not really caring about this temperament business.

Equal temperament just means that the distance between any two semitones is exactly the same throughout the octave. Before equal temperament there were just intonation and meantone and other stuff. Perish the thought you should actually read the book.

If you go around the circle of fifths, when you get to the original note it will be off, too high. Now right there he is being illogical. To get the circle of fifths to come out even with the octave, I need to adjust the top note of the fifth down slightly. A circle of these slightly diminished fifths will come out even with the octave. By doing a circle of fifths I will have generated all 12 notes of the scale, n'est pas? Why aren't I done now? This is the process that creates equal temperament.

He wants a lot more than 12 notes because he says the equal temperament major third is too big and sounds bad. This is really his whole argument.

Almost any tuning system has the purpose of limiting the number of keys, notes, finger combinations to 12 distinct notes for each octave. No effort is made to distinguish F# from Gb. The piano is hard enough to play without adding another set of sharp/flat notes. I for one would have to throw in the towel.

There needs to be some serious thought here. A pipe organ will require stable tuning more than any other instrument. It's a lot of work to tune a pipe organ, and once it's tuned, it will stay that way for months or years. Pianos are probably next in terms of permanence of tuning. But a touring professional pianist will want his piano tuned prior to performance. And as we saw recently, the harpsichordist will need to be able to tune the harpsichord before a concert. A harp is tuned for each performance, but the pitch of a harp is very much a special case involving pedals that change the pitch for different keys. Let's leave the harp out.

Keyboards are really the only instruments that require equal temperament. The other instruments can all manipulate the pitch in performance. Horns can lower the pitch by stopping with their hands. Trombones slide. Woodwinds move their fingers slightly off of the holes to get pitch changes. All of them can manipulate the pitch with their mouths. On strings only the open notes are fixed pitches. Everything else can be changed in context.

Tuning systems and the music played with them have influenced each other throughout history. A natural, valveless horn tunes its notes according to the overtone series and not according to any tuning system whatsoever. The only thing you can mechanically tune is the bottom note. When we had natural horns and trumpets, we made them in different pitches or chose the key of a composition based on the notes available in the lower part of the overtones of those instruments. The presence of these natural instruments in the orchestration limited the keys available to the composer. If I add valves, something that happened in the second quarter of the nineteenth century, then I have a lot more keys I can use.

The availability of all the keys led to increased freedom of modulation. Wagner is not possible without the valved horn. All the other wind instruments of a modern orchestra were similarly redesigned in the nineteenth century in order to get a louder, more tonally flexible orchestra. They were going for loud, not pretty. If you have attended an indoor performance of Schoenberg's Gurrelieder, you will understand what I am talking about. Amplification is just not necessary.

If I have so carefully constructed the instruments of the orchestra to allow for modulation to any key, equal temperament seems the logical tuning system for their construction. With earlier tuning systems the farther away you are from C, the more out of tune the scale becomes.

My son the horn player says that he once discussed this with Dave Krebel, the former first horn of the San Francisco Symphony. How does a first rank professional orchestra address the complex issues of tuning? Does a symphony orchestra actually play in equal temperament? Remember the whole point of the book we are discussing is to tell us we are playing in equal temperament and shouldn't be.

According to Dave, the orchestra would match against specific instruments and players to achieve its tuning. If the ensemble includes a keyboard, the orchestra will tune with that instrument. This will be in equal temperament. Perhaps in a piece with brasses, the orchestra would tune with them, emphasizing the pitches from the overtone series. Other times they would tune with the woodwinds. The actual intonation of the orchestra is a fluid, flexible phenomenon probably not reflecting any particular tuning system. It is part of what makes them professionals.

Chris said that it is easier to get classical pieces to sound in tune if you leave out the continuo. The keyboard with its rigidly fixed pitches is seen as an obstacle to proper sound. How fascinating.

Duffin starts his book with a description of the Cleveland Orchestra playing Beethoven's Ninth Symphony. When they modulated from d minor to Bb major, the conductor wasn't satisfied with the sound of the major chord. Maybe Cleveland isn't as good as San Francisco.

I am ready to concede one point: all these new early instrument ensembles might be well advised not to tune their harpsichords in equal temperament. They don't have to concern themselves with free modulation to all 24 keys like a symphony orchestra or a solo pianist would. I suppose a harpsichordist might tune the harpsichord any way he wants.


Anonymous said...

Tke a look at this new recenty developed temperament at

Dr.B said...

By all means look. I personally prefer that making music remains an art form. I have enjoyed thinking about this subject, and have become aware that each family of instruments has its own unique acoustical properties and pitch problems. The art comes from blending them together. Blending them is more difficult with early instruments, and this may explain my sense that these ensembles don't play in tune. It's simply harder for them.