I’m partial to the 13th

A recent post in my husband’s blog (Steven Cornelius) describes his disciplined approach to ear training. At one point he mentions the overtone series. I can relate. This is currently at the center of my musical existence as my quartet continues to record Composer Ben Johnston‘s string quartet cycle. It also happens to be at the root of our Western harmonic language.

What is an overtone? They are beautifully synchronized pitches that are neatly folded inside almost every note we hear.

The pitch of a string is determined by the rate at which it vibrates. On the violin, for example, the D string vibrates in a single arc from one fixed end to the other at a rate of 293 cycles a second. That perceived pitch is the first partial or harmonic, aka the fundamental. However, the string is simultaneously vibrating in smaller divisions (halves, thirds etc.). Each of these segments creates its own pitch as well.

Overtones vibrate in direct proportional relationship with the fundamental. For example, each half vibrates twice as fast as the whole (2:1), which produces the first overtone, the octave. Three equal divisions of the string creates a vibration ratio of 3:2. From this you get the second overtone, the fifth (one octave higher). Each subsequent division produces another overtone, always higher in pitch than the previous one. Because the vibrations of the overtones are perfectly synchronized with the fundamental, there are no interference patterns in the sound waves. The intervals are pure; their sound is smooth and harmonious.

Steven embedded a chart of the overtone series in his post. Certain overtones are marked as being perceived as “out of tune.” The plain fact is, if you are using equal temperament (ET) as your litmus test, every single overtone will be out of tune, except those that produce octaves of the fundamental (2nd, 4th, 8th 16h overtones and so on). The ones marked as out of tune in the chart are just the most extreme examples. The 7th partial is about 31 cents lower than ET (about 1/6 of a step), the 11th is 53 cents higher (approximately a quarter tone) and the 13th is 27 cents higher than ET. 

Ben Johnston has chosen to move outside the limitations of ET and inhabit this expanded pitch world of pure relationships – the world of just intonation. Imagine a chord with the 13th partial sounding in one of the voices, and then imagine modulating to that partial – building chords using the overtones it generates. Welcome to Ben’s world.

Right now Kepler is tackling Johnston’s String Quartet No. 7 – a piece that has, to our knowledge, never been played. Small wonder, as it has a vocabulary of over 1,200 pitches to the octave. I have been compiling a chart of the accidentals, and so far (first movement only) have found 85 distinct combinations of Ben’s various modifiers.

During yesterday’s rehearsal, we managed to pick through 5 (five) measures of music – figuring out the actual pitches, their functions, and listening to them. A few more days and we will be ready to bring the first movement to Ben. He will answer our questions, and we will begin the long road to the recording studio.

Wish us Bon Voyage…

To Boldly Go…

This blog has been dormant for so long, I almost forgot it existed. Now seemed an excellent time to weigh in, as I have been thinking a lot about Ben Johnston and his explorations in extended just tuning, having recently written about him for the American String Teachers’ Association publication. Also, Kepler is deep into SQ No. 6. With yesterday’s recording session, we passed the half way mark on the third and final disc of the quartet cycle.

Some experiences change us. I know that the 11 years I spent playing in Marimolin transformed my understanding of rhythm. The same is true after 12 years of playing Ben’s music. I am certainly a different person and a different musician than I was before.

Playing Johnston has been like traveling to a new universe. It may seem distant, but it is tightly coiled inside the one we know – as close as a breath – or a couple of cents, which will open a door into new, undreamt of dimensions.

Talking to Ben about his life in music, one gets the sense that ultimately, his quest has been spiritual in nature. His work is an attempt to infuse meaning into life through the composition and practice of music. I ended my article with the following quote from Ben,

“There are two approaches to life. One is linear and melodic – the hero’s journey. But there is another – the vertical, harmonic way – concerned with perfect relationships. I have grown to find this a much richer experience. It is the same in music. I don’t mean to say that I am a better person than others, and therefore this is better music. But I do believe that working with this music has the potential to make me a better person. This is true for anybody who deals with it. If it is used right, it has that sort of potential. It’s not just a question of what the composer has put down on paper and how accurately it is realized. It’s a matter of finding meaning, and what actions this meaning might invoke.”

 

The Shape of Things….

Last Friday I visited the Racine Art Museum, where they had a show of works by Barbara Sorensen and Karen Gunderson. Walking through Sorensen’s ‘speleothems‘ installation was a dizzying, surreal experience. Pacing around and between these stalagmite and stalactite shaped forms, each step revealing new and unexpected perspectives, was like entering a cave on another planet in a distant universe.

Adjacent to this were Gunderson’s black canvases: oil on linen… black paint laid on in blocks with grooves as fine as an infant’s hair. Light reflecting off these grooves makes the painting look literally 3-D. I don’t think I have ever seen a canvas look so sculptural. As one moves past, the waves dance and ripple. I had to get close to the wall and look at them from the side to convince myself that they were really flat. The effect of movement on these sculptures and paintings echoed my experience of music and how it unfolds through time.

Going to the Source

On January 14, Gramercy Trio will premiere a new trio by Gunther Schuller*. It is a fantastic piece, and we are keenly aware of our good fortune, although in commissioning Gunther we knew we would get a winner.

We were thrilled when Gunther came to a rehearsal. He put us through the wringer for 4 hours.

It is fascinating for me to work closely again with Gunther after intervening years of working with Ben Johnston. The beauty of Ben’s notation is that everything depends on function. Gunther, on the other hand, uses a row. … the same one since 1976. It has produced an amazing body of work.

Working directly with the composer can be crucial. It is a direct path into their thoughts and intentions. For example, at one point the violin has a C# against a E flat chord. Thinking from the angle of ‘spelling denotes function’, it did not occur to me that my C# is intended to function as a dominant seventh. But, lo-and-behold, it does. With Gunther there to clarify, I lowered the pitch to his satisfaction.

*This commission has been made possible by the Chamber Music America Classical Commissioning Program, with generous funding provided by The Andrew W. Mellon Foundation, and the Chamber Music America Endowment Fund.

Haiku for a Cold Morning

Hats, mittens, sweaters,

Down coats and boots are great – but

Pockets are heaven.