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Monday, March 8, 2010

The Bohlen-Pierce scale

Boston is hosting an interesting symposium and concert series this week (March 7-9, 2010). It began yesterday and continues through tomorrow evening.

The event is drawing a diverse crowd of composers, musicians, mathematicians, music theorists, computer scientists, researchers, neurologists, and musical instrument builders from all over the world - all because of an intriguing and unifying idea.

The idea that has caught their imagination is a new scale. The scale was conceived independently by two microwave engineers and a computer scientist in the 1970s and 80s. It is now referred to as the Bohlen-Pierce or "BP" scale. Heinz Bohlen, Kees van Prooijen, and John R. Pierce all had a hand in it's discovery.

The BP scale is rather unique. There are several variants, but the primary idea is that BP utilizes the 3:1 ratio instead of the 2:1 ratio that defines the traditional even-tempered scale used in most Western music.

With traditional Western music, the octave is a basic and primary interval. It's derived from the 2:1 ratio, and from that we divide the octave into 12 equal steps. BP replaces the octave with something they call a "tritave." Arriving at the tritave in the notes of a rising BP scale does provide a melodic sense of closure or completion.

With the BP scale, the 3:1 ratio defines the lower and upper degrees of the scale (which happen to be the span of what we usually think of as an octave and a fifth). That range is then divided into 13 steps.

The Bohlen-Pierce Symposium and Concerts are sponsored by the Boston Microtonal Society and Georg Hajdu (Hamburg Hochschule für Musik und Theater) in partnership with the Goethe Institute of Boston, the Berklee College of Music, Northeastern University, and New England Conservatory. The conference website is

I was intrigued by the idea of this new scale, and attended the first concert at the Fenway Center at Northeastern University last evening to hear what composers are doing with it. The concert featured nine pieces - although the BP conference in total will showcase 24 premieres of pieces written by composers from around the globe who are utilizing the BP scale.

My first impressions of this new musical structure are mixed.

While there seems to be a solid theoretical basis for BP, how composers and musicians apply the raw material of sound is the ultimate proof in the pudding. There seems to be a number of aesthetic and logistical issues regarding the execution.

First, it's pretty hard to abandon the interval of an octave. It's so universal and ingrained in virtually all the music we have known up to this point, that skipping over the octave seems strange. In the BP sound world, the octave is an an invisible elephant sitting on the stage.

Electronic realizations of the BP scale sound so much more convincing than realizations produced by singers or instruments. I'm not convinced that musicians have yet attained the needed hearing and performance skills to accurately render the BP scale. Nor have our ears grown familiar enough with it.

For instance, one of the more successful works on the concert was Five Moods by Anthony De Ritis. De Ritis recorded BP clarinetist Amy Advocat and produced a tape piece based on those sounds and pitches. From his piece, I could hear the totality of the scale, and how it has some very consonant properties.

All music is cultural. The basic premise that the BP system seems to ride on is a notion that the current 12-note equal-tempered scale is somehow inferior. The BP scale, while still imperfect, strives (at least theoretically) to make a better map onto the frequencies implied by Nature's Grand Dame - the overtone series.

My beef with that objective is one of personal bias. Who says that musical systems should follow Nature's lead? Why the heck should human-kind not divide musical intervals as they please. I like to hear my music served up on a plate with "in-harmonic" intervals. I like the sound of notes and their overtones beating "out of tune." I like dissonance. I like tone clusters, scalar symmetry, and the certainty of an equally loaded 12-gage keyboard. The traditional semi-tone is one of my favorite intervals, and I don't desire anything smaller - particularly when it is dispersed using octave-equivalence over several spanning registers. Octave equivalence is an amazing property.

As with the Early Music folks, the BP advocates seem to want just intonation and tonal consonance. They believe that the modern day piano is corrupt, evil, and ugly. Frankly, I just don't share that point of view.

I'm a composer who works mostly in an atonal universe. For that sound scape, a 12-note even-tempered scalar system works rather nicely. Musicians are trained to hear it, read it, and perform it. It doesn't require relearning a new system.

A very good notational system exists for the 12-tone system which has evolved through the collective efforts of musicians over centuries of practical use and applicaton.

BP music notation (or the prevailing version of it) uses the standard five-line music staff and traditional clefs that musicians are familiar with, but the seven notes C-D-E-F-G-A-B are augmented with H and J. The thing that throws me off is that while the musicians may be reading the note G - what actually sounds (and the interval it creates with the preceding note) is something entirely different. BP notation and keyboards need to go through a lot more development.

Will BP catch on and become mainstream?

Probably not. It's hard to create a tradition when only six BP tuned clarinets exist in the entire world (four of which are in Boston for the concert series). The BP clarinet should be the hallmark for this scale, since the clarinet is acoustically ideal for it. It over blows in the correct ratio, and it's "square wave" timbre nicely reinforces the gestalt of the scale by providing energy on the odd-numbered overtones.

The bottom line is that composers will end up writing what they want to hear. What they want to hear is, in the end, approximated by whatever system or scale they happen to be using. Musical ideas fall onto a pitch-frequency grid, and while the grid can vary, the musical ideas themselves transcend the surface characteristics of the aural medium. There is no magic bullet, and no substitute for genuine and substantive musical ideas regardless of the tuning system it is constructed on top of. Tuning systems are secondary - almost arbitrary.

There were some pieces on last evening's program that caught my attention. For example Liebesleid (2010) , a short work by James Bergin, seemed classical in conception. Bergin took a rather conservative approach to the BP scale, and worked within the constraints of a simple melodic materials. His piece was straight-forward and elegant. His intervals in the BP language sounded large compared to other pieces that I've heard from him, although the same unique composers' voice still comes through regardless of the underline pitch system.

Julia Werntz's piece Imperfections (2010) was also for solo BP clarinet. It too was short and simple, and to me sounded like a transcription of her 72-note microtonal music. In fact, she converted the BP scale and notation into a subset of the language she usually composes in (a 72-note system devised by Ezra Sims), and back again after the piece was conceived. Having heard her music before, Imperfections sounded like a subset of her normal sound world. The ending of the piece intrigued me. The wide leaps did point to a coherence in the BP scale. It did make me wonder if BP is actually a universal chord, rather than a scalar set of distinct stand-alone pitches related to one-another. When heard as a chord, all the notes seem to be cut from the same cloth, and seem intuitively related - like members of a family.

I want to keep abreast of developments in the BP field. But at present, I don't see it as a new panacea or musical Shangri-La. I'm quite content to keep composing in the system that has done me well over all of these years. I'm find no shortage of relationships to exploit in the 12-pitch even-tempered system. It's not lacking in any way. In fact, 12-pitches per octave is about all that I can handle.