There is much more to an octave than the twelve equally spaced tones we listeners and practitioners of western classical music have become accustomed to today. While Schoenberg and the rest of the decidedly dodecaphonic Neue Wiener Schule may have been content to arrange and rearrange rows of the twelve tones of the equal tempered scale, other composers felt trapped by the finite color choices and harmonic landscapes available in these arbitrary twelve pitches (after all, there are only 479,001,600 – 12 factorial – possible tone rows).
Some composers joined the search for more pitch colors and added another twelve equal tones “in the cracks” between those already widely used, thus adding quarter-tones to their musical languages. Others experimented with “alternative” equal temperaments – why use twelve equal tones per octave when twenty-eight or fifteen would do just as well? Finally, some composers turned to historical non-equal temperaments in search of viable alternatives to equal temperament.
Among many people who have experimented with microtonal writing, one of my favorites is Ben Johnston. I currently have the entirety of his 10th String Quartet stuck in my head. In the case of the microtonal materials in this particular quartet, Johnston based his harmonic language on the upper partials of the harmonic sequence while relying heavily on principles of just intonation. A sample:
“Microtones are the least of it. Microtones are the byproduct of what I’ve asked for. I’m dealing with getting music very precisely in tune, and this means that the level of accuracy has got to be higher than usual.”
— Ben Johnston
Last year I heard the Del Sol String Quartet play Johnston’s Tenth Strong Quartet twice – first at Old First Church and then at The Hub (the old Chronicle Building) downtown. This work features Johnston’s fully developed tonal language: based on the eighth through sixteenth partials of the overtone series (although not consciously, Charlton Lee, Del Sol’s violist, mentioned that when he figured this out after hours of score study he asked Johnston about it, and Johnston said “oh, why yes, I suppose so…”). The piece is in four movements, each showing how the alternate tonality can ever so slightly shift out understanding of the music. Dissonances become more “crunchy,” consonances more singing, purer.
In addition to his innovative use of microtones to bring out his relatively simple harmonic changes, Johnston employs extremely complex rhythmic patterns (4 against 5 against 6 with hemiolas against 7 in the second movement!), and uses the famous Irish Air “Oh Danny Boy” to great effect in the last movement. One doesn’t notice the tune at first, because it begins the movement in inversion, only “re-inverting” to its true form in the very end of the movement. The last movement also charts a history of western music, setting Inverted Danny’s Air in the style of “Isaac, Machaut, Montiverdi, Bach, and finally moving into something modern, or maybe post modern.”
I looked over the score for the quartet, and discovered that Johnston had devised a very clever way of indicating how each note is to be “tweaked” into tune: he used flat and sharp signs in conjunction with upwards and downwards arrows, as well as little numbers (7, 11, 13; sometimes with flat signs) to indicate with variant of the given pitch (based on a frequency from the implied fundamental’s overtone series) he wanted. Each “chord” in the quartet is built either upwards (as is standard) or downwards (which is quite new and different) from a fundamental pitch. Of particular interest is where Johnston creates and “upside-down” overtone series descending from a high fundamental pitch. The ratios that define each interval in the series are identical to those going upwards (as we are used to, 1:1; 2:1; 3:2, etc) except that the distance is inverted. This is, in my view, part of what makes Johnston’s microtonal harmonic language so very interesting. The fundamentals, whether high or low, may or may not actually be present in the score (although in the copy I examined somebody had written the implied fundamentals in based on a complicated mathematical process deducing them from the pitches indicated). However, every single note each musician plays are based on the harmonic series from each of these constantly shifting implied fundamentals, which guarantees absolutely pure intonation. Johnston has in fact found one possible solution to the age old issue of the “left over bits” that form the comma.