An uneasy symmetry?

As part of our 2017-2018 season we’re continuing to give each of our core singers a turn at the helm of the blog. The below post below comes from our bass, Steven Hrycelak.


So much of the history of Western music centers around tonic and dominant harmonies, as well the dominant’s functional cousin, the subdominant.

For those of us obsessed with symmetry, however, it is worth noting that the thing that divides the octave in half is the tritone — which is exactly in between the fourth and fifth scale degrees, upon which the subdominant and dominant chords are built.

To achieve a scale that contains these fourth and fifth scale degrees, major and minor scales are made of various combinations of whole and half steps. Scale degree four and five are a whole step apart, but a scale of only whole steps would contain neither of these pitches; that is, neither a perfect fourth nor a perfect fifth above the root would be in this scale.

How, then, to achieve something more symmetrical? More contemporary composers have explored two options. First, the whole tone scale, which divides the octave into six equal whole steps, and the tritone into three equal whole steps. Dominant and subdominant harmonies are not a part of compositions employing this scale, and any given scale degree has less prominence, but a feeling of completion or circularity may still be felt as the octave is achieved, depending on how the composer uses this scale. The other frequently employed option — more of a technique than a scale, per se — is based on minor thirds, which can stack indefinitely to create diminished triads. This divides the octave into four equal parts, or the tritone into two equal parts. I find that this configuration further downplays the prominence of scale degrees, meaning that nothing feels like a root as diminished triads endlessly invert.

Chris Trapani, in his piece End Words, explores a further division of this symmetry — and one that we are not used to either performing or hearing. In the second movement this piece, the building block is a scale in which the minor third is cut in half; in other words, each scale degree is equal to 1.5 semitones. In this way, the octave is divided into eight equal parts; the tritone, into four.

In my experience in working on this piece, this adds to a further lack of grounding, or a feeling of weightlessness, as the size of the interval is not one that we encounter regularly. But, since each interval is the same size, perhaps there is also something grounding in that? Maybe you have another reaction altogether? I’d love to know what you think, when you come to hear us on Friday night!

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