From Terry Riley, With Complements

….the last bar of Terry Riley’s Y Bolanzero, for guitar orchestra–a wierd 8-note collection with no G#, no F#, no B, no D#….

Austrian guitar virtuoso Yvonne Zehner will be principal player with a crack group of Queens College guitarists at Symphony Space on November 2. Y Bolanzero will finish the 3rd set in a 1-day guitar festival featuring Yvonne Zehner. Tickets HER

I approach this piece humbly. It surprises continually.

There are integrators and bridge burners. Sometimes one person tries both in one lifetime.
Terry Riley is an integrator. Carter was integrative in the ’50s; a bridge-burner in the ‘60’s & 70’s.

We see in the last bar, all the things D minor handed to us at once, like one of those Picasso paintings where an image is seen from mulitple views at once.

What would “pan-diatonic” mean for harmonic minor? Y Bolanzero has an answer, and it is surprising. “Pan-diatonic” in harmonic minor begs for complementation.

Before seeing the piece in that obvious way ( all things D harmonic minor ), I looked at it as if it were a Carter pitch field, all based on what we see in the last 2 bars, a funny thing to do. And yet there are some lovely things to examine that way. I now have no doubt that Terry Riley exhibits a sensibility that is integrative, conscious of both post-tonal developments, and utterly unfearful of integrating those with tonal (scale-degree) contexts.

The pitches in the last bar offer two contexts for the major 7 chord. The major 7 chord can be a I maj7 in tonal music, extended by its *diatonic* transposition, the IV maj7. The last bar has all the notes in the F major scale, and then some. We see Bb maj7 and Fmaj7. We see another context for the maj7 chord in this last bar. It has 5/6ths of this bizarre scale: 014589, alternating semitones and minor 3rds (1’s and 3’s). This scale is the maj7 chord transposed through the 4 cycle. Fmaj7, Amaj7, Dbmaj7. There is no Ab in the last bar. Ab is one missing component, but we see it in the preceding bar. There is also an incomplete octotonic scale. All of these elements have their moments in the piece. The basic sound of the piece is F-C#-E, a sound-signature of 014589. [ Note: the last 2 bars lack F#, D#, and B. ]

If harmonic minor reeks of E hexachord, then certainly, harmonic minor in // major 3rds will double that. We see that in bar 9, and we see that the Ab that is missing from the last bar and from the opening bars appears in this passage, fleshing out the E hexachord ( augmented triad with passing tones ). Ab is there, but still no F#.

Add the name Terry Riley to the list of E Hexachord pioneers.

[ In measure 6, F# appears fleetingly as a completion of the octotonic scale that begs for completion in Riley’s pitch field. ]

In the climactic passage in 7/4 we hear [F, C, E] gloriously extended decorated by the [A, C#] dyad. This is 5/6ths of the E Hexachord. Slonimsky calls it the augmented triad with passing tones. Until this point, Bb maj7 never serves as the immediate foil for the F major7. In the first 3 beats of these 7/4 bars, Bb maj7 is superimposed upon F maj7–the diatonic extension of the maj7 sound; The [ A, C# ] dyad we see landed sqarely on the 4th beat is the E hexachord context of the F maj7. **This E hexachord is complemented.**

The big moments in the piece could arguably have to do with complementation. In the same wonderful 7/4 celebration, The [F, C, E] – [A, C#] interplay has a foil, the same thing down a second. Too few are aware of the fact that the augmented triad with passing tones (aka “E Hexachord”) has one tidy complement–its transposition by 2, by a major second ( up, or down– the two are the same ). [ Eb, Bb, D ] highlighted by glimmers of [ G, B ] dyad, 5/6ths of another E hexachord, the complement of the first.

Note: Each of the 2 complementary E hexachords are muddied in the bass guitar 1 part. Bb is added to the [F, C, E] + [A, C#]; Ab is added to [ Eb, Bb, D ] + [ G, B ]. The two missing components in the two E hexachords here are G# & F#. The G# appears with the [ Eb, Bb, D ] + [ G, B ]. This creates the tension between the two contexts of the the [ 0, 1, 5 ] collection. So the missing pitch is F#.

So, let’s look for the F#. It appears earlier as an extension of the incomplete octotonic material in the last bar. Still working this out. At the moment I am thrilled to find a composer who has figured out how to avoid being OCD about interval content, while being utterly faithful to a contextual principal for a work of music. Riley shows that we can be consistent without throwing out the baby with the bathwater. By this I mean, simply, that Riley is returning to the Elliott Carter of the 1950’s, who did not fear scale-degree associations. Bring them on! JS Bach is all over this. The Bourree of the E minor suite for Lautenwerk shows an uncanny balance of set class consciousness as it falls on scale-degree associations.

Complementation–isn’t this very clear? No Bb’s until measure 17:

There are many examples of 11-note gamuts, setting up a completion.

The E Hexachord emerges in Beethoven, Brahms, Schoenberg Babbitt, and finally, Terry Riley. Terry Riley brings the E Hexachord back to earth, back to a context where the scale degree context is not erased, destroyed.

In his op.88, Brahms demonstrated an awareness of this non-diatonic context for the maj7 chord lurks in the background of the tertiary harmonic relationships that we find in Beethoven’s work (Diabelli Variations). I’m calling this context the E hexachord out of habit. It is the maj7 chord transposed through the 4-cycle (the major third cycle, the augmented triad). The E hexachord was explored further by Schoenberg & Babbitt. Take a major 7 chord and transpose it by major thirds, and you get what Donald Martino called the E hexachord, a “scale” that alternates minor 2nds and minor 3rds, a pattern that repeats after 6 notes.

The last bar of Y Bolanzero has these features:
7 notes of the diatonic septachord (a complete diatonic septachord)
5 consecutive notes of the E hexachord
4 consecutive whole tones
4 consecutive notes of the octotonic
3 consecutive notes of a chromatic scale
Terry Tiley’s representation is echt 21st Century–the familiar diatonic septachord contrasted by the rest of the list.
Carter was all over this sort of interval-vector parsing.

Bb & F are very familiar, the most ancient musical relationship—what Pythagoras heard on the blacksmiths’ anvils.

The E hexachord, the crazy thing that came out of Beethoven, Brahms, Schoenberg and Babbitt, is a precious, pristine mountaintop with rarefied air. For Brahms it was a mountaintop, for Schoenberg it was another planet.

Terry Riley is not afraid to show the connection between simple things and the fancy things. The tune we hear in the very opening sets forth some of the key elements of the E hexachord as every day materials found in harmonic minor music.

This is simply D harmonic minor, and it enfolds the kernel of the E hexachord–F, C#, E, the 0 harmony of the piece (the focal harmony of the piece). Carter was careful to avoid tonal associations after a certain point. I am drawn to Terry Riley’s music for his daring to divulge these tonal contexts of post-tonal things. Is it unfair to say that concealing these relationships leads to a *partial* representation of musical realities? Is it fair to say that the 20th Century way was to avoid such aural connections?

Often Dowland’s most chilling sounds come from augmented triads; his augmented triads over-foreground his glorious suspensions. Think also of Bach’s Sarabande from the Cello Suite No. 5, and notice how that augmented triad move sneaks into the Gavotte and other movements. See Duke Ellington.

Carter avoided familiar associations. I admire Terry Riley for his fearless sounding of the familiar, for bringing things together, fearless reconcilings of old and new, plain and fancy, occurring in various ways and over various timescales. The soundworld throughout Y Bolanzero is intensely E hexachord, a post-tonal thing, but with reminders of the I maj7–IV maj7 diatonic relationship.

I see that, like Carter, Terry Riley avoids straight symmetries. He breaks them, always. The last measure has only 5/6ths of the E hexachord. Throughout, there are “scales” redolent of the octotonic, but always interrupted by consecutive major 2nds or consecutive minor seconds. That is lovely. The last measure has a complete F diatonic septachord. The E hexachord is a straight symmetry, like the octotonic scale. What Donald Martino called the E Hexachord, Slonimsky called an augmented triad with passing tones. It is a “scale” that alternates semitones and minor thirds, repeating after 6 notes, just as the octotonic scale is a diminished triad with passing tones, aka the “diminished scale”, alternating semitones and whole tones, and repeating after 8 notes. These are scales of limited transposition (Messian). They are what they are. I see Terry Riley here sharing Carter’s concern to avoid strait up symmetries. Why avoid anything? Because in a symmetrical scale such as the E hexachord & the octotonic scale, every pitch has only 2 meanings. The symmetry limits the profile of each pitch. In the E hexachord, any pitch will be followed by either a semitone or a minor third. In the octotonic scale, any pitch will be followed by either a semi-tone or a whole-tone. Other sound worlds are free of this poverty of contextual richness. In the diatonic hexachord, there are no tritones, only one minor 2nd, two major thirds, three minor thirds, four fourths. The usual proceeding is for the music to float on the symmetrical “scales” until finally landing in a context where each pitch in the “scale” has more profile. The diatonic septachord has only one tritone, making the tritone the defining element of a “key”.

The last bar of Y Bolanzero is a gathering of the E hexachord and the diatonic septachord. The E hexachord floats with a Baudelairean anti-positivism, the diatonic is a landing place where up is up and down is down. Y Bolanzero is very floaty. It really doesn’t quite ever land, but it constantly flirts with landings and other old things. I am struck, at this juncture, by the post-tonal aspects of the work.

Symmetrical scales are deprived of the unique multiplicities of intervals seen the in the diatonic hexachord and the chromatic hexachord.

Another way to look at this:

–E hexachord is 5ths through the 4 cycle (through the major third cycle)
–Octotonic is 5ths through the 3 cycle (through the minor third cycle)

I thank Frank Brickle for bringing Terry Riley’s recent music to my attention.

Thanks to my team of guitarists at Queens College:

Ricardo Arias (thanks for 90 minutes today), James Artache, Kyle Miller, Pascual Araujo, Jonathan Ramirez, Charlee Ray Price, Ebin Samuel, Pablo Sanchez, Xavier Paez Haubold, John Coughlin, Austin Tobia, distinguished alumnus John Chang

–William Anderson