The next in the series begun with the 1971 original, Nocturne for orchestra, Olympic Shoreswas scored for wind ensemble. A large 1974 work for double choir, brass, and tape, Shores of Infinity, preceded it. While the same textural approach to a large instrumental ensemble continued, the title reflected my Pacific Lutheran University experience in Washington state the previous year.
Olympic Shores
Clark 1975 (TC-31)
NTSU (now UNT) Symphony Band
A chamber music piece titled Shores (TC-44) followed in 1978, which opened a new stream of writing for me with its completely non-metric time notation, bright arpeggiated pitch constellations, and oscillations animating the harmony and the texture.
Though it was performed in 1978 in Denton by the NTSU New Music Performance Lab, I’ve not been able to salvage an old recording.
Three pieces of the early 20th century, which I studied deeply in the 1970s and later used extensively in my teaching of modern music, were each masterful explorations of musical sound color:
Claude Debussy’s La Mer (1905), an iconic tone poem of Impressionistic musical painting with an orchestral palette
Arnold Schoenberg’s “Farben (Summer Morning by a Lake: Chord-Colors”, the third of his Five Pieces for Orchestra, Op. 16 (1909) — a gentle study of orchestral sound color
Anton Webern’s Symphony, Op. 21 (1928), whose first movement is a delicate gem of pointillistic color canon built on one enormous, static, symmetrical 13-pitch constellation
After fifty years, these works are embedded more deeply than ever in my musical consciousness. Farben pays special homage to Schoenberg’s masterpiece, layering kaleidoscopic wind-instrument colors to build massive, morphing constellations, echoing Webern’s hidden chord-color symmetry.
This musical material goes all the way back to a solo trombone piece I started writing in 1969. Night Songs, which I premiered in Ann Arbor on bass trombone, exemplifies the dark atonal pitch language I was beginning to explore as a composition student of George Balch Wilson at Michigan.
Its first movement, “Elegy,” is somber in expression and amorphous in rhythm, a feature I use as an example of rhythm “beyond meter” in current writing and talks about Time. The line’s sonorous darkness now becomes a fertile theme for exploratory variations, suggesting the liquid life of mysterious creatures in ocean depths.
As the musical line ascends to a high-register bubbly surface level, it eventually sheds its atonal sharps and flats to become a lighter, diatonic pitch pattern. (Listen carefully at 2:27 and again at 3:40.)
Having begun composing in 1963, I started formal composition study in 1968 at the University of Michigan in Ann Arbor. American composer Eugene Kurtz, based in Paris but filling in that semester at Michigan, was assigned to teach the new freshman. A proponent of modern French music, his compositional models included Debussy and Ravel. He assigned me to immerse myself in deep study of their music, in particular Ravel’s Sonatine (1905). Fifty years later in my career as a more experimental composer, my compositional style began to adopt a gentler Impressionistic approach and a lush, bright harmonic language reminiscent of Debussy and Ravel.
Sonatine is spun from a single harmonic progression, seven chords each stacking a Perfect Fifth interval high above another.
This material (what Schoenberg would call a Grundgestalt) generates melodic lines and many arpeggiation patterns, in successive variations of changing register, intensity, and rhythmic pace.
1985-2022 . . . Fourteen canonic studies in three voices (19 minutes)
My compositional fascination with canons began in the early 1970s with study (at the University of Michigan) of Ockeghem’s 15th-century polyphony, the 10 canons in Bach’s 18th-century The Musical Offering, and Webern’s 20th-century Symphonie Op.21. As a young professor in the 1980s teaching 16th-century counterpoint at what was then North Texas State University (now UNT), I used canon as a challenging contrapuntal writing assignment. In 1985, a wind ensemble piece, Parallel Horizons (Homage to Schoenberg), was my first formal composition constructed by canon. In Dark Matter, other contrapuntal writing surrounds an extended canon. Now canon pervades much of my 21st-century writing, a challenging yet stimulating and gratifying approach to texture and continuity of material.
In notes on a recent composition, Frost Serenade, I described “changing tonal temperature.” Here is a deep dive into what that meant.
The metaphor of tonal color and temperature has to do with what we normally call consonance and dissonance in a chord or other harmonic entity.
Centuries-old tradition classified musical pitch-intervals as pure, perfect consonances (“Perfect Fifth” and “Perfect Octave” for example); major or minor (exp. “Major Third” or “minor Sixth”); or problematic (“Augmented Fourth” and “diminished Fifth”). Some major and minor intervals (thirds and sixths) were considered imperfect consonances; the others (seconds and sevenths) were considered dissonant. Every music student learns these categories while studying 16th-century model counterpoint.
Using the color spectrum in temperature order:
Let’s convert the consonance/dissonance concept to think of a pitch-interval’s acoustic complexity. Every musical tone has a fundamental pitch, plus faint overtones that give the sound its color. They are of fading intensity and felt (as color) more than actually heard as the distinct pitches they are. Discovered by Pythagoras as partial vibrations in whole-number fractions, the overtones are always in a fixed interval ladder rising from the fundamental: Up an octave, then a Perfect Fifth, then a Perfect Fourth, a Major third, minorthird, then to the eccentric seventh partial, which is out of tune by our scale-trained pitch perception (and shown a darker gray below), and on to the eighth partial, which is three octaves above the fundamental. (An octave is a multiply-by-2 operator, so partials 2, 4, 8, and 16 of the C overtone series are also the pitch-class C. Likewise, partials 3, 6, and 12 are all octave related.)
Two different fundamental pitches sounding together each bring into the acoustical mix their distinct overtones. The overtones from one either match (simple) or clash with (complex) overtones of the other. This is what makes the sonic complexity or perceived purity of the interval between two fundamental pitches. Using this relationship, we theorize that the higher we need to go to start finding matching overtones between the two pitches, the more complex is the interval. Following this logic, here is an overtone-match analysis of all harmonic intervals smaller than an octave.
PERFECT CONSONANCES
The rather pure Perfect Fifth interval between fundamental pitches, C up to G, matches overtones at G’s partial 2, a low level in the series, matching the C’s partial 3. The interval makes four such matches in this lowest-two-octaves span. The pitch match up of the G’s 2nd partial with the C’s 3rd partial (both are the same pitch, G) will be duplicated in all higher octaves, making this an acoustically simple interval. The two pitches’ overtones mostly match and don’t interfere with each other much.
IMPERFECT CONSONANCES
The triadic consonantMajor 3rd interval between fundamental pitches, C up to E, matches overtones at a somewhat higher level in the series, partial 4, and makes two matches in this lowest-two-octaves comparison.
DISSONANCES
The dissonantminor 7th interval between fundamental pitches, C up to Bb, matches overtones makes only one match in this lowest-two-octaves comparison, at partial 5. That means its harmonic quality is more complex, with most of the lower overtones interfering, not matching. Not a strong dissonance, but more complex than the others.
By contrast, with the more complex Major Seventh interval (ex. C up to B), you have to go all the way up three octaves to the B’s 8th partial (matching the C’s 15th partial!) to find an overtone that matches and doesn’t conflict/interfere. The Major 7th interval can be considered much more complex at a rating of 8 than a Perfect 5th at rating 2.
The most complex interval analyzed, the minor 2nd, clashes all the way up until the 15th partial.
Summarizing the analysis with a complexity rating number for each interval:
minor 2nd = 1 semitone
15
Major 2nd = 2 semitones
8
minor 3rd = 3 semitones
5
Major 3rd = 4 semitones
4
Perfect 4th = 5 semitones
3
Augmented 4th = 6 semitones
10
Perfect 5th = 7 semitones
2
minor 6th = 8 semitones
5
Major 6th = 9 semitones
3
minor 7th = 10 semitones
5
Major 7th = 11 semitones
8
Now we can add up the ratings of each interval in a chord and take an average complexity quotient. And we can think of complex as darker than simple, or we can invoke the color spectrum. In digital photo imaging, we use a temperature metaphor, seeing red as warmest (infrared heat) down through orange, yellow, green, down to blue, the coolest. The “hottest,” most complex harmonic interval is the minor 2nd. The “coolest,” purest (other than the octave) is the Perfect 5th.
The intervals in the following example are shown in semitones. Each chord has four pitch classes and six intervals between them. The Blue chord has an average complexity rating of 3.8. Green chord is slightly more complex, at 4.3. Yellow, which includes the more complex 11-semitone Major 7ths, rates 5.5. And Orange, with the only minor 2nd 1-semitone hot dissonance, is warmest at 6.2. Try to hear the differences. (No attempt here to demonstrate a red-hot cluster mashup of pitch!)
Here is a little demonstration phrase using those four chord types to build a progression of tonal temperature colors. Again, as you listen, try to feel the temperature warm up then cool back down.
2024 . . . Four Small Tonal Studies for piano (4:00)
Recent compositions have shifted from my longstanding focus on contrapuntal writing, especially canons, and animated sound masses to chordal development of my personal harmonic language. Crystallography and Folio explore arpeggiated chords, pitch constellations of four or more pitches forming a mixture of pure, consonant, and mildly dissonant intervals. The changing tonal color of these sonorities in succession, from bright to dark, prompted this small tonal study. As the color or brightness differences are subtle, pastel water color painting is an appropriate visual metaphor.
A video cross-dissolving my own digital images combined with synthesized sound makes a multimedia version viewable on YouTube:
Pastels — Four Small Studiesof Tonal Color for piano:
Inspired by wonderful colleagues (and also my two daughters) who played viola, my love continues for its beautiful rich lyric voice.
The title is a double reference, both to the still iciness of an autumn night and morning, and to a great American poet. Robert Frost’s “Stopping By Woods” was the inspiration for Before I Sleep, a 2018 unaccompanied work for Texas State violist Ames Asbell. Much melodic material was drawn from it for this Serenade. The two parts, “Twilight bridge” and “Snowy dawn,” grow lyric lines out of intricately articulated harmonies of changing tonal “temperature.”
At this stage in my 60-year composing career, I feel free to explore whatever intrigues me and, however complex or simple, craft a tranquil listening experience.
2024 . . . Serenade for viola and strings . . . 8 minutes
This is not a musical sketch about bridges. Its impetus is a musical idea, the exploration of complex patterns for articulating a chord.
An arpeggio is the pitches of a chord sounded one at a time instead of as a block simultaneity. The order is usually straight up from lowest to highest pitch (Moonlight Sonata), or up and back down, or jumping around (Alberti bass). On a piano the damper pedal is usually used to let each pitch continue to sound with the others, bringing together the complete harmony.
In contrapuntal textures, individual voices each contribute a member pitch of the chord, either simultaneously (chorale) or at different moments, but again sustaining all pitches over time into a pitch constellation (like Orion).
In Night Bridge, pitch constellations build up from a single pitch to four pitches before dissipating back to a single tone; then a reflective pause before another constellation starts to build. A solitary musical voice floats above the resulting liquid waves of tone.
Back to the bridges metaphor: their spanning is more mysterious at night, when lights may reflect off ripples in a peaceful passage over a flow of dark water. The most venerable bridge I’ve traversed, the Charles Bridge over the great river Vltava, inspired the contrapuntal chamber music in my Karlův most (2018). Night Bridge echoes that music.
Here’s another favorite bridge, viewed at night from Chicago’s Michigan Ave. bridge:
I have reveled in composing what I call multi-phase ostinato music ever since my first exposure as a performer in the 1970s to the grandfather of the genre, Terry Riley’s famous In C (1964). The style (commonly categorized and misnamed as minimalist music) involves small melodic repeated-pattern ostinato chains overlapping with each other canonically as they weave a rich, pulsating rhythmic and harmonic fabric out of simple threads. Dancing Water is a retrospective medley of my works in this style, from fresh 2024 writing all the way back to my first ostinato piece, Effulgence(1984).
The pieces flow together in one continuous listening (or dancing!) stream.
“Horace’s Fountain” (2024) recalls my 1950s childhood joy of watching the geyser of the Horace Rackham Memorial Fountain at the Detroit Zoo cascade over charming sculpted bears.
“Shore Birds” was music originally composed for my 1993 ballet score, PTACI(“Birds”), based on the musical bird call sketches of the Moravian composer Leoš Janáček. Here the music suggests the flight of birds over the sparkling surf of Mustang Island.
“Buckingham Fountain” is one of my Chicago Sketches(2019) originally scored for flutes, inspired by Reich’s Vermont Counterpoint (1982) commissioned and recorded by flutist Ransom Wilson. The fountain in Grant Park is a magnificent symphony of dancing water.
“Rainbow” portrays the hopeful search for sunlight refracted through water vapor after a storm. Its music is from Looking for the Rainbow (2021), composed during the pandemic as a prequel to Rainbow Rising(2016), an earlier canonic piece for cellos.
“Otter Creek” flows eagerly into Lake Michigan, where its water shines over rippled sand as it spreads out to join the Great Lake’s waves. The music represented WATER, one of Aristotle’s Elements (2022).
“Vltava” the great Czech river flowing through Prague, was celebrated as one tone poem in Smetana’s Ma Vlast. In my string orchestra composition Three States of Water (2021) the music represented water’s LIQUID state, contrasted with the SOLID state of “Ice Dunes”.
“Effulgence” from the 1984 piece that started all this, is a celebration of radiant, resplendent light energetically sparkling on the wind-blown waves of Lake Michigan’s cold blue water.
Thomas Clark - composer / digital artist 