Landform Variations


The Landform Variations are not sonic representations of specific landforms (i.e. a cascading mountain range, sea cave, sand dune, alluvial fan, etc.). However, some attributes of natural terrains and the variety of life they support have conceptually influenced the formal construction. Also of interest was the concept of an ecotone, a transitional area between two (or more) environments featuring attributes of both, sometimes including unusual overlaps in geology and plant and animal life.

Examination of any environments – global to microbial – reveal that different combinations of a small set of natural features (mineral and soil composition, altitude, temperature, water/humidity, sunlight etc.) result in a variety of landscapes, each populated by a unique sub-set of the fauna and flora such places might support. This can be seen both by an eye attuned to subtlety on a walk in a mundane local park or by even those otherwise oblivious when displayed on a magnificent scale in America’s celebrated national parks. Examples include places like the Grand Canyon, Carlsbad Caverns, and Arches – where erosion created awe inspiring formations – as well as Sequoia, Joshua Tree and Seguaro – where conditions support clusters of highly unusual plant life.

In recent years, I have sometimes used the metaphor of topographical variation as a loose model for creating variety within a musical work. While my pitch relationships are often sketched first, perhaps the most important phase of my creative process is to sketch the musical “texture” (landscape) and determine how it varies over time and what musical features it would support (in ways unobtrusive, brazen, or awkward). While the Landform Variations are largely “about” contrasting groups of scales, it is the musical textures and settings in which they are contained – the “landforms” – which hopefully sustain the listener’s interest.

Another more general way in which concepts of place have influenced my compositions stems from some of my early listener feedback. Upon hearing some of my first shorter experimental pieces, an audience member without prior exposure to such music said I had placed her in an unfamiliar world. While this was initially interesting to her, the things which happened within this “world” were difficult to understand and appreciate because she was still not acclimated to her surroundings. She speculated that for people who had prior experience in a similar musical “world”, the experience might be different. But for her, the experience was essentially one of interested disorientation.

While “interested disorientation” can be a desirable short-term state for me to pursue in creating a piece, I have always believed in the importance of communication in art. This need becomes intensified by the higher demands placed on the audience’s attention when creating outside of an easily identified genre. One way I have learned (from the example of Morton Feldman) to deal with this issue of inaccessibility is to utilize longer forms and durations and thereby enable listeners to “get their bearings” in my musical “world” more easily. I feel the combination of “experimental” and “traditional” elements in my music is more digestible when they have a longer span of revelation and juxtaposition within larger, slowly emerging structures. (Hence the title of my 2008 piece Everything Will Make Sense Given Time.) Furthermore, longer durations enable me to create a “world” which is more detailed than in a shorter work, even when I utilize fewer musical contents.


Unlike traditional theme-and-variations form, Landform Variations does not have a theme but instead juxtaposes 38 pentatonic (5-note) scales. Some of the variations add  other scale-forms and polychords to the pitch-material as well.

In one of my better pieces of juvenilia, I used pitch material consisting of a list of every equal-tempered pentatonic scale within one octave (each starting on C to avoid transpositions of the same pattern of interval sizes). In 2008, I returned to this list of scales to generate source material for a new piece. I excluded most of the scales I thought would be overly reminiscent of familiar scales like the major and minor scales, church modes, the chromatic scale, whole tone scales, the blues scale, and scales which reminded me of specific non-western musical traditions. The proportions of consonance and dissonance in the intervals of these scales suited one of my aesthetic goals – producing music which has few cultural and emotional reference points (i.e. major being the happy scale, minor being the sad scale, 3- and 4-beat martial/dance rhythms, etc).

After selecting the scales, I listened to them in different sequences and developed several “rules” (made to be selectively broken) to govern the composition. These helped avoid an overabundance of repetition and assured fluidity of melody (if they were to be played as an unbroken monophonic line). The scales also took on specific melodic functions and structural roles for improvisation.


Each of the variations highlights a different combination of scales based on shared attributes. Variations with similar attributes are further grouped into the 3 books. Books 1 and 3 are further divided into 4 and 2 sections respectively. The average # of scales per variation is approximately 8.5 with the most used being 27 and the fewest being 1. Within each variation, all possible combinations of sequences between the available scales are explored (subject to the “rules” explained above).

The descriptions of the variations below omit certain possible variations which would stem from the same mathematical derivations as those included. There are 2 possible reasons for this. First, some of these omitted variations would have had too many scales to retain a distinctive flavor. Second, some of these omitted variations would have resulted in zero scales (no content) and would therefore be silent variations.

Book 1

Section 1: in which the 2nd scale degree is a…
Variation 1: minor 2nd
Variation 2: major 2nd
Variation 3: minor 3rd
Variation 4: major 3rd

Section 2: in which the 3rd scale degree is a…
Variation 5: major 2nd
Variation 6: minor 3rd
Variation 7: major 3rd
Variation 8: perfect 4th
Variation 9: perfect 5th

Section 3: in which the 4th scale degree is a…
Variation 10: major 3rd
Variation 11: perfect 4th
Variation 12: tritone
Variation 13: perfect 5th
Variation 14: minor 6th
Variation 15: major 6th
Variation 16: minor 7th

Section 4: in which the 5th scale degree is a…
Variation 17: tritone
Variation 18: perfect 5th
Variation 19: minor 6th
Variation 20: major 6th
Variation 21: minor 7th
Variation 22: major 7th

Book 2: in which all scales include the pitch (with C=0)…
Variation 23: C#/Db (1) (same as Variation 1)
Variation 24: D (2)
Variation 25: D#/Eb (3)
Variation 26: E (4)
Variation 27: F (5)
Variation 28: F# (6)
Variation 29: G (7)
Variation 30: G#/Ab (8)
Variation 31: A (9)
Variation 32: A#/Bb (10)
Variation 33: B (11) (same as Variation 22)

Book 3

Section 1: in which all scales include the interval…
Variation 34: minor 3rd
Variation 35: major 3rd
Variation 36: perfect 4th
Variation 37: tritone
Variation 38: perfect 5th

Section 2: in which all scales include in their intervals…

Variation 39: both a minor 3rd and a major 3rd
Variation 40: two occurrences of a minor 3rd
Variation 41: both a minor 3rd and a perfect 4th
Variation 42: both a minor 3rd and a tritone
Variation 43: none greater than a major 2nd