Seven Etudes in Modulating Modality (2018)

Listen to “Some Sorrow in A” from The Magic Clavier, Book II

Noam Lemish, piano

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Composer’s Notes

This is the second of the two volumes of The Magic Clavier, which I’ve composed with dual intentions. The first, unsurprisingly, is to invite the musical delight and insight that pure listening offers. The second is to demonstrate the wide array of musical moods and colors made available by “extended modality.”

Our modern tuning system, called twelve-tone equal temperament, specializes in the contrast between reasonably clear harmonic meaning and a matrix of harmonic ambiguities. To offer an analogy, in spoken language individual phonemes take on divergent meanings as a function of context (to, two, too, tutu). Similarly, in musical language, context imbues individual tones with meaning. As musical contexts shift around in equal temperament, the shifts accumulate, resulting in a kind of sonic shimmering. Clarity can suddenly emerge from this ambiguity like the sun or the moon emerging from behind clouds. The overall effect lends a sense of heightened possibility to the music and can be a powerfully transformative magic. It also gives us a passport to travel freely from one tonal center, or “key,” to any other — myriad journeys of mysterious beauty fashioned from only twelve tones. My book Harmonic Experience rigorously details the method behind the magic.

Book I of The Magic Clavier — Twelve Etudes in Extended Modality, investigates how far the ear is able to travel from the home key without actually leaving it — a maximally expansive view of home. The possibilities that arise, taken all together, I call “the magic mode.” The CD liner notes of Book I offer a brief explanation of the subject, and some of the history of that practice, with reference to our connection with J. S. Bach’s The Well-Tempered Clavier.

Book II of The Magic Clavier — Seven Etudes in Modulating Modality, investigates how the harmonic scope of the magic mode, with all of its innate clarity and skein of ambiguities, carries the ear forward into modulation. It follows a simple overall plan, modulating, etude by etude, from a given tonal center to progressively distant keys, then returning, eventually, to the original key. Assuming one’s home is Omaha, modulation might be like traveling southwest to San Diego (adding flats), then up to Portland, Oregon (mixture of sharps and flats), then back through Omaha, then way up and over to Portland, Maine (all sharps), then way down to Miami (sharps and flats mixed), and finally back home to Omaha. This territorial analogy uncannily resembles how we actually hear and process harmonic narrative. And, just as plot is the blueprint of a novel, harmonic narrative is the blueprint of a tonal composition, the secret of its intrinsic wisdom.

The etudes in Book II of The Magic Clavier, although composed in a variety of keys, follow a simple overarching harmonic design. The first piece does not modulate at all but, like the magic mode etudes in Book I, explores the modal possibilities within its home key only. The second piece does modulate a litle bit: by one harmonic move up to the sharp — or “overtonal” — side of the harmonic spectrum, and one harmonic move down to the flat — or “reciprocal” — side; we’ll call this ±1. The next piece ventures a little further afield: up and down by two moves, which we’ll call ±2. The next piece expands the range to three moves up and three moves down: ±3. The next piece is ±4, and the next is ±5 — far-flung travel indeed! The last piece begins with a tuneful theme that modulates to the extreme overtonal reach, adding 6 sharps, returns to the home key, proceeds reciprocally to the key of 6 flats, and then finds its way back home again: ±6. This is followed by five variations on that theme, each traveling a closely similar harmonic path, and one of which (guess which) is a sympathetic replication (by Noam) of a shamelessly bravura improvisation (by me).

Now that you know about this lovely formal scheme, the composer’s sincere request is that you forget it. This music is made ideally for pure listening, to be heard trusting that the heart knows what it’s hearing. If you listen with an empty mind, that would be a sky-blue blessing upon the ears of the world.

Noam Lemish, once my student and now my colleague (and isn’t it sweet how that works), performs these pieces with flashing clarity and profound nuance of feeling. Indeed, this music was composed with Noam in mind and heart, as is true for another cycle I’ve recently composed, called Seven Affections, soon to be released through Cold Mountain Music.

– W. A. Mathieu

Performer’s Notes

Learning this set of compositions has been a multilayered gift. I’ve had the joy of internalizing its harmonic landscapes, of benefitting from the composer’s guidance, and of having the work’s wisdom with me for life. I’m deeply grateful to Allaudin for entrusting me with this beautiful, magical music.

– Noam Lemish


Composer and pianist William Allaudin Mathieu is known for his songs, chamber music, solo piano albums, and his four books on music. In the 1960s he wrote music for Stan Kenton and Duke Ellington, and was the musical director of both The Second City in Chicago (which he helped found) and San Francisco’s Committee Theater. In the 70s he taught at The San Francisco Conservatory and Mills College, and directed The Sufi Choir. Since 1980 he has devoted himself to composition, recording, teaching, and writing from his home in Northern California.

Noam Lemish is a pianist, composer, scholar, and educator. He holds a doctor of musical arts (DMA) in jazz performance and a master’s degree in composition from the University of Toronto. He has performed across the US, Canada, Europe, Israel, and in Bhutan, and has released numerous albums including, most recently, Pardes (2018). His compositions include chamber, choral, piano, and jazz works. Dr. Lemish is currently teaching and doing research at the University of Toronto’s jazz studies program and codirects the Israeli-Iranian Musical Initiative. (Please visit