Rosalie Kaplan and Noah Kaplan standing in front of a dump near a river overlooking the Manhattan skyline.
Notes from Underground: Ivan Wyschnegradsky’s Manual of Quarter-Tone Harmony
Photo by Reed Lerner.

Notes from Underground: Ivan Wyschnegradsky’s Manual of Quarter-Tone Harmony

[Ed. Note: Some of the unusual melodies and harmonies on the indie rock band Dollshot’s latest album Lalande, two singles from which were just released today on Bandcamp and Spotify, were inspired by an unusual source—the theories of early 20th century avant-garde classical composer Ivan Wyschnegradsky, a Russian émigré in Paris who was a pioneer of microtonal music. Probing deeper, it turns out that Dollshot’s co-leaders, vocalist Rosie K and saxophonist Noah K, are immersed in a very wide range of musical styles. Noah fronts a jazz quartet that has recorded two discs on hatOLOGY and participated in last year’s New Jersey Symphony Orchestra Edward T. Cone Composer Institute at Princeton University. Rosie has composed original works for chamber ensembles and electronics and has also recorded a re-imagining of Benjamin Britten’s Songs from the Chinese with electric guitarist Marco Cappelli. We asked Rosie and Noah to write about how they became interested in Wyschnegradsky, why they translated his 1932 Manual of Quarter-Tone Harmony, and what the implications of Wyschnegradsky’s ideas are for music being created today in all genres.—FJO]

In 1932, Ivan Wyschnegradsky wrote a short yet profound book introducing twelve new tones into the language of classical harmony. Historically excluded from the edifice of harmony constructed around 12-tone equal temperament, these tones from outside the system open new expressive possibilities and expose hidden beauty. The Manual of Quarter-Tone Harmony rewrites the past for the future and pulls back the curtain on the realm of ultrachromatic music.

The Manual of Quarter-Tone Harmony rewrites the past for the future.

The Manual traces the history of Western harmony and systematically injects quarter tones into each stage of its development. Beginning with Baroque-like usages of quarter tones as ornaments and embellishments, it then introduces quarter-tone non-harmonic tones and altered triads, suggesting the harmonic practice of the Classical period. The treatment of quarter tones then extends from simple diatonic progressions to modulations in new quarter-tone keys, then on to quarter-tone chromatic harmony. Part Two introduces artificial quarter-tone scales, followed by quarter-tone atonality and poly-tonality. Wyschnegradsky weaves quarter tones into the fabric of our common musical syntax, showing us how they can enrich—and supersede—our grammar.

Though a return to the strictures of classical harmonic theory may seem opposed to contemporary practice, the operative concept of the tradition of harmonic development is progress, and it is this progressive spirit which animates the Manual. Mapping new harmonies over the old ones offers a comprehensive methodology for the use of quarter tones that composers can choose to follow or reject completely. Wyschnegradsky frees us from circling back over well-trodden territory. The circle is transfigured as harmony steps forward.

Shortly after completing the Manual of Quarter-Tone Harmony, Wyschnegradsky wrote the first edition of his 24 Preludes, Op. 22 in 1934, which would turn out to be a lifelong project and a landmark within his oeuvre. The preludes show a mastery of styles including Romanticism, jazz, and atonality, and they elaborate and exemplify many of the ideas discussed in the Manual beyond the text’s examples. The preludes are based on a quasi-diatonic scale, the chromatic scale diatonicized to 13 tones. In this scale (pictured below), Wyschnegradsky found structural analogies to the major scale; its two heptachords, which include a series of semitone intervals followed by a quarter-tone interval are analogous to the two tetrachords made up of whole tones followed by a semitone that constitute a diatonic major scale (C-D-E-F & G-A-B-C).

Musical notation of Wyschnegradsky's scale of 13 quarter tones in ascent.

Wyschnegradsky’s “chromatic scale diatonicized to 13 tones”

In addition, the chromatic scale diatonicized to 13 tones unifies 13 descending major fourths—a perfect fourth plus a quarter tone—in the space of an octave, beginning from a major fourth above the tonic, F quarter-high, and descending through the cycle of major fourths to B quarter-high. This is analogous to the unification of seven descending perfect fourths in the major scale beginning from a fourth above the tonic, F, and descending through the cycle of perfect fourths to B. This latter feature allows for a scheme of modulations based on the ascending major fourth resolution, as opposed to the ascending perfect fourth (or descending perfect fifth) relationship intrinsic to previous tonal music.

A diagram in musical notation showing how Wyschnegradsky's 13-note scale was derived from a chain of half-augmented 4th (which are a very close approximation of the 11th overtone).

Late in his life, Wyschnegradsky returned to the preludes and dramatically revised them, saturating his original “diatonic” pieces in 24-note ultrachromaticism. This revision coincided with the publication of his article “Ultrachromaticism and Non-Octavian Spaces” (1972) in La Revue Musicale, a new English edition of which will be published by Underwolf Editions in the next year. The 24 Preludes—a highly original work that offers a bold vision of the expansion of harmony—illustrates the depth and utility of the ideas introduced in the Manual.

Yet since its publication 75 years ago, the Manual has passed the years in relative obscurity. There are few records of the book, and the only English translation is long out of print and unavailable. We were both living in Princeton, writing music and developing techniques for playing and singing microtones, when we came across a mention of the Manual in the library. We began a correspondence with Martine Joste of the Association Wyschnegradsky in Paris, who sent us a copy of the book in its original French. We were immediately captivated by its ideas, and the project of translating and publishing a new edition began. In addition to the text, the Underwolf edition includes an audio companion rendering Wyschnegradsky’s musical examples, realized by composer and theorist Christopher Douthitt.

Since its publication 75 years ago, the Manual has passed the years in relative obscurity.

The book went with us everywhere as we prepared the translation, working in coffee shops in Los Angeles, New York, and Montreal, where we traveled to meet Wyschnegradsky’s disciple Bruce Mather. Martine had introduced us to Bruce through a letter. A great composer in his own right, Bruce taught the Manual during his tenure at McGill University. He and his wife, Pierrette LePage, an accomplished pianist and teacher, live between Montreal and France, where they present concerts and perform contemporary microtonal works. Bruce and Pierrette’s living room is taken up almost entirely by two baby grand pianos tuned a quarter tone apart, positioned so that the players face one another. Together, the pianos function like the combined moving parts of a single, profoundly expressive instrument. The musical lines divided between the keyboards crystallize into the most intensely nuanced passages, and the resonance of the quarter tones is strikingly vivid.

Bruce Mather standing beside an upright piano that has been retuned to 96-tone equal temperament (the Carrillo piano).

Bruce Mather with the Carrillo 96-tone piano

While we were visiting Bruce, he took us to the Conservatoire de musique de Montréal so that we could hear the sixteenth-tone “Carrillo piano” that had been specially built for him by the German piano maker Sauter. The piano appears to be an ordinary upright piano, but it has an extended 97-note keyboard whose entire range encompasses one octave, C1 (middle C) to C2. The question of whether one can hear sixteenth tones was decidedly answered for us when Bruce sat down and demonstrated a “glissando” by playing a passage of ultra-ultrachromatic notes. Each sixteenth tone illuminates a distinct, reverberant sound-space. The instrument’s most poignant feature is the surreal and uncanny quality of the resonance warping between such precisely and closely tuned strings. Bruce played some of his piece Etude VII A, in which tonal and quartertonal sonorities bleed into one another, stretched apart by sixteenth tone alterations. The harmonics collide to create a sound akin to a piano being played underwater, the sound waves bent and distorted by the thickness of the substance through which they travel. Bruce organizes a concert each winter in Montreal featuring works written for his special piano.

Hearing the sixteenth-tone piano piqued our interest in its inventor, Julián Carrillo. A contemporary of Wyschnegradsky, Carrillo was an indigenous Mexican composer active in the early 20th century, who traveled from his home in Mexico City to Leipzig to learn what he referred to as the “glorious German music tradition.” After writing music that sounds a lot like Brahms and Wagner, including an impressive opera Matilde o México (1910), Carrillo devoted himself, starting in the 1920s, to composing with microtones. In an artful narrative, Carrillo often recounted how he discovered the existence of microtones in 1895 during an experiment in which he used a razor’s edge to stop the G string on a violin in increments until he reached the note A. Within the whole step G to A he found sixteen discreet sounds. His microtonal system, which he called Sonido 13 (the thirteenth sound), communed with the mysteries beyond 12-note equal temperament. Carrillo had lofty ambitions for Sonido 13, prophesying that “[t]he thirteenth sound will tune the world.” In 1926 he moved to New York where his Sonata casi fantasía was heard by Stokowski, who then commissioned a work for the Philadelphia Orchestra from him. Carrillo reworked the Sonata into his 1927 Concertino in which, in a brilliant stroke of practical ingenuity, he had a chamber ensemble playing microtones against the “normally” tuned orchestra. The composite result was an eminently playable microtonal orchestral piece. Like Wyschnegradsky, Carrillo mastered the history of his art and the dominant style of his time before plunging, out of an inner necessity, headlong into the deep waters of microtonality. And like Wyschnegradsky, he remains an underheard innovator of 20th-century music.

Noah standing in the middle of a recording studio which is cluttered with a drum, a music stand, a speaker and other pieces of electronic equipment.

Noah in the recording studio for Lalande.

The mysterious immediacy of microtones is what initially attracted us to writing and playing ultrachromatic music. Over the past few years, we formed our language of microtones through free improvisation. We experimented with dissonance and sinuous melodic lines, finding beauty in the chilling nearness of tones. When we began writing a new album, Lalande, for our band Dollshot, we envisioned songs composed from the poetics of these new pitches, using quarter tones explicitly to illustrate lyrics and lyricism. They give the music more specificity, more color and conflict.

Lalande is about the tension between selves within the self, mirrored by tones between the tones.

In “Swan Gone,” quarter tones, first introduced in a grinding bassline, finally infect a dreamlike vocal line singing madness from beyond the threshold. In “She” (a setting of a text by Geoffrey Chaucer), quarter tones dramatize psychological friction, the ecstasy and the bitter frustration of a young woman praying to the goddess Diana to protect her from the yoke of marriage and motherhood. Lalande is about the tension between selves within the self, mirrored by tones between the tones. Though the music of Lalande is worlds apart from Wyschnegradsky’s, its source is the same mystical fascination with the expressive power of microtones from which he drew his inspiration.

The democratization of sound as music, the dissolution of genre, and our engagement with machines for creating and producing new music were once escapes from the confines of tradition.

Now, more than seventy-five years after the initial publication of the Manual of Quarter-Tone Harmony, new tones are still all too often treated as belonging to a shadow world, lurking behind a pleasing, preferred reality. Inherited aesthetics still reign, circumscribing the attributes of creative work and imposing criteria for its judgment. The popular acceptance of new tonalities lags behind the revolutions of the last century. The democratization of sound as music, the dissolution of genre, and our engagement with machines for creating and producing new music were once escapes from the confines of tradition. Ultrachromaticism—in which all possible tones are treated as real tones–lies in waiting. How many times do we walk by the door and not open it? The Manual of Quarter-Tone Harmony is the key. The moment has arrived to unleash a flood of radical new expression.

Rosie K standing in front of a microphone in a recording studio, which some sheet music nearby.

Rosie in the recording studio for Lalande.

Over his lifetime, Wyschnegradsky used many different divisions of the octave in his music. The use of quarter tones and equal temperament is one decidedly pragmatic way forward. Quarter tones are easy to play on most instruments and double the resolution of the pitch spectrum, as if we were suddenly seeing an image with much greater clarity. Hidden details that were always there but whose visage and meaning eluded us are brought into relief. Ways of seeing, perhaps, can point towards ways of hearing. The enhanced equal-tempered octave reorients our musical thinking, leading to new perspectives in the treatment of consonance and dissonance, voice leading, and modulation. These potentialities are explored in the Manual. The 24-note equal-tempered octave is not an end, but a beginning. A vista where the ultrachromatic landscape becomes visible, unfolding before us. The Manual does not prescribe, it beckons.

The 24-note equal-tempered octave is not an end, but a beginning.

There is hardly a more abstract investigation of possibility than in writing music. The most unnatural yet naturally expressive realities of sound and form are imagined, then heard. To hear beyond what history and culture dictate is visionary. The expansion of our musical language must draw from within.

It is only by going under that we can cross over.


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Rosie K is a composer and vocalist from Virginia. She co-leads the band Dollshot, whose second album Lalande will be out in 2018. Recent recordings include an EP reimagining Benjamin Britten’s Songs from the Chinese with electric guitarist Marco Cappelli, and a collaboration with sound artists Desmond Knight. She has performed and recorded with Rinde Eckert, Federico Ughi, Quinn Collins, Caroline Park, Jeff Snyder, Christopher Douthitt, Marco Kappelli, Kevin McFarland, and Sarah Bernstein, among others. As composer, she writes predominantly for small ensembles and electronics. Read more »


Noah K is a composer and saxophonist from Topanga, CA who blends the dark energy of free jazz with Romantic lyricism in new realms of tonality. His music has been performed by the New Jersey Symphony, Orchestra 2001, JACK quartet, PRISM quartet, So Percussion, and the American Modern Ensemble, among others. He co-leads the indie pop band Dollshot and is currently collaborating with screenwriter Hampton Fancher (Blade Runner, Blade Runner 2049) on Salvation, an opera trilogy. As an improviser, Noah has performed and/or recorded with Joe Morris, Anthony Coleman, David Tronzo, Peter Erskine, Alan Pasqua, Rinde Eckert, Mat Maneri and Joe Maneri, among others. The Noah Kaplan Quartet has recorded two albums for HatHut Records, Descendants (2011) and Cluster Swerve (2017).Read more »


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