Other Harmony: Beyond Tonal and Atonal

by Tom Johnson

Noted composer, theorist, and critic Tom Johnson explores the theoretical discoveries of classical music's forgotten thinkers and composers, (Euler, Hauer, Slonimsky, Obouhow, Schillinger, and Messiaen), before taking the reader on a guided tour of his own investigations into the structure of harmony. He thoroughly analyzes chord families (in the style of Forte) and provides a number of his own techniques as alternate methods for classifying chords.

This brief, accessible work provides a survey of alternative harmonic practices, and it is tailored to the composer who wishes to sample some fruitful methods of composition beyond strictly tonal or atonal harmonic practice. The work reflects Johnson's fascination with the mathematical underpinnings of harmonic structures.

Genres: Music

252 pages, Paperback

Published January 1, 2015

About the author

Librarian Note: There are more than one author in the Goodreads database with this name.

Reviews

[Peter · Rating 4 out of 5]

Johnson writes in a wonderfully practical and conversational style, sharing his insights not as a theorist per se, but as a composer. He writes of the book in the Introduction,

"Without pretending to have researched the subject thoroughly, it would be enough just to explain how... many kinds of Other harmony have been evolving, and how my own harmonic practices fit into this context."

To this end, Johnson provides an easygoing and accessible survey of alternative harmony, beginning first with the topics of tonality and atonality before examining the harmonic languages of other theorists and composers. These chapters are as follows:

1. Tonality
2. Atonality
3. Euler Harmonies
4. Hauer
5. Slonimsky
6. Obouhow
7. Schillinger
8. Messiaen

While Euler is primarily a mathematician, and is a much earlier figure than the other five composer/theorists, his abstract musings on the materia of musical harmony provide a nice foreshadowing of Johnson's later harmonic systems. The remaining figures come from a wide variety of rather systematic theories of composition and harmony. (I was unfamiliar with Hauer and Obouhow before reading this work, and I was very pleased by Johnson's descriptions of their work and historical context). While it would be impossible to provide a comprehensive overview (much less an extensive comparison) of these composers' harmonic methods, Johnson's survey provides numerous opportunities for the interested reader to conduct some further research.

The remaining chapters are as follows:

9. Equal and Complete
10. Heights and Sums
11. Advancing
12. Adjacent Intervals
13. Sums Modulo n
14. All-Interval Tetrachords and Other Homometries
15. Block Designs
16. Parallel Classes
17. Almost Not

These chapters deal with further (mathematical) methods of constructing harmonic spaces for compositions. The first chapter of this section (9. Equal and Complete) is essential for setting the context of the discussion. Johnson is primarily concerned with harmonic systems that treat all their elements equally. These elements may be pitch classes, but Johnson focuses on systems where families of chords comprise the elements that are to be treated equally. Similarly, he specifically looks at such cases where the composer employs the complete set of elements that can be produced from such a system. The remaining chapters enumerate a variety of such systems, many of which Johnson has employed in his own compositions. For further reference, see Johnson's website related to Other Harmony at http://oh.editions75.com/

While the work is certainly technical, Johnson is careful to make the mathematics accessible through a variety of diagrams and explanations. A mathematics addendum can be found at the back of the book. While the reader doesn't need to be familiar with advanced algebra or trigonometry, some knowledge of basic combinatorics is certainly helpful. The reader ought to be familiar with tonality, atonality, tone rows, and perhaps the basics of musical set theory. At the end of each chapter, Johnson provides a splendid collection of investigative exercises that a curious composer, theorist, or enthusiast may explore in his/her spare time.

My only regret was that Johnson didn't write more! Other Harmony has provided a nice starting point for further investigation, and I look forward to reading his Self Similar Melodies.

[Mike Zavorskas · Rating 4 out of 5]

A lot of great concepts, sometimes a little difficult (as a non-mathematician musician) to wrap my head around exactly what Johnson is saying. But some great ideas, and presented in a way that one could quickly build upon those foundations. Besides presenting original ideas for harmony, the book begins with a reintroduction of tonal and atonal theory, and puts the harmonic ideas of Messiaen, Schillinger, Slonimsky, and others into context.

[Jason Cady · Rating 5 out of 5]

This book is an excellent reminder of all the alternative ways of thinking about harmony. I do wish the various chapters were a little longer. Also, despite not being about atonality it is heavily indebted to Allen Forte's "Structure of Atonal Music," so if like me, you have not read Forte, Other Harmony can be difficult to understand in a few place. I plan to read Forte and then return to Other Harmony.