Other Harmony: Beyond Tonal and Atonal

As a composer, I truly adore this book. It doesn’t go into great detail about any singular technique, but it is a superb introduction to a great number of non-“common practice” methods of organizing harmony. It’s truly a fountainhead of inspiration.Just keep in mind that the book is providing a broad overview of practices and theories, and is not itself a text book to teach you all of the intricacies of each method. For examples, you’ll get a useful introduction to a method like set theory, but if your interest is peaked by the book, then you’ll want to buy a whole separate book (or books) on set theory.

Having an interest in music theory for nearly fifty years now, I was intrigued by the title. It very much lives up to its name. Not only did I find new areas to explore, but concepts I'd previously encountered were enhanced by clear explanations and examples. As he states, the author is interested in providing new resources for the contemporary composer, and not so much in providing analyses for the musicologist. I've already created a few etudes using the material, and have ideas for several longer works...after only a week or so after getting the book. One of the best books I've bought since Schoenberg's Theory of Harmony.

It is sad that this book has not found the attention that it deserves. It is well-written and fun to read, unlike many of the stuffy books dealing with complex music theory issues. Tom Johnson is a composer, so you can expect clear, concise and practical ideas, combined with information that cannot be found anywhere else. Some theory knowledge is needed, but even if you have holes in your theory background, you will be able to grasp what the author is talking about. I would identify this book as a survey+guide that would lead you to a significantly broader understanding of how harmony works. Five stars without any hesitation.

This is another book that unfortunately insists on reducing our sonic universe to 12 objects and then plays some math with them. Octave equivalence, prime forms, inversionally related sets, together with the insistence that dissonance is cultural instead of a (well understood) physical phenomenon produce results that completely disregard the reality of sound and that no appeal to an imaginary “different hear” can rescue.Examples abound: the treatment of chord inversions as identical; Forte’s cataloguing of chords (which makes, for example, a major triad and a minor triad considered the same); “chords of equal interval sum” which, for example, ends up including dyadic, triadic and quartal harmonies (Fig.2 page 123) in the same family; “sums modulo N” which obtain a colossal number of chord families that end up being undistinguishable from picking chords at random; the chord progressions described in “Parallel Classes”, that are selected from the possible millions based on some arbitrary mathematical property.And there lies the problem with this misuse of mathematics: there is no isomorphism between 12 ordered objects, and their possible combinations over a uniform metric, and a much larger class of ordered objects (the 88-90 tempered pitches) for which combinations are ordered by a complex metric (see e.g. Sethares, W. A. Tuning, timbre, spectrum, scale. 2nd edn, [Springer-Verlag, 2005].).You might as well play math with colored pebbles, obtain exactly the same results described in this book, and not move much in the direction of understanding how musical composition works.

This book was mostly beyond my level of intelligence. I am not being sarcastic and I do not want this to sound like a negative review. If you have a strong mathematics background and good computer skills you will like this book. It uses numbering systems for the 12 note chromatic ( like Forte 0,1,2... equals c, c#, d) to generate matrices of harmonies, tetra chords, scales etc. The chapters on some lesser known composers were good.

Tom Johnson has done composers a favor in writing this book. The technical stuff is interesting and worthwhile, and Johnson also works in some of his own compositional concerns (for example, equality and completeness). Composers constantly evaluate how their technical means and aesthetic principles interact. Johnson's book offers some side-roads that might get us home (aesthetically) faster than the main streets.

Very mind opening

If you spend time thinking about different musical theories you will love this book

Initially I bought this because of its explorations of the idea that giving all pitches an equal role in composition does not inexorably lead to 12 tone serialism (not that there's anything wrong with that). And here's a book which gave me the kind of insight into folk like Hauer which left other explanations seeming rather opaque. And who doesn't have a soft spot for Slonimsky? And then there's a discussion of Block Designs, also an inherently 'democratic' disposition of objects in sets (so why not musical pitches, or dynamics, or note lengths, or even timbres). Even if you're not a fan of equal opportunity, there's material on smaller sets like all-interval tetrachords.Naturally, once one has discovered renderings of mathematical structures as music - quite capable of holding its own without any help from such (literally, I suppose) 'abstract expressionists' - there's nothing at all to stop you from applying the ideas presented here to systems other than 12-tone. Although you can be sure that you won't find any all-interval sets in Harry Partch's 43-tone octaves, you might be minded to come up with a 43 heptachord symmetric block design.In short, truly inspiring.