Book Review: Harmony for Computer Musicians
No matter what kind of music you are involved in, the harmonic foundations of the 18th and 19th centuries are probably of relevance to your composition. Here’s a good resource for learning the subject.
by David Baer, May 2014
This is a review of a book on music harmony, Harmony for Computer Musicians by Michael Hewitt. It is a book suitable as a first primer on the subject, assuming the reader possesses knowledge of basic music theory: notation, key signaturesand so forth. But before discussing whether it is worth one’s time to purchase and study this book, it might be worthwhile to discuss why any musician, computer or otherwise, might benefit from learning about harmony.
Today’s popular Western music, be it rock, country, pop, musical theater and most other mainstream genres embraces a set of rules, or at least conventions, that govern what is acceptable in harmonic progressions – in other words, what chord sequences listeners will find engaging. These rules and conventions were largely established in the 18th and 19th centuries, during which time they evolved only slightly.
Just prior to the 20th century, composers started really pushing the boundaries, experimenting with breaking the rules and inventing new ones. One movement occurring in the early 20th century, atonalism, sought to demolish the rules entirely, replacing them with a draconian set of laws that abolished the long-established basis of having music gravitate around tonal centers, i.e., music that was in specific “keys”. The atonal movement largely failed. Most CD collections in the homes of lovers of “serious” music anywhere will have few, if any, works from the atonal school.
Apart from the atonal school, in the realm of “classical” music there was much invention and expansion that commenced with the late Romantic era composers and continues to this day. But the foundation established in the preceding two centuries is very much present and in good health.
Another development in the latter half of the 20th century, “modern” jazz, also diverged from traditional harmony, but in its own unique way. Rather than reinventing it, it sought ways to adhere to traditional harmony while altering a note here and/or adding a note there, so that the traditional comfort level is always being challenged with something unexpected and exciting.
So, no matter what kind of music you are involved in, the harmonic foundations of the 18th and 19th centuries are of relevance. That resolved, the question remains, do you need to understand it? The degree to which knowledge of harmony is relevant will depend on what your role in music is. Certainly a composer should unquestionably be educated in this subject – and by “composer” I mean someone who writes any kind of music, whether it is a symphony or a pop song. Likewise, an arranger should know more than just what instruments complement each other if even they don’t formally “compose”.
One could argue that some musicians have no need of this knowledge, however. A virtuoso pianist who performs concertos and sonatas will rarely play notes not already written by someone else (at least they will work diligently to avoid such!), so why should such a musician waste time learning harmony when they could be practicing? I think the answer is that even one who only “performs”must be a sensitive interpreter. Interpretational insights will be enhanced by understanding what lies beneath the notes. I would make the case that any musician will become a better one by learning harmony. If you don’t agree, then I’m surprised you’ve read this far. J
So perhaps those still with me all agree that it will be beneficial to learn harmony. How does one go about it? Taking a formal class is probably the most assured way, assuming a teacher of adequate skill is in charge. There will be assignments, exercises and tests. Most students will be motivated to stay with the program. Doing it on one’s own takes rather more discipline. However, if that discipline is present, a good book on the subject can assume the role of teacher. And this brings us to Harmony for Computer Musicians.
A Platform for the Study of Harmony
The author, Michael Hewitt, earned his doctorate in music, specializing in composition. He actively composes, but also is a tutor in musical technology in the UK. He has authored other books, in somewhat of a series, including Music Theory for Computer Musicians and Composition for Computer Musicians. He certainly seems to have sufficient credentials.
But what makes this book especially relevant to computer musicians? Actually, there’s not all that much in my opinion. But that’s not a significant criticism of the book’s value. The author does two things to justify the “computer musicians” qualifier in the title. In diagrams throughout the book, he includes DAW piano roll view images to augment scores (see accompanying image). The other (somewhat more relevant) device employed is the inclusion of exercises that incorporate simple MIDI files.
I’m going to suggest that this book would be a fine one as a first encounter with harmony for any musician. And what music student these days doesn’t deal with some form of MIDI data in any case? So neither embrace nor reject this book based on your status as “computer musician”. I prefer to judge it on how well it explains harmony to a musician, period.
Long story short: it does this rather well. I must confess that this is the first book on harmony that I’ve read, so I have nothing to compare it to. I can say that the subject is presented at a reasonable pace and in just about the right amount of detail for a first-time harmony student.
The order of presentation is also quite logical, although I suspect that some of the order is governed by common sense and that all harmony tutorials must follow somewhat the same path. We must learn intervals before triads and triads before seventh chords. Any other sequence just wouldn’t be comprehensible.
No surprise, we do begin by learning about intervals – two notes played simultaneously (we can’t call multiple notes a “chord” until there’s at least three, it turns out). This is followed with a presentation on the basics of Western tonality: the diatonic scale (in which there are two “half steps” and five “whole steps” in a one-octave scale).
Next we learn about triads, three notes that are the most fundamental arrangement in Western music. In this early going, some of the material is so basic and obvious that it’s tempting at times to think “Well, duh!” while reading. But try to avoid that mindset. Some absolutely essential groundwork is being laid for some far more complex material to follow.
Before we venture further into the mysteries of chords, some time is spent considering the rules of part writing. When we move from one chord to another, there are good ways and bad ways to effect the transition. For example, having parallel jumps of octaves of fifths is unsatisfying. The book explains why – and you’ve just had your first lesson in composition!
Along the way we’ll learn further advice about lead lines and how they relate to underlying chords. We’ll learn different ways to voice simple triads. In fact, we need to get to almost the halfway point of this 270 page book before we encounter a chord with four distinct notes: the dominant seventh chord, the most important penultimate chord in all of Western music.
The Plot Thickens!
Most pianists will know, if only intuitively, that a G7 chord obviously resolves to a C major chord. By the same token, guitarists will probably first encounter the dominant seventh as B7, which resolves to E. There is an entire (albeit brief) chapter on just the dominant seventh. And then we have more chapters on the seventh chords on other degrees of the scale.
At this point we start to see the somewhat different rules in play for major and minor keys. Minor keys take a bit more understanding, since there are three versions of the minor scale: natural (A minor on the keyboard, all white keys), harmonic (A minor with G# rather than G), and melodic (add F# rather than F to A minor harmonic, but only on the way up). So when we talk about harmony in a minor key, we need to know which version of minor is the context.
I found the chapter on modulation to be one of the more interesting. Of the term “modulation”, the computer musician is likely to think of altering pitch with an LFO, or something to that effect. But “modulation” in harmony means the manner of transitioning from one key to another key (with a different key signature) in a graceful or logical manner. It turns out that some chords can be enharmonically identical (have the exact same keyboard notes) but be spelled differently. A G sharp is the same pitch as an A flat in modern practice, but the two notations can imply different key contexts. So, in one key, we can find a logical way to get to a chord. Change the spelling of that chord, if only in our mind, and a new pathway to another chord in another key is revealed. How could any geek … er, I mean computer musician … not love this stuff?
From here, the going gets increasingly complex. Add another triad to the seventh chord and we get the ninth. Add another to the ninth and we get the eleventh chord. Fortunately this progression stops at the thirteenth chord.
As the book draws to a close, we touch upon the subject of modal harmony. “What’s that?” you say. Consider only the white keys on the keyboard. The notes from A to A constitute a natural minor scale and from C to C a major scale. What about from D to D? Here we have half steps between the second and third degrees of the scale and between the sixth and seventh. There’s a name for this sequence: it’s called the Dorian mode. In fact there’s a mode named for any of the possible forms of the diatonic scale played on the white keys of the keyboard. Each of them can form the basis of a structure of harmony.
The harmonic system of any of the modes could probably warrant an entire book. Harmony for Computer Musicians only presents a tantalizing glimpse. That glimpse may be more than enough for many readers, although jazz musicians in particular may well be chomping at the bit to learn more.
Is This Book for You?
If you know nothing about the formal subject of harmony, then I can suggest that the answer is absolutely “yes”, whether you want to learn enough to simply appreciate the subject or need a starting point for deeper study. At some point the serious student will probably want to tackle Walter Piston’s Harmony, the considered the “bible” by many harmony teachers. But for an individual studying solo, that might be too much to confront as a first encounter.
The book has a few problems with errors in the illustrations. While annoying, I was able to puzzle my way out of the seeming contradictions without wasting too much time.
Readers who can hear chords in their mind when seeing a four-part chord written in a score will be at an advantage, since the book will not easily lay flat when wishing to play the examples at the keyboard.
There is one other concern, although many will regard it a benefit. The discussion is almost always limited to the “easy keys”, C major, A minor and C minor. The well versed harmony student will be able the “think” in any key. They will not be challenged on that front here. But that may be for the good. The subject of harmony is challenging enough upon first encounter even when sticking to the easy keys.
I’m writing this about a month after I finished the bulk of the article. During that time I’ve acquired and started to study the Walter Piston Harmony book mentioned just above. I’m finding that attempting to do this as a self-taught endeavor is formidable – Piston was a Harvard professor, after all, so what can one expect?
A thorough study of harmony with only a book as a teacher is far from easy. Unlike, say, a subject such as calculus, in harmony a study exercise will often have no single correct answer (although it will always have innumerable wrong ones). A math exercise will usually have a single answer, and those checking the answers to exercises allow you to gauge your progress. Not so with harmony, and without a teacher or peer students, assessing your progress is elusive.
But if I’m struggling now, I can only think how much more intimidating it would be having not first read Harmony for Computer Musicians. If you are intent on learning harmony and don’t have the benefits of a classroom situation, I’m all the more convinced that Harmony for Computer Musicians is an excellent first exposure to the topic. Yes, it’s lightweight compared to Piston’s comprehensive treatment, but if you’re doing this your own, that’s probably just what will best suit.