The subdominant is a mystery. Every standard Western scale and church mode except the Lydian contains it, but where did it come from? Nicolas Slonimsky once pointed out, in an effort to dissuade readers from the idea that Western tonality is the inevitable result of how we hear (as opposed to a largely artificial invention), that no matter how high one goes in the harmonic series, a fundamental pitch will not produce a perfect fourth above the fundamental.
That’s a slight overstatement, but not by much. The closest harmonic to the perfect fourth, either equal-tempered or just intonation, is the 85th, with the 43rd a few cents away. (For a cent-by-cent table of 700 pitches found within an octave, and many of their corresponding places in the overtone series, see Kyle Gann’s indispensable Anatomy of an Octave.) It’s clear from this why the major pentatonic, the basis of a nearly infinite store of melody around the world, lacks a fourth step. The subdominant would seem to be an arbitrary construct.
But what would happen if we were to build a diatonic scale that truly embodied the first seven pitch classes to appear in the overtone series? The fifth and the major third show up easily and quickly; respectively, they are the third and fifth harmonics. The ninth harmonic gives us the second degree of our scale. The sixth step makes its appearance as the 13th harmonic, though it is woefully “out of tune” unless adjusted. Now we have C-D-E-G-A, the major pentatonic scale that has been the fount of many a beautiful melody, from early folksong to George M. Cohan to alternative rock.
Adding fourth and seventh steps is a lot trickier. Just as Slonimsky opined, the perfect fourth above the tonic is nowhere to be found. For a fourth degree, it is easier and more natural to grab the 11th harmonic. This is 551.318 cents above a given tonic, almost exactly midway between the current, equal-tempered perfect fourth (500 cents) and augmented fourth (600 points). In just intonation, however, the perfect fourth lies at about 498 cents, some 53 cents distant from the 11th harmonic, while the augmented fourth is at 582-plus cents, significantly closer at 31 cents away. Conceptually, too, the 11th harmonic feels closer to a flat-tuned augmented fourth than to a sharp-leaning perfect fourth. The augmented fourth, then, takes the place of the standard perfect fourth in our natural diatonic scale.
With the elimination of the perfect fourth, the functionality of the subdominant is swept away. The old IV chord was one of three major triads in any major key, forming the familiar primary structure I-IV-V. In our new form of the major scale, only I and II are major triads. The new IV chord becomes a diminished triad, perhaps better integrated as the top three-quarters of a “dominant seventh” chord built on the supertonic (in C: D-F-sharp-A-C).
What about the seventh step? Our familiar leading tone wouldn’t be there, either. Unlike the subdominant, the leading tone does show up among the first 20 harmonics: 15th place. But it’s beat out by the lowered seventh’s appearance in both the 7th and 14th positions. In fact, the lowered seventh is the first note to appear in the series that does not belong to the tonic triad. This makes B-flat the seventh step in a scale based on C, and alters the tonic seventh chord into a “dominant” seventh. It gives pause to realize that a system truly based on the strongest overtones would posit a major chord with a minor seventh as stable.
Our new scale, drawn solely from the first 13 harmonics, spelled on C:
C – D – E – F-sharp – G – A – B-flat.
This is also known as the Lydian Dominant, a favorite mode for bebop musicians in the 1940s and ’50s. The upper four notes are the same as the upper four in the octatonic scale, which—like the pentatonic and whole-tone scales—also lacks a subdominant.
So, how did we get the major scale we have, instead of this one? Short of being able to ask Guido D’Arezzo, we’ll never know for sure. We’re all told in early music history that medieval musicians utilized hexachords, and that these hexachords all contained, as their fourth degrees, perfect fourths above the tonic. They didn’t just throw them in. They had to hear them first.
Play around with the Lydian dominant on C. Improvise melodies on the scale and structure some changes. Staying within this new diatonic framework, you’ll quickly feel you’re actually toying with the notes of an ascending minor scale based on G; the pitches are the same. Within the notes given, the only functional progression in C will be the II7 chord resolving to V; or V7 to I in G minor. The sharped fourth degree and the flatted seventh have altered the so-called Dominant seventh and robbed it of its central place in the tonal scheme.
One other dominant does exist, however: the one built on the tonic itself. It resolves, not to any note within the scale, but to a foreign pitch—the so-called subdominant. Thus the perfect fourth above the tonic enters the scene, not as part of a stable major scale, but as a tempter, a seducer, a built-in modulation away from the true tonic. The perfect fourth, and not the tritone, is the true “devil in music.” It’s no “subdominant.” It’s the phantom tonic.
This is from the book Music and Sound, published in 1937 by the English organist, composer, and theorist Llewelyn Southworth Lloyd:
All the evidence shows that, in the early stages of a scale developed in the attempt to sing melody, one of two intervals, the fourth as an interval approached downwards, or the fifth, would almost certainly provide its first essential note other than the octave. (Emphasis added.)
Later in the same paragraph:
Our subdominant is a true fifth below its (the fundamental’s) octave.
Not a fourth above, but a fifth below: the phantom tonic.
When we resolve to the phantom tonic, we suddenly have three new pitch classes. Resolving from the Lydian dominant on C, we would get the scale: F-G-A-B-C-D- E-flat. The F, B (natural) and E-flat are new. The Lydian Dominant on F being no more stable than the Lydian Dominant that resolved to it, we would soon resolve to B-flat below F, where the A-flat is added, and then to the E-flat below that, where D-flat completes the 12-tone party. The true circle of fifths moves down, not up, and it supplies us with all 12 tones of the chromatic scale much sooner than the ascending version.
What difference does this make to us as composers?
We pick a pitch and call it the tonic. We know that assigning tonic status to the pitch is arbitrary; obviously, we can call tonic any note we please. But it is also true, and far less understood, that the concept of tonic is itself arbitrary. We may choose to call B-flat home base, but in the equal-tempered world of 12 pitch classes, no single pitch is ever just the tonic; it is at one and the same time the dominant of the phantom tonic, the supertonic of the pitch a whole step below, the leading tone to the pitch a half-step above, etc.
Debussy averred that music is made only of rhythm and color. Pitch is a function of color; a matter of where, in the span of some universal monochord with infinite fundamentals, it falls, and of what other pitches are sounding at the same time. In the German-based tonal system we’ve inherited and many of us still use, a B-flat is tonic because we say so and it remains tonic until we say otherwise by modulating away from it. In the French way of comprehending harmony, you can’t do that, for even if you play only a C minor chord and return to the B-flat, that B-flat chord is now changed forever. It has a different sonic context and is therefore a different entity. Its relationship to other pitch classes and to its own internal elements has shifted.
Roman numeraling is an illusion based on the mistaken idea that tonal relationships must be codifiable or they cannot be tonal relationships. We are told to call the German system “tonality” when, in fact, all relationships of pitch are inherently tonal—not in the sense of adhering to an arbitrary system that posits stable tonics, but in the sense that every pitch in some way suggests every other pitch. There is not and cannot be any such thing as “atonal” music.
This might seem to some to lead in the direction of eliminating hierarchy altogether and embracing the principle underlying dodecaphony: absolute independence of one pitch from another. It would seem to do so, that is, if you insist that hierarchy cannot admit ambiguity. If the tonic cannot be the tonic securely and without challenge, if its existence implies the phantom tonic below, and very shortly all 12 tones, then the only alternatives are either a sonic world of 12 fiercely independent pitch classes (dodecaphony), or one in which every pitch class connects to every other pitch class in a web of complex relational flux. I think this latter was too French an idea for the Germans who determined much of our music history. Better to disavow the validity of necessary relationship altogether, than to recognize the subtleties and paradoxes of an uncodified tonality.
Until our 12-pitch scale changes to something else, if it ever does, the business of a composer is to intuit the shifting relationships that grow from playing with the intervals of that scale, and shaping these into attractive structures, framed by rhythm and timbre. This would be true 12-tone music. Everything else is merely system, grounded either in an arbitrary tonic or in the equally arbitrary denial of tonal relationships.
Kenneth LaFave’s music has been performed by the Phoenix Symphony, the Tucson Symphony Orchestra, the Chicago String Quartet, the Kansas City Chorale, Close Encounters with Music, and many other artists and organizations. With librettist Robert Kastenbaum, LaFave has composed the 30-minute cabaret opera Closing Time, the full-length musical Outlaw Heart, and American Gothic, a full-length opera in one act. LaFave’s most recent commissions include Gateways, a concerto for electric guitar and wind symphony; and The Medicine Gift, for two horns, piano and narrator, set to a text by his wife, Susan LaFave.