2.1.1 Past Doubling Theories

[1] There are four general categories of theories that are used to justify various rules of chord-tone doubling. These are based on:

• harmonic series,
• sonority,
• key structure, and
• voice-leading.

Doubling to Fit a Harmonic Series

[2] The most popular theory of voice-doubling, one that now dominates modern thinking about doubling rules, holds that a triad is an extension of its root, and the organization of pitches within a triad serves to emphasize the root. The scaffolding for that organization is the harmonic series, and the fundamental of the harmonics is the root of the triad. Thus the most obvious PC to double is that of the root. The fifth of the triad is the next tone in the harmonic series, and the third is the last in the triad to appear. The fifth is therefore the next best candidate for doubling, and the third is the worst.

[3] Rameau, as the father of modern harmonic theory and the inventor of the concept of a triad “root,” was the first to propose a version of this theory. Although only a couple of short paragraphs are devoted to the topic in his Treatise on Harmony, he carried the logic forward in a convincing manner: A triad is a projection of the harmonic series of the root. If a triad is in first inversion, then the root has already been doubled in an upper octave, and any of the notes in the triad can be doubled equally well.⁽¹⁰⁾

[4] Although Rameau was the first to interpret triads in terms of overtones, he was certainly not the last. Nor did later theorists interpret the relationship between triads and harmonic series in the same way, although the basic theory continued to reappear almost unchanged into the twentieth century.⁽¹¹⁾

[5] Riemann also believed that chords are derived from the harmonic series, but took a subtly different position. As explained in Harmony Simplified, the choice of doubled pitches emphasizes either natural or unnatural harmonics of the root. Unlike Rameau’s conception, these are not tangible harmonics that can be influenced by inversions, but the abstractions of harmonics forming an ideal series. The exact nature of the series is ambiguous, however. For the minor triad, Riemann discarded the generating note (the “fifth” in normal nomenclature) in favor of its Unterklang (the “root”), because he acknowledged that the lowest note generates the strongest harmonic series.⁽¹²⁾

[6] More recent variants on this theory include those of Mitchell,⁽¹³⁾ who warned against emphasizing the weak harmonics by doubling them, and Weidig,⁽¹⁴⁾ who encouraged the doubling of strong harmonics.

Doubling for a Pleasing Sonority

[7] The second argument for avoiding particular doublings claims that certain arrangements of pitches are particularly “striking” or “harsh,” and are therefore undesirable. Most of Schoenberg’s theory of doubling, for instance, is based on this premise.⁽¹⁵⁾ The third of a triad is an example of a striking note, since it defines the character of the triad, and should generally not be doubled. However, according to Schoenberg, in a diminished triad the third is acceptable, since the triad is neither major nor minor. Instead, the most striking triad member is the fifth, which defines the tritone. The root is, as always, perfectly acceptable to double (!). (Later in the text he offers different advice about how to treat the diminished triad.)⁽¹⁶⁾

[8] Generally, most theorists who find the third overly harsh make exception for the minor triad. This is apparently a phenomenological appeal, but Weidig also proposed that the thirds of all major triads are in fact leading tones, and should not be doubled because of their tendency to create bad voice-leading.⁽¹⁷⁾

Doubling to Fit the Key

[9] A smaller number of theorists suggest note doubling should reinforce the sense of key. The strong notes of the key are the tonic, dominant, subdominant (and perhaps supertonic or mediant), and deserve to be doubled in that order of occurrence. Prout was the strongest advocate of this point of view, and made it his first rule of doubling.⁽¹⁸⁾ A few other theorists decided this was the best practice only for first-inversion triads.⁽¹⁹⁾ Most recently, Huron has found empirical support for Prout’s theory.⁽²⁰⁾

[10] First-inversion triads have attracted particular attention from most theorists. Numerous theories have been proposed about how doubling should operate in the case where the third is found in the bass. One approach is to double the note that is in the soprano.⁽²¹⁾ This is difficult to reconcile with any of the theories mentioned so far. If the soprano note is “striking,” then might doubling it not sound “harsh”? If the soprano deserves to be reinforced because it is so prominent, why should this be true only for first inversion? An alternate proposal is that first-inversion triads have no vertically-defined rules at all.⁽²²⁾

[11] Regardless of theoretical specifics, the larger question is why inversions matter at all, if the root is—according to the prevailing convention—the perceptible organizing sound of all triads. For these theorists, there seems to be some unresolved conflict, an uneasy truce between the importance of the bass of the triad and its root.

Doubling for Good Voice-Leading

[12] The most agreed-upon voice doubling rule is probably the dictum to avoid doubling the leading tone, or other “tendency” tones. The explanation for this phenomenon, when given, is always the same. A tendency tone almost always moves to a particular pitch, so doubling that tone will result in parallel octaves.⁽²³⁾ This tendency is sometimes described as an “overactive” melodic character which should not be made over-prominent by doubling it.⁽²⁴⁾ It is worth observing, however, that avoiding the leading tone can also work to reinforce the sense of key, since the leading tone is the least common diatonic scale tone.

[13] What is probably the most idiosyncratic theory of all was proposed by Robinson,⁽²⁵⁾ who claimed that all traditional rules of voice doubling (i.e., to favor the root and fifth) can be reduced to a tendency rule. In other words, all doubling rules derive directly from (rather than being artifacts of) the attempt to avoid doubling tendency notes.

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