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What’s in a Name?

Dr. J. Scott Brubacher
The main article addresses changes in chord nomenclature that appear in the Piano Syllabus, 2015 Edition. Here we will delve a little deeper into a theoretical understanding of why the cadential six-four can be symbolized as V 6/4. (See Example 1)
As stated earlier, chords have meaning in relation to each other within a harmonic, metric, and formal context. By using the word “context,” what we are really describing is tonal function with all of its implied hierarchies. Just like melodies can have non-harmonic tones, such as passing and neighbour notes that are not as hierarchically important as the consonant notes that they decorate, so too can chords exist in passing and neighbour roles, based on their position within the harmonic and metrical context. This understanding of functional harmony is different from the mere identification of sonorities. 
The main confusion around the cadential six-four chord lies in the analytic symbols, not the understanding of harmony. Roman-numeral figured-bass analysis (called functional chord symbols in the theory curriculum) is an unhappy marriage of two different analytic systems. The figured bass numbers describe vertical sonorities, intervals built above the sounding bass note. We inherited these symbols from performance practice of continuo playing in the 17th and 18th centuries. Roman numeral analysis, which developed in the early 19th century, describes harmonic function as tied to specific scale degrees. When the two systems of analysis are joined together in a “convenient” short-hand, the results can sometimes be misleading.
Example 2 shows a typical 4–3 suspension over the dominant chord in C major. The suspended fourth is held over from the preceding tonic chord and resolves down by step to B. Example 3 shows a somewhat less common 6–5 suspension, where the E is held over and resolves down by step. In Example 2, since the figured bass number 4 does not exist as a short-hand for any triad inversion, there is no doubt that V is the appropriate Roman numeral for this chord. In Example 3, if you were to isolate the initial chord with G in the bass, you might analyze it as iii6. In this context, however, it is clear that the E is a suspended note, delaying chord member D. The G chord is functionally a dominant harmony with a non-harmonic tone in the soprano voice. The functional chord symbol V6–5 does not suggest that this is a first-inversion G chord, but rather that there is a 6–5 voice-leading motion over the G chord. When the two suspensions occur at the same time, the function of the chord with G in the bass does not change. It is still a dominant harmony, now with two non-harmonic tones delaying the actual chord members. This interpretation is supported by the harmonic rhythm (the harmony is changing every 2 beats) and the metric placement (the cadential chord appears on a strong beat). To identify this as a tonic chord in second inversion ignores these aspects of musical context.

The non-harmonic 6 and 4 above the bass note can be prepared as suspensions, as we have seen, or approached as accented passing and neighbour tones. Example 4 shows a combination of these approaches, where the dominant chord is approached by its own dominant (V6/5 of V). The fact that the cadential 6/4 chord follows the applied dominant of V further supports its identity as a dominant function. 
It is important to remember that figured bass numbers and Roman numerals describe different things. Although they are often written as a unit, when working with students it may be helpful to separate the two layers of analysis onto different vertical planes. To think of the cadential six-four as an independent unit (I 6/4) loses the richer understanding that arises when the Roman numerals are separated from the figured bass to express two different types of analysis. 
The main article ended by asking when the I 6/4 symbol is correct, and when V 6/4 in C major does mean a G chord with D in the bass. The cadential six-four is just one type of 6/4 chord—often called an accented six-four. In terms of tonal function, this type of accented six-four is hierarchically quite significant. But there are other types of six-four chords, including passing, neighbor, and arpeggiating six-four chords, which as their names imply occupy a lower level in tonal hierarchy. These are the musical contexts in which the I 6/4 and traditional understanding of the V 6/4 symbol are more likely to be correct.