3.5 The Passing 6/4

The opening phrase of the second movement of Mozart's Sonata K. 330 , above, has a voice exchange expansion between F and A which is itself expanded by intervening notes. Mozart inserted the passing tone, G, in the highest and lowest lines as they move in opposite directions between F and A. In addition a lower neighbor E is inserted in an inner voice as a C sustains from the previous eighth note.

These inserted notes, (from the bottom: octave G's, C, E and G) can also be interpreted as a second inversion dominant triad--see the Roman numeral V below the 6/4. In a situation similar to the cadential 6/4, whether we call these notes a triad in its own right (in this case an inverted V chord) or simultaneous nonharmonic tones (in this case expanding a tonic triad) depends on our level of analysis. So in the Roman numeral analysis below the staffs, the V above the bracket is a result of a purely vertical interpretation, while the Roman numeral I below the bracket implies that these notes are nonharmonic tones (aside from the C which sustains) expanding a one-and-a-half beat long tonic triad. In any case the notes highlighted in red are called a passing 6/4, after the passing tone in the bass.

As an aside, the last measure contains a cadential 6/4 which does not resolve to I. A V chord at the end of phrase makes the listener anticipate another phrase of music, and is called a half cadence.
To see how a figured bass with passing 6/4 is realized, watch the video below while following the accompanying explanation. If Example a is taken as the standard, Example b shows that voice exchange can go in reverse--with the first inversion tonic preceding the root position tonic (as in the Mozart Example above). Example c shows that the soprano is not necessarily the voice involved in voice exchange, and Example d shows that, despite the same figures and starting chord as Example b, the voice leading may differ.
At 0:02 Roman numerals are placed below the staff with a bracket indicating that the voice exchange and intervening passing 6/4 are expansions of tonic.
At 0:06 the note involved with voice exchange appears in red in the last chord of measure 1. The first note in the bass is also red showing that these two notes have the same letter name. (The intervening 6/4 has been disregarded for the moment.)
At 0:12 passing tones are inserted in the voices involved in voice exchange.
At 0:17 the remaining voices in measure 1 are filled in either according to the smoothest voice leading with notes of a V chord or according to the following tonic expansion: Scale degree 1 is decorated with a lower neighbor while scale degree 5 is repeated. These two descriptions are equivalent and equally valid.
At 0:24 the notes of the dominant are filled in. When this chord is approached by a first inversion tonic triad as in Examples a. and c., there is often a choice of where the doubled notes go. For instance, in Example a. the soprano falls to the leading tone and the tenor rises to scale degree 2. The reverse would also have been possible, with the soprano rising and the tenor falling. However this choice is not always available because of restrictions on spacing. In Example c., for example, the soprano could not have ascended with the alto descending because this voice leading would have resulted in an interval greater than an octave between these two voices. Intervals greater than an octave are not allowed between soprano and alto and between alto and tenor
At 0:29 the final tonic triad is filled in according to Common-Tone Stepwise voice leading in three of the four examples. In Example c. the tenor drops by a third and three roots and a third result in the final chord.
At 0:33 the four phrases are played.

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