History
Voice crossing appears in free organum, with examples appearing as early as John Cotton's treatise De musica (1100). Voice crossing is inherent in voice exchange, which became an important compositional technique in the 12th and 13th centuries. Later, as different voices were thought of occupying more distinct vocal ranges, crossing is less frequent. In the 15th-century English discant style, such as in the Old Hall manuscript, the three voices rarely cross. In the three-part music of Guillaume Dufay, a special use of voice crossing at the cadence involves a Landini cadence but has lower voice crossing to give a bass progression as in the modern dominant-tonic cadence. As four-part music became more established by the time of Johannes Ockeghem, the top and bottom parts were less likely to cross, but the inner voices continued to cross frequently.
Voice crossing appears frequently in 16th-century music, to such a degree that Knud Jeppesen, in his analysis of Renaissance polyphony, said that without voice crossing "no real polyphony is possible." Voice crossing is less common when it involves the lowest voice, as it creates a new bass line for the calculation of the upper voices, though still it is by no means uncommon. Though it is common in the repertoire, voice crossing is sometimes avoided in strict counterpoint pedagogical exercises, especially when involving few voices. This is not always the case, however; Gradus ad Parnassum (1725), probably the most famous species counterpoint instruction book, includes an example using crossed voices early in the text.
In 18th-century contrapuntal writing, voices may cross freely, especially among voices in the same pitch location. It is, however, quite restricted in invertible counterpoint, since it makes the crossing in the inversion impossible. Canons at small harmonic intervals usually necessitate considerable voice crossing, and in a crab canon it is inevitable at the midpoint. For this reason, many authors find that canons sound better when performed by voices of different timbre. In four-part chorale writing, voice crossing is infrequent, and again the most frequently crossed voices are the alto and tenor. Voice crossing is usually forbidden in pedagogical exercises in common practice chorale-style voice-leading, especially when involving an outer voice.
Read more about this topic: Voice Crossing
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