to sing, approach and follow leaps with movement in the opposite direction, and correctly handle tendency tones (primarily, the leading-tone, but also the , which often moves down to ). To be independent, they should avoid parallel fifths and octaves. Contrapuntal conventions likewise consider permitted or forbidden melodic intervals in individual parts, intervals between parts, the direction of the movement of the voices with respect to each other, etc. Whether dealing with counterpoint or harmony, these conventions emerge not only from a desire to create easy-to-sing parts but also from the constraints of tonal materials and from the objectives behind writing certain textures. These conventions are discussed in more detail below. Harmonic roles As the Renaissance gave way to the Baroque era in the 1600s, part writing reflected the increasing stratification of harmonic roles. This differentiation between outer and inner voices was an outgrowth of both tonality and homophony. In this new Baroque style, the outer voices took a commanding role in determining the flow of the music and tended to move more often by leaps. Inner voices tended to move stepwise or repeat common tones. A Schenkerian analysis perspective on these roles shifts the discussion somewhat from "outer and inner voices" to "upper and bass voices." Although the outer voices still play the dominant, form-defining role in this view, the leading soprano voice is often seen as a composite line that draws on the voice leadings in each of the upper voices of the imaginary continuo. Approaching harmony from a non-Schenkerian perspective, Dmitri Tymoczko nonetheless also demonstrates such "3+1" voice leading, where "three voices articulate a strongly crossing-free voice leading between complete triads [...], while a fourth voice adds doublings," as a feature of tonal writing. Neo-Riemannian theory examines another facet of this principle. That theory decomposes movements from one chord to another into one or several "parsimonious movements" between pitch classes instead of actual pitches (i.e., neglecting octave shifts). Such analysis shows the deeper continuity underneath surface disjunctions, as in the Bach example from BWV 941 hereby. References Further reading McAdams, S. and Bregman, A. (1979). "Hearing musical streams", in Computer Music Journal 3(4): 26–44 and in Roads, C. and Strawn, J., eds. (1985). Foundations of Computer Music, p. 658–698. Cambridge, Massachusetts: MIT Press. "Voice Leading Overview", Harmony.org.uk. Voice Leading: The Science Behind a Musical Art by David Huron, 2016, MIT Press "Mathematical Musick – The Contrapuntal Formula