<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><blockquote type="cite"><div><div class="MsoNormal"><font class="Apple-style-span" size="5"><span class="Apple-style-span" style="font-size: 18px;">Another example of a sequence where the typical part-writing is opposite the smoothest idealized voice leading is the ubiquitous descending fifth sequence. We usually associate descending part writing with the descending fifths sequence, but it has idealized ascending voice leading. </span></font></div></div></blockquote><br></div><div>This is an important point.</div><div><br></div><div>In "strong" progressions, the root moves (diatonically) by descending third, descending fifth, or ascending step. When you're using plain triads, the most efficient voice leading for a strong progression is ascending. This creates a conflict between two tonal imperatives: 1) using efficient voice leading, and 2) creating phrases that use descending melodic contours. (Hello, Heinrich, nice to see you again!) Typically, then, a harmonic cycle such as I-IV-V-I or I-ii-V-I involves at least one non-minimal voice leading. The descending fifth sequence is a case in point -- usually one of the two voice leadings is non-minimal, as in (C, E, G)->(C, F, A)->(B, D, F)->(B, E, G), where the nonminimal voice leading is (C, F, A)->(B, D, F).</div><div><br></div><div>With seventh chords, the situation is reversed -- now the most efficient voice leadings for strong progressions descend. This means that you can create sequences, or harmonic cycles, using maximally efficient descending voice leadings. You start to see this more and more often in nineteenth-century music, and it eventually becomes central to jazz voice-leading practice.</div><div><br></div><div>DT</div><div><br></div><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div>Dmitri Tymoczko</div><div>Associate<span class="Apple-converted-space"> </span>Professor of Music</div><div>310 Woolworth Center</div><div>Princeton, NJ 08544-1007</div><div>(609) 258-4255 (ph), (609) 258-6793 (fax)</div><div><a href="http://music.princeton.edu/~dmitri">http://music.princeton.edu/~dmitri</a></div><div><br class="khtml-block-placeholder"></div><div><br class="khtml-block-placeholder"></div><br class="Apple-interchange-newline"></span><br class="Apple-interchange-newline"> </div><br></body></html>