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Folks,<div><br></div><div>I wish I had time to write about this more fully. In haste, with a meeting looming, I have time only for a few isolated points:</div><div><br></div><div>1. My own preference is to use descriptions for chords that capture what is going on in the bass. Calling a Tonic-prolonging progression over a 1-7-1 or 3-4-3 bass a neighbour progression (and the middle chord a neighbour chord) seems reasonable and appropriate under this assumption. I would prefer to describe the succession of Tonic to IV 6/4 to Tonic as a pedal succession (rather than a neighbour succession) for just the same reason, because the common-tone (pedal) bass is what governs the succession; upper-voice patterns seem to have so much less to do with the larger impact of the harmony.</div><div><br></div><div>2. Of the four neighbour progressions that prolong Tonic (1-7-1, 1-2-1, 3-2-3, and 3-4-3), the 1-2-1 and 3-2-3 are clearly the rarest. Now that the question has been raised, I wonder whether a 6/4 chord ever appears over the bass 2 in a 3-2-3 neighbour...but haven't had time to check my notebooks of examples.</div><div><br></div><div>3. When 1-2-1 does occur, the bass 2 almost never supports a 6/4 or a 6/5 chord (the latter a slight correction that needs to be made to Matt's fine post below). What does tend to appear is a 6/3 or (most often) a 4/3 chord. A first hypothesis about this might be that the 3rd above the 2 is necessary, perhaps as a tendency-tone pointing down to 3, to compensate for the lack of a tendency-tone in the bass. (NB the common neighbour basses both involve tendency-tones!) This hypothesis might seem to be falsified by the rarity of the 6/5 chord—except that its infrequent appearance over a 2-1 bass can be accounted for by voice-leading issues—avoiding the parallel/direct 5th of 6-5 over the bass 2-1. Other possible falsifications of this hypothesis will likely occur to all of you, as they have to me, but I don't have a better one yet.</div><div><br></div><div>4. In the end, I am no more (and no less) puzzled by the absence of an apparently grammatical progression in the literature than I am by the idiomatic eccentricities of any language.</div><div><br></div><div>I well remember learning Russian in England in my teens, from a set of two lovely OUP books that I still have: the first entitled <i>Russian Grammar</i>, which explained all the declensions and conjugations and what they entailed, and the second <i>Russian Syntax</i> (probably not the term linguists would use these days) which highlighted which forms were actually used in the language and which weren't. It has always seemed to me that harmony instruction has tended to be relatively deficient in this second area. I find it quite gratifying that Dmitri, Matt, and others have begun to focus more on this aspect of harmony in recent years; it is a subject that occupies me, as well, in whatever time I can spare these days.</div><div><br></div><div>Cheers,</div><div>Charles</div><div><div><div><br></div><div><br></div><br class="Apple-interchange-newline"><blockquote type="cite">Dear Colleagues:<br><br>I'm heartened to see the volume of dialogue my brief query has initiated. I must say, however, I'm not sure I've found among the many worthy musings a convincing answer to my original question. Perhaps there isn't one. At the risk of repeating myself, let me rephrase the question and append some relevant commentary from three of the responses to the SMT list below.<br> <br>Given that ^1-^2-^1 bass paradigms that expand tonic seem to be considerably rarer than either passing ^1-^2-^3 bass lines prolonging tonic or than ^1-^7-^1 and ^3-^4-^3 bass neighbor motions prolonging tonic for reasons many on this list have hypothesized, is it true that when ^1-^2-^1 bass lines prolonging tonic do occur, unaccented 6/4 chords above ^2 in the bass are rarer than other harmonizations of the same figure (say, with V 4/3 or vii65 [RATHER vii°6?] chords), or is ^1-^2-^1 just such a rara avis that it almost never occurs as a tonic prolongation figure in common-practice music regardless of how it is harmonized? In either case, why? Is mode a factor?<br> <br>Let me also say that the scare quotes around "Neighboring" in my original post title were intentional. I was taught that unaccented 6/4 chord labels, like sequence labels, followed no consistent logic. They were named for a variety of functions, sometimes describing the upper voices, sometimes the bass, sometimes either. More specifically, a "neighboring" 6/4 was an unaccented, tonic-prolonging sonority in which the upper voices moved 5/3 - 6/4 - 5/3. More recently, textbooks have been naming unaccented 6/4 chords consistently by the bass motion, calling what I have described above a "pedal" 6/4. Using this nomenclature, is there such a thing as a "neighboring" 6/4 in which a harmonized upper neighbor in the bass line serves to prolong a given sonority? (A related—one might say "inverted"—question is do unaccented passing tones in the soprano harmonized by 6/4 chords appear with any regularity as prolongational devices in common-practice music?) Does anyone have a database that could begin to answer such questions?<br> <br>Thanks to the three scholars below for their understanding and augmentation of my initial query:<br><br clear="all">Olli Väisälä:<br><br>What is written above does not help much to explain the original question in this thread. Why does I–V6/4–I occur so rarely, even though the progression would seem correct in both harmonic and contrapuntal terms? The previous mails contain several valuable points, the multitude of which helps to remind us that for questions about compositional practice we should not expect to find simple explanations, based on a single factor alone, since successful compositional solutions usually combine several desirable features. For what it's worth, however, here is a summary of the factors that I find most crucial in this case: First, passing motion is a more effective and fundamental way of dissonance treatment than neighboring motion; therefore I–V6/4–I6 arises more readily than I–V6/4–I. Second, for a bass line ^1–^2–^1 there is a very effective harmonization in I–V4/3–I (or I–VII6–I) involving parallel tenths; hence no need to use a neighboring V6/4 easily arises. Third, neighboring chords involving only upper-voice motions are much less weighty in character than those involving the bass; therefore I–IV6/4–I arises more readily than I–V6/4–I.<br><br>Ed Klorman:<br>Of course, none of this answers Matt's original query regarding why a second-inversion dominant appears commonly as a passing chord but rarely as an upper neighbor to I (with bass ^1-^2-^1) or, for that matter, as a lower neighbor to I6 (with bass ^3-^2-^3). My best instinct, which is not at all rigorous, would appeal to a the Gestalt principle of "good continuation" and to an idea of musical momentum or inertia. That is, a bass motion of ^1 to ^2 would most naturally continue on to ^3 (as in the passing progression I V 6/4 I6). In contrast, in a neighbor progression such as I V 6/5 I, the bass goes from ^1 to ^7, but the strong pull from leading tone up to tonic forces the bass to change direction; the tendency-tone principle presents the bass from continuing downward. The same principle explains I6 V 4/2 I6 (with bass of ^3 ^4 ^3, where ^4 is pulled back to ^3 because it is a tendency tone).<br><br>Scott Murphy:<br>For those with corpora at their beck and call, here's one test suggested to me by Edward's cogent reply that might tease things out: compare minor to major. Regardless of what immediately follows the progression (i.e. putting the distinctions between passing and neighbor aside) or other details as listed above, does "tonic in 5/3 followed by major dominant in 6/4" with a non-modulatory continuation appear in minor (e.g. the Beethoven example) significantly more often than it does in major? If so, why, and could the answer be related to an answer to Matt's original query? <br><br>Best,<br><br>Matt<br><br>________________________________<br><br>Matthew Bribitzer-Stull<br>Associate Professor of Music Theory<br>University of Minnesota School of Music<br> <br>*** Emails sent from this account are often personal in nature. Whether personal or professional, emails sent from this account do not necessarily reflect the views of the University of Minnesota or members of the University community. ***<br> <br><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Smt-talk mailing list</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="mailto:Smt-talk@lists.societymusictheory.org">Smt-talk@lists.societymusictheory.org</a></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><a href="http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org">http://lists.societymusictheory.org/listinfo.cgi/smt-talk-societymusictheory.org</a></div> </blockquote></div><br><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; 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: 0px; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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: 0px; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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: 0px; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; 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: 0px; "><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-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: 0px; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; 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; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><span class="Apple-style-span" style="border-collapse: separate; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; 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; -webkit-text-decorations-in-effect: none; text-indent: 0px; -webkit-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><div>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^</div><div>Prof. Charles J. Smith</div><div>Slee Chair of Music Theory & Chair of the Department</div><div>Music Department, 220 Baird Hall, University at Buffalo</div><div>Buffalo, NY 14260</div><div><a href="mailto:cjsmith@buffalo.edu">cjsmith@buffalo.edu</a></div><div>Private Office Line: 716-645-0639</div><div>Office Fax: 716-645-3824</div><div><br></div><br class="Apple-interchange-newline"></span></span></span><br class="Apple-interchange-newline"></span></span></span></span> </div><br></div></body></html>