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Dmitri Tymoczko writes: <BR> <BR>
<EM>A number of you have made the sensible-sounding suggestion that we should teach both specific idioms and general principles ... The problem, in this specific instance, is that when you look carefully at classical music, you find shockingly few varieties of "passing" and "neighboring" 6/4 chords. There are only two common kinds of "neighboring 6/4 chords", to wit I->IV6/4->I and V->I6/4->V, and basically just one common variety of "passing 6/4," namely IV6- I6/4->[IV or ii6 or ii6/5].<BR>> <BR>> So the idea that there is some complicated practice which can be subsumed into a single unifying framework -- that of "passing" or "neighboring" 6/4 chords -- is not really backed up by this music. There are precisely three idiomatic non-cadential 6/4 progressions, and together these account for the vast majority of examples that students are going to encounter. The concepts "neighboring" and "passing 6/4" allow you to knock these three idioms down to two categories, but at the expense of forcing you to explain to your students that a vast number of the newly-sanctioned theoretical possibilities (ii-V6/4-ii, etc.) don't ever occur in the literature. <BR> In this sense, I think the cost of the proposed "general principles" might be greater than the benefit.<BR></EM><BR>
As important as it is to know what's common (and your findings are illuminating), it's also important to recognize that what falls outside the bounds of the usual is not necessarily abnormal, perverted, or wrong. As with left-handedness or sexual orientation, recognizing only the majority denies the contribution of the minority thus rendered invisible. <BR>
For example, here are two instances I find at hand of neighboring 6/4s expanding VI, (VI-"II6/4"-VI), a category you may not have mentioned: <BR>
Bach, <SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT size=2 face=Verdana><EM>Christmas Oratorio </EM><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT size=2 face=Verdana>BWV 248: </FONT></SPAN>Part 1, No. 9 (“Ach, mein herzliebes Jesulein!”) m.3; </FONT></SPAN><BR>
<SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"></SPAN><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT size=2 face=Verdana>Beethoven, <I style="mso-bidi-font-style: normal">Sechs geistlicher Lieder von Gellert</I>, Op. 48, No. 3, “Vom Tode” mm. 36-40 (VI-VIx7-Passingdim7-“[‘Phrygian’]II6/4”-VIx7 respelled enharmonically to prepare cadential 6/4). </FONT></SPAN></SPAN><BR>
<SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT style="FONT-SIZE: 10pt" size=2 face=Verdana>Also Schubert uses unusual 6/4 neighbors in <EM>Winterreise</EM>, "Der Wegweiser" mm. 11 and 13, and of course the passing 6/4s in the chromatic wedges at the end of that song. </FONT></SPAN></SPAN><BR>
<SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT style="FONT-SIZE: 10pt" size=2 face=Verdana>So really there's an abundant variety of passing and neighboring 6/4s in the repertoire, even if the vast majority fall into a few categories. Why some are not only unusual but utterly foreign to the tonal style is a valuable question you are correct to point out our discipline has yet to address adequately. Also you might find some of these "stones the builders rejected" in modal and neo-modal repertoires (Sibelius, Janacek, etc.). </FONT></SPAN></SPAN><BR>
<SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT size=2 face=Verdana></FONT></SPAN></SPAN> <BR>
<SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT size=2 face=Verdana>Richard Porterfield</FONT></SPAN></SPAN><BR>
<SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT size=2 face=Verdana>Instructor, Mannes College of Music</FONT></SPAN></SPAN><BR>
<SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT size=2 face=Verdana>Ph.D. Candidate in Music Theory, CUNY GC</FONT></SPAN></SPAN><BR>
<SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT size=2 face=Verdana>Co-founder, Lionheart</FONT></SPAN></SPAN><BR>
<SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><SPAN style="LINE-HEIGHT: 115%; FONT-FAMILY: 'Calibri','sans-serif'; FONT-SIZE: 11pt; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA"><FONT size=2 face=Verdana><A href="mailto:porterfr@hotmail.com">porterfr@hotmail.com</A></FONT></SPAN></SPAN><BR> <br /><hr />Your E-mail and More On-the-Go. Get Windows Live Hotmail Free. <a href='http://clk.atdmt.com/GBL/go/196390709/direct/01/' target='_new'>Sign up now.</a></body>
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