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</o:shapelayout></xml><![endif]--></head><body bgcolor=white lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal>Nicolas,<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Are we really going to play the game of a close reading of Schenker? (I played the game once, in an <i>MTO </i>article entitled “The Bridges that Never Were.”)<o:p></o:p></p><p class=MsoNormal>Surely the statement “there are no other tonal spaces than those of 1–3, 3–5, and 5–8,” which of course cannot be taken literally (due to such “tonal spaces” as 2-1-7, 4-3-2, etc.), essentially equates “tonal space” with “diatonic system.” That Schenker (apparently) wants us to believe that his <i>Urlinie</i> is conceptually prior to the diatonic system is one of his many conceits.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Eytan Agmon<o:p></o:p></p><p class=MsoNormal>Bar-Ilan University<o:p></o:p></p><p class=MsoNormal> <o:p></o:p></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'> Nicolas Meeùs [mailto:nicolas.meeus@paris-sorbonne.fr] <br><b>Sent:</b> Sunday, July 17, 2011 9:17 PM<br><b>To:</b> Eytan Agmon<br><b>Cc:</b> 'SMT Talk'<br><b>Subject:</b> Re: [Smt-talk] prolongation<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Le 17/07/2011 17:15, Eytan Agmon a écrit : <o:p></o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'>(and that, as Ildar told us, the second I is not the same as the first).<o:p></o:p></p><p class=MsoListParagraph style='text-indent:-18.0pt'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>A chord progression Y-X-Y assumes that X and Y occupy the same “tonal space” (=diatonic system).</span><o:p></o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'>For Schenker, the "tonal space" certainly is not the diatonic system. The concept is described mainly in <i>Erläuterungen</i> (<i>Der Tonwille</i> IX and X, <i>Das Meisterwerk </i>I and II). Schenker writes: <br> <i>Die Tonräume des Klanges misst die Urlinie aus und bringt den Klang so erst zum Ausdruck, zum Bewustsein</i>. <i>Die Urlinie ist ersters Durchgang, als solcher erste Melodie und zugleich Diatonie. Andere Taunräume als 1-3, 3-5, 5-8 gibt est nicht, eienen anderen Ursprung des Durchganges, der Melodie gibt es nicht. <br> </i>In Ian Bent's translation: "The Urlinie measures out the tonal spaces within the chord, and thereby articulates the chord for the first time, bringing it to consciousness . The Urlinie is the first passing-tone progression [<i>erster Durchgang</i>]. As such it constitutes the first melody, and at the same time provides the diatonic content [<i>Diatonie</i>]. There are no other tonal spaces than those of 1–3, 3–5, and 5–8. There is no other origin for passing-tone progressions, or for melody."<i><br> </i>Remarks about the translation (none of these are extremely important, I would hate to seem pedant about this; but they are slightly irritating):<br>– One possible translation of <i>Ausmessen</i> is "to pace": it is by pacing the tonal spaces that the Urlinie takes their measure, and the pacing may be more important than the measure. [Note that the Urlinie, in this particular text, is an ascending line. It is changed in a descending one in fig. 4 of <i>Free Composition</i>, where Schenker nevertheless stresses its articulation on ^8 ^5 (^3) ^1 and its relation to the chord from which it emanates. The "diatony" (which is not exactly the diatonic system) results from the pacing of the space.<br>– Schenker really writes "...thereby brings the chord for the first time to expression, to consciousness". Ian Bent translation of <i>Ausdruck</i> in "articulate" might refer to an expression in words, but this remains unclear.<br>– "The Urlinie ... <u>is</u> the first melody and at the same time <u>is</u> the <i>Diatonie</i>"; Schenker does not seem to refer to <u>providing</u> a diatonic <u>content</u><i>.</i><br><br>Tonal spaces are at first empty spaces. Any filling is dissonant, while the spaces themselve must be consonant [let's leave aside the problem of 7th chords]: <i><br> Der este Urlinie-Durchgang is dissonierend (Sekund, Quart, Sept). Die Dissonanz wird in eine Konsonanz verwandelt, weil im Gegensatz zu jener nur diese allein mit ihren Tonräumen (siehe oben) wieder zu neuen Durchgängen, zu neu sich zweigender Melodie führen kann. Dies geschieht nun durch Prologationen in immer neuen Stimmführungsschichten</i>, etc. <br> Ian Bent translates: "The first passing-tone progression comprised by the Urlinie generates dissonance (second, fourth, seventh). Dissonance is transformed into a consonance because only consonance, with its tonal spaces (as shown earlier) can, by contrast with dissonance, promote new passing-tone progressions and freshly burgeoning melodies. This comes about through prolongations in ever-renewing layers of voice-leading..."<br> Remarks about the translation:<br>– Schenker does not say that the Urlinie <u>generates</u> dissonance, but that it <u>is dissonant</u>.<br>– The new tonal spaces do not <u>promote</u>, they <u>lead to</u> new passing-tone progressions.<br>– <i>sich zweigender</i> belongs to Schenker's sophisticated German; it means "developing into new branches".<br> <br>X does not occupy the same tonal space as Y: insofar as it is made consonant (by other parts of the voice leading), it creates a <u>new</u> tonal space, probably within the same diatony. I suspect however that Schenker is not strict about keeping to the diatony: passing notes may include a b7 or a #4...<br> The chord (<i>Klang</i>) has no conscious existence before it is expressed in prolongation. This confirms the idea of the chord initially being but an abstraction, a concept (<i>Harmonienbegriff</i>), as already stated in <i>Harmonielehre</i>.<br><br><o:p></o:p></p><p class=MsoListParagraph style='margin-bottom:12.0pt'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>There exists a logical interdependence between the vertical and horizontal dimensions, in particular, between progressions involving triads and seventh chords and what I call (<i>Musikometrika</i> 3, 1991) “efficient” voice leading. </span><o:p></o:p></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>Therefore, as far as I can see, the Y-X-Y model “lets Y grow” in much the same sense as Schenker’s. (Melodic prolongation is analogous, yet distinct from harmonic prolongation.)</span><o:p></o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'>We are speaking of descriptions. The Y–X–Y model appears merely to describe a 'pendular' situation, what Sadaï names the "a–b–a pattern". Schenker's description as prolongation appears to add strong precisions about how X relates to Y through voice leading (and certainly not by mere juxtaposition). Isn't the efficient voice leading merely a consequence of the structure of chords as piling 3ds, with the result that any note in between the borders of the tonal spaces is adjacent to at least one (and often both) of these borders?<br> In addition, not all prolongations result in embedded chords.<o:p></o:p></p><p class=MsoNormal>Nicolas Meeùs<br>Université Paris-Sorbonne<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>