Editing Schenkerian analysis (section)

==Schenkerian notation==
Graphic representations form an important part of Schenkerian analyses: "the use of music notation to represent musical relationships is a unique feature of Schenker's work".{{sfn|Beach|1983|loc=ch. "Schenker's Theories: A Pedagogical View", p. 27}} Schenkerian graphs are based on a "hierarchic" notation, where the size of the notes, their rhythmic values and/or other devices indicate their structural importance. Schenker himself, in the foreword to his ''Five Graphic Analyses'', claimed that "the presentation in graphic form has now been developed to a point that makes an explanatory text unnecessary".<ref>H. Schenker, ''Fünf Urlinie-Tafeln'' (''Five Analyses in Sketchform''), New York, Mannes Music School, 1933; ''Five Graphic Analyses'', New York, Dover, 1969. The Foreword is dated 30 August 1932.</ref> Even so, Schenkerian graphs represent a change of semiotic system, a shift from music itself to its graphical representation, akin to the more usual change from music to verbal (analytic) commentary; but this shift already exists in the score itself, and Schenker rightly noted the analogy between music notation and analysis.<ref>On this most interesting topic, see Kofi Agawu, "Schenkerian Notation in Theory and Practice", ''Music Analysis'' 8/3 (1989), pp. 275–301.</ref> One aspect of graphic analyses that may not have been enough stressed is the desire to abolish time, to represent the musical work as something that could be apprehended at a glance or, at least, in a way that would replace a "linear" reading by a "tabular" one.

[[File:Chopin op 10 1 Czerny.png|thumb|upright=2.5|Rhythmic reduction of the first measures of Chopin's Etude, Op. 10, no. 1. Simplified version of the analysis of the "ground-harmony" in Czerny's ''School of Practical Composition'', 1848<br />[[File:Chopin op 10 1 Czerny score.mid|thumb|left|Original]][[File:Chopin op 10 1 Czerny.mid|thumb|Reduction]]]]
The first step of the analytic rewriting often takes the form of a "rhythmic" reduction, that is one that preserves the score, but "normalizes" its rhythm and its voice-leading content.<ref name = idea>William Rothstein, "Rhythmic Displacement and Rhythmic Normalization", ''Trends in Schenkerian Research'', A. Cadwallader ed., New York, Schirmer, 1990, pp. 87–113. Rothstein's idea is that ornamentations such as retardations or syncopations result from displacements with respect to a "normal" rhythm; other diminutions (e.g. neighbor notes) also displace the tones that they ornate and usually shorten them. Removing these displacements and restoring the shortened note values operates a "rhythmic normalization" that "reflects an unconscious process used by every experienced listener" (p. 109).</ref> This type of reduction has a long tradition, not only in counterpoint treatises or theory books,<ref>Kofi Agawu, "Schenkerian Notation in Theory and Practice", ''op. cit.'', p. 287, quotes Czerny's representation of the "ground-harmony" of Chopin's Study op. 10 n. 1 (in his ''School of Practical Composition'', 1848), reproduced here in a somewhat simplified version.</ref> but also in the simplified notation of some Baroque works, e.g. the Prelude to Händel's Suite in A major, HWV 426, or early versions of Bach's C major Prelude of Book I of the Well Tempered Keyboard. One indirect advantage of rhythmic reduction is that it helps reading the voice leading: Czerny's example hereby transforms Chopin's arpeggios into a composition in four (or five) voices. Edward Aldwell and [[Carl Schachter]] write that the first rewriting should "produce a setting that is reasonably close to note-against-note."<ref>Edward Aldwell, [[Carl Schachter]] and Allen Cadwallader, ''Harmony and Voice Leading'', 4th edition, Schirmer, Cengage Learning, 2011, p. 692.</ref> Allen Cadwallader and David Gagné suggest a special type of rhythmic reduction that they call "imaginary [[Figured bass#Basso continuo|continuo]]",<ref>Allen Cadwallader and David Gagné, ''Analysis of Tonal Music: A Schenkerian Approach'', New York, OUP, 3/2011, pp. 66–68.</ref> stressing the link between the rhythmic reduction and a notation as a melody with figured bass. Basically, it consists in imagining a figured bass line for the work analyzed, and writing a chordal realization of it.

Schenker himself usually began his analyses with a rhythmic reduction that he termed ''Urlinietafel''. From 1925 onwards, he complemented these with other levels of representation, corresponding to the successive steps leading to the fundamental structure. At first, he mainly relied on the size of the note shapes to denote their hierarchic level, but later abandoned this system as it proved too complex for contemporary techniques of musical engraving. Allen Cadwallader and David Gagné propose a description of Schenker's system of graphic notation which, they say, "is flexible, enabling musicians to express in subtle (and sometimes different) ways what they hear and how they interpret a composition". They discuss open noteheads, usually indicating the highest structural level, and filled-in noteheads for tones of lower levels; slurs, grouping tones in an arpeggio or in linear motions with passing or neighbor tones; beams, for linear motions of higher structural level or for the arpeggiation of the bass; broken ties, for repeated or sustained tones; diagonal lines to realign displaced notes; diagonal beams, connecting successive notes that belong to the same chord ("unfolding"); etc.<ref>''Op. cit.'', Appendix, Introduction to Graphic Notation, pp. 384-402: "We discuss the symbols in the following categories, which are not mutually exclusive: 1. Open noteheads [p. 385]; 2. Slurs and filled-in noteheads [pp. 385-88]; 3. Beams [pp. 388-90]; 4. Broken ties [p. 390]; 5. Stem with flags [pp. 390-91]; 6. Diagonal lines [pp. 391-92]; 7. Diagonal lines and beams [pp. 392-95]; 8. Rhytmic notation at lower levels [pp. 395-96]; 9. Roman numerals [pp. 396-398]" They conclude with sample graphic analyses for study [pp. 398-401.]</ref>