A Corpus-Based Model of Voice Leading in Tonal Music

Transcription

1 A Corpus-ased Model of oice Leading in Tonal Music Robert T. Kelley igure : igured ass xercise Table : Renaming Harrison s Scale-Degree unctions New unction Name Tonic Member(s) Subdominant Dominant Other Names oundation () ˆ ˆ ˆ ase (Harrison), Trigger (Quinn) Active Tone () ˆ ˆ ˆ Agent (Harrison), Trigger (Quinn) Primary Stabilizer () ˆ ˆ ˆ2 Associate (Harrison and Quinn) Secondary Stabilizer () ˆ ˆ2 ˆ Associate (Quinn) Chordal Dissonance () ˆ ˆ ˆ, ˆ unctional Dissonance (Quinn) Non-Chord Tone () ˆ2, ˆ ˆ, ˆ ˆ, (ˆ) Non-unctional Diss. (Quinn) Table 2: An xcerpt from the Data Set, Showing the Hymn Tune Americus, by Charles H. Gabriel #americus.mid T; T; S; T; T; T; S; T; T; D; T; S; T; D; T; D2; D2; D; T; D; S; D; D; T; D; T; T; S; T; S; S2; T; D; T; T; D; D; T; T; S; T; S; S2; T; T; T; S; D; D2; T; T; T; S; T; T; T; S; T; T; D; T; S; T; D; T; D; D; D2; T; D2; S; D; D; T; D2; T; T; S; T; S; S; T; D; T; T; D; D2; T; T; S; T; S; S; T; T; T; S; D; D; T; T; T; S; T; T; T; S; T; T; D; T; S; T; D; T; D; D; D; T; D; S; D; D; T; D; T; T; S; T; S; S; T; D; T; T; D2; D; T; T; S; T; S; S; T; T; T; S; D; D; T; T; T; S; T; T; T; S; T; T; D2; T; S; T; D2; T; D; D; D; T; D2; S2; D; D; T; D2; T; T; S; T; S; S; T; D2; T; T; D; D; T; T; S2; T; S; S; T; T; T; S; D; D; T; % % 2 Dˆ % Tˆ % Sˆ Dˆ % % Sˆ2 Tˆ % % % % 2 Tˆ % Dˆ Sˆ % % % % % Tˆ 0% Dˆ % Sˆ % 2 Tˆ 2 Sˆ Dˆ Dˆ % Sˆ Tˆ % Sˆ % % 2 % igure 2: Hidden Markov Model of Scale-Degree unctions

2 Tˆ Tˆ Tˆ Tˆ Tˆ Tˆ Tˆ Tˆ % % 8 Dˆ 8 Dˆ Dˆ Dˆ % Dˆ % % Dˆ Sˆ 0% Tˆ 90% 2% Tˆ % % % % Sˆ2 % Sˆ 2 % % Sˆ Sˆ Sˆ Sˆ 2 Dˆ Dˆ Dˆ % % 2 2 Dˆ Dˆ % Tˆ % % % % Tˆ % % 2 % Dˆ 9% Sˆ % % % % 0% % % % % % Sˆ2 Sˆ 8 % Sˆ Sˆ Sˆ Sˆ % 80% (a) Authentic Progression Scale-Degree Tendencies (b) Plagal Progression Scale-Degree Tendencies Dˆ % % 0% % % % % % % % Dˆ % % % Dˆ % % % % % Dˆ % Dˆ % % % Dˆ % % Tˆ Tˆ Tˆ Tˆ Tˆ Tˆ % 2 Sˆ % 2 % % % % 2 % Sˆ2 % % Sˆ % 0% Sˆ % % % % Sˆ % % Sˆ % Sˆ % % % % (c) Scale-Degree Tendencies with No Change of Harmonic unction igure : Resolution Tendencies of All Scale-Degree unctions in All Harmonic Contexts 2

3 (a) Harrison s igures.2.: Agent Discharges T T, S S, D D T S, S D, D T T D, D S, S T Step Ant.=CT, T=Down by rd, Others=Step ree Down by Step CT ree Step: M, M R, L S, T D nfl. or S CT Step or Dim. rd in Direction of nflection ree Step CT ree CT Step ree ree ree Table : Active Tone Resolution Tendencies (b) Chart of Active Tone Resolutions ˆ TONC ˆ ˆ ˆ ˆ T S discharge ˆ ˆ2 T D discharge ˆ ˆ S T, S D discharge ˆ ˆ D S, D T discharge ˆ2 DOMNANT ˆ Plag Auth ˆ Plag Auth Auth ˆ Plag ˆ ˆ SUDOMNANT igure 2: Chart of Active Tone Resolutions Table : oice-leading The S Choral Procedures Texture When completing part-writing exercises, the student will work under the assumption that their No unction Change Authentic Progression (AP) Plagal Progression (PP) T T, S S, D D T S, S D, D T T D, D S, S T music should be easily performable by a four-voice mixed choir (S). When completing more practical projects, such as composing or arranging for a jazz ensemble, symphonic band, piano, or string quartet, some of the constraints of S choral writing can be relaxed. The principles of DN=rd, Others=Step Ant.=CT, T=Down by rd, Others=Step singable lines, proper voice leading, and restricting the range of each voice, however, will still assure that music for any type of ensemble will be easily performable and will sound natural to the listener. ree Down by Step CT Table provides the constraints to which the students should adhere in their choral writing. ree Step: M, M R, L S, T D Doubling nfl.,, or CT Step or Dim. rd in Direction of nflection Ordinarily, only triads will require doubling of one of the chord members. When the fifth must be left out of a chord for voice-leading reasons, however, then a chord member must be doubled in ree Step CT seventh chords. f the fifth must be left out of a triad, then more than one chord member may be ree CT, Down by rd or th, or Up by th Step doubled or a single chord member tripled. Table gives a procedure for determining which note to double in a chord, and which notes never to double. ree ree ree Table : Doubling Procedures. f a primary or secondary stabilizer is in the bass voice, double it. 2. f not, then if the foundation note is in the chord, double it.. f not, then double the bass note.. oice leading may overrule the doubling indicated by the first three rules.. Never double dominant active tones, chordal dissonances, or inflections other than modal mixture. Table : Part-Writing Priorities. Top Priorities 2. mportant Considerations. Do Whenever Possible,,, nfl. &S Resolutions Law of the Shortest Way Resolutions in nner oices Doubling Procedure Avoiding Consecutive Ps Doubling Procedures Avoiding Consecutive Ps & P8s ncluding the th in Triads ncluding the th in th Chords Range, Spacing, Avoiding Crossing Avoiding oice Overlaps Resolutions in Passing Chords

4 M: T M: T A/ [] [] [] [] S [Tped] /D C m / T S /G m /A / S T Dp2 [] [] [] [] T / 8 Dcad T D D A/ [] [] [] S [Tped] T [] T T /A 2 M: Dp Dp2 [] [] / Dp2 [] [] [] [] C m /G vi Tp [D] [] [] [] [] /G T / Dp2 sus / /G A [] [] / D/ S S T A [] Sn o /A T [] [] /G / T Dp2 A/ [] [] [] [] [] [] [] [] S [Tped] /G A T S T / D/ [T] / Dcad igure : Harmonic Analysis of Americus with Scale-Degree unction Analysis D D A S T M: T [] [] [] D/ [T] [] S2 D/i [D2] [] [] [] [] T D/ S D/ [S] [] [] [] [] [] [] [] [] D D/vi [D] Tx S D igure : Two-Layer Analysis Technique for Applied Dominants D T unctional Part Writing Manual

5 References Aarden, ret, and Paul T. von Hippel Rules for Chord Doubling (and Spacing): Which Ones Do We Need? Music Theory Online, vol. 0/2. < hippel frames.html>. urstein, L. Poundie, and Joseph N. Straus. 20. Concise ntroduction to Tonal Harmony. W. W. Norton. Harrison, Daniel G. 99. Harmonic unction in Chromatic Music: A Renewed Dualist Theory and an Account of ts Precedents. University of Chicago Press. Kostka, Stefan, and Dorothy Payne. 98. Tonal Harmony, with an ntroduction to Twentieth- Century Music. th ed., 20. New York: A. A. Knopf. Motte, Diether de la. 9. The Study of Harmony: A Historical Perspective. Translated by J. L. Prater. Dubuque, owa: W. rown, 99. Quinn, an Harmonic unction Without Primary Triads. Paper delivered at the Twenty- ighth Annual Meeting of the Society for Music Theory in oston, November 200. Quinn, an, and Panayotis Mavromatis. 20. oice-leading Prototypes and Harmonic unction in Two Chorale Corpora. dited by Carlos Agon, Moreno Andreatta, Gérard Assayag, mmanuel Amiot, Jean resson, and John Mandereau, Mathematics and Computation in Music: Third nternational Conference, MCM 20, Paris, rance, June, 20. Proceedings. Springer erlin Heidelberg. Quinn, an, and Christopher White. 20. xpanding Notions of Harmonic unction Through a Corpus Analysis of the ach Chorales. Paper delivered at the Annual Meeting of the Society for Music Theory A Corpus-ased Model of Harmonic unction in Popular Music. Paper delivered at the Annual Meeting of the Society for Music Theory. Shaffer, Kris, and Robin Wharton, eds. 20. Open Music Theory. Hybrid Pedagogy Publishing. <