Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature...
Transcript of Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature...
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Bass Lines and Harmonic StructureThe nature of the lowest voice and its relationship to harmonic structure
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Three Fundamental Classes
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Three Fundamental Classes
✦ Tonic (T) class
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Three Fundamental Classes
✦ Tonic (T) class✦ Intermediate (int) or “predominant” class
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Three Fundamental Classes
✦ Tonic (T) class✦ Intermediate (int) or “predominant” class✦ Dominant (D) class
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Tonic (T) Class
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Tonic (T) Class
✦ I - I6
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Tonic (T) Class
✦ I - I6✦ Two chords, but just a prolongation of one tonic idea
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Tonic (T) Class
✦ I - I6✦ Two chords, but just a prolongation of one tonic idea
✦ I - vii6 - I6
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Tonic (T) Class
✦ I - I6✦ Two chords, but just a prolongation of one tonic idea
✦ I - vii6 - I6✦ Adds a passing chord between I and I6, connecting the
root and third of the tonic
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Intermediate (int) Class
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Intermediate (int) Class
✦ IV - ii6 - V
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Intermediate (int) Class
✦ IV - ii6 - V✦ The two intermediate chords (descending root) prepare
the dominant
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Intermediate (int) Class
✦ IV - ii6 - V✦ The two intermediate chords (descending root) prepare
the dominant✦ I - vi - IV
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Intermediate (int) Class
✦ IV - ii6 - V✦ The two intermediate chords (descending root) prepare
the dominant✦ I - vi - IV
✦ The vi acts both as a prolongation of T and a bridge into the int chord as well
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Chord and Harmony
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Chord and Harmony
✦ Schenkerian analysis makes a distinction between chord and harmony
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Chord and Harmony
✦ Schenkerian analysis makes a distinction between chord and harmony
✦ The chord is the actual labelled harmonic event
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Chord and Harmony
✦ Schenkerian analysis makes a distinction between chord and harmony
✦ The chord is the actual labelled harmonic event✦ The harmony is the overall function of that harmonic
event, viewed either singly but more often together with other chords as a larger unit
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Mozart: Sonata K. 545, II
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Mozart: Sonata K. 545, II
✦ The V43 on the third beat provides harmonic variety, but it also serves to prolong the initial tonic harmony
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Mozart: Sonata K. 545, II
✦ The V43 on the third beat provides harmonic variety, but it also serves to prolong the initial tonic harmony
✦ The bass line in the first two measures outlines an upper neighbor tone
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Mozart: Sonata K. 545, II
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Mozart: Sonata K. 545, II
✦ The 6-4 chord in bar three is a neighboring 6-4, an embellishment which serves to prolong the tonic
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Mozart: Sonata K. 545, II
✦ The 6-4 chord in bar three is a neighboring 6-4, an embellishment which serves to prolong the tonic
✦ The common-tone diminished seventh chord on the third beat is also an embellishment, creating incomplete neighbor chords (contrapuntal chords)
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Mozart: Sonata K. 545, II
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Mozart: Sonata K. 545, II
✦ The reduced analysis here shows the neighboring functions of the V43, IV64, and common-tone diminished chords
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Mozart: Sonata K. 545, II
✦ The reduced analysis here shows the neighboring functions of the V43, IV64, and common-tone diminished chords
✦ The reduction also analyzes the melody, using stems to show primary tones and identifying embellishments
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Mozart: Sonata K. 545, II
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Mozart: Sonata K. 545, II
✦ Bars 5-6 display a continuation of the tonic prolongation
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Mozart: Sonata K. 545, II
✦ Bars 5-6 display a continuation of the tonic prolongation✦ The neighboring V43 is repeated in bar 5
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Mozart: Sonata K. 545, II
✦ Bars 5-6 display a continuation of the tonic prolongation✦ The neighboring V43 is repeated in bar 5✦ In bar 6, a motion from I through vi moves to I6—this is
essentially the same motion as if moving upwards from I to I6.
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Mozart: Sonata K. 545, II
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Mozart: Sonata K. 545, II
✦ Bar 7 is intermediate harmony—a “predominant” function leading us to the
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Mozart: Sonata K. 545, II
✦ Bar 7 is intermediate harmony—a “predominant” function leading us to the
✦ half-cadence in bar 8 and the dominant harmony
!"!"
!"!"
#$ % & & & & & ! & & ' & ! & & & & & &$ & ! & & '($ & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & &$ &$ & & & & & & & & & & & & &
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Mozart: Sonata K. 545, II!"!"
!"!"
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A Reminder
!"## $# $ $# $
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A Reminder
✦ The cadential six-four is really an intensified dominant
!"## $# $ $# $
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A Reminder
✦ The cadential six-four is really an intensified dominant✦ Therefore, the notation which analyzes it as a dominant with
non-chord tones resolving to chord tones is more descriptive than
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A Reminder
✦ The cadential six-four is really an intensified dominant✦ Therefore, the notation which analyzes it as a dominant with
non-chord tones resolving to chord tones is more descriptive than
✦ the more logically-correct notation
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Bach: “Wach’ auf, mein Herz”
!"!"
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Bach: “Wach’ auf, mein Herz”
✦ At first glance, one might think that the IV in bar 2 is the intermediate, or predominant, chord
!"!"
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Bach: “Wach’ auf, mein Herz”
✦ At first glance, one might think that the IV in bar 2 is the intermediate, or predominant, chord
✦ It is followed by a dominant
!"!"
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Bach: “Wach’ auf, mein Herz”
✦ At first glance, one might think that the IV in bar 2 is the intermediate, or predominant, chord
✦ It is followed by a dominant✦ The dominant then resolves to a tonic.
!"!"
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Bach: “Wach’ auf, mein Herz”
!"!"
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Bach: “Wach’ auf, mein Herz”
✦ However, the opening tonic is actually prolonged over two measures, extending from the upbeat to the third beat of measure 2
!"!"
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Bach: “Wach’ auf, mein Herz”
!"!"
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Bach: “Wach’ auf, mein Herz”
✦ What appears at first to be a cadence in bar 2 is an evaded cadence (or an implied) cadence, a technique used specifically to extend ideas—i.e., it’s a prolongation technique.
!"!"
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Bach: “Wach’ auf, mein Herz”
!"!"
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Bach: “Wach’ auf, mein Herz”
✦ Therefore, the intermediate chord is found on the downbeat of bar 3
!"!"
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Bach: “Wach’ auf, mein Herz”
✦ Therefore, the intermediate chord is found on the downbeat of bar 3
✦ It leads to a prolonged dominant on beat 2
!"!"
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Bach: “Wach’ auf, mein Herz”
✦ Therefore, the intermediate chord is found on the downbeat of bar 3
✦ It leads to a prolonged dominant on beat 2✦ And the final tonic on the downbeat of bar 4
!"!"
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Bach: “Wach’ auf, mein Herz”
!"!"
!"
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Bach: “Wach’ auf, mein Herz”
✦ The reduced version of the bass line helps make the components clear.
!"!"
!"
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Dominant Class
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Dominant Class
✦ The half-cadence at the end of the antecedent requires a resolution
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Dominant Class
✦ The half-cadence at the end of the antecedent requires a resolution
✦ However, the beginning of the consequent doesn’t provide the resolution
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Dominant Class
✦ The half-cadence at the end of the antecedent requires a resolution
✦ However, the beginning of the consequent doesn’t provide the resolution
✦ The end of the consequent is the true resolution
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Dominant Class
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Dominant Class
✦ We tend to hear the end of the antecedent, and the beginning of the consequent, as an interruption before the dominant finally achieves full closure
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Beethoven: Sonata Op. 13, II
!"!"
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Beethoven: Sonata Op. 13, II
✦ Different uses of dominant chords
!"!"
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Beethoven: Sonata Op. 13, II
✦ Different uses of dominant chords✦ Dominants in bars 1 and 2 act as incomplete neighbors
!"!"
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Beethoven: Sonata Op. 13, II
✦ Different uses of dominant chords✦ Dominants in bars 1 and 2 act as incomplete neighbors✦ In bar 4, the V is in root position and articulates a half
cadence
!"!"
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Beethoven: Sonata Op. 13, II
!"!"
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Beethoven: Sonata Op. 13, II
✦ Different uses of dominant chords
!"!"
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Beethoven: Sonata Op. 13, II
✦ Different uses of dominant chords✦ The V in bar 4 resolves through V42 to I6—therefore
the dominant persists through bar 5 as well
!"!"
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Beethoven: Sonata Op. 13, II
!"!"
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Beethoven: Sonata Op. 13, II
✦ Different uses of dominant chords
!"!"
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Beethoven: Sonata Op. 13, II
✦ Different uses of dominant chords✦ The V in bar 4 also acts so as to divide an overall bass
motion from I to I
!"!"
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Beethoven: Sonata Op. 13, II
✦ Different uses of dominant chords✦ The V in bar 4 also acts so as to divide an overall bass
motion from I to I✦ And also acts to prepare the long-term motion to the ii in
bar 7
!"!"
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Beethoven: Sonata Op. 13, II
!"!"
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Beethoven: Sonata Op. 13, II
✦ A “dividing dominant” is indicated in the analysis with a bracketed [V]
!"!"
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Beethoven: Sonata Op. 13, II
✦ A “dividing dominant” is indicated in the analysis with a bracketed [V]
✦ Note important features:
!"!"
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Beethoven: Sonata Op. 13, II
✦ A “dividing dominant” is indicated in the analysis with a bracketed [V]
✦ Note important features:✦ The dotted slur (indicated a prolongation)
!"!"
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Beethoven: Sonata Op. 13, II
✦ A “dividing dominant” is indicated in the analysis with a bracketed [V]
✦ Note important features:✦ The dotted slur (indicated a prolongation)✦ Stems indicating the primary bass line notes
!"!"
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Beethoven: Sonata Op. 13, II
✦ A “dividing dominant” is indicated in the analysis with a bracketed [V]
✦ Note important features:✦ The dotted slur (indicated a prolongation)✦ Stems indicating the primary bass line notes✦ Flags indicating neighbor tones
!"!"
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Beethoven: Sonata Op. 13, II
✦ A “dividing dominant” is indicated in the analysis with a bracketed [V]
✦ Note important features:✦ The dotted slur (indicated a prolongation)✦ Stems indicating the primary bass line notes✦ Flags indicating neighbor tones✦ Large-scale tonic prolongation
!"!"
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”!"!"
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Two root-position tonic chords are connected by a dominant chord in root position—octave leap subdivided by a fifth
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Two root-position tonic chords are connected by a dominant chord in root position—octave leap subdivided by a fifth
✦ Soprano moves from ^1 to ^3; thus the tonic triad is fully outlined in both voices.
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”!"!"
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Register transfer back to original octave; motion from I to I6 via a passing vii6.
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Register transfer back to original octave; motion from I to I6 via a passing vii6.
✦ Return to root-position tonic by means of a V43.
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Register transfer back to original octave; motion from I to I6 via a passing vii6.
✦ Return to root-position tonic by means of a V43.✦ Motion from ^3 to ^6 of the tonic triad
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”!"!"
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Arrival at a dominant chord at bar 4, however the chord is not entirely stable
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Arrival at a dominant chord at bar 4, however the chord is not entirely stable
✦ The soprano note is the leading tone
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Arrival at a dominant chord at bar 4, however the chord is not entirely stable
✦ The soprano note is the leading tone✦ Bass moves back through V42 to I63
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Arrival at a dominant chord at bar 4, however the chord is not entirely stable
✦ The soprano note is the leading tone✦ Bass moves back through V42 to I63
✦ Thus this is a “dividing” dominant
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”!"!"
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Return to I; notice the combination of stepwise motion and leaps in the bass.
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Return to I; notice the combination of stepwise motion and leaps in the bass.
✦ There is a voice exchange between the outer voices in this motion from I6 to I
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”!"!"
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Modulation to III.
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Modulation to III.✦ F is established as a key area in its own right
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Modulation to III.✦ F is established as a key area in its own right✦ The ‘f’ in the soprano serves as the melodic goal of the
phrase, and also initiates a new melodic ascent in the next phrase
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Modulation
![Page 99: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/99.jpg)
Modulation
✦ Although in a modulation the piece does “change key”, as a rule it is the very tension created by the key change—and the eventual return to the original tonic—which makes modulation useful in musical structure.
![Page 100: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/100.jpg)
Modulation
✦ Although in a modulation the piece does “change key”, as a rule it is the very tension created by the key change—and the eventual return to the original tonic—which makes modulation useful in musical structure.
✦ Therefore, the new key is both a new tonic, and still retains whatever secondary quality in the old key (i.e., if you modulate to V in a major key, the V is a new key, but still acts like the dominant in the original key.)
![Page 101: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/101.jpg)
Modulation
✦ Although in a modulation the piece does “change key”, as a rule it is the very tension created by the key change—and the eventual return to the original tonic—which makes modulation useful in musical structure.
✦ Therefore, the new key is both a new tonic, and still retains whatever secondary quality in the old key (i.e., if you modulate to V in a major key, the V is a new key, but still acts like the dominant in the original key.)
✦ Because of that, Schenker referred to modulation as motion to an “illusory key.”
![Page 102: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/102.jpg)
Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”!"!"
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Tonic prolonged to bar 8
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Tonic prolonged to bar 8✦ Int harmony from 8 - 15
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![Page 105: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/105.jpg)
Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
✦ Tonic prolonged to bar 8✦ Int harmony from 8 - 15✦ D harmony at 15
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Bach: Chorale “Ihr Gestirn, ihr hohen Lüfte”
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Imaginary Continuo
![Page 108: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/108.jpg)
Imaginary Continuo
✦ An imaginary continuo creates a harmonic representation of a composition, removing melodic and harmonic embellishment
![Page 109: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/109.jpg)
Imaginary Continuo
✦ An imaginary continuo creates a harmonic representation of a composition, removing melodic and harmonic embellishment
✦ Feel free to move between three and six voices
![Page 110: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/110.jpg)
Imaginary Continuo
✦ An imaginary continuo creates a harmonic representation of a composition, removing melodic and harmonic embellishment
✦ Feel free to move between three and six voices✦ Try to stay with relatively “pure” voice leading, unless to do
so means to seriously misrepresent the composition
![Page 111: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/111.jpg)
Imaginary Continuo
✦ An imaginary continuo creates a harmonic representation of a composition, removing melodic and harmonic embellishment
✦ Feel free to move between three and six voices✦ Try to stay with relatively “pure” voice leading, unless to do
so means to seriously misrepresent the composition✦ Generally think of piano style—the RH plays complete
chords, while the LH plays single bass notes
![Page 112: Bass Lines and Harmonic Structure - · PDF fileBass Lines and Harmonic Structure The nature of the lowest voice and its relationship to harmonic structure](https://reader031.fdocuments.us/reader031/viewer/2022012923/5a797a527f8b9ade698bff20/html5/thumbnails/112.jpg)
Beethoven: Sonata Op. 10 No. 1, II
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Beethoven: Sonata Op. 10 No. 1, II
✦ The imaginary continuo follows the original pretty closely.
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Beethoven: Sonata Op. 10 No. 1, II
✦ The imaginary continuo follows the original pretty closely.✦ Note: my version is a bit different from the text; I think their
version in bars 6 & 7 was a bit too “convenient” and slightly misrepresented the music.
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