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Harmony and Figured Bass

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REFERENCE INDEX Accidentals in four-part harmony, 49 Neapolitan 6 Chord, 50 Antecedent-consequent, 65 Normal Progressions, 44 Apparent seventh chords, 52 Normal Uses of Diatonic Chords, 43 Applied Chords, 47, 48 Parallel octaves, fifths, or unisons, 32 Augmented-six chords, 51 Period, 65 Binary form, 69ff. Phrases and other groupings, 65 Cadences, 66 Plagal Use of IV, 41 Cadential six-four, 35 Rondo form, 74 Charting Phrases, 66 Second-Species Counterpoint, 59 Choral style, 31 Sentence structure, 65, 66 Chord Doublings, 52 Sequences, 45 Chord Repetition, 46 Sonata Form, 72 Consonance and Dissonance, 54 Species Counterpoint, 53 Consonant Three-Part Sonorities, 54 Subphrase, 65 Dominant "13th" chord, 37 Ternary form, 71 Dominant chord with altered fifths, 38 Third-Species Counterpoint, 60 dominant functions, 37 Unusual Diatonic Chords, 42 Double-Neighbor Figure, 61 V 4-3, 36 Ending fourth or fifth species V 8-7, 33 counterpoint, 64 V of V (V/V 48 Expansion of phrases, 67 V6 and Vyg , 34 Fifth-Species Counterpoint, 62 Figured Bass, 30 VI Chord, 39 First-Species Counterpoint, 58 vii Æ7, 37 Forephrase-afterphrase, 65 vii o 7, 37 Form, 65 Voice-Leading Rules, 32 Fourth-Species Counterpoint, 61 V4/3 and viio6, 35 Harmony and Figured bass, 30 I, I6, and V chords, 33 keyboard style, 31 II , 38 Koch, 66-67 II7 and IV7, 39 Labeling a Species Counterpoint III chord, 41 Exercise, 57 IV and II6 chords, 38 Leading tone, 32 IV6 Chord, 40 Melody Rules For Species Counterpoint, V chord, 33 56 Mixture, 46 Modulations, Tonicizations, and Pivot Chords, 49 page 30 Reference Harmony and Figured Bass HARMONY AND FIGURED BASS Figured Bass Figured bass is a notation used to indicate chords that was developed by composers and music theorists of the Baroque era. A figured bass symbol indicates the appropriate intervals (or their compound equivalents) above the bass. Thus, for instance, the figures: 7 Indicate one should play a 7th, 4th, and 2nd above the bass (or their compound 4 equivalents, such as an octave plus a seventh or two octaves plus a seventh). 2 Sometimes a type of shorthand is used to indicate the notes to be played in a figured bass. According to this shorthand (which must be memorized): This figure: is shorthand for: [nothing underneath the 5 bass]; 5; 3; 8 or any 3 combination of these three numbers 6 6 3 6 6 5 5 3 4 6 3 4 3 4 or 2 6 ( remember: don’t double the bass, since there is a “2” 2 4 among the figures) 2 4 5 4 7 7 [BUT SEE 7 6 below!] 5 3 7 6 7 6 3----- (note: 7/3 chord does not have a 5th above the bass with a 7-6!) 9 9 5 3 (note: 9th of chord must be at least a 9th above the bass and also a 9th above any doubling of the bass) # 5 #3 4 # 5 ------- 4 #3 (note: 4 # does not equal #4! Students often seem to make careless mistakes with this figure!) 6 6 # #3 page 31 Reference Harmony and Figured Bass 8 7 8 --- 7 ( 5 ------) 3 ------- 5 5 (remember: don’t double the bass!) 2 2 Note that any accidental (sharp or flat) in front of a number alters that interval above the bass. Thus, for instance, a “#6” means to sharp the 6th above the bass. An accidental alone refers to a third above the bass. A dash in a figured bass symbol means “move the bass only, keep the upper voices stationary.” Usually, a dash is used when the bass line is a passing tone or when the bass line moves by arpeggio. Doubling in realizing a figured bass: Often a tone will need to be doubled when realizing a figured bass in four-part harmony. In most such cases, the leading tone should not be the tone that is doubled, nor (in most cases) should a chromaticized tone be doubled. Also, one should not double a dissonance (a seventh above a bass, for instance, is almost always a dissonance). Usually, it is a good idea to double the bass; however, the bass should not be doubled the bass if the number “2” is among the figures (since the bass will be a dissonance), nor should the bass be doubled if it is the leading tone. Choral style and keyboard style In four-part choral style format, the treble and alto voices are always written in treble clef, and the tenor and bass are always written in bass clef. The soprano and tenor are always stemmed up, and the alto and bass are always stemmed down. The soprano and alto should be within an octave of one another, and the alto and tenor should be within an octave of one another. In keyboard style format, the top three voices are all written in the treble clef and there should be no more than an octave between the alto and tenor (if there were more than an octave, the stretch would be too great for the pianist’s right hand). When there are two different rhythms in the same hand at the same time in keyboard style, they must be stemmed in opposite directions. The example shown in (a) below looks amateurish; it looks as though all of the notes on the downbeats are only an eighth note long. The example in (b) is much better. (a) (b) page 32 Reference Harmony and Figured Bass Basic Voice-Leading Rules for harmony and figured bass exercises (see Aldwell- Schachter, pages 63-77). Main rules: (a) Don’t have parallel octaves, fifths, or unisons. Also, note that a perfect fifth may move to a diminished fifth, but a diminished fifth may not move to a perfect fifth.1 (b) Don’t double the leading tone. (c) Chordal dissonances should resolve down by step and not be doubled. Examples of chordal dissonances include sevenths of seventh chords and the fourth above the bass of a cadential six-four. (d) Use the proper tones of a chord, with proper accidentals. Remember that scale-degree 7^ must be raised to create a leading tone in minor keys. The root or third of a chord may not be omitted. Secondary rules (a) Use the proper range, avoid notes needing more than one ledger line. (b) Use proper spacing. In chorale style, you should not have more than an octave between adjacent upper voices. In keyboard style, the upper voices should be within an octave of one another. (c) The upper voices should move smoothly. The bass voice can leap large intervals (though the bass should not leap the interval of a seventh). However, the upper voices usually do not move more than a third when one chord moves to another chord. (The upper voices usually leap only if there is a chord repetition or in other special circumstances.) (d) Do not use augmented melodic intervals. In particular, avoid leaping an augmented fourth (even in the bass voice) and avoid moving an augmented ^ second (an interval which may accidentally crop up in between scale degrees 6 ^ and 7 in minor). (e) Avoid hidden fifths or octaves in between the outer voices if the upper voice leaps. Other instances of hidden fifths and octaves are not that faulty. (A hidden interval occurs when the interval is approached in similar motion; a hidden interval is also referred to as a similar or direct interval.) (f) Usually the bass of a chord should be doubled. If the chord is in first inversion, any voice may be doubled. However, leading tones or dissonances should never be doubled, even if they are in the bass. (g) Avoid overlap and voice crossing. 1 The only time a diminished fifth may move to a perfect fifth is when a viio6 or V4/3 moves to a I6. page 33 Reference Harmony and Figured Bass I, I6, and V chords (See Aldwell-Schachter, pp. 81-99.) Basic Outline: The I and V are the most basic harmonies. The V chord resolves to a I. Main Uses: (a) The I and I6 are chords of tonal resolution. A root position I chord should appear at the end of a harmony exercise and at its main cadence points. The I6 can substitute for I in other places in order to provide variety in the bass line. (b) A V chord resolves to a I or I6 chord (not to a I 6/4 chord!). Specifically, a V chord should (i) resolve to a I or I6; (ii) be followed by another V or similar chord; or (iii) more rarely, a root position (not inverted) V or V7 may move to a root position VI. A V, V7, or similar chord may not move to any other chord. (c) When a V or V7 resolves to a I, the leading tone (scale degree 7,^ the third of the V chord) must resolve up to the tonic if it is in the soprano voice. If the leading tone is in an inner voice, it need not resolve up to tonic. (d) A V7 functions in a manner similar to a V triad, except that it is a bit more intense. A V7 is too unstable to appear at a half cadence. The seventh of the V7 (the subdominant scale degree) must resolve down by step to the third of the I chord (the mediant scale degree). V7 may not resolve to a I6. (e) The fifth of the I, V, or V7 may be omitted. The roots and thirds of these chords may not be omitted, however.
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