##### Joaquín Rodrigo Superior Conservatory of Music of Valencia ###### Harmony and Counterpoint Practice 1st Year **Exercise Dossier to be completed**
Professor: Joan Alborch
###### Harmonic Series - **Triad Chords** - **Types of Triad Chords:** - Major - Minor - Augmented - Diminished ###### Types of Cadences - **Perfect Cadence** - **Plagal Cadence** - **Imperfect Cadence** - **Half Cadence** (on the dominant) - **Deceptive Cadence**
###### Scale Formation Major and Minor Scales - **Major Chords** - **Minor Chords** - **Circle of 5ths** - Major Scale Range - Minor Scale Range
###### Table of Harmonic Intervals - **Consonances (Stable Intervals):** - Perfect: - 8ths, 5ths, 4ths perfect - Note: The perfect 4th from the bass is considered dissonant. - Imperfect: - 3rds, 6ths Major and Minor - **Dissonances (Dynamic Intervals):** - Absolute: - 2nds, 7ths Major and Minor - Apparent or conditional: - Most augmented and diminished intervals. - **Tritone:** - Augmented 4th - Diminished 5th - **Compound Intervals:** - They share the same condition as their simple version.
###### Table of Chord Figuring - **Root Position** - **1st Inversion** - **2nd Inversion** - **3rd Inversion** - 5, 8, 3 or none - **Triad Chords** - Figure 4 +6 - **7th Degree Chord** - 5, 3, +4 - **Dominant 7ths:** - 7 +6 - **7th Degree 7ths (extension of the 5th degree)** - Diminished 7th, half-diminished - Diatonic Major 7th: 9 6 4 - Minor 7th: b9 7 +6 - **Accidental Alterations** - Applied before the corresponding number. - If no number is present, they affect the third of the chord.
###### Basses - Root Position in 4 voices - **Examples of Basses:** - P. Hindemith - Chord Progressions: I IV V I, IV V I
###### Harmony Basses Melody and Minor Mode - **Examples of Melodies:** - With and without degree indications - Progressions: I IV V
###### Chords in Inversion 6th Chords - The 6th chord is found between harmonics 5-6-8 - **Figuring:** - Simply avoid doubling the bass unless it is a tonal degree of the scale. - **General Effect of Inversion:** - Related to the connection with chords in root position.
###### Chords Regularly Used in Inversion - VII and III of the minor mode - Exercises With Chord Connection Rules - Overcoming connection rules to improve the melody
###### Inversion of Chords Second Inversion - **Brief Theoretical Explanation:** - Appears between harmonics 3-4-5. - Considered dissonant with an auxiliary chord function. - Preferred note to double is the bass. - Avoid doubling the tritone.
###### Cadences and 6/4 Chords - **Cadences:** - Passing 6/4 (neighboring chord) - 4th prepared and resolved - Cadential 6/4: divides the dominant function in 2. - **Examples of Figured Basses:** - Series of 7ths with exceptional resolution
###### Diatonic and Chromatic Modulation - **Different Types of Modulation:** - Cadences in C Major and A minor - **Chromatism** - Enharmonic Modulation - **Examples:** - Resolution of the Tritone
###### Dominant 7th Chord Theoretical Explanation - **Origin of the Chord** - **Inversions and Resolutions:** - Inversions affecting dominant 7ths - **Aural Training:** - Identification of chords and corresponding figuring.
Foundations of the Harmonic Series and Triad Formation
The study of harmony starts from the harmonic series to determine the nature of chords. Triads are classified according to the combination of thirds: - **Major:** Major 3rd + Minor 3rd (Perfect 5th). - **Minor:** Minor 3rd + Major 3rd (Perfect 5th). - **Augmented:** Major 3rd + Major 3rd (Augmented 5th). - **Diminished:** Minor 3rd + Minor 3rd (Diminished 5th). Table of Intervals and their Stability In counterpoint practice, interval classification determines the movement of voices: 1. **Consonances (Stable Intervals):** - **Perfect:** 8ths, 5ths, and perfect 4ths. Remember that the perfect 4th, when produced against the bass, behaves as a dissonance requiring resolution. - **Imperfect:** 3rds and 6ths (major and minor). These are the most flexible intervals for parallel movement. 2. **Dissonances (Dynamic Intervals):** - **Absolute:** Major and minor 2nds and 7ths. - **Apparent:** Includes most augmented and diminished intervals (such as the augmented 4th or diminished 5th / Tritone). Function of Triads in Scales Depending on the mode, the function and stability of degrees change: - **Major Scale:** Tonal degrees (I, IV, V) are consonant. Modal degrees (II, III, VI) are considered dynamic, and VII is diminished. - **Natural Minor Scale:** Degrees I, IV, V are minor (stable), whereas III, VI, VII are major. - **Harmonic Minor Scale:** The appearance of the leading tone alters the nature of chords: - V and VI are major. - II and VII are diminished. - III is augmented. Rules for Figuring and 4-Voice Distribution The figuring indicates the intervals from the bass to the upper voices: - **Root Position:** Figured with 5, 8, 3 or left blank. Typically, the root is doubled. - **First Inversion (6):** Figured with a 6 (or 6/3). - **Doubling rule:** Avoid doubling the bass to prevent weakening the sonority of the chord, unless the bass is a tonal degree (I, IV, V). - **Second Inversion (6/4):** Figured with 6 and 4. - Considered a passing or auxiliary chord. - **Doubling rule:** The preferred note to double is the bass (the 5th of the chord). - **Types of 6/4:** 1. **Passing:** The bass moves by stepwise motion. 2. **Cadential:** Precedes the absolute dominant, placed on the strong beat. 3. **Neighboring or Pedal:** The bass remains stationary while the upper voices move. The Dominant 7th Chord (7) This chord is built on the V degree and contains the tonal tritone (augmented 4th or diminished 5th) between the leading tone and the 7th of the chord. - **Obligatory Resolution:** - The **leading tone** must resolve up to the tonic. - The **7th** must resolve down by step to the third of the tonic chord. - **Inversions:** Depending on which note is in the bass, the figuring changes to +6 (1st inv.), +4 (2nd inv.), or 2 (3rd inv.). The "+" sign indicates the presence of the leading tone. Modulation To change key diatonically, a pivot chord belonging to both keys is used. In chromatic modulation, a note from the original key is altered to lead to the new leading tone or characteristic note of the new mode.
In-Depth Explanation: How to Realize Figured Bass
Theoretical Concept
Figured bass (also known as Basso Continuo) is a system where numerals are placed below or above the bass line to represent intervals above the bass. These intervals determine the harmonies to be filled in by the upper voices (Soprano, Alto, Tenor).
The Numerical Code
Default/Hidden Intervals: If a bass note has no number, it is assumed to be a triad in root position (5/3). Similarly, a single 6 implies a 6/3 chord.
Interval Subtraction/Addition: Intervals are always calculated from the bass note up. For example, a G in the bass with a 6 and a 4 indicates the notes C (4th) and E (6th).
Compound Intervals: Figures usually refer to simple intervals. Even if you place the note an octave or two higher, you still write 3, 5, or 6 rather than 10, 12, or 13.
Handling Accidentals
Independent Accidentals: If a #, b, or \natural appears alone, it always applies to the third above the bass.
Attached Accidentals: If an accidental is next to a number (e.g., b6), it modifies that specific interval relative to the key signature.
Slashed Numbers or Pluses: A slash through a number or a + next to it (like +4 or +6) indicates that the note should be raised by a semitone. In dominant chords, this often denotes the leading tone.
Practical Step-by-Step Realization
Identify the Key: Look at the key signature and the final cadence to determine the tonal center.
Decode the Chord: Look at the bass note and the figure to identify the chord's quality (Major, Minor, etc.) and inversion.
Voice Leading:
Start by positioning the Soprano voice to create a melodic line.
Place the Alto and Tenor voices to complete the harmony, ensuring no two voices exceed an octave distance (except between Bass and Tenor).
Parallelism: Check strictly for parallel 5ths or 8ths; these are forbidden in classical harmony.
Doubling Priority:
Root Position: Double the root.
First Inversion (6): Double a tonal degree (I, IV, or V) if it's in the chord; otherwise, double the soprano or root.
Second Inversion (6/4): Always double the bass.