Discuss the process of building and analyzing chords, including triads and extended chords.

Building and analyzing chords is a fundamental aspect of music theory and understanding harmony. Chords are created by combining multiple notes played simultaneously, and they form the harmonic foundation of a piece of music. Two primary types of chords are triads and extended chords, each with its own structure and characteristics.

1. Triads:
Triads are three-note chords consisting of a root, a third, and a fifth. The quality of the triad (major, minor, diminished, or augmented) is determined by the intervals between these three notes.

* Major Triad: A major triad has a root, a major third (four semitones above the root), and a perfect fifth (seven semitones above the root). For example, a C major triad includes the notes C, E, and G.
* Minor Triad: A minor triad has a root, a minor third (three semitones above the root), and a perfect fifth. For example, a C minor triad includes the notes C, Eb, and G.
* Diminished Triad: A diminished triad has a root, a minor third, and a diminished fifth (six semitones above the root). For example, a C diminished triad includes the notes C, Eb, and Gb.
* Augmented Triad: An augmented triad has a root, a major third, and an augmented fifth (eight semitones above the root). For example, a C augmented triad includes the notes C, E, and G#.
2. Extended Chords:
Extended chords are chords that go beyond the basic triad structure by adding additional notes. These additional notes are typically seventh, ninth, eleventh, or thirteenth intervals above the root. The most common extended chords are seventh chords.

* Major Seventh Chord: A major seventh chord adds a major seventh interval (eleven semitones above the root) to a major triad. For example, a C major seventh chord includes the notes C, E, G, and B.
* Dominant Seventh Chord: A dominant seventh chord adds a minor seventh interval (ten semitones above the root) to a major triad. For example, a C dominant seventh chord includes the notes C, E, G, and Bb.
* Minor Seventh Chord: A minor seventh chord adds a minor seventh interval to a minor triad. For example, a C minor seventh chord includes the notes C, Eb, G, and Bb.
* Diminished Seventh Chord: A diminished seventh chord adds a diminished seventh interval (nine semitones above the root) to a diminished triad. For example, a C diminished seventh chord includes the notes C, Eb, Gb, and Bbb.

Analyzing chords involves identifying the individual notes that make up a chord and determining its quality and function within a harmonic context. This process includes understanding the intervals between the chord tones, recognizing common chord progressions, and interpreting their role in the overall tonal structure of a piece. Chord analysis helps musicians and composers in creating and arranging harmonies, improvising melodies, and understanding the harmonic choices made by other composers.