Open Music Theory

Open Music Theory is organized into several major pedagogical domains. You can navigate the curriculum through the following high-level modules:

• Fundamentals: Basic notation, meter, pitches, scales, intervals, and triads.
• Voice-leading and model composition: Strict counterpoint (species), thoroughbass, and melodic keyboard style.
• Harmony: Musical functions, harmonic syntax, cadences, and modulation.
• Form: Classical thematic structures (sentence, period), Sonata form, Rondo form, and Galant schemata.
• Post-tonal music: Pitch-class set theory, modular 12 arithmetic, and twelve-tone theory.
• Pop/rock music: Rhythm (syncopation), harmony (common progressions), and formal structures.
• Text and music: Analyzing poetry.

Classical musical themes can be categorized into several structural types based on William Caplin’s Classical Form. These types include:

• Sentence: A specific structural type (see sentence.html).
• Period: A specific structural type (see period.html).
• Hybrid themes: Themes that combine characteristics of other types (see hybridThemes.html).
• Compound themes: Complex structures such as Compound periods or Compound sentences.
• Small Ternary: A specific structural type (see smallTernary.html).
• Small Binary: A specific structural type (see smallBinary.html).

For a functional analysis of these structures, refer to the Classical theme functions guide.

Intervals can be categorized along a scale from most concrete to most abstract:

1. Ordered Pitch Interval (Most Concrete): Specific pitches, specific direction (+/-).
2. Unordered Pitch Interval: Specific pitches, shortest distance.
3. Ordered Pitch-Class Interval: Pitch classes, clockwise direction.
4. Unordered Pitch-Class Interval / Interval Class (Most Abstract): Pitch classes, shortest distance.

An appoggiatura is a specific type of accented incomplete neighbor tone.

Key characteristics:

• Approach: Approached by leap (usually up).
• Resolution: Followed by step (usually down, but always in the opposite direction of the preceding leap) to a more stable tone.

The Recapitulation is the A' section of the minuet's small ternary structure. To identify a recapitulation, look for these three definitive characteristics:

1. Return of the basic idea: The return of the material from the A section at the beginning.
2. Return of the home key: The return of the tonic key at the beginning.
3. Final PAC: A final Perfect Authentic Cadence (PAC) in the home key.

While it typically copies the thematic and phrase-structural features of the exposition, it often alters the secondary theme to end in the tonic and may expand the exposition's closing phrase.

A Hybrid 1 theme is a combination of an antecedent phrase and a continuation phrase.

In this structure, the antecedent phrase typically follows a complete presentation–continuation–cadential function progression. The subsequent continuation phrase is incomplete, often characterized by fragmentation and increased surface rhythm, eventually leading to a cadential function (e.g., a V:PAC).

In pop/rock, rhythms often approximate triplets using simple divisions (2, 4, 8) rather than true triplets. These are known as fake triplets.

Fake Triplets

Instead of dividing a beat into three equal parts, a beat (or two) is divided into almost-equal groups. The most common grouping is 3+3+2 (e.g., two dotted-eighth notes followed by an eighth note to fill a half note). Other possible groupings include:

• 3+2+3
• 2+3+3

Fake Sextuplets

This pattern occurs when the 3+3+2 grouping is doubled, resulting in a 3+3+3+3+2+2 pattern. This is often used when playing subdivisions like sixteenth notes.

Closing functions occur at the end of a theme or phrase to provide resolution.

• Cadential function: Involves a cadential harmonic progression and a conventional descending melodic pattern. It moves from the last chord of tonic prolongation to a cadential arrival (PAC, IAC, or HC).
• Consequent function: Similar to the antecedent function, it presents a basic idea followed by a contrasting one. However, unlike the antecedent, the consequent brings completion to the thematic unit and ends with a strong cadence, typically a Perfect Authentic Cadence (PAC).

A direct modulation occurs when a chord in the previous key is followed immediately by a chord in the new key without a smooth transition or overlap.

If this occurs at a phrase boundary (e.g., the old-key tonic ends a phrase and the new-key tonic begins the next), it is called a phrase modulation. This is common at the end of an exposition in minuet or sonata forms.

Notation for harmonic analysis: Follow the last chord in the old key with the new key, a colon, and then the first chord in the new key.

Example (G major to A minor): G: I II V I Am: I . . .

Example (Functional notation): G: T1 S4 D5 T1 Am: T1 . . .

A deceptive resolution occurs when a D5 (V or V⁷) chord progresses to VI instead of the expected I (authentic cadence).

Implementation Details

• Tendency Tone Resolution: It is critical that ti resolves to do (as it would in an authentic cadence) rather than la/le. This ensures the role of the tendency tone is fulfilled and avoids the dissonant augmented second (ti–le) in minor keys.
• Doubling: This resolution results in a non-standard doubling of the VI chord (do, rather than the bass).

The Essential Sonata Closure (ESC) is the primary harmonic goal of the recapitulation and the entire sonata movement.

To identify the ESC:

1. Look for a I:PAC (Tonic:Perfect Authentic Cadence).
2. Locate the point that typically corresponds to the same thematic position as the EEC (Essential Expositional Closure) in the exposition.
3. Check if the music is a transposition of the exposition's secondary key material into the home key.