Music Theory

pitch and intervals

Pitch defines how high or low a sound is, as quantified by frequency, and is organized into repeating notes (A-G) across octaves. Intervals measure the distance between two pitches and are named numerically (unison, second, third, etc.) and by quality (perfect, major, minor, diminished, augmented). Perfect intervals are unison, fourth, fifth, and octave, and major and minor are applied for seconds, thirds, sixths, and sevenths. Diminished and augmented intervals are formed by lowering or raising a note by a semitone. Intervals form melodies and harmonies, establishing the structure and emotional quality of music.

major and minor scales

Major and minor scales are the foundation of music in the Western tradition, each consisting of seven notes in a specific pattern of whole and half steps. The major scale uses the pattern W-W-H-W-W-W-H (C-D-E-F-G-A-B-C) and is bright and cheerful in sound. The minor scale exists in three forms: natural minor (W-H-W-W-H-W-W), harmonic minor (the 7th note is raised), and melodic minor (raising the 6th and 7th notes when ascending). Minor scales generally have a darker, more sombre sound. Minor scales dictate melodies and harmonies and thus the mood and tonal centre of music.

modes

Modes are forms of the major scale, each starting on a different degree and with a unique pattern of whole and half steps. The seven modes are Ionian (major scale, happy and stable), Dorian (minor with raised 6th, jazzy sound), Phrygian (minor with flattened 2nd, exotic flavour), Lydian (major with raised 4th, dreamy sound), Mixolydian (major with flattened 7th, blues sound), Aeolian (natural minor, sad), and Locrian (minor with flattened 2nd and 5th, tense and unstable). Each mode creates distinct harmonic and melodic flavours, influencing various music styles.

keys and key signatures 

Keys and key signatures specify the tonal centre of a piece of music and identify naturally sharp or flat notes. A key is focused around a major or minor scale, establishing the home note (tonic) and mood. Key signatures are at the beginning of a staff and consist of sharps or flats that apply for the length of the work. There are 12 major and 12 minor keys, each with its own unique signature (e.g., C major has no sharps or flats, G major has one sharp, F major has one flat). Key signatures enable the performer to immediately identify the tonal structure and organization of a work.

melody writing

Melody writing is the act of composing a series of notes that form an expressive and memorable musical line. An effective melody combines stepwise motion (motion by small intervals) and leaps (jumps by larger intervals) with a clear rhythmic structure. Melodies typically follow a scale or mode and are delineated by phrasing, contour, and repetition to create coherence. Successful melodies will emphasize the tonic, dominant, and other chord tones to create harmonic stability. Techniques like motif development, call-and-response, and variation increase musical interest. A good melody is singable, expressive, and fits the harmonic and rhythmic nature of the piece.

functional harmony

Functional harmony is the structure of the interrelation among chords that create movement and resolution in tonal music. It relies on the tonic (I), dominant (V), and subdominant (IV) chords that create tension and release. Tonic is the tonic chord, dominant creates tension that is eager to resolve, and subdominant is contrasting. Passing or intermediate harmonies are the other chords such as supertonic (ii), mediant (iii), and submediant (vi). Standard patterns like I-IV-V-I or ii-V-I promote tonal stability. Functional harmony guides chord progression, shaping musical phrasing and affect through predictable but varied relations.

circle of 5ths 

The Circle of Fifths is a chart that places keys into proximity with each other in ascending perfect fifths. Starting at C major (no sharps or flats), each move to the right adds one sharp (G, D, A, etc.), and to the left one flat (F, B♭, E♭, etc.). It also shows relative minor keys, which share the same key signature as their major counterparts (A minor for C major, for instance). The circle makes it easy to understand key relationships, chord progression, and modulation, and is thus essential for composition, improvisation, and harmonic analysis.

modal interchange

The Circle of Fifths is a diagrammatic tool that organizes keys by their relationship to each other in ascending perfect fifths. Starting with C major (no sharps or flats), clockwise every step adds one sharp (G, D, A, etc.), and counter clockwise adds one flat (F, B♭, E♭, etc.). It also shows relative minor keys, with the same key signature as the major equivalent (e.g., A minor to C major). The circle helps musicians understand key relationships, chord progressions, and modulation and is therefore an essential tool in composition, improvisation, and harmonic analysis.

dominant 7th and extended chords

Dominant 7th and extended chords add harmonic richness and tension. A dominant 7th chord (V7) is a major triad with a minor seventh (e.g., G7: G-B-D-F) and creates a strong tendency to the tonic, commonly used in cadences. Extended chords go beyond the 7th by adding 9ths, 11ths, or 13ths (e.g., C9: C-E-G-B♭-D), which introduce harmonic colour and complexity. They are essential in jazz, blues, and contemporary music, contributing depth and expressiveness as well as harmonic progression and voice leading guidance.

secondary dominants

Secondary dominants are chords that temporarily function as the dominant (V) of a non-tonic chord and create tension and more powerful harmonic motion. Notated as V/x (as in V7/V for "five of five"), they temporarily tonicize a fresh chord within a key. In C major, for example, D7 (V7 of G) is a secondary dominant resolving on G (V). They produce colour, tension, and modulation-like effects without changing the key entirely, thus producing more dynamic and richer-sounding progressions. They have wide applications in classical, jazz, and pop music.

note values

Note values determine the length for which a note or a rest must be sounded. The most common note values are:

• -Whole note (semibreve) – 4 beats

• Half note (minim) – 2 beats

• Quarter note (crotchet) – 1 beat

• Eighth note (quaver) – 1/2 beat

• Sixteenth note (semiquaver) – 1/4 beat

Rests are symbols representing silence and share the same values (whole rest, half rest, etc.). Brief note values (like triplets or dots) divide or extend the length, adding rhythmic interest. Note values need to be understood for playing back, writing, and playing music properly.

time signatures

Time signatures inform us about how many beats in a measure and what note value takes one beat. The top number informs us about how many beats in a measure, and the bottom number informs us about which note takes one beat. Some of the most common time signatures are:

• 4/4 (common time)– Four beats in a measure, quarter note gets one beat

• 3/4 – Three beats in a measure, quarter note receives one beat (most often used in waltz)

• 2/4 – Two beats to a bar, quarter note gets one beat

• 6/8 – Six to the measure, eighth note takes one beat (widely used in compound time)

Time signatures govern the rhythm of a work, determining the way the music is organized, phrased, and played.

rhythm and beats 

Rhythm is the pattern of silence and sound in music, derived from the arrangement of rests and notes in time. Beats are the unit of time within music, normally heard as the constant pulse that underpins a piece. Rhythmic values (e.g., whole, half, quarter, eighth note) specify how long each sound or silence. Rhythms can be simple, with equally spaced beats, or complex, with syncopation (stressing off-beats) and polyrhythm (simultaneous multiple rhythms). The relationship between rhythm and beats creates the groove and motion of a work, determining the feel and general movement of the music.

tempo

Tempo refers to the speed at which a piece of music is played, typically measured in beats per minute (BPM). It determines the pace of the music, affecting its overall energy and mood. Some standard tempo markings include:

• Largo– Very slow

• Adagio– Slow

• Andante– Moderately slow

• Moderato– Moderate pace

• Allegro-  Fast

• Presto– Very quick

Changes in tempo, like accelerando (gradually slower) or ritardando (gradually faster), add expressiveness and movement to music. Tempo is important in determining how a piece is played and how its rhythmic elements are heard.

dynamics

Dynamics are the loudness or volume of sound in music, informing us how loudly or softly a piece is to be played. They add emotion and contrast to music. Some dynamic markings are as follows:

• Piano (p)– Soft

• Forte (f)– Loud

• Mezzo piano (mp)– Moderately soft

• Mezzo forte (mf)– Moderately loud

• Crescendo (cresc.)– Gradually getting louder

• Decrescendo (decresc.) or Diminuendo (dim.)– Gradually getting softer

Dynamics, including sudden variations (known as sforzando or sfz) or subtle nuances, contribute to expressiveness, helping in the building of emotional effect and overall structure of a musical composition.

articulations

Articulations are musical markings that govern the way the notes should be played or sung, with some effect upon their attack, duration, and release. Articulations communicate style and expression. Some common articulations are:

• Staccato– Detached short notes

• Legato– Connected smooth notes without separation between them

• Accent – A single note played louder or with greater attack

• Tenuto– The note is held to its full value, often with a slightly accented attack

• Marcato– The note is attacked with a forceful, accented stroke

• Fermata– The note or rest is held longer than its specified value

Articulations help to form the contours of phrasing and expression in music as well as further establish the nature and mood of a performance.

terms

Terms are defined in music as specific directions or descriptions that guide the performance, interpretation, and structure of a piece of music. They tend to be in Italian and serve to determine the manner in which the music will be performed. Common terms include:

• Allegro– Spirited and brisk

• Adagio– Majestic and slow

• Vivace– Highly spirited and rapid

• Andante– Slow but not slow, usually translated as "walking speed"

• Fermata– Pause or hold on a note or rest

• Crescendo– Getting louder gradually

• Decrescendo or Diminuendo– Getting softer gradually

• D.C. al Fine– Go back to the start and play until fine

• Coda-  Final section of a piece

They help performers to understand the stylistic and emotional content of the music so that performances are consistent in interpretation and expression.