Intervals are the building blocks of music, defining the relationships between pitches. They play a crucial role in creating melodies, harmonies, and chords. Understanding interval sizes and qualities is essential for musicians to analyze and create music effectively.

This topic explores various interval types, from unisons to octaves and beyond. It covers how to identify, construct, and invert intervals, as well as their role in musical context. Mastering intervals enhances overall musicianship and deepens one's understanding of musical structures.

Interval sizes

• Intervals are the distance between two pitches, measured by the number of staff positions or scale steps they encompass
• Interval size is determined by counting the lines and spaces on the staff, including the starting and ending notes
• Intervals can be categorized based on their size, ranging from unison to intervals larger than an octave

Unison intervals

• Unison intervals occur when two notes have the same pitch and are played together
• Unison intervals can be written on the same line or space on the staff
• Examples of unison intervals include two C notes played simultaneously or two G notes played together

Second intervals

• Second intervals encompass two adjacent notes on the staff, either a line and a space or two adjacent lines or spaces
• Second intervals can be major (whole step) or minor (half step) depending on the number of semitones between the notes
• Examples of second intervals include C to D (major second) and E to F (minor second)

Third intervals

• Third intervals span three notes on the staff, skipping one note in between the starting and ending notes
• Third intervals can be major (two whole steps) or minor (whole step + half step) based on their semitone content
• Examples of third intervals include C to E (major third) and D to F (minor third)

Fourth intervals

• Fourth intervals encompass four notes on the staff, skipping two notes between the starting and ending notes
• Perfect fourth intervals consist of two whole steps and one half step (five semitones)
• Examples of fourth intervals include C to F (perfect fourth) and F to B (augmented fourth or tritone)

Fifth intervals

• Fifth intervals span five notes on the staff, skipping three notes between the starting and ending notes
• Perfect fifth intervals are composed of three whole steps and one half step (seven semitones)
• Examples of fifth intervals include C to G (perfect fifth) and B to F (diminished fifth or tritone)

Sixth intervals

• Sixth intervals encompass six notes on the staff, skipping four notes between the starting and ending notes
• Sixth intervals can be major (nine semitones) or minor (eight semitones) based on their semitone content
• Examples of sixth intervals include C to A (major sixth) and E to C (minor sixth)

Seventh intervals

• Seventh intervals span seven notes on the staff, skipping five notes between the starting and ending notes
• Seventh intervals can be major (eleven semitones) or minor (ten semitones) depending on the number of semitones
• Examples of seventh intervals include C to B (major seventh) and D to C (minor seventh)

Octave intervals

• Octave intervals encompass eight notes on the staff, spanning from one note to the same note in the next higher or lower octave
• Octave intervals consist of twelve semitones and are considered perfect intervals
• Examples of octave intervals include C to C' (one octave higher) and G to G, (one octave lower)

Intervals larger than octave

• Intervals larger than an octave exceed the span of eight notes on the staff
• These intervals are named by combining the interval quality with the number of octaves plus the interval size within the additional octave
• Examples of intervals larger than an octave include C to E' (major tenth, one octave plus a third) and F to D'' (perfect eleventh, one octave plus a fourth)

Interval qualities

• Interval quality refers to the specific type of interval based on the number of semitones it contains
• The five main interval qualities are perfect, major, minor, diminished, and augmented
• Interval quality is determined by the relationship between the two notes in terms of their position in the major or minor scale

Perfect intervals

• Perfect intervals are highly consonant and stable, occurring naturally in the major scale
• Perfect intervals include unison, fourth, fifth, and octave
• Examples of perfect intervals include C to G (perfect fifth) and F to F' (perfect octave)

Major intervals

• Major intervals are formed by the intervals of a second, third, sixth, and seventh in a major scale
• Major intervals are wider than their minor counterparts by one semitone
• Examples of major intervals include C to E (major third) and G to B (major third)

Minor intervals

• Minor intervals are one semitone smaller than their corresponding major intervals
• Minor intervals include the second, third, sixth, and seventh intervals in a natural minor scale
• Examples of minor intervals include D to F (minor third) and A to C (minor third)

Diminished intervals

• Diminished intervals are one semitone smaller than their corresponding minor intervals or one semitone smaller than perfect intervals
• Diminished intervals can be formed by lowering the upper note or raising the lower note of a minor or perfect interval by a half step
• Examples of diminished intervals include C to G♭ (diminished fifth) and F to B (diminished fifth or tritone)

Augmented intervals

• Augmented intervals are one semitone larger than their corresponding major intervals or one semitone larger than perfect intervals
• Augmented intervals can be formed by raising the upper note or lowering the lower note of a major or perfect interval by a half step
• Examples of augmented intervals include C to F♯ (augmented fourth or tritone) and E to C♯ (augmented sixth)

Interval naming conventions

• Interval naming conventions provide a standardized way to describe and categorize intervals based on their characteristics
• The three main categories for naming intervals are diatonic vs chromatic, simple vs compound, and consonant vs dissonant
• Understanding these naming conventions is essential for effective communication and analysis of intervals in music theory and practice

Diatonic vs chromatic intervals

• Diatonic intervals are formed by notes within the same diatonic scale (e.g., C major scale) without any accidentals
• Chromatic intervals involve notes outside the diatonic scale and include one or more accidentals (sharps, flats, or naturals)
• Examples of diatonic intervals include C to E (major third in C major) and G to B (major third in G major), while examples of chromatic intervals include C to E♭ (minor third) and F to B (tritone)

Simple vs compound intervals

• Simple intervals are intervals that are smaller than or equal to an octave (unison up to seventh)
• Compound intervals are larger than an octave and can be reduced to a simple interval by subtracting one or more octaves
• Examples of simple intervals include C to G (perfect fifth) and E to C (minor sixth), while examples of compound intervals include C to E' (major tenth, compound third) and G to F' (minor seventh, compound second)

Consonant vs dissonant intervals

• Consonant intervals are intervals that sound stable, harmonious, and resolved, often found in triads and stable chord progressions
• Dissonant intervals create tension, instability, and a need for resolution, often used to add interest and movement to a musical piece
• Perfect intervals (unison, fourth, fifth, octave) and major/minor thirds and sixths are considered consonant, while major/minor seconds and sevenths, along with all diminished and augmented intervals, are considered dissonant

Interval inversion

• Interval inversion is the process of flipping an interval upside down by moving one of the notes up or down an octave
• Inverting an interval changes its size and quality while maintaining the same overall sound and function within the musical context
• Understanding interval inversion is crucial for analyzing and creating harmonies, as well as for transposing and rearranging musical passages

Inversion process

• To invert an interval, move either the upper note down an octave or the lower note up an octave
• The resulting inverted interval will have a complementary size that adds up to nine (e.g., a third inverts to a sixth, a fourth inverts to a fifth)
• Examples of interval inversion include inverting a C to E interval (major third) to E to C' (minor sixth) by moving the upper note down an octave, or inverting a G to D interval (perfect fifth) to D to G' (perfect fourth) by moving the lower note up an octave

Resultant interval qualities

• When inverting an interval, the quality of the resulting interval changes according to a specific pattern
• Perfect intervals (unison, fourth, fifth, octave) remain perfect when inverted
• Major intervals become minor, and minor intervals become major
• Augmented intervals become diminished, and diminished intervals become augmented
• Examples of resultant interval qualities include inverting a C to E interval (major third) to E to C' (minor sixth), or inverting a C to G♯ interval (augmented fifth) to G♯ to C' (diminished fourth)

Inversion of compound intervals

• Compound intervals can be inverted by first reducing them to their simple interval equivalents, inverting the simple interval, and then adding octaves back to the resulting interval
• The inversion process for compound intervals follows the same rules as for simple intervals regarding size and quality changes
• Examples of inverting compound intervals include inverting a C to A' interval (major sixth, compound third) to A to C' (minor third) by reducing it to a simple interval, inverting, and adding an octave back, or inverting an E to F'' interval (minor ninth, compound second) to F to E' (major seventh) using the same process

Interval identification

• Interval identification is the skill of recognizing and naming intervals in both aural and visual contexts
• Developing the ability to identify intervals quickly and accurately is essential for sight-reading, transcription, improvisation, and overall musicianship
• Interval identification can be practiced through various exercises and techniques, including aural recognition, visual identification in notation, and interval ear training

Aural recognition of intervals

• Aural recognition involves identifying intervals by ear, without the aid of visual notation
• Strategies for improving aural recognition include associating intervals with familiar songs or melodies, singing intervals using solfege or scale degrees, and practicing with interval recognition software or apps
• Examples of aural recognition exercises include identifying intervals played on a piano, guitar, or other instrument, or recognizing intervals within a melodic or harmonic context in a musical recording

Visual identification in notation

• Visual identification involves recognizing intervals as they appear in written musical notation
• Strategies for improving visual identification include analyzing the distance between notes on the staff, considering accidentals and key signatures, and relating intervals to common scales, chords, and melodic patterns
• Examples of visual identification exercises include naming intervals in a written melody, identifying intervals within a chord progression, or analyzing intervals in a full musical score

Interval ear training exercises

• Interval ear training exercises are designed to help musicians improve their aural recognition skills through targeted practice and repetition
• These exercises can include interval comparison (identifying whether two intervals are the same or different), interval singing (reproducing intervals using the voice), and interval dictation (notating intervals played by an instructor or recording)
• Online resources, such as ear training websites and mobile apps, offer a variety of interval ear training exercises that can be customized to individual skill levels and learning goals

Interval construction

• Interval construction is the process of building intervals on a staff or by using semitones, either within a specific key or in a more general context
• Understanding how to construct intervals is essential for composition, arranging, and analyzing musical structures
• Interval construction can be approached through various methods, including visual placement on a staff, counting semitones, and considering the context of a particular key or tonality

Interval construction on staff

• Constructing intervals on a staff involves placing notes on the appropriate lines and spaces to create the desired interval size and quality
• This method relies on visual recognition of the distance between notes and an understanding of how accidentals (sharps, flats, and naturals) affect interval quality
• Examples of interval construction on a staff include building a major third above a given note by counting three half steps up on the staff, or constructing a perfect fifth below a note by counting seven half steps down

Interval construction by semitones

• Constructing intervals by semitones involves counting the number of half steps between two notes to determine the size and quality of the interval
• This method is particularly useful for understanding the relationship between interval size and quality, as well as for constructing intervals outside of a specific key or tonal context
• Examples of interval construction by semitones include building a minor sixth by counting eight half steps above a given note, or constructing an augmented fourth (tritone) by counting six half steps above a note

Interval construction in different keys

• Constructing intervals within the context of a specific key requires an understanding of the key signature and the role of accidentals in modifying interval qualities
• In this method, intervals are constructed using the diatonic notes of the key, with accidentals introduced as needed to create the desired interval quality
• Examples of interval construction in different keys include building a major third in the key of D major (F♯ to A), or constructing a diminished fifth in the key of B minor (F♯ to C)

Intervals in musical context

• Intervals play a crucial role in creating the melodic, harmonic, and structural elements of music
• Understanding how intervals function within various musical contexts is essential for composition, improvisation, and analysis
• Intervals can be examined in terms of their use in melody, harmony, and chord construction, each of which contributes to the overall character and emotional impact of a piece of music

Intervals in melody

• Melodic intervals are the building blocks of melodies, determining the shape, contour, and expressive qualities of a musical line
• Composers and improvisers use a variety of intervals to create melodic interest, tension, and resolution, often combining stepwise motion (seconds) with leaps (thirds, fourths, fifths, and larger intervals) to create a sense of direction and phrasing
• Examples of intervals in melody include the opening theme of Beethoven's "Fifth Symphony" (minor third, major second, and perfect fourth), or the iconic opening of "Somewhere Over the Rainbow" (octave leap followed by a descending major sixth)

Intervals in harmony

• Harmonic intervals are the foundation of chords and chord progressions, creating the vertical sonorities that support and enrich the melodic and rhythmic elements of a piece
• Consonant intervals (thirds, sixths, perfect fourths, and fifths) are often used to create stable, pleasing harmonies, while dissonant intervals (seconds, sevenths, and tritones) add tension and a sense of movement or instability
• Examples of intervals in harmony include the stacked thirds of a C major triad (C-E, E-G) or the perfect fifth and major third of a D dominant seventh chord (D-A, F♯-C)

Intervals in chord construction

• Chords are built by stacking intervals above a root note, with the quality and type of chord determined by the specific intervals used
• Triads, the most basic type of chord, are constructed using a root, third, and fifth, with the quality of the third and fifth determining whether the triad is major, minor, diminished, or augmented
• Seventh chords and extended chords are created by adding additional thirds above the basic triad structure, with the quality of these additional intervals contributing to the chord's overall sound and function
• Examples of intervals in chord construction include the major third and perfect fifth of a major triad (C-E-G), or the minor third, diminished fifth, and minor seventh of a half-diminished seventh chord (B-D-F-A)