Intervals are the building blocks of music, measuring the distance between pitches. They're crucial for understanding scales, chords, and harmony. Mastering interval identification and construction is key to developing your musical ear and theory knowledge.

In this section, we'll explore how to identify and construct intervals. You'll learn to measure pitch distances, determine interval sizes and qualities, and analyze melodic and harmonic intervals. This knowledge will help you read music, compose, and understand chord progressions better.

Interval Identification

Measuring Distance Between Pitches

• An interval is the distance between two pitches, measured by the number of half steps or whole steps between them
• Half steps and whole steps are the building blocks of intervals
  • A half step is the smallest possible interval in Western music, equivalent to the distance between two adjacent keys on a piano (white to black, black to white, or white to white)
  • A whole step is equal to two half steps, equivalent to the distance between two keys with one key in between them on a piano (white to white, skipping over a black key)

Determining Interval Size

• Interval size is determined by counting the number of letter names (inclusive) between the two pitches, with the starting pitch counted as 1
• Intervals can range from a unison (same pitch) to a 15th or beyond
  • Intervals up to an octave are called simple intervals (unison, 2nd, 3rd, 4th, 5th, 6th, 7th, octave)
  • Intervals larger than an octave are called compound intervals (9th, 10th, 11th, 12th, 13th, 14th, 15th, etc.)

Determining Interval Quality

• Interval quality is determined by the number of half steps between the two pitches, relative to the major scale of the lower pitch
• The five main interval qualities are perfect, major, minor, augmented, and diminished
  • Perfect intervals (unison, 4th, 5th, octave) are neither major nor minor and remain perfect when inverted
    • Augmented and diminished intervals are alterations of perfect intervals (augmented 4th, diminished 5th)
  • Major intervals (2nd, 3rd, 6th, 7th) can be made minor by lowering the upper pitch by a half step, or augmented by raising the upper pitch by a half step
  • Minor intervals can be made diminished by lowering the upper pitch by a half step

Interval Construction

Constructing Intervals Above a Given Note

• To construct an interval above a given note, first determine the letter name of the upper note based on the interval size, then adjust accidentals to match the desired quality
  • For example, to construct a major 6th above C, first find the 6th letter name above C (counting C as 1), which is A. Then, adjust the accidentals to create a major 6th (9 half steps) by adding a sharp to A, resulting in A♯
• Constructing a compound interval (larger than an octave) involves the same process as constructing a simple interval within an octave, then displacing the upper note by one or more octaves
  • For example, to construct a major 13th above C, first construct a major 6th (A♯) and then displace the upper note up an octave, resulting in a major 13th from C to A♯

Constructing Intervals Below a Given Note

• To construct an interval below a given note, first determine the letter name of the lower note based on the interval size, then adjust accidentals to match the desired quality
  • For example, to construct a perfect 5th below D, first find the 5th letter name below D (counting D as 1), which is G. Then, adjust the accidentals to create a perfect 5th (7 half steps) by leaving G natural
• Constructing a compound interval below a given note involves the same process as constructing a simple interval within an octave, then displacing the lower note by one or more octaves
  • For example, to construct a perfect 12th below A, first construct a perfect 5th (E) and then displace the lower note down an octave, resulting in a perfect 12th from A down to E

Interval Analysis

Melodic Intervals

• Melodic intervals occur between two pitches sounded consecutively (one after the other) as part of a melody
• Analyzing melodic intervals involves identifying the quality and size of intervals between successive pitches
  • For example, in the melody C-E-G-C, the melodic intervals are a major 3rd (C to E), a minor 3rd (E to G), and a perfect 4th (G to C)
• Understanding melodic intervals helps in recognizing melodic patterns, motifs, and overall melodic structure

Harmonic Intervals

• Harmonic intervals occur between two pitches sounded simultaneously (together) as part of a chord
• Analyzing harmonic intervals involves identifying the quality and size of intervals between concurrent pitches
  • For example, in a C major triad (C-E-G), the harmonic intervals are a major 3rd (C to E), a minor 3rd (E to G), and a perfect 5th (C to G)
• Harmonic interval analysis aids in understanding chord structure, harmonic progression, and the overall tonality of a musical passage

Consonance vs Dissonance

Defining Consonance and Dissonance

• Consonance and dissonance refer to the perceived stability or instability of an interval, which can vary depending on musical style and context
• Consonant intervals are generally considered stable and pleasant sounding
  • Perfect intervals (unison, 4th, 5th, octave) and major/minor 3rds and 6ths are typically treated as consonant
• Dissonant intervals are generally considered unstable and tense sounding, often requiring resolution to a consonant interval
  • Major/minor 2nds and 7ths, along with all augmented and diminished intervals, are typically treated as dissonant

Factors Affecting Consonance and Dissonance

• The consonance or dissonance of an interval can be affected by its harmonic context, as well as its preparation and resolution within a musical passage
  • For example, a perfect 4th is considered consonant when used as part of a consonant triad (C-F-A), but can be perceived as dissonant when used as a melodic interval requiring resolution (F-B resolving to E-C)
• Musical style and cultural norms also play a role in determining the perceived consonance or dissonance of intervals
  • For example, in medieval music, perfect 4ths were considered consonant, while in later Western classical music, they were often treated as dissonant when used melodically