5.2 Interval inversion
7 min read•august 20, 2024
is a key concept in music theory that involves flipping intervals upside down by switching the positions of notes. This technique changes the sound and properties of intervals while maintaining their relationship, allowing for variety in melodies and harmonies.
Understanding interval inversion is crucial for analyzing and composing music. It follows specific rules, such as the principle and quality changes. Mastering this concept helps musicians create interesting musical structures and develop their ear training skills.
Definition of interval inversion
- Interval inversion is a fundamental concept in music theory that involves flipping an interval upside down by switching the positions of the upper and lower notes
- Inverting an interval changes its sound and properties while maintaining a close relationship to the original interval
- Understanding interval inversion is crucial for analyzing and composing music, as it provides a way to create variety and interest in melodic and harmonic structures
Concept vs notation
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- The concept of interval inversion refers to the idea of reversing the positions of the notes in an interval, with the lower note becoming the upper note and vice versa
- In notation, interval inversion is represented by writing the above or below the original interval, using the same note names but with different accidentals and octave placement
- Inverted intervals are often labeled with the same interval number as the original interval, but with a different quality (such as major becoming minor or perfect becoming perfect)
Inversion of harmonic intervals
- Harmonic intervals are intervals in which the two notes are played simultaneously, creating a vertical sonority
- When a harmonic interval is inverted, the resulting inverted interval will have a different quality and sound, but will still be recognizable as related to the original interval
- Inverting harmonic intervals can create interesting chord voicings and harmonies, as the inverted intervals will have different relationships to the root note of the chord
Inversion of melodic intervals
- Melodic intervals are intervals in which the two notes are played sequentially, creating a horizontal melody line
- Inverting a melodic interval involves reversing the direction of the interval, so that an ascending interval becomes descending and vice versa
- Inverted melodic intervals will have the same interval number as the original interval, but with a different quality and a reversed direction, creating a mirror image of the original melody
Interval inversion rules
- There are several key rules and patterns that govern the process of interval inversion, which can help in quickly determining the properties of inverted intervals
- Understanding these rules is essential for accurately analyzing and notating inverted intervals in music theory and practice
- The interval inversion rules relate to the sum of the original and inverted intervals, the changes in , and the changes in interval number
Inversion sum of 9
- One of the fundamental rules of interval inversion is that the sum of an interval and its inversion always equals 9
- For example, a (interval number 5) inverted becomes a perfect fourth (interval number 4), and 5 + 4 = 9
- This rule holds true for all simple intervals, and can be used to quickly determine the interval number of an inverted interval by subtracting the original interval number from 9
Interval quality changes
- When an interval is inverted, its quality (such as major, minor, perfect, augmented, or diminished) will change according to a specific pattern
- Perfect intervals (unison, fourth, fifth, and octave) remain perfect when inverted
- Major intervals become minor when inverted, and minor intervals become major
- Augmented intervals become diminished when inverted, and diminished intervals become augmented
Interval number changes
- The interval number (such as second, third, sixth, or seventh) also changes in a predictable way when an interval is inverted
- The new interval number of an inverted interval can be determined by subtracting the original interval number from 9
- For example, a second (interval number 2) becomes a seventh (interval number 7) when inverted, as 9 - 2 = 7
- A third becomes a sixth, a fourth becomes a fifth, and so on, with the sum of the original and inverted interval numbers always equaling 9
Inverting specific intervals
- While the general rules of interval inversion apply to all intervals, it can be helpful to examine the specific properties and patterns of inverted intervals for each interval quality
- Understanding how perfect, major, minor, augmented, and diminished intervals behave when inverted can aid in quickly recognizing and notating inverted intervals in music
- Each quality of interval has its own unique sound and musical effect, both in its original form and when inverted
Inversion of perfect intervals
- Perfect intervals (unison, fourth, fifth, and octave) remain perfect when inverted
- A perfect unison inverts to a perfect octave, a perfect fourth inverts to a perfect fifth, and vice versa
- The perfect intervals are the most stable and consonant intervals, and their inverted forms maintain this stability and consonance
Inversion of major intervals
- Major intervals (second, third, sixth, and seventh) become minor when inverted
- A major second becomes a minor seventh, a becomes a minor sixth, and so on
- The bright, happy sound of major intervals becomes darker and more melancholic when inverted to their minor counterparts
Inversion of minor intervals
- Minor intervals (second, third, sixth, and seventh) become major when inverted
- A minor second becomes a major seventh, a minor third becomes a major sixth, and so on
- The sad, introspective sound of minor intervals becomes brighter and more optimistic when inverted to their major counterparts
Inversion of augmented intervals
- Augmented intervals (second, third, fourth, fifth, sixth, and seventh) become diminished when inverted
- An augmented second becomes a diminished seventh, an augmented fourth becomes a diminished fifth, and so on
- The tense, unstable sound of augmented intervals becomes even more dissonant and unsettled when inverted to their diminished counterparts
Inversion of diminished intervals
- Diminished intervals (second, third, fourth, fifth, sixth, and seventh) become augmented when inverted
- A diminished third becomes an augmented sixth, a diminished fifth becomes an augmented fourth, and so on
- The harsh, jarring sound of diminished intervals becomes slightly less dissonant but still tense and unstable when inverted to their augmented counterparts
Compound interval inversion
- Compound intervals, which are intervals larger than an octave, can also be inverted using the same principles as simple intervals
- However, the process of inverting compound intervals involves an additional step of octave reduction, which can affect the resulting interval quality and number
- Understanding how to invert compound intervals is important for analyzing and composing music that spans a wide range, and for recognizing the relationships between intervals across multiple octaves
Octave equivalence in inversion
- When inverting a , the first step is to reduce the interval to its simple interval equivalent by removing any octaves
- This is because intervals that are an octave apart are considered to be equivalent in terms of their and musical effect
- For example, a compound major tenth (an octave plus a major third) would first be reduced to a simple major third before being inverted
Calculating compound interval inversions
- Once the compound interval has been reduced to its simple interval equivalent, the inversion can be calculated using the same rules as for simple intervals
- The inverted simple interval can then be expanded back into a compound interval by adding one or more octaves as needed
- For example, a compound major tenth (an octave plus a major third) would be reduced to a major third, inverted to a minor sixth, and then expanded to a compound minor thirteenth (an octave plus a minor sixth)
Applications of interval inversion
- Interval inversion is not just a theoretical concept, but has many practical applications in the composition, analysis, and performance of music
- Composers can use interval inversion to create interesting melodic and harmonic structures, to vary and develop musical themes, and to modulate to different keys
- Music theorists and analysts can use interval inversion to identify patterns and relationships in musical works, and to understand the underlying structure and logic of a composition
Interval inversion in composition
- Composers often use interval inversion as a tool for generating new musical ideas and creating coherence and unity within a piece
- By inverting a melodic or harmonic interval, a composer can create a sense of balance and symmetry, or can introduce tension and contrast
- Inverting a melody can also help to fit it within a desired range or to create a counter-melody that complements the original
Interval inversion in analysis
- Music theorists and analysts use interval inversion to identify and describe the relationships between different musical elements within a composition
- By examining the intervals between notes and comparing them to their inversions, analysts can uncover hidden patterns and structures that give a piece its unique character and form
- Interval inversion can also be used to track the development and transformation of musical themes and motifs throughout a work
Interval inversion in ear training
- Interval inversion is an important concept for musicians to understand and recognize by ear, as it can help them to identify and reproduce musical passages more accurately
- By practicing interval inversion drills and exercises, musicians can train their ears to recognize inverted intervals and to sing or play them correctly
- Developing a strong sense of interval inversion can also aid in sight-reading, transposition, and improvisation, as musicians can more easily recognize and manipulate the relationships between notes in real-time.
Key Terms to Review (22)
Augmented Interval: An augmented interval is a musical interval that is one half step larger than a perfect or major interval. These intervals create a sense of tension and can be used to enhance musical expression, making them important in various contexts. Understanding augmented intervals is crucial for identifying relationships between notes, as well as for recognizing how they function in chord progressions and when intervals are inverted.
Compound interval: A compound interval is an interval that spans more than an octave, meaning it consists of a distance larger than 8 scale degrees. These intervals can be understood as extensions of simple intervals, which are the distances within one octave. Knowing about compound intervals is important because they help musicians understand harmonic relationships and the expansion of melodies across larger ranges.
Counterpoint: Counterpoint is a compositional technique that involves the relationship between two or more independent melodies that are played simultaneously, creating harmonic and rhythmic interplay. It is fundamental to Western music, enriching harmonic progression and enhancing melodic sight-singing, as well as facilitating score analysis and interpretation.
Diminished interval: A diminished interval is a musical distance that is one half-step smaller than a perfect or minor interval. This type of interval creates a tense or unstable sound, often used to evoke emotions or enhance musical tension. Understanding diminished intervals is crucial for recognizing how they function within harmonic progressions and how they relate to the concept of interval inversion.
Harmonic function: Harmonic function refers to the role that chords and intervals play within a musical context, defining how they relate to each other and contribute to the overall structure of a piece. This term highlights how different chords can create tension, resolution, or a sense of movement in music. Understanding harmonic function is essential for grasping how interval inversion can affect the perception and effectiveness of these relationships in a musical composition.
Harmonic Progression: Harmonic progression refers to a sequence of chords that create a sense of movement and direction in music. This concept is fundamental in establishing the tonal framework of a piece, guiding listeners through various emotional landscapes and key centers. It often involves the relationships between chords that are built on specific scales or modes, allowing composers to convey tension and resolution effectively.
Interval Inversion: Interval inversion is a music theory concept that occurs when the notes of an interval are rearranged so that the lower note becomes the higher note, and vice versa. This process changes the quality and size of the interval, and helps in understanding how different intervals relate to each other. Recognizing these transformations is crucial for identifying intervals accurately, assessing their qualities and sizes, and exploring their harmonic implications.
Interval Quality: Interval quality refers to the characteristic that defines the specific sound of an interval, which can vary based on the number of half steps between two pitches. It includes distinctions such as major, minor, perfect, augmented, and diminished, each conveying different emotional and harmonic implications. Understanding interval quality is essential for recognizing how intervals function in musical contexts and how they influence the overall sound of melodies and harmonies.
Interval Recognition: Interval recognition is the ability to identify the distance between two pitches, measured in terms of steps and half steps. This skill is essential for musicians as it allows them to understand melodies, harmonies, and the overall structure of music. Mastering interval recognition helps with ear training, which is vital for sight-singing and reading music accurately.
Interval Symbol: An interval symbol is a concise notation that represents the distance and quality between two pitches in music. It uses a combination of numbers and letters to indicate both the size of the interval (such as seconds, thirds, etc.) and its type (like major, minor, perfect, augmented, or diminished). This symbolization is essential for understanding how notes relate to each other in harmony and melody, particularly when examining the concepts of intervals and their inversions.
Intervallic distance: Intervallic distance refers to the measurable difference between two pitches, expressed as the number of letter names or scale degrees between them. This concept is foundational in understanding how intervals function within music, influencing interval recognition, defining their qualities and sizes, and playing a crucial role in interval inversion. Understanding intervallic distance allows musicians to categorize and describe intervals accurately, which is essential for performance, composition, and analysis.
Inverted Interval: An inverted interval occurs when the notes of a musical interval are switched, meaning the lower note becomes the higher note and vice versa. This transformation affects the quality and distance of the interval, which can lead to interesting harmonic relationships in music theory. Inversion can change the function of an interval within a musical context, impacting how melodies and chords are constructed.
Major interval: A major interval is a type of musical interval that is defined by its specific distance in pitch between two notes, typically encompassing two whole steps plus one half step in the major scale. Major intervals create a bright and happy sound, commonly found in melodies and harmonies, contributing significantly to the emotional quality of music. They play an important role in establishing the character of chords and scales.
Major Third: A major third is an interval that spans four half steps or semitones, typically creating a bright and happy sound. It serves as a foundational building block in harmony, playing a crucial role in chord construction and recognition. The major third connects to various concepts in music such as interval recognition, chord quality, and melodic structures, allowing musicians to understand how melodies and harmonies interact.
Melodic Dictation: Melodic dictation is the process of listening to a melody and accurately transcribing it in musical notation. This skill is crucial for developing aural skills, as it requires the ability to recognize pitches, rhythms, and intervals, which are essential in understanding and creating music. Mastering melodic dictation can greatly enhance one's sight-singing abilities, facilitate effective use of the movable-do system, and improve overall musical literacy when reading scores or playing at the keyboard.
Minor interval: A minor interval is a specific type of musical interval that is characterized by a smaller distance between two pitches compared to a major interval. In Western music, minor intervals are typically one half step smaller than their major counterparts, creating a distinct sound that often conveys a sense of melancholy or tension. Understanding minor intervals is essential for recognizing their role in harmony and melodic construction, as well as in the context of interval inversion, where the quality of an interval can change depending on how it is arranged.
Perfect Fifth: A perfect fifth is a musical interval that spans seven half steps, creating a harmonious and stable sound. This interval is crucial in music theory as it forms the foundation of many chords and is essential for recognizing harmonic structures, which can enhance both composition and performance.
Perfect interval: A perfect interval is a type of musical interval that is characterized by a specific consonance and includes the unison, fourth, fifth, and octave. These intervals are considered 'perfect' because they produce a stable and harmonious sound when played together. The nature of perfect intervals makes them fundamental in music theory, especially when discussing their role in harmonic progressions and how they behave during interval inversion.
Staff notation: Staff notation is a system of writing music that uses a set of horizontal lines and spaces to represent different pitches. Each line and space corresponds to a specific musical note, making it easier for musicians to read and interpret music. This notation system serves as a universal language for musicians, connecting various musical concepts such as intervals, scales, and chords.
Sum of 9: The sum of 9 refers to a specific relationship between musical intervals where the total of the two intervals equals nine. This concept is significant in understanding how interval inversions work, as inverting an interval changes its quality and can often lead to a new interval that, when added to the original, sums to 9. Recognizing this pattern helps musicians create harmonic and melodic structures effectively.
Tension and resolution: Tension and resolution refers to the musical concept where tension builds up through harmonic, melodic, or rhythmic elements, and then resolves to a more stable or restful state. This interplay is essential in creating emotional depth and movement in music, as tension invites anticipation and resolution provides closure. It can be expressed through various techniques such as dissonance and consonance, with specific structures like modes, extended chords, and interval inversions enhancing the overall musical narrative.
Voice Leading: Voice leading is the practice of composing music in a way that ensures smooth and logical movement from one chord to another by focusing on how individual melodic lines or 'voices' transition between notes. This technique is crucial for creating harmonic progressions that are pleasing to the ear, ensuring that intervals between successive notes are handled with care to maintain clarity and coherence in the musical texture.