In music, harmony is the process by which the composition of individual sounds, or superpositions of sounds, is analysed by hearing. Usually, this means simultaneously occurring frequencies, pitches (tones, notes), or chords.
Harmony is a perceptual property of music, and along with melody, one of the building blocks of Western music. Its perception is based on consonance, a concept whose definition has changed various times throughout Western music. In a physiological approach, consonance is a continuous variable. Consonant pitch relationships are described as sounding more pleasant, euphonious, and beautiful than dissonant relationships which sound unpleasant, discordant, or rough.
The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them.
Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line, or the "horizontal" aspect.
Counterpoint, which refers to the relationship between melodic lines, and polyphony, which refers to the simultaneous sounding of separate independent voices, are therefore sometimes distinguished from harmony.
In popular and jazz harmony, chords are named by their root plus various terms and characters indicating their qualities. In many types of music, notably baroque, romantic, modern, and jazz, chords are often augmented with "tensions". A tension is an additional chord member that creates a relatively dissonant interval in relation to the bass.
Typically, in the classical common practice period a dissonant chord (chord with tension) "resolves" to a consonant chord. Harmonization usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds. In simple words, that occurs when there is a balance between "tense" and "relaxed" moments.
The term harmony derives from the Greek ἁρμονίαharmonia, meaning "joint, agreement, concord", from the verb ἁρμόζωharmozō, "(Ι) fit together, join". In the past, harmony often referred to the whole field of music, while music referred to the arts in general.[ citation needed ] In Ancient Greece, the term defined the combination of contrasted elements: a higher and lower note. Nevertheless, it is unclear whether the simultaneous sounding of notes was part of ancient Greek musical practice; harmonía may have merely provided a system of classification of the relationships between different pitches.[ citation needed ] In the Middle Ages the term was used to describe two pitches sounding in combination, and in the Renaissance the concept was expanded to denote three pitches sounding together. Aristoxenus wrote a work entitled Harmonika Stoicheia , which is thought the first work in European history written on the subject of harmony.
It was not until the publication of Rameau's Traité de l'harmonie (Treatise on Harmony) in 1722 that any text discussing musical practice made use of the term in the title, although that work is not the earliest record of theoretical discussion of the topic. The underlying principle behind these texts is that harmony sanctions harmoniousness (sounds that please) by conforming to certain pre-established compositional principles.
Current dictionary definitions, while attempting to give concise descriptions, often highlight the ambiguity of the term in modern use. Ambiguities tend to arise from either aesthetic considerations (for example the view that only pleasing concords may be harmonious) or from the point of view of musical texture (distinguishing between harmonic (simultaneously sounding pitches) and "contrapuntal" (successively sounding tones).In the words of Arnold Whittall:
While the entire history of music theory appears to depend on just such a distinction between harmony and counterpoint, it is no less evident that developments in the nature of musical composition down the centuries have presumed the interdependence—at times amounting to integration, at other times a source of sustained tension—between the vertical and horizontal dimensions of musical space. [ page needed ]
The view that modern tonal harmony in Western music began in about 1600 is commonplace in music theory. This is usually accounted for by the replacement of horizontal (or contrapuntal) composition, common in the music of the Renaissance, with a new emphasis on the vertical element of composed music. Modern theorists, however, tend to see this as an unsatisfactory generalisation. According to Carl Dahlhaus:
It was not that counterpoint was supplanted by harmony (Bach’s tonal counterpoint is surely no less polyphonic than Palestrina’s modal writing) but that an older type both of counterpoint and of vertical technique was succeeded by a newer type. And harmony comprises not only the ("vertical") structure of chords but also their ("horizontal") movement. Like music as a whole, harmony is a process. [ page needed ]
Descriptions and definitions of harmony and harmonic practice often show bias towards European (or Western) musical traditions, although many cultures practice vertical harmonyIn addition, South Asian art music (Hindustani and Carnatic music) is frequently cited as placing little emphasis on what is perceived in western practice as conventional harmony; the underlying harmonic foundation for most South Asian music is the drone, a held open fifth interval (or fourth interval) that does not alter in pitch throughout the course of a composition. Pitch simultaneity in particular is rarely a major consideration. Nevertheless, many other considerations of pitch are relevant to the music, its theory and its structure, such as the complex system of Rāgas, which combines both melodic and modal considerations and codifications within it.
So, intricate pitch combinations that sound simultaneously do occur in Indian classical music—but they are rarely studied as teleological harmonic or contrapuntal progressions—as with notated Western music. This contrasting emphasis (with regard to Indian music in particular) manifests itself in the different methods of performance adopted: in Indian Music improvisation takes a major role in the structural framework of a piece,whereas in Western Music improvisation has been uncommon since the end of the 19th century. Where it does occur in Western music (or has in the past), the improvisation either embellishes pre-notated music or draws from musical models previously established in notated compositions, and therefore uses familiar harmonic schemes.
Emphasis on the precomposed in European art music and the written theory surrounding it shows considerable cultural bias. The Grove Dictionary of Music and Musicians (Oxford University Press) identifies this clearly:
In Western culture the musics that are most dependent on improvisation, such as jazz, have traditionally been regarded as inferior to art music, in which pre-composition is considered paramount. The conception of musics that live in oral traditions as something composed with the use of improvisatory techniques separates them from the higher-standing works that use notation.
Yet the evolution of harmonic practice and language itself, in Western art music, is and was facilitated by this process of prior composition, which permitted the study and analysis by theorists and composers of individual pre-constructed works in which pitches (and to some extent rhythms) remained unchanged regardless of the nature of the performance.
Early Western religious music often features parallel perfect intervals; these intervals would preserve the clarity of the original plainsong. These works were created and performed in cathedrals, and made use of the resonant modes of their respective cathedrals to create harmonies. As polyphony developed, however, the use of parallel intervals was slowly replaced by the English style of consonance that used thirds and sixths.[ when? ] The English style was considered to have a sweeter sound, and was better suited to polyphony in that it offered greater linear flexibility in part-writing.
Carl Dahlhaus (1990) distinguishes between coordinate and subordinate harmony. Subordinate harmony is the hierarchical tonality or tonal harmony well known today. Coordinate harmony is the older Medieval and Renaissance tonalité ancienne, "The term is meant to signify that sonorities are linked one after the other without giving rise to the impression of a goal-directed development. A first chord forms a 'progression' with a second chord, and a second with a third. But the former chord progression is independent of the later one and vice versa." Coordinate harmony follows direct (adjacent) relationships rather than indirect as in subordinate. Interval cycles create symmetrical harmonies, which have been extensively used by the composers Alban Berg, George Perle, Arnold Schoenberg, Béla Bartók, and Edgard Varèse's Density 21.5 .
Close harmony and open harmony use close position and open position chords, respectively. See: Voicing (music) and Close and open harmony.
Other types of harmony are based upon the intervals of the chords used in that harmony. Most chords in western music are based on "tertian" harmony, or chords built with the interval of thirds. In the chord C Major7, C–E is a major third; E–G is a minor third; and G to B is a major third. Other types of harmony consist of quartal and quintal harmony.
A unison is considered a harmonic interval, just like a fifth or a third, but is unique in that it is two identical notes produced together. The unison, as a component of harmony, is important, especially in orchestration.In pop music, unison singing is usually called doubling, a technique The Beatles used in many of their earlier recordings. As a type of harmony, singing in unison or playing the same notes, often using different musical instruments, at the same time is commonly called monophonic harmonization.
An interval is the relationship between two separate musical pitches. For example, in the melody "Twinkle Twinkle Little Star", between the first two notes (the first "twinkle") and the second two notes (the second "twinkle") is the interval of a fifth. What this means is that if the first two notes were the pitch C, the second two notes would be the pitch "G"—four scale notes, or seven chromatic notes (a perfect fifth), above it.
The following are common intervals:
|Root||Major third||Minor third||Fifth|
Therefore, the combination of notes with their specific intervals—a chord—creates harmony.[ citation needed ] For example, in a C chord, there are three notes: C, E, and G. The note C is the root. The notes E and G provide harmony, and in a G7 (G dominant 7th) chord, the root G with each subsequent note (in this case B, D and F) provide the harmony.[ citation needed ]
In the musical scale, there are twelve pitches. Each pitch is referred to as a "degree" of the scale. The names A, B, C, D, E, F, and G are insignificant.[ citation needed ] The intervals, however, are not. Here is an example:
As can be seen, no note will always be the same scale degree. The tonic, or first-degree note, can be any of the 12 notes (pitch classes) of the chromatic scale. All the other notes fall into place. For example, when C is the tonic, the fourth degree or subdominant is F. When D is the tonic, the fourth degree is G. While the note names remain constant, they may refer to different scale degrees, implying different intervals with respect to the tonic. The great power of this fact is that any musical work can be played or sung in any key. It is the same piece of music, as long as the intervals are the same—thus transposing the melody into the corresponding key. When the intervals surpass the perfect Octave (12 semitones), these intervals are called compound intervals, which include particularly the 9th, 11th, and 13th Intervals—widely used in jazz and blues Music.
Compound Intervals are formed and named as follows:
The reason the two numbers don't "add" correctly is that one note is counted twice.[ clarification needed ] Apart from this categorization, intervals can also be divided into consonant and dissonant. As explained in the following paragraphs, consonant intervals produce a sensation of relaxation and dissonant intervals a sensation of tension. In tonal music, the term consonant also means "brings resolution" (to some degree at least, whereas dissonance "requires resolution").[ citation needed ]
The consonant intervals are considered the perfect unison, octave, fifth, fourth and major and minor third and sixth, and their compound forms. An interval is referred to as "perfect" when the harmonic relationship is found in the natural overtone series (namely, the unison 1:1, octave 2:1, fifth 3:2, and fourth 4:3). The other basic intervals (second, third, sixth, and seventh) are called "imperfect" because the harmonic relationships are not found mathematically exact in the overtone series. In classical music the perfect fourth above the bass may be considered dissonant when its function is contrapuntal. Other intervals, the second and the seventh (and their compound forms) are considered Dissonant and require resolution (of the produced tension) and usually preparation (depending on the music style).[ citation needed ]
Note that the effect of dissonance is perceived relatively within musical context: for example, a major seventh interval alone (i.e., C up to B) may be perceived as dissonant, but the same interval as part of a major seventh chord may sound relatively consonant. A tritone (the interval of the fourth step to the seventh step of the major scale, i.e., F to B) sounds very dissonant alone, but less so within the context of a dominant seventh chord (G7 or D♭7 in that example).[ citation needed ]
In the Western tradition, in music after the seventeenth century, harmony is manipulated using chords, which are combinations of pitch classes. In tertian harmony, so named after the interval of a third, the members of chords are found and named by stacking intervals of the third, starting with the "root", then the "third" above the root, and the "fifth" above the root (which is a third above the third), etc. (Note that chord members are named after their interval above the root.) Dyads, the simplest chords, contain only two members (see power chords).
A chord with three members is called a triad because it has three members, not because it is necessarily built in thirds (see Quartal and quintal harmony for chords built with other intervals). Depending on the size of the intervals being stacked, different qualities of chords are formed. In popular and jazz harmony, chords are named by their root plus various terms and characters indicating their qualities. To keep the nomenclature as simple as possible, some defaults are accepted (not tabulated here). For example, the chord members C, E, and G, form a C Major triad, called by default simply a C chord. In an A♭ chord (pronounced A-flat), the members are A♭, C, and E♭.
In many types of music, notably baroque, romantic, modern and jazz, chords are often augmented with "tensions". A tension is an additional chord member that creates a relatively dissonant interval in relation to the bass. Following the tertian practice of building chords by stacking thirds, the simplest first tension is added to a triad by stacking, on top of the existing root, third, and fifth, another third above the fifth, adding a new, potentially dissonant member a seventh away from the root (called the "seventh" of the chord) producing a four-note chord called a "seventh chord".
Depending on the widths of the individual thirds stacked to build the chord, the interval between the root and the seventh of the chord may be major, minor, or diminished. (The interval of an augmented seventh reproduces the root, and is therefore left out of the chordal nomenclature.) The nomenclature allows that, by default, "C7" indicates a chord with a root, third, fifth, and seventh spelled C, E, G, and B♭. Other types of seventh chords must be named more explicitly, such as "C Major 7" (spelled C, E, G, B), "C augmented 7" (here the word augmented applies to the fifth, not the seventh, spelled C, E, G♯, B♭), etc. (For a more complete exposition of nomenclature see Chord (music).)
Continuing to stack thirds on top of a seventh chord produces extensions, and brings in the "extended tensions" or "upper tensions" (those more than an octave above the root when stacked in thirds), the ninths, elevenths, and thirteenths. This creates the chords named after them. (Note that except for dyads and triads, tertian chord types are named for the interval of the largest size and magnitude in use in the stack, not for the number of chord members : thus a ninth chord has five members [tonic, 3rd, 5th, 7th, 9th], not nine.) Extensions beyond the thirteenth reproduce existing chord members and are (usually) left out of the nomenclature. Complex harmonies based on extended chords are found in abundance in jazz, late-romantic music, modern orchestral works, film music, etc.
Typically, in the classical Common practice period a dissonant chord (chord with tension) resolves to a consonant chord. Harmonization usually sounds pleasant to the ear when there is a balance between the consonant and dissonant sounds. In simple words, that occurs when there is a balance between "tense" and "relaxed" moments. For this reason, usually tension is 'prepared' and then 'resolved',where preparing tension means to place a series of consonant chords that lead smoothly to the dissonant chord. In this way the composer ensures introducing tension smoothly, without disturbing the listener. Once the piece reaches its sub-climax, the listener needs a moment of relaxation to clear up the tension, which is obtained by playing a consonant chord that resolves the tension of the previous chords. The clearing of this tension usually sounds pleasant to the listener, though this is not always the case in late-nineteenth century music, such as Tristan und Isolde by Richard Wagner.
A number of features contribute to the perception of a chord's harmony.
Tonal fusion contributes to the perceived consonance of a chord,describing the degree to which multiple pitches are heard as a single, unitary tone. Chords which have more coinciding partials (frequency components) are perceived as more consonant, such as the octave and perfect fifth. The spectra of these intervals resemble that of a uniform tone. According to this definition, a major triad fuses better than a minor triad and a major-minor seventh chord fuses better than a major-major seventh or minor-minor seventh. These differences may not be readily apparent in tempered contexts but can explain why major triads are generally more prevalent than minor triads and major-minor sevenths are generally more prevalent than other sevenths (in spite of the dissonance of the tritone interval) in mainstream tonal music.
In organ registers, certain harmonic interval combinations and chords are activated by a single key. The sounds produced fuse into one tone with a new timbre. This tonal fusion effect is also used in synthesizers and orchestral arrangements; for instance, in Ravel’s Bolero #5 the parallel parts of flutes, horn and celesta resemble the sound of an electric organ.
When adjacent harmonics in complex tones interfere with one another, they create the perception of what is known as "beating" or "roughness". These precepts are closely related to the perceived dissonance of chords.To interfere, partials must lie within a critical bandwidth, which is a measure of the ear's ability to separate different frequencies. Critical bandwidth lies between 2 and 3 semitones at high frequencies and becomes larger at lower frequencies. The roughest interval in the chromatic scale is the minor second and its inversion, the major seventh. For typical spectral envelopes in the central range, the second roughest interval is the major second and minor seventh, followed by the tritone, the minor third (major sixth), the major third (minor sixth) and the perfect fourth (fifth).
Familiarity also contributes to the perceived harmony of an interval. Chords that have often been heard in musical contexts tend to sound more consonant. This principle explains the gradual historical increase in harmonic complexity of Western music. For example, around 1600 unprepared seventh chords gradually became familiar and were therefore gradually perceived as more consonant.
Individual characteristics such as age and musical experience also have an effect on harmony perception.
The inferior colliculus is a mid-brain structure which is the first site of binaural auditory integration, processing auditory information from the left and right ears.Frequency following responses (FFRs) recorded from the mid-brain exhibit peaks in activity which correspond to the frequency components of a tonal stimulus. The extent to which FFRs accurately represent the harmonic information of a chord is called neural salience, and this value is correlated with behavioral ratings of the perceived pleasantness of chords.
In response to harmonic intervals, cortical activity also distinguishes chords by their consonance, responding more robustly to chords with greater consonance.
The creation and destruction of harmonic and 'statistical' tensions is essential to the maintenance of compositional drama. Any composition (or improvisation) which remains consistent and 'regular' throughout is, for me, equivalent to watching a movie with only 'good guys' in it, or eating cottage cheese.— Frank Zappa, The Real Frank Zappa Book, page 181, Frank Zappa and Peter Occhiogrosso, 1990
In music, counterpoint is the relationship between two or more musical lines which are harmonically interdependent yet independent in rhythm and melodic contour. It has been most commonly identified in the European classical tradition, strongly developing during the Renaissance and in much of the common practice period, especially in the Baroque. The term originates from the Latin punctus contra punctum meaning "point against point", i.e. "note against note".
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
Music theory is the study of the practices and possibilities of music. The Oxford Companion to Music describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation ; the second is learning scholars' views on music from antiquity to the present; the third a sub-topic of musicology that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built."
In music theory, a leading-tone is a note or pitch which resolves or "leads" to a note one semitone higher or lower, being a lower and upper leading-tone, respectively. Typically, the leading tone refers to the seventh scale degree of a major scale, a major seventh above the tonic. In the movable do solfège system, the leading-tone is sung as ti.
A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth is the fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones.
In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.
A seventh chord is a chord consisting of a triad plus a note forming an interval of a seventh above the chord's root. When not otherwise specified, a "seventh chord" usually means a dominant seventh chord: a major triad together with a minor seventh. However, a variety of sevenths may be added to a variety of triads, resulting in many different types of seventh chords.
A chord, in music, is any harmonic set of pitches/frequencies consisting of multiple notes that are heard as if sounding simultaneously. For many practical and theoretical purposes, arpeggios and broken chords, or sequences of chord tones, may also be considered as chords in the right musical context.
Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is called the tonic. The root of the tonic chord forms the name given to the key; so in the key of C major, the note C is both the tonic of the scale and the root of the tonic chord. Simple folk music songs often start and end with the tonic note. The most common use of the term "is to designate the arrangement of musical phenomena around a referential tonic in European music from about 1600 to about 1910". Contemporary classical music from 1910 to the 2000s may practice or avoid any sort of tonality—but harmony in almost all Western popular music remains tonal. Harmony in jazz includes many but not all tonal characteristics of the European common practice period, sometimes known as "classical music".
In classical music, a third is a musical interval encompassing three staff positions, and the major third is a third spanning four semitones. Along with the minor third, the major third is one of two commonly occurring thirds. It is qualified as major because it is the larger of the two: the major third spans four semitones, the minor third three. For example, the interval from C to E is a major third, as the note E lies four semitones above C, and there are three staff positions from C to E. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones.
The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees of a major scale are called major.
In music theory, a minor chord is a chord that has a root, a minor third, and a perfect fifth. When a chord has these three notes alone, it is called a minor triad. For example, the minor triad built on C, called a C minor triad, has pitches C–E♭–G:
In music theory, the concept of root is the idea that a chord can be represented and named by one of its notes. It is linked to harmonic thinking—the idea that vertical aggregates of notes can form a single unit, a chord. It is in this sense that one speaks of a "C chord" or a "chord on C"—a chord built from C and of which the note C is the root. When a chord is referred to in Classical music or popular music without a reference to what type of chord it is, it is assumed a major triad, which for C contains the notes C, E and G. The root need not be the bass note, the lowest note of the chord: the concept of root is linked to that of the inversion of chords, which is derived from the notion of invertible counterpoint. In this concept, chords can be inverted while still retaining their root.
In music theory, a ninth chord is a chord that encompasses the interval of a ninth when arranged in close position with the root in the bass.
The ninth chord and its inversions exist today, or at least they can exist. The pupil will easily find examples in the literature [such as Schoenberg's Verklärte Nacht and Strauss's opera Salome]. It is not necessary to set up special laws for its treatment. If one wants to be careful, one will be able to use the laws that pertain to the seventh chords: that is, dissonances resolve by step downward, the root leaps a fourth upward.
Chromaticism is a compositional technique interspersing the primary diatonic pitches and chords with other pitches of the chromatic scale. Chromaticism is in contrast or addition to tonality or diatonicism and modality. Chromatic elements are considered, "elaborations of or substitutions for diatonic scale members".
Not only at the beginning of a composition but also in the midst of it, each scale-step [degree] manifests an irresistible urge to attain the value of the tonic for itself as that of the strongest scale-step. If the composer yields to this urge of the scale-step within the diatonic system of which this scale-step forms part, I call this process tonicalization and the phenomenon itself chromatic.
Chromaticism is almost by definition an alteration of, an interpolation in or deviation from this basic diatonic organization.
Throughout the nineteenth century, composers felt free to alter any or all chord members of a given tertian structure [chord built from thirds] according to their compositional needs and dictates. Pronounced or continuous chordal alteration [and 'extension'] resulted in chromaticism. Chromaticism, together with frequent modulations and an abundance of non-harmonicism [non-chord tones], initially effected an expansion of the tertian system; the overuse of the procedures late in the century forewarned the decline and near collapse [atonality] of the system [tonality].
Chromaticism is the name given to the use of tones outside the major or minor scales. Chromatic tones began to appear in music long before the common-practice period, and by the beginning of that period were an important part of its melodic and harmonic resources. Chromatic tones arise in music partly from inflection [alteration] of scale degrees in the major and minor modes, partly from secondary dominant harmony, from a special vocabulary of altered chords, and from certain nonharmonic tones.... Notes outside the scale do not necessarily affect the tonality....tonality is established by the progression of roots and the tonal functions of the chords, even though the details of the music may contain all the tones of the chromatic scale.
Sometimes...a melody based on a regular diatonic scale is laced with many accidentals, and although all 12 tones of the chromatic scale may appear, the tonal characteristics of the diatonic scale are maintained. ... Chromaticism [is t]he introduction of some pitches of the chromatic scale into music that is basically diatonic in orientation, or music that is based on the chromatic scale instead of the diatonic scales.
In music, a guitar chord is a set of notes played on a guitar. A chord's notes are often played simultaneously, but they can be played sequentially in an arpeggio. The implementation of guitar chords depends on the guitar tuning. Most guitars used in popular music have six strings with the "standard" tuning of the Spanish classical guitar, namely E-A-D-G-B-E' ; in standard tuning, the intervals present among adjacent strings are perfect fourths except for the major third (G,B). Standard tuning requires four chord-shapes for the major triads.
In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.
In musical set theory, an interval vector is an array of natural numbers which summarize the intervals present in a set of pitch classes. Other names include: ic vector, PIC vector and APIC vector
In music theory, an inversion is a type of change to intervals, chords, voices, and melodies. In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory.
The harmonic seventh intervalPlay (help·info), also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio. This is somewhat narrower than and is, "particularly sweet," "sweeter in quality" than an "ordinary" just minor seventh, which has an intonation ratio of 9:5.
Richard Parncutt is an Australian-born academic. He has been professor of systematic musicology at Karl-Franzens-Universität Graz in Austria since 1998. His research focuses on the psychology of music.
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