A chordioid, also called chord fragment or fragmentary voicing [1] or partial voicing, [1] is a group of musical notes which does not qualify as a chord under a given chord theory, but still useful to name and reify for other reasons. Almost all types of chordioid are at least ancohemitonic, allowing the possibility that the resultant scale be at least ancohemitonic itself.
The main use of chordioids is to form "legitimate" chords enharmonically in 12TET by adding one or more notes to this base. [2] It is typical of chordioids that many different resultant chords can be created from the same base depending on the note or combination of notes added. [2] The resultant chords on a single chordioid are somewhat related, because they can be progressed between using motion of just one voice. Theorists – or practical music teachers – writing of chordioids usually go so far as to advise that students learn them in the practical manner of chords generally: in all transpositions, ranges, permutations, and voicings, for reading, writing, and playing. [1] [2] [3] It is the case, also, that "legitimate chords" can be used as chordioids to create resultant chords by the same process. [4] Perhaps this is whence the non-chord chordioids come. The Italian augmented 6th chord (It+6) is one example, from which proceed the French augmented 6th chord (Fr+6) and German augmented 6th chord (Gr+6) by addition of one note. Rawlins (2005) asserts that the notion derives from practice of such composers as Eric Satie, Claude Debussy, Maurice Ravel, and Gabriel Fauré, and was first used in jazz by Bill Evans. [1]
Two chordioids may potentially be combined, as well. Typically, duplication of notes will result in a reduced number of unique notes in the resultant.
Chordioids as a technique is related to polychords insofar as polychords are the result of an additive process, but differs in that the basis of polychords is the addition of two known chords. Chordioids is related also to upper structures as a technique insofar as upper structures represent groups of notes not commonly taken to be "legitimate" chords, but differs in that chordioids as a technique uses a priori structures held in common rather than a free selection of color tones appropriate for a lower integral chord. Chordioids is related to slash chords as a technique insofar as known chords may be used as chordioids to create resultant scales, but differs in that chordioids used are not exclusively known chords.
Nicolas Slonimsky named "master chord" [2] that chordioid described in jazz chord theory as 7no5, e.g.: { C D F♯ }. The sonority of the chordioid itself is identical to that of the It+6, a subset of the wholetone scale and so subject to some of the symmetries and homogeneity for which that scale is known, and anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
The chord buttons of the accordion usually play master chords, allowing the bass buttons (or a second chord button) to supply the variable note (or notes) to complete the sonority.
The new name and concept, "master chord", thus does not imply either jazz derivation, completeness of the sonority as an independent chord, nor connection to other use as a chord of dominant function. It does not speciously denote anything to be "missing", or posit that the listener should ever hear a note not actually present. It rejects the tertian chordal basis as pertaining at all. These, the practicality of application, and the variety of use, are the logical basis of chordioids.
The following table shows the resultant chord for each of the possible added notes:
Master Chord: C D F♯ | |||
---|---|---|---|
Added Note | Resultant Chord | Intervals | Audio |
D♭ | D♭♭9 sus4 | 0 5 7 e 1 | |
E♭ | D7♭9 | 04 7 t1 | ⓘ |
E | E9♯5 | 08t2 | ⓘ |
F | F13♭9 | 0 4 7 t 1 5 9 | |
G | GM7sus4 | 0 5 7 e | |
G♯ | G♯(♯11), Fr+6 to D♭ | 04 7 t 2 6, 046t | ⓘ , ⓘ , ⓘ |
A | D7, Gr+6 to D♭ | 047t | ⓘ , ⓘ |
B♭ | C9♭5, B♭9♯5 | 0 4 6t2, 048 t 2 | ⓘ , ⓘ |
B | Bm7♭9 | 0 3 7 t 1 |
Robert Rawlins based his theory of chordioids off the above as well as permutations of other major and minor 7th chords. [1] He described his chordioids as the interval of a 2nd below the interval of a 3rd. [1]
Based upon M7no5, e.g.: { C D♭ F }: [1]
C D♭ F [5] | |
---|---|
Added Note | Resultant Chord |
E♭ | E♭13 |
F♯ | F♯M7♯11 |
G | G11♭5 |
A♭ | D♭M7 |
A | A(♭13♯9) |
B♭ | Csus4♭9, B♭m add2 |
Based upon mM7no5, e.g.: { C D♭ F♭ }: [1]
C D♭ E [5] | |
---|---|
Added Note | Resultant Chord |
E♭ | E♭13♭9 |
G | G13/11♭5 |
A♭ | D♭mM7 |
B♭ | B♭m9♭5 |
Based upon m7no5, e.g.: { C D F }, [1] the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
C D F [5] | |
---|---|
Added Note | Resultant Chord |
E | E(♭13♭9) |
G | G7sus4 |
A | Dm7 |
B♭ | B♭add2 |
Joseph Schillinger based his theory of chordioids off the above as well as those irregular voicings of 7th chords in which the 5th is present but the 3rd absent, and of 9th chords in which the 5th and 3rd are both absent. [6]
Based upon 7no3, e.g.: { C G B♭ }, [4] the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
C G B♭ [4] | |
---|---|
Added Note | Resultant Chord |
D | D(♭13) |
E♭ | E♭6 |
E | C7 |
A♭ | A♭M9 |
A | Am7♭9 |
Based upon M7no3, e.g.: { C G B }: [4]
C G B [4] | |
---|---|
Added Note | Resultant Chord |
D | D13 |
E | CM7 |
A♭ | A♭M♯9 |
A | Am9 |
Based upon 7♭5no3, e.g.: { C G♭ B♭ }, [4] the sonority of the chordioid itself is identical to that of the base triad of the Fr+6, a subset of the wholetone scale and so subject to some of the symmetries and homogeneity for which that scale is known, and anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
C G♭ B♭ [4] | |
---|---|
Added Note | Resultant Chord |
D | D(♭13) |
E♭ | Cm7♭5, E♭m6 |
E | C7♭5 |
A♭ | A♭9 |
Based upon M7♭5no3, e.g.: { C G♭ B }, [4] the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
C G♭ B [4] | |
---|---|
Added Note | Resultant Chord |
D | D13 |
E♭ | CmM7♭5 |
E | CM7♭5 |
A♭ | A♭(♯9) |
Based upon 7♯5no3, e.g.: { C G♯ B♭ }, [4] the sonority of the chordioid itself is a subset of the wholetone scale and so subject to some of the symmetries and homogeneity for which that scale is known, and anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
C G♯ B♭ [4] | |
---|---|
Added Note | Resultant Chord |
D | D7alt5 |
E | C7♯5 |
A | AmM♭9 |
Based upon M7♯5no3, e.g.: { C G♯ B }: [4]
C G♯ B [4] | |
---|---|
Added Note | Resultant Chord |
D | D13♭5 |
E | CM7♯5 |
A | AmM9 |
Based upon 9no5no3, e.g.: { C D B♭ }, [4] the sonority of the chordioid itself is a subset of the wholetone scale and so subject to some of the symmetries and homogeneity for which that scale is known, and anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
C D B♭ [4] | |
---|---|
Added Note | Resultant Chord |
E♭ | Cm9 |
E | C9 |
F | Dm(♭13) |
F♯ | D(♭13) |
Based upon M9no5no3, e.g.: { C D B }: [4]
C D B [4] | |
---|---|
Added Note | Resultant Chord |
E♭ | CmM9 |
E | CM9 |
F | Dm13 |
F♯ | D13 |
Based upon ♭9no5no3, e.g.: { C D♭ B♭ }, [4] the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
C D♭ B♭ [4] | |
---|---|
Added Note | Resultant Chord |
E♭ | Cm♭9 |
E | C(♭9), D♭mM13 |
F | D♭M13 |
Based upon M♭9no5no3, e.g.: { C D♭ B }, [4] the sonority of the chordioid itself is cohemitonic assuring that the resultant scale be cohemitonic itself.
C D♭ B [4] | |
---|---|
Added Note | Resultant Chord |
E♭ | CmM♭9 |
E | CM(♭9) |
Based upon ♯9no5no3, e.g.: { C D♯ B♭ }, [4] the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
C D♯ B♭ [4] | |
---|---|
Added Note | Resultant Chord |
E | C(♯9) |
G | Cm7 |
Based upon M♯9no5no3, e.g.: { C D♯ B }: [4]
C D♯ B [4] | |
---|---|
Added Note | Resultant Chord |
E | CM♯9 |
G | CmM7 |
Based upon 11no5no9 (or 7sus4), e.g.: { C F B♭ }, [4] the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
C F B♭ [4] | |
---|---|
Added Note | Resultant Chord |
D | Dm♭13 |
G | Gm11 |
Based upon M11no5no9 (or M7sus4), e.g.: { C F B }: [4]
C F B [4] | |
---|---|
Added Note | Resultant Chord |
D | Dm13 |
G | G11 |
Harmonically, augmented sixth chords (+6ths) in prime position require three things:
Given these requirements, which are minimally fulfilled by the Italian sixth (It+6), e.g.: { A♭ C F♯ }, it is possible to derive all potential +6 chords from the It+6. The following table illustrates: [9]
Italian +6th Chord: A♭ C F♯. [10] [11] | |
---|---|
Added Note(s) | Resultant Chord |
B♭/A♯ | A♭ B♭/A♯ C F♯ |
E /D | A♭ C E /D F♯ |
E♭/D♯ | A♭ C E♭/D♯ F♯ |
E/D | A♭ C E/D F♯ |
B♭/A♯ & E /D | A♭ B♭/A♯ C E /D F♯ |
B♭/A♯ & E♭/D♯ | A♭ B♭/A♯ C E♭/D♯ F♯ |
B♭/A♯ & E/D | A♭ B♭/A♯ C E/D F♯ |
D & E | A♭ C D E F♯ |
B♭/A♯, D & E | A♭ B♭/A♯ C D E F♯ |
Joseph Schillinger also used basic triads and the master chord as chordioids in building bigger structures, textures, and strata. His 7th chords were based upon single notes added below major, minor, diminished, or augmented triads; [12] some of his hybrid 4-part harmony (including 11th and 13th chords) [4] likewise.
In music theory, a scale is "any consecutive series of notes that form a progression between one note and its octave", typically by order of pitch or fundamental frequency.
An altered chord is a chord that replaces one or more notes from the diatonic scale with a neighboring pitch from the chromatic scale. By the broadest definition, any chord with a non-diatonic chord tone is an altered chord. The simplest example of altered chords is the use of borrowed chords, chords borrowed from the parallel key, and the most common is the use of secondary dominants. As Alfred Blatter explains, "An altered chord occurs when one of the standard, functional chords is given another quality by the modification of one or more components of the chord."
An octatonic scale is any eight-note musical scale. However, the term most often refers to the ancohemitonic symmetric scale composed of alternating whole and half steps, as shown at right. In classical theory, this symmetrical scale is commonly called the octatonic scale, although there are a total of 43 enharmonically inequivalent, transpositionally inequivalent eight-note sets.
In jazz, the altered scale, altered dominant scale, or super-Locrian scale is a seven-note scale that is a dominant scale where all non-essential tones have been altered. This means that it comprises the three irreducibly essential tones that define a dominant seventh chord, which are root, major third, and minor seventh and that all other chord tones have been altered. These are:
In Western music theory, a chord is a group of notes played together for their harmonic consonance or dissonance. The most basic type of chord is a triad, so called because it consists of three distinct notes: the root note along with intervals of a third and a fifth above the root note. Chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in contemporary classical music, jazz, and other genres.
In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, was further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.
In music theory, tertian describes any piece, chord, counterpoint etc. constructed from the intervals of thirds. An interval such as that between the notes A and C encompasses 3 semitone intervals and is termed a minor third while one such as that between C and E encompasses 4 semitones and is called a major third. Tertian harmony principally uses chords based on thirds; the term is typically used to contrast with quartal and quintal harmony which uses chords based on fourths or fifths.
In music and music theory, a polychord consists of two or more chords, one on top of the other. In shorthand they are written with the top chord above a line and the bottom chord below, for example F upon C: F/C.
In jazz, the term upper structure or "upper structure triad" refers to a voicing approach developed by jazz pianists and arrangers defined by the sounding of a major or minor triad in the uppermost pitches of a more complex harmony.
In music, a triad is a set of three notes that can be stacked vertically in thirds. Triads are the most common chords in Western music.
The diminished seventh chord is a four-note chord composed of a root note, together with a minor third, a diminished fifth, and a diminished seventh above the root:. For example, the diminished seventh chord built on B, commonly written as Bo7, has pitches B-D-F-A♭:
A heptatonic scale is a musical scale that has seven pitches, or tones, per octave. Examples include:
In music and music theory, a hexatonic scale is a scale with six pitches or notes per octave. Famous examples include the whole-tone scale, C D E F♯ G♯ A♯ C; the augmented scale, C D♯ E G A♭ B C; the Prometheus scale, C D E F♯ A B♭ C; and the blues scale, C E♭ F G♭ G B♭ C. A hexatonic scale can also be formed by stacking perfect fifths. This results in a diatonic scale with one note removed.
The mathematical operations of multiplication have several applications to music. Other than its application to the frequency ratios of intervals, it has been used in other ways for twelve-tone technique, and musical set theory. Additionally ring modulation is an electrical audio process involving multiplication that has been used for musical effect.
In music, especially modern popular music, a slash chord or slashed chord, also compound chord, is a chord whose bass note or inversion is indicated by the addition of a slash and the letter of the bass note after the root note letter. It does not indicate "or". For example, a C major chord (C) in second inversion is written C/G or C/G bass, which reads "C slash G", "C over G" or "C over a G bass". Some chords may not otherwise be notated, such as A♭/A. Thus, a slash chord may also indicate the chord form or shape and an additional bass note.
In music, harmonization is the chordal accompaniment to a line or melody: "Using chords and melodies together, making harmony by stacking scale tones as triads".
Post-tonal music theory is the set of theories put forward to describe music written outside of, or 'after', the tonal system of the common practice period. It revolves around the idea of 'emancipating dissonance', that is, freeing the structure of music from the familiar harmonic patterns that are derived from natural overtones. As music becomes more complex, dissonance becomes indistinguishable from consonance.
Musicology commonly classifies scales as either hemitonic or anhemitonic. Hemitonic scales contain one or more semitones, while anhemitonic scales do not contain semitones. For example, in traditional Japanese music, the anhemitonic yo scale is contrasted with the hemitonic in scale. The simplest and most commonly used scale in the world is the atritonic anhemitonic "major" pentatonic scale. The whole tone scale is also anhemitonic.
The Hungarian major scale is a heptatonic scale subset of the octatonic scale with an omitted ♭2 degree. It has the following interval structure in semitones: 3, 1, 2, 1, 2, 1, 2, giving it the notes C D♯ E F♯ G A B♭ in the key of C. It is, "used extensively in Hungarian gypsy music [sic]", as well as in classical music by composers including Franz Liszt and Zoltán Kodály ," as well as in Thea Musgrave's Horn Concerto (1971). As a chord scale, Hungarian Major is both a dominant and a diminished scale, with a fully diminished seventh chord composed of C, D#, F#, and A, and a dominant seventh chord composed of C, E, G, and Bb. This is an enharmonic mode of Bb Harmonic Major, along with G Harmonic Minor and E Hungarian Minor. The root note of D Aeolian Dominant is raised a semitone to D#, and the root note of B Phrygian Dominant lowered a semitone to Bb. There is also a ♮6 & ♮2 with the Bb Super Lydian Augmented scale, lowering the C# & G# to C♮ & G♮.
The Romanian major scale is a heptatonic scale subset of the octatonic scale with an omitted ♭3 degree. It is noted for its flattened 2nd and sharpened fourth degrees, the latter a distinctive feature of Romanian traditional music. It has the following interval structure in semitones: 1, 3, 2, 1, 2, 1, 2, giving it the notes C, D♭, E, F♯, G, A, B♭ in the key of C. Though it is called a major scale, it is typically played over a C13 dominant chord. This is an enharmonic mode of B Harmonic Minor, along with D Harmonic Major. The root note of F Harmonic Major is raised a semitone to F#, and the root note of D Aeolian Dominant lowered a semitone to Db. There is also a ♮6 with the Db Super Lydian Augmented scale, lowering the B♮ to Bb.