Chordioid

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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.

Contents

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.

Master chord

Master chordioid resultant chords: added note = square note heads, implied notes=parenthesis Master chord chardiod resultant chords.png
Master chordioid resultant chords: added note = square note heads, implied notes=parenthesis

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 some of the possible added notes:

Master Chord: C D F
Added NoteResultant ChordIntervalsAudio
ED7904 7 t1 Play on C
EE9508t2 Play on C
GG(11),
Fr+6 to D
04 7 t 2 6,
046t
Play on C ,
Play on C ,
Fr+6 in C
AD7,
Gr+6 to D
047t Play on C ,
Gr+6 in C
BC95,
B95
0 4 6t2,
048 t 2
Play on C ,
Play on C

Non-dominant seventh chordioids

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 chordiods as the interval of a 2nd below the interval of a 3rd. [1]

Major

Based upon M7no5, e.g.: { C D F }: [1]

C D F [5]
Added NoteResultant Chord
EE13
FFM711
GG115
ADM7
AA(139)
BCsus49, Bm add2

Major-minor

Based upon mM7no5, e.g.: { C D F }: [1]

C D E [5]
Added NoteResultant Chord
EE139
GG13/115
ADmM7
BBm95

Minor

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 NoteResultant Chord
EE(139)
GG7sus4
ADm7
BBadd2

Incomplete sevenths and ninths chordioids

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]

Dominant seventh

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 NoteResultant Chord
DD(13)
EE6
EC7
AAM9
AAm79

M7

Based upon M7no3, e.g.: { C G B }: [4]

C G B [4]
Added NoteResultant Chord
DD13
ECM7
AAM9
AAm9

75

Based upon 75no3, 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 NoteResultant Chord
DD(13)
ECm75, Em6
EC75
AA9

M75

Based upon M75no3, e.g.: { C G B }: [4]

C G B [4]
Added NoteResultant Chord
DD13
ECmM75
ECM75
AA(9)

75

Based upon 75no3, 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 NoteResultant Chord
DD7alt5
EC75
AAmM9

M75

Based upon M75no3, e.g.: { C G B }: [4]

C G B [4]
Added NoteResultant Chord
DD135
ECM75
AAmM9

Dominant 9

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 NoteResultant Chord
ECm9
EC9
FDm(13)
FD(13)

M9

Based upon M9no5no3, e.g.: { C D B }: [4]

C D B [4]
Added NoteResultant Chord
ECmM9
ECM9
FDm13
FD13

Dominant 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 NoteResultant Chord
ECm9
EC(9), DmM13
FDM13

M9

Based upon M9no5no3, 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 NoteResultant Chord
ECmM9
ECM(9)

Dominant 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 NoteResultant Chord
EC(9)
GCm7

M9

Based upon M9no5no3, e.g.: { C D B }: [4]

C D B [4]
Added NoteResultant Chord
ECM9
GCmM7

Incomplete 11ths chordioids

Dominant 11

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 NoteResultant Chord
DDm13
GGm11

Major 11

Based upon M11no5no9 (or M7sus4), e.g.: { C F B }: [4]

C F B [4]
Added NoteResultant Chord
DDm13
GG11

Augmented sixth chords

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/AA B/A C F
E Doubleflat.svg /DA C E Doubleflat.svg /D F
E/DA C E/D F
E/D DoubleSharp.svg A C E/D DoubleSharp.svg F
B/A & E Doubleflat.svg /DA B/A C E Doubleflat.svg /D F
B/A & E/DA B/A C E/D F
B/A & E/D DoubleSharp.svg A B/A C E/D DoubleSharp.svg F
D & EA C D E F
B/A, D & EA B/A C D E F

Other known chords as chordioids

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.

See also

Related Research Articles

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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 non-equivalent, transpositionally non-equivalent 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:

<span class="mw-page-title-main">Chord (music)</span> Harmonic set of three or more notes

A chord, in music, is any harmonic set of pitches consisting of multiple notes that are sounded simultaneously, or nearly so. For many practical and theoretical purposes, arpeggios and other types of broken chords may also be considered as chords in the right musical context.

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<span class="mw-page-title-main">Polychord</span>

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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.

<span class="mw-page-title-main">Heptatonic scale</span> Musical scale with seven pitches

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.

<span class="mw-page-title-main">Harmonic major scale</span> Musical scale

In music theory, the harmonic major scale is a musical scale found in some music from the common practice era and now used occasionally, most often in jazz. In George Russell's Lydian Chromatic Concept it is the fifth mode (V) of the Lydian Diminished scale. It corresponds to the Raga Sarasangi in Indian Carnatic music.

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<span class="mw-page-title-main">Slash chord</span> A chord whose bass note is indicated by a slash

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Musicians use various kinds of chord names and symbols in different contexts to represent musical chords. In most genres of popular music, including jazz, pop, and rock, a chord name and its corresponding symbol typically indicate one or more of the following:

  1. the root note,
  2. the chord quality,
  3. whether the chord is a triad, seventh chord, or an extended chord,
  4. any altered notes,
  5. any added tones, and
  6. the bass note if it is not the root.

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.

References

  1. 1 2 3 4 5 6 7 8 9 Rawlins, Robert, et al. (2005) Jazzology: The Encyclopedia of Jazz Theory for All Musicians, p. 86. Winona: Hal Leonard. ISBN   0634086782.
  2. 1 2 3 4 Slonimsky, Nicholas. (1947) Thesaurus of Scales and Melodic Patterns, p. v. New York: Charles Scribner Sons. ISBN   002-6118505.
  3. Slonimsky, Nicholas. (1947) Thesaurus of Scales and Melodic Patterns, p. 241. New York: Charles Scribner Sons. ISBN   002-6118505.
  4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Schillinger, Joseph. (1941) The Schillinger System of Musical Composition, Vol. 1, p. 478. New York: Carl Fischer. ISBN   0306775212
  5. 1 2 3 Rawlins, Robert, et al. (2005) Jazzology: The Encyclopedia of Jazz Theory for All Musicians, pg. 87. Winona: Hal Leonard. ISBN   0634086782.
  6. Schillinger, Joseph. (1941) The Schillinger System of Musical Composition, Vol. 1, p. 478. New York: Carl Fischer. ISBN   0306775212
  7. Christ, William (1966). Materials and Structure of Music, v. 2, pp. 153ff. Englewood Cliffs: Prentice–Hall. LOC 66-14354.
  8. Tymoczko, Dimitri. (2011) A Geometry of Music, pp. 61ff. New York: Oxford University. ISBN   978-0195336672 .
  9. Prout, Ebenezer. (1889) Harmony: Its Theory and Practice, pp. 197ff. London: Augener.(
  10. Chadwick, G. (1897) Harmony: A Course of Study, p. 134. Boston: B. F. Wood.
  11. Hanson, Howard. (1960) Harmonic Materials of Modern Music, pp. 356ff. New York: Appleton-Century-Crofts. LOC 58-8138.
  12. Schillinger, Joseph. (1941) The Schillinger System of Musical Composition, Vol. 1, p. 447. New York: Carl Fischer. ISBN   0306775212