Chordioid

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 some preferred chord theory or other, but still useful to name and reify for other reasons.

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 Faure, 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 chardiod 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 Note	Resultant Chord	Intervals	Audio
E♭	D7♭9	0 4 7 t 1	Play on C
E	E9♯5	0 8 t 2	Play on C
G♯	G♯(♯11), Fr+6 to D♭	0 4 7 t 2 6, 0 4 6 t	Play on C , Play on C , Fr+6 in C
A	D7, Gr+6 to D♭	0 4 7 t	Play on C , Gr+6 in C
B♭	C9♭5, B♭7♯5	0 4 6 t 2, 0 4 8 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 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

Major-minor

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

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 Note	Resultant Chord
E	E(♭13♭9)
G	G7sus4
A	Dm7
B♭	B♭add2

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.^[4]

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 Note	Resultant Chord
D	D(♭13)
E♭	E♭6
E	C7
A♭	A♭M9
A	Am7♭9

M7

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

7♭5

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

M7♭5

Based upon M7♭5no3, e.g.: { C G♭ B }:^[4]

C G♭ B^[4]
Added Note	Resultant Chord
D	D13
E♭	CmM7♭5
E	CM7♭5
A♭	A♭(♯9)

7♯5

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

M7♯5

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

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 Note	Resultant Chord
E♭	Cm9
E	C9
F	Dm(♭13)
F♯	D(♭13)

M9

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

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 Note	Resultant Chord
E♭	Cm♭9
E	C(♭9), D♭mM13
F	D♭M13

M♭9

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)

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 Note	Resultant Chord
E	C(♯9)
G	Cm7

M♯9

Based upon M♯9no5no3, e.g.: { C D♯ B }:^[4]

C D♯ B^[4]
Added Note	Resultant Chord
E	CM♯9
G	CmM7

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 Note	Resultant Chord
D	Dm♭13
G	Gm11

Major 11

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

C F B^[4]
Added Note	Resultant Chord
D	Dm13
G	G11

Augmented sixth chords

Main article: Augmented sixth chord

Harmonically, augmented sixth chords (+6ths) in prime position require three things:

the interval of a major third up from the bottom note,
the interval of an augmented sixth up from the bottom note, and
strict anhemitonia: that there be no semitones present.^[6]^[7]

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:^[8]

Italian +6th Chord: A♭ C F♯.^[9]^[10]
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♯

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;^[11] some of his hybrid 4-part harmony (including 11th and 13th chords)^[4] likewise.

References

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

Chords

By form

Triad	Major Minor Augmented Diminished Suspended

Seventh	Major Minor Dominant Dominant seventh flat five Diminished Half-diminished Diminished major Minor-major Augmented major Augmented minor Altered seventh Nondominant Harmonic seventh

Extended	Ninth Eleventh Thirteenth Upper structure Dominant 7♯9 Polychord Tone cluster

Added / omitted	Sixth Augmented sixth Lydian Seven six

Specific	Alpha Bridge Complexe sonore Dream Elektra Farben Grandmother Magic µ Mystic Northern lights Petrushka Psalms So What Tristan Viennese trichord

General	Mixed interval Secundal Tertian Quartal Synthetic chord

By function

Diatonic	Tonic Dominant Subdominant Supertonic Mediant Submediant Leading / Subtonic

Altered	Approach Borrowed Chromatic mediant Neapolitan Passing

Secondary	Secondary dominant Secondary leading-tone Secondary supertonic

Other	Common Contrast Primary triad Subsidiary

Techniques

Other

Jazz theory & improvisation

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