A chordioid, also called ''chord fragment'' or ''fragmentary voicing''
[Rawlins, Robert, et al. (2005) ''Jazzology: The Encyclopedia of Jazz Theory for All Musicians'', p. 86. Winona: Hal Leonard. .] or ''partial voicing'',
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.
The main use of chordioids is to form "legitimate" chords
enharmonic
In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that is equivalent to some other note, interval, or key signature but "spelled", or named differently. The enharmonic spelling of a written n ...
ally in
12TET
Twelve-tone equal temperament (12-TET) is the musical system that divides the octave into 12 parts, all of which are equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2 ( ≈ 1.05946). That resulti ...
by adding one or more notes to this base.
[Slonimsky, Nicholas. (1947) ''Thesaurus of Scales and Melodic Patterns'', p. v. New York: Charles Scribner Sons. .] 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.
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
In the Hebrew Bible and in the Old Testament, the word ranges has two very different meanings.
Leviticus
In Leviticus 11:35, ranges probably means a cooking furnace for two or more pots, as the Hebrew word here is in the dual number; or perhaps ...
,
permutations
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...
, and
voicings
''Voicings'' was the last recording by the Minneapolis jazz vocal group Rio Nido. The album was one of the early recordings to feature live "direct to digital" recording techniques.
Track listing
# "Northern Lights" (D. Karr, L. Ball)
# "I'm ...
, for reading, writing, and playing.
[Slonimsky, Nicholas. (1947) ''Thesaurus of Scales and Melodic Patterns'', p. 241. New York: Charles Scribner Sons. .]
It is the case, also, that "legitimate chords" can be used as chordioids to create resultant chords by the same process.
[Schillinger, Joseph. (1941) ''The Schillinger System of Musical Composition, Vol. 1'', p. 478. New York: Carl Fischer. ] 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
Eric Alfred Leslie Satie (, ; ; 17 May 18661 July 1925), who signed his name Erik Satie after 1884, was a French composer and pianist. He was the son of a French father and a British mother. He studied at the Paris Conservatoire, but was an und ...
,
Claude Debussy
(Achille) Claude Debussy (; 22 August 1862 – 25 March 1918) was a French composer. He is sometimes seen as the first Impressionist composer, although he vigorously rejected the term. He was among the most influential composers of the ...
,
Maurice Ravel
Joseph Maurice Ravel (7 March 1875 – 28 December 1937) was a French composer, pianist and conductor. He is often associated with Impressionism along with his elder contemporary Claude Debussy, although both composers rejected the term. In ...
, and
Gabriel Fauré
Gabriel Urbain Fauré (; 12 May 1845 – 4 November 1924) was a French composer, organist, pianist and teacher. He was one of the foremost French composers of his generation, and his musical style influenced many 20th-century composers ...
, and was first used in jazz by
Bill Evans
William John Evans (August 16, 1929 – September 15, 1980) was an American jazz pianist and composer who worked primarily as the leader of his trio. His use of impressionist harmony, interpretation of traditional jazz repertoire, block ch ...
.
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
polychord
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,Policastro, Michael A. (1999). ''Understanding How to Build ...
s 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 structure 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.Ellenberger, K ...
s 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 chord
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 no ...
s 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
Nicolas Slonimsky
Nicolas Slonimsky ( – December 25, 1995), born Nikolai Leonidovich Slonimskiy (russian: Никола́й Леони́дович Сло́нимский), was a Russian-born American conductor, author, pianist, composer and lexicographer. B ...
named "master chord"
that chordioid described in
jazz
Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana in the late 19th and early 20th centuries, with its roots in blues and ragtime. Since the 1920s Jazz Age, it has been recognized as a major ...
chord theory as
7no5, e.g.: The sonority of the chordioid itself is identical to that of the
It+6
It or IT may refer to:
* It (pronoun), in English
* Information technology
Arts and media Film and television
* ''It'' (1927 film), a film starring Clara Bow
* ''It! The Terror from Beyond Space'', a 1958 science fiction film
* ''It!'' (1967 f ...
, a subset of the
Wholetone scale
In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or ''hexatonic'' ...
and so subject to some of the
symmetries
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
and
homogeneity
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
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
Accordions (from 19th-century German ''Akkordeon'', from ''Akkord''—"musical chord, concord of sounds") are a family of box-shaped musical instruments of the bellows-driven free-reed aerophone type (producing sound as air flows past a reed ...
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
In music, the dominant is the fifth scale degree () of the diatonic scale. It is called the ''dominant'' because it is second in importance to the first scale degree, the tonic. In the movable do solfège system, the dominant note is sung as "So( ...
. 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:
Non-dominant seventh chordioids
Robert Rawlins based his theory of chordioids off the above as well as
permutation
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...
s of other major and minor
7th chords.
[ He described his chordiods as the interval of a 2nd below the interval of a ]3rd
Third or 3rd may refer to:
Numbers
* 3rd, the ordinal form of the cardinal number 3
* , a fraction of one third
* Second#Sexagesimal divisions of calendar time and day, 1⁄60 of a ''second'', or 1⁄3600 of a ''minute''
Places
* 3rd Street (d ...
.
Major
Based upon M7no5, e.g.: :
Major-minor
Based upon mM7no5, e.g.: :
Minor
Based upon m7no5, e.g.:
, the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
Incomplete sevenths and ninths chordioids
Joseph Schillinger
Joseph Moiseyevich Schillinger (Russian: Иосиф Моисеевич Шиллингер, (other sources: ) – 23 March 1943) was a composer, music theorist, and composition teacher who originated the Schillinger System of Musical Composition ...
based his theory of chordioids off the above as well as those irregular voicings of 7th
7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube (algebra), cube.
As an early prime number in the series of positive integers, the number seven has greatly symbolic associations in religion ...
chords in which the 5th is present but the 3rd
Third or 3rd may refer to:
Numbers
* 3rd, the ordinal form of the cardinal number 3
* , a fraction of one third
* Second#Sexagesimal divisions of calendar time and day, 1⁄60 of a ''second'', or 1⁄3600 of a ''minute''
Places
* 3rd Street (d ...
absent, and of 9th
9 (nine) is the natural number following and preceding .
Evolution of the Arabic digit
In the beginning, various Indians wrote a digit 9 similar in shape to the modern closing question mark without the bottom dot. The Kshatrapa, Andhra and ...
chords in which the 5th and 3rd
Third or 3rd may refer to:
Numbers
* 3rd, the ordinal form of the cardinal number 3
* , a fraction of one third
* Second#Sexagesimal divisions of calendar time and day, 1⁄60 of a ''second'', or 1⁄3600 of a ''minute''
Places
* 3rd Street (d ...
are both absent.
Dominant seventh
Based upon 7no3, e.g.:
, the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
M7
Based upon M7no3, e.g.: :
75
Based upon 75no3, e.g.:
, the sonority of the chordioid itself is identical to that of the base triad of the Fr+6, a subset of the Wholetone scale
In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or ''hexatonic'' ...
and so subject to some of the symmetries
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
and homogeneity
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
for which that scale is known, and anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
M75
Based upon M75no3, e.g.: :
75
Based upon 75no3, e.g.:
, the sonority of the chordioid itself is a subset of the Wholetone scale
In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or ''hexatonic'' ...
and so subject to some of the symmetries
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
and homogeneity
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
for which that scale is known, and anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
M75
Based upon M75no3, e.g.: :
Dominant 9
Based upon 9no5no3, e.g.:
, the sonority of the chordioid itself is a subset of the Wholetone scale
In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or ''hexatonic'' ...
and so subject to some of the symmetries
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
and homogeneity
Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
for which that scale is known, and anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
M9
Based upon M9no5no3, e.g.: :
Dominant 9
Based upon 9no5no3, e.g.:
, the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
M9
Based upon M9no5no3, e.g.: , the sonority of the chordioid itself is cohemitonic assuring that the resultant scale be cohemitonic itself.
Dominant 9
Based upon 9no5no3, e.g.:
, the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
M9
Based upon M9no5no3, e.g.: :
Incomplete 11ths chordioids
Dominant 11
Based upon 11no5no9 (or 7sus4), e.g.: , the sonority of the chordioid itself is anhemitonic allowing the possibility that the resultant scale be anhemitonic or at least ancohemitonic itself.
Major 11
Based upon M11no5no9 (or M7sus4), e.g.: :
Augmented sixth chords
Harmonically, augmented sixth chords (+6ths) in prime position require three things:
* the interval of a major third
In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () is a third spanning four semitones. Forte, Allen (1979). ''Tonal Harmony in Concept and P ...
up from the bottom note,
* the interval of an augmented sixth
In classical music from Western culture, an augmented sixth () is an interval produced by widening a major sixth by a chromatic semitone.Benward & Saker (2003). ''Music: In Theory and Practice, Vol. I'', p.54. . Specific example of an A6 not g ...
up from the bottom note, and
* strict anhemitonia
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'' sc ...
: that there be no semitones present.
Given these requirements, which are minimally fulfilled by the Italian sixth (It+6), e.g.: , it is possible to derive all potential +6 chords from the It+6. The following table illustrates:
Other known chords as chordioids
Joseph Schillinger
Joseph Moiseyevich Schillinger (Russian: Иосиф Моисеевич Шиллингер, (other sources: ) – 23 March 1943) was a composer, music theorist, and composition teacher who originated the Schillinger System of Musical Composition ...
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
Major (commandant in certain jurisdictions) is a military rank of commissioned officer status, with corresponding ranks existing in many military forces throughout the world. When used unhyphenated and in conjunction with no other indicators ...
, minor
Minor may refer to:
* Minor (law), a person under the age of certain legal activities.
** A person who has not reached the age of majority
* Academic minor, a secondary field of study in undergraduate education
Music theory
*Minor chord
** Barb ...
, diminished, or augmented triads;[Schillinger, Joseph. (1941) ''The Schillinger System of Musical Composition, Vol. 1'', p. 447. New York: Carl Fischer. ] some of his hybrid 4-part harmony (including 11th and 13th chords) likewise.
See also
* Factor (chord)
In music, a factor or chord factor is a member or component of a chord (music), chord. These are named root (chord), root, third (chord), third, fifth (chord), fifth, sixth chord, sixth, seventh (chord), seventh, ninth (compound interval, compo ...
References
{{Jazz theory
Chords
Jazz techniques
Musical techniques
Jazz terminology
Musical terminology