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PolychordCategory:Chords
In music and music theory a polychord consists of two or more chords, one on top of the other, multiple chords. It is implied, however, that the two chords are constructed in different manners or are taken as a unit. Thus, while simultaneous chords in a bitonal piece may be called polychords, this is rarely found useful.
See also: secundal, tertian, quartal.
Category:ChordsCategory:Musical terminology
Main article: Chord (music).
Chord (music)In music and music theory, a chord (from the Middle English cord) short for accord is two or more different notes or pitches sounding simultaneously, or nearly simultaneously, over a period of time. For example, if you simultaneously play any three (or more) keys of a piano, you have just played a chord. Likewise, if you simultaneously play three or more strings of a guitar, you have just played a chord on the guitar. Every chord is given a specific name, based on the notes that constitute the chord and the distances, or intervals, between them.
Originally, a chord simply meant the sounding together of different tones, the resultant of these tones. Broadly, any combination of three or more notes is a chord, although during the common practice period in western music and most popular music some combinations were given more prominence than others. Thus in common usage a chord is only those groups of three notes which are tonal or have diatonic functionality. Chords being directly perceived units, sonorities of two pitches are often interpreted as fragments of three- or four-note chords.
A chord is then also only the harmonic function of the group of three notes, and it is unnecessary to have all three notes form a simultaneity. Less than three notes may and often do function, in context, as a simultaneity of all notes of chord. One example is a power chord, another is a broken chord or arpeggio, where each note in a chord is sounded one after the other. One of the most familiar broken chord figures is Alberti bass. See accompaniment.
Although, as Jean-Jacques Nattiez (1990, p.218) explains, "we can encounter 'pure chords' in a musical work," such as in the following example from the "Promenade" of Modest Mussorgsky's Pictures at an Exhibition:
Pictures at an Exhibition
But "often, we must go from a textual given to a more abstract representation of the chords being used," as in the following example where the chords on the second stave are abstracted from the actual notes written on the first:
Pictures at an Exhibition
"For a sound configuration to be recognized as a chord, it must have a certain duration." Goldman (1965, p.26) elaborates: "the sense of harmonic relation, change, or effect depends on speed (or tempo) as well as on the relative duration of single notes or triadic units. Both absolute time (measurable length and speed) and relative time (proportion and division) must at all times be taken into account in harmonic thinking or analysis."
Music is said to be chord-based when the melody is determined by the chords and not by melodic concerns such as modal frames.
Nonchord tones and dissonance
A nonchord tone is a dissonant or unstable tone which is not a part of the chord that is currently playing and in most cases quickly resolves to a chord tone.
Chord sequences
Chords are commonly played in sequence, much as notes are played in sequence to form melodies. Chord sequences can be conceptualised either in a simplistic way, in which the root notes of the chords play simple melodies while tension is created and relieved by increasing and decreasing dissonance, or full attention can be paid to each note in every chord, in which case chord sequences can be regarded as multi-part harmony of unlimited complexity.
Listen to an example of a chord sequence from Erik Satie's Sarabande no. 3.
Harmonic analysis and construction
Chords are named for how many notes they contain, more commonly for what type of intervals they are constructed from, and by the root note and bass note.
The easiest way to name a chord, or limit its construction, is according to the number of notes included. The simplest and possibly most frequently used chords are trichords, meaning they have three ("tri") notes (before any doubling of notes, that is), four notes being a tetrachord, six a hexachord, etc.
It is more informative to label a chord based on what type of intervals it contains, rather than how many notes, because no matter how many notes a similar interval apart you stack on top of each other, the chord still retains a characteristic sound. The chords most traditionally used in Western music are those with notes fundamentally a third apart (that is, before any inversions and doublings, discussed below), called tertian chords. Chords constructed from seconds are secundal, and from fourths are quartal.
Chords are also distinguished and notated by the scale degree, pitch, or note of their root and bass, although there are many different conventions for indicating the quality of the chord, and the inversion of the chord (determined by which note of the chord serves as the bass note); see Inverted triads below). For example, since the first scale degree of the C major scale is the note C, a triad built on top of the note C would be called the one chord, which might be notated 1, I, or even C, in which case the assumption would be made that the key signature of the particular piece of music in question would indicate to the musician what function a C major triad was fulfilling, and that any special role of the chord outside of its normal diatonic function would be inferred from the context.
Chords are labelled with chord symbols.
The triad
The most commonly used chords in Western music, triads are the basis of diatonic harmony, and are tertian trichords. That is, they are composed of three notes: a root note, a note which is a third above the root, and a note which is a third above that note, and therefore a fifth above the root.
Each note has a function within the chord: the note the chord is built on is called the root of the chord, the second note (a third above the root) is called the third of the chord, and the third note (a third above the second note) is called the fifth of the chord. This is true of all triads, regardless of key, inversion, or quality. For example, in an F triad, F is always the root, A (sharp, natural, or flat) is always the third, and C (sharp, natural, or flat) is always the fifth.
For another example, consider an octave of the C major scale, consisting of the notes C D E F G A B C:
major scale
Fig 1. The C major scale
The triad formed using the C note as the root would consist of C (the root note of the scale), E (the third note of the scale) and G (the fifth).
major scale
Fig 2. C, E and G - The C major triad
Using the same scale (and thus, implicitly, the key of C major) a chord may be constructed using the D as the root note. This would be D (root), F (third), A (fifth).
It should be immediately apparent on hearing these two chords that they have a different quality to them: one which does not stem merely from the difference in pitch between their roots C and D. Examination at the piano keyboard will reveal that there are four semitones between the root and third of the chord on C, but only 3 semitones between the root and third of the chord on D (while the outer notes are still a perfect fifth apart).
This triad on C is therefore called a major triad, or major chord, since the interval from C to E is a major third. A minor chord, such as the triad on D, has a smaller interval from root to third called a minor third, and the chord is D minor.
A triad can be constructed on any note of the C major scale. These will all be either minor or major, with the exception of the triad on B, the leading-tone (the last note of the scale before returning to a C, in this case), which is diminished. See also Mathematics of the Western music scale.
Types of triads
As well as major and minor, there can also be augmented and diminished triads. These four terms describe the quality of a chord. For instance a triad built on top of a root D in the key of C would be said to be minor or have a minor quality.
Augmented triads are composed of the root, a note a major third from the root, but then a note an augmented fifth from the root (unlike the major and minor triads); or equivalently, a major third on top of a major third (same as a major triad, except the top note has been raised by a semitone). Diminished triads have the root, a note a minor third from the root, but then a note a diminished fifth from the root, or a minor third on a minor third (same as a minor triad, except the top note has been lowered by a semitone.) These rules summarise the type of triads encountered so far:
- Major triad (M): root, major 3rd, perfect 5th
- Minor triad (m): root, minor 3rd, perfect 5th
- Augmented triad (A): root, major 3rd, augmented 5th
- Diminished triad (d): root, minor 3rd, diminished 5th
Inverted triads
Triads are said to be inverted when a note other than the root serves as the bass note (that is, it is the lowest note sounded). There are three positions that triads can have, two of which are inversions:
- Root position is when the chord is as described above: in ascending thirds with its root note in the bass, creating an interval of a fifth, and a third (i.e. the tonic root position is marked, "I" in a figured bass).
- First inversion is when the third of the chord is in the bass, with the fifth of the chord next above, and the root highest, creating an interval of a sixth and a third (this is marked as, "I6".).
- Second inversion is when the fifth of the chord in the bass, with the root next above, and the third of the chord highest, forming an interval of a sixth, and a fourth (This is marked "I6/4"). Second inversion is the most unstable chord position.
For one traditional system of notation for inverted chords, see figured bass. Most Western music of any sophistication makes extensive use of inversion, since without it the harmonic resources available would be severely limited.
For example, a I6/4 (second inversion of the tonic) often had cadential function in early western music since scale degree 5 is in the bass.
Listen to some triads: the first three chords played are C major root position, first inversion, second inversion; then C minor root position, first inversion, second inversion.
Seventh chords
:Main article: Seventh chord.
Seventh chords may be thought of as the next natural step in composing tertian chords. Seventh chords are constructed by adding a fourth note to a triad, at the interval of a third above the fifth of the chord. This creates the interval of a seventh above the root of the chord. There are various types of seventh chords depending on the quality of the original chord and the quality of the seventh added.
Extended chords
:Main article: Extended chord.
Extended chords are tertian chords (built from thirds) or triads with notes extended, or added, beyond the seventh. Thus ninth, eleventh, and thirteenth chords are extended chords. After the thirteenth, any notes added in thirds duplicate notes elsewhere in the chord, so there are no fifteenth chords, seventeenth chords, and so on.
Augmented sixth chords
:Main article: Augmented sixth chord.
An augmented sixth chord is a chord which contains two notes which are separated by an augmented sixth (or, by inversion, a diminished third - though this inversion is rare in compositional practice). The augmented sixth is generally used as a dissonant interval which resolves by both notes moving outward to an octave.
In Western music, the most common use of these chords is to resolve to a dominant chord in root position (that is, a dominant triad with the root doubled to create the octave to which the augmented sixth chord resolves), or to a tonic chord in second inversion (a tonic triad with the fifth doubled for the same purpose). In this case, the tonic note of the key is included in the chord, sometimes along with an optional fourth note, to create one of the following (illustrated here in the key of C major):
- Italian Augmented Sixth Chord: A flat, C, F sharp
- French Augmented Sixth Chord: A flat, C, D, F sharp
- German Augmented Sixth Chord: A flat, C, E flat, F sharp
Added tone chords
:Main article: Added tone chord.
An added tone chord is a traditional chord with an extra "added" note, such as the commonly added sixth (above the root). This includes chords with an added second (ninth) or fourth (eleventh), or a combination of the three. These chords do not include "intervening" thirds as in an extended chord.
Sustained chords
:Main article: Sustained chord.
A sustained chord, or "sus chord" (also suspended chord), is a chord where the second or most often the fourth is played with or replaces the third. For instance, Csus4 is C, F, and G. These chords are called "sustained" because you typically arrive at them when you perform a V7-I progression but don't resolve the seventh of the V7. This is similar to a suspension, where the harmony shifts from one chord to another, but one or more notes of the first chord are held over into the second. However in a sustained chord the note may never resolve as is required of a suspension. In jazz, sus chords are usually played as a major triad with the second in the bass, e.g. a major C with a D bass is a Dsus7.
Borrowed chords
:Main article: Borrowed chord.
Borrowed chords are chords borrowed from the parallel minor or major. If the root of the borrowed chord is not in the original key, then they are named by the accidental. For instance, in major, a chord built on the parallel minor's sixth degree is a "flat six chord", written bVI. Borrowed chords are an example of mode mixture.
Neapolitan sixth chord
The Neapolitan sixth chord is a major triad with the lowered supertonic scale degree as its root. The chord is referred to as a "sixth" because it is almost always found in first inversion (first inversions being traditionally named like this, from their characteristic interval of a sixth from the bass). Though a technically accurate roman numeral analysis would be bII6, it is generally labelled N6. In C major, the chord is spelled (assuming root position) D flat, F, A flat.
Because it uses lowered altered tones, this chord is often grouped with the borrowed chords. However, the chord is not borrowed from the parallel major or minor, and may appear in both major and minor keys.
Other types of chords
"Power chords" consist of perfect fifths and fourths and may be considered triads which lack the third and thus double the root or fifth to create a third note. The lack of the third makes their quality ambiguous. Popularized by heavy metal music they are used extensively in many kinds of rock music, especially (see below). Polychords are two or more chords superimposed on top of one another. See also altered chord, secundal chord, and Tristan chord.
See also
- Block chord
- Mu major chord
References
- Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). Studies in the Origin of Harmonic Tonality, p.67. Princeton University Press. ISBN 0691091358.
- Nattiez, Jean-Jacques (1990). Music and Discourse: Toward a Semiology of Music (Musicologie générale et sémiologue, 1987). Translated by Carolyn Abbate (1990). ISBN 0691027145.
- Goldman (1965).
Further reading
- Twentieth Century Harmony: Creative Aspects and Practice by Vincent Persichetti, ISBN 0393095398.
- Benward, Bruce & Saker, Marilyn (2002). Music in Theory and Practice, Volumes I & II (7th ed.). New York: McGraw Hill. ISBN 0-07-294262-2.
- Piston, Walter (1987). Harmony (5th ed.). New York: W.W. Norton & Company. ISBN 0-393-95480-3.
External links
- [http://www.knowchords.com Understanding Chords for Keyboard] Note: this is a commercial site.
- [http://www.jazzguitar.be/jazz_guitar_chords.html Jazz Guitar Chords]
- [http://www.outsideshore.com/primer/primer/ms-primer-6-1.html#ChordVoicings Jazz Chord Voicings]
- [http://www.geocities.com/melatefet/chordsr.htm Chords Generator]
- [http://www.chordfind.com/ Guitar Chord Finder]
- [http://www.banjolin.co.uk/chordtheory/chords.htm Chord Theory] (Chord theory for Mandolins, Mandolas etc)
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BitonalThe use of more than one key simultaneously is known in music as polytonality. Bitonality is the use of only two different keys at the same time. While initially polytonality referred simply to "contrapuntally juxtaposed tonalities" it quickly was applied to any "simultaneous tonalities...that cross, overlap, complement or even oppose each other." (Reti, 1958)
A well known example is the fanfare at the beginning of Igor Stravinsky's ballet, Petrushka. The first clarinet plays a melody in C major, while the second clarinet plays nearly the same melody in F sharp major:
image:Stravinsky-petrushka-fanfare.png
image:Stravinsky-petrushka-fanfare.png
Although this example consists of just two melodic lines, some examples of bitonality contrast fully harmonised sections of music in different keys. Examples of this rather more dissonant kind of bitonality can be found in the work of Charles Ives, whose use of the technique in later additions (1909-1910) to his Variations on "America" (1891) is one of the first in classical music. Earlier examples, such as Wolfgang Amadeus Mozart's Ein musikalischer Spass(1787), tend to use the technique for comic effect.
Debussy's works often employ nascent polytonality (Reti, 1958). Bitonality was used quite often by members of the French group, Les Six, and especially by Darius Milhaud, who perhaps used it more than any other composer. Many composers today who are interested in using tonality are also interested in bitonality, such as Philip Glass in his Symphony No. 2 which exploits polytonality for ambiguity of key. Aaron Copland is also known for his use of polychords and polytonality:
polychord
Although the word bitonality is most often used when talking about relatively modern classical music (written in the last one hundred years or so), it is quite a common technique in folk music, especially in eastern Europe.
Milton Babbitt, Paul Hindemith, and other theorists have "questioned and even dismissed as a viable auditory possibility," polytonality. Hindemith called polytonality a, "self-contradictory expression which, if it is to possess any meaning at all, can be used only to designate a certain degree of expansion of the individual elements of a well-defined harmonic or voice-leading unit." (Beach 1983) For example, the perception of polytonality and polychords is complicated by the fact that a complete ninth, eleventh, and thirteenth chords consist of separate chords:
voice-leading
However, examples such as the following taken from Beethoven's Sonata in Eb for Piano suggest that polytonality originated from extended chords:
voice-leading
Bitonality is also suggested by the use of added tone chords with an added tone a perfect fourth below the root of the chord:
voice-leading
Bimodality is the use of two pitch collections ("scales" with contextual pitch centers rather than hierarchical tonics), one example being the opening (mm. 1-14) of Béla Bartók's "Boating" from Mikrokosmos in which the right hand uses pitches of the pentatonic scale on Eb and the left hand uses those of either G mixolydian or dorian:
dorian
Bartók also uses the white-key and black-key collections (diatonic scale and its penatonic complement) in no.6 of the Eight Improvisations, with the pentatonic as foreground, and in mm.50-51 of the third movement of his Fourth Quartet, with the diatonic as foreground. (Wilson 1992, p.25)
Paul Wilson argues against analyzing Bartók's "Diminished Fifth" (no.101, vol. 4, Mikrokosmos) and "Harvest Song" (no.33 of the Forty-Four Duos for two violins) as bitonal since in both the octatonic collection is partitioned into two (symmetrical) four-note segments (4-10 or 0235) of the natural minor scales a tritone apart and "the larger octatonic collection embraces and supports both supposed tonalities." (ibid, p.27)
See also: List of pieces which use polytonality, musical mode, polymodal chromaticism.
Sources
- Reti, Rudolph (1958). Tonality, Atonality, Pantonality: A study of some trends in twentieth century music. Westport, Connecticut: Greenwood Press. ISBN 0313204780.
- Beach, David, ed. (1983). "Schenkerian Analysis and Post-Tonal Music", Aspects of Schenkerian Theory. New Haven: Yale University Press.
- Hindemith, Paul (1942). The Craft of Musical Composition, vol. 1, p.156. New York: Associated Music Publishers.
- Babbitt, Milton (1949). "Quartets of Bartok", Musical Quarterly 35, p.380.
- Wilson, Paul (1992). The Music of Béla Bartók. ISBN 0300051115.
Category:Musical techniques
TertianIn music or music theory, tertian is the quality of a chord constructed from thirds, and other things constructed from thirds such as counterpoint.
Chords which may be considered as built from sixths, because of inversion, are actually tertian.
See also
- secundal
- quartal and quintal harmony
- polychord
Category:Chords
Quartal:For the meaning in music theory, see Quartal and quintal harmony.
The quartal numeral system is the base four system, and uses the digits 0-3. Two quartal digits contain a nybble; four contain a byte. A single quartal digit can be described by two bits.
Quartal numerals can be made from binary numerals by grouping consecutive digits into pairs (from right).
E.g.: The binary representation for decimal 74 is 1001010, which groups into 1 00 10 10. So the quartal representation is 1022.
Compare: binary, octal, hexadecimal.
See also: computer numbering formats. லட்சம்ஒரு இலட்சம் (Lakh) என்பது, எண்ணிக்கையில் நூறு ஆயிரங்களுக்கு சமமாகும். நூறு இலட்சங்கள் சேர்ந்து ஒரு கோடியாகும், இது, இந்தியாவில் பயன்படுத்தப்பட்டு வரும் பழங்கால எண்ணிக்கை முறையாகும். இம்முறையில் எண்களை எழுதும் போது, எண்களுக்கு இடையே தடுப்பான்களை பயன் படுத்தும் இடங்களும் மாறுபடுகின்றன.
எடுத்துக்காட்டு
அயல் நாடுகளில் 3 மில்லியனை 3,000,000 என எழுதுவர். இதுவே இலட்ச அடிப்படையில் எழுதும் பொழுது, 30,00,000 என எழுதப்படும்.
Category:எண்ணிக்கை
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