The Magic Chord is a chord and installation (1984) created by La Monte Young, consisting of the pitches E, F, A, B♭, D, E, G, and A, in ascending order and used in works including his The Well-Tuned Piano and Chronos Kristalla (1990). The latter was performed by the Kronos Quartet and features all notes of the magic chord as harmonics on open strings. The quartet has been described as, "offer[ing] perhaps the ultimate challenge in performing in a just environment."
Described as, "complex and throbbing," the chord does not contain its fundamental (see root (chord)), ♭, and is a subset of the Romantic Chord, G-Dorian in eight octaves, spelled G,A,B,C,D,E,F♯,G. "When the Magic Opening Chord is obtained by playing the Opening Chord at one end of a room while the Magic Chord is played at the other (as Young set it up for me), the feeling-changes of the stereo effect as you move back and forth[-]are dazzling." The opening chord consists of E♭, B♭, C, E♭, F, B♭ (ratios 4:6:7:8:9:12
The Well-Tuned Piano is based on a pitch lattice of perfect fifths and harmonic sevenths, tuned as follows:
|Note sounded relative to E♭ (Ben Johnston notation)||(E♭)||F7++||F+||A7b+||B7b+||Bb||(D7b)||E7b+|
For example, G (21/16) is the harmonic seventh of the perfect fifth (7/4 * 3/2 = 21/16):
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In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios of frequencies. Any interval tuned in this way is called a just interval. Just intervals consist of members of a single harmonic series of a (lower) implied fundamental. For example, in the diagram, the notes G and middle C are both members of the harmonic series of the lowest C and their frequencies will be 3 and 4 times, respectively, the fundamental frequency; thus, their interval ratio will be 4:3. If the frequency of the fundamental is 50 Hertz, the frequencies of the two notes in question would be 150 and 200.
In music, an octave or perfect octave is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". The interval between the first and second harmonics of the harmonic series is an octave.
In music theory, an interval is the difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones. For instance, the interval from F up to the B above it is a tritone as it can be decomposed into the three adjacent whole tones F–G, G–A, and A–B. According to this definition, within a diatonic scale there is only one tritone for each octave. For instance, the above-mentioned interval F–B is the only tritone formed from the notes of the C major scale. A tritone is also commonly defined as an interval spanning six semitones. According to this definition, a diatonic scale contains two tritones for each octave. For instance, the above-mentioned C major scale contains the tritones F–B and B–F. In twelve-equal temperament, the tritone divides the octave exactly in half as 6 of 12 semitones or 600 of 1200 cents.
La Monte Thornton Young is an American composer, musician, and artist recognized as one of the first American minimalist composers and a central figure in post-war avant-garde music. He is best known for his exploration of sustained tones, beginning with his 1958 composition Trio for Strings. His works have called into question the nature and definition of music, most prominently in the text scores of his Compositions 1960. Despite having released very little recorded material throughout his career—much of it currently out of print—some sources have described him as "the most influential living composer today". The Observer wrote that his work has had "an utterly profound effect on the last half-century of music."
In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.
In music theory, the cycle or circle of fifths is the relationship among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space.
Benjamin Burwell Johnston Jr. was an American contemporary music composer using just intonation. He was called "one of the foremost composers of microtonal music" by Philip Bush (1997) and "one of the best non-famous composers this country has to offer" by John Rockwell (1990).
In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions, and the major sixth is one of two commonly occurring sixths. It is qualified as major because it is the larger of the two. The major sixth spans nine semitones. Its smaller counterpart, the minor sixth, spans eight semitones. For example, the interval from C up to the nearest A is a major sixth. It is a sixth because it encompasses six note letter names and six staff positions. It is a major sixth, not a minor sixth, because the note A lies nine semitones above C. Diminished and augmented sixths span the same number of note letter names and staff positions, but consist of a different number of semitones.
The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees (of a major scale are called major.
In Western classical music, a minor sixth is a musical interval encompassing six staff positions, and is one of two commonly occurring sixths. It is qualified as minor because it is the smaller of the two: the minor sixth spans eight semitones, the major sixth nine. For example, the interval from A to F is a minor sixth, as the note F lies eight semitones above A, and there are six staff positions from A to F. Diminished and augmented sixths span the same number of staff positions, but consist of a different number of semitones.
In music theory, a minor chord is a chord that has a root, a minor third, and a perfect fifth. When a chord has these three notes alone, it is called a minor triad. For example, the minor triad built on C, called a C minor triad, has pitches C–E♭–G:
Minimal music is a form of art music or other compositional practice that employs limited or minimal musical materials. Prominent features of minimalist music include repetitive patterns or pulses, steady drones, consonant harmony, and reiteration of musical phrases or smaller units. It may include features such as phase shifting, resulting in what is termed phase music, or process techniques that follow strict rules, usually described as process music. The approach is marked by a non-narrative, non-teleological, and non-representational approach, and calls attention to the activity of listening by focusing on the internal processes of the music.
In music theory, chord substitution is the technique of using a chord in place of another in a progression of chords, or a chord progression. Much of the European classical repertoire and the vast majority of blues, jazz and rock music songs are based on chord progressions. "A chord substitution occurs when a chord is replaced by another that is made to function like the original. Usually substituted chords possess two pitches in common with the triad that they are replacing."
In music, a guitar chord is a set of notes played on a guitar. A chord's notes are often played simultaneously, but they can be played sequentially in an arpeggio. The implementation of guitar chords depends on the guitar tuning. Most guitars used in popular music have six strings with the "standard" tuning of the Spanish classical guitar, namely E-A-D-G-B-E' ; in standard tuning, the intervals present among adjacent strings are perfect fourths except for the major third (G,B). Standard tuning requires four chord-shapes for the major triads.
Otonality and utonality are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: 1/1, 2/1, 3/1,... or 1/1, 1/2, 1/3,....
An Otonality is that set of pitches generated by the numerical factors (...identities)...over a numerical constant in the denominator. Conversely, a Utonality is the inversion of an Otonality, a set of pitches with a numerical constant in the numerator over the numerical factors...in the denominator.
The harmonic seventh interval
The Well-Tuned Piano is an ongoing, improvisatory, solo piano work by composer La Monte Young. Begun in 1964, Young has never considered the composition or performance "finished", and he has performed incarnations of it several times since its debut in 1974. The composition utilizes a piano tuned in just intonation.
7-limit or septimal tunings and intervals are musical instrument tunings that have a limit of seven: the largest prime factor contained in the interval ratios between pitches is seven. Thus, for example, 50:49 is a 7-limit interval, but 14:11 is not.
Among alternative tunings for the guitar, an overtones tuning selects its open-string notes from the overtone sequence of a fundamental note. An example is the open tuning constituted by the first six overtones of the fundamental note C, namely C2-C3-G3-C4-E4-G4.
A decatonic scale is a ten note musical scale. If the notes are ordered, a decatonic set has 3,628,800 permutations, however, in twelve tone equal temperament only six unordered ten note sets exist, 10-1—10-6: