Neutral third
Encyclopedia
A neutral third is a musical interval wider than a minor third
but narrower than a major third
. Three distinct intervals may be termed neutral thirds:
These intervals are all within about 12 cents and are difficult for most people to distinguish. Neutral thirds are roughly a quarter tone
sharp from 12 equal temperament minor thirds and a quarter tone flat from 12-ET major thirds. In just intonation, as well as in tunings such as 31-ET
, 41-ET
, or 72-ET
, which more closely approximate just intonation, the intervals are closer together.
A neutral third can be formed by stacking a neutral second
together with a whole tone. Based on its positioning in the harmonic series, the undecimal neutral third implies a root
one whole tone below the lower of the two notes.
A triad formed by two neutral thirds is neither major nor minor, thus the neutral thirds triad is ambiguous. While it is not found in twelve tone equal temperament it is found in others such as the quarter tone scale and 31-tet .
and also before intervals as large as a perfect fourth
or larger.
, James Tenney
, and Gayle Young
.
(see also Arab tone system
). Undecimal neutral thirds appear in traditional Georgian music
. Neutral thirds are also found in American folk music.
s (a note found in country music
, blues
, and some rock music
) on the third note of a scale can be seen as a variant of a neutral third with the tonic, as they fall in between a major third and a minor third. Similarly the blue note on the seventh note of the scale can be seen as a neutral third with the dominant. Unlike most classical music, blue notes do not have exact values.
, 34-ET
, 41-ET
, 72-ET
, and slightly less closely by 53-ET
.
Close approximations to the tridecimal neutral third appear in 53-ET
and 72-ET
. Both of these temperaments distinguish between the tridecimal (16:13) and undecimal (11:9) neutral thirds. All the other tuning systems mentioned above fail to distinguish between these intervals; this can be interpreted as tempering out the comma 144:143.
Minor third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...
but narrower than a major third
Major third
In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...
. Three distinct intervals may be termed neutral thirds:
- The undecimal neutral third has a ratio of 11:9 between the frequencies of the two tones, or about 347.41 cents .
- A tridecimal neutral third has a ratio of 16:13 between the frequencies of the two tones, or about 359.47 cents. This is the largest neutral third, and occurs infrequently in music, as little music utilizes the 13th harmonicHarmonicA harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...
.
- An equal-temperedEqual temperamentAn equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
neutral third is characterized by a difference in 350 centsCent (music)The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...
between the two tones, a hair wider than the 11:9 ratio, and exactly half of an equal-tempered perfect fifth.
These intervals are all within about 12 cents and are difficult for most people to distinguish. Neutral thirds are roughly a quarter tone
Quarter tone
A quarter tone , is a pitch halfway between the usual notes of a chromatic scale, an interval about half as wide as a semitone, which is half a whole tone....
sharp from 12 equal temperament minor thirds and a quarter tone flat from 12-ET major thirds. In just intonation, as well as in tunings such as 31-ET
31 equal temperament
In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO , , is the tempered scale derived by dividing the octave into 31 equal-sized steps...
, 41-ET
41 equal temperament
In music, 41 equal temperament, often abbreviated 41-tET, 41-EDO, or 41-ET, is the tempered scale derived by dividing the octave into 41 equally-sized steps . Each step represents a frequency ratio of 21/41, or 29.27 cents , an interval close in size to the septimal comma. 41-ET can be seen as a...
, or 72-ET
72 equal temperament
In music, 72 equal temperament, called twelfth-tone, 72-tet, 72-edo, or 72-et, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps...
, which more closely approximate just intonation, the intervals are closer together.
A neutral third can be formed by stacking a neutral second
Neutral second
A neutral second or medium second is a musical interval wider than a minor second and narrower than a major second. Three distinct intervals may be termed neutral seconds:...
together with a whole tone. Based on its positioning in the harmonic series, the undecimal neutral third implies a root
Root (chord)
In music theory, the root of a chord is the note or pitch upon which a triadic chord is built. For example, the root of the major triad C-E-G is C....
one whole tone below the lower of the two notes.
A triad formed by two neutral thirds is neither major nor minor, thus the neutral thirds triad is ambiguous. While it is not found in twelve tone equal temperament it is found in others such as the quarter tone scale and 31-tet .
In infants' song
Infants experiment with singing, and a few studies of individual infants' singing found that neutral thirds regularly arise in their improvisations. In two separate case studies of the progression and development of these improvisations, neutral thirds were found to arise in infants' songs after major and minor seconds and thirds, but before intervals smaller than a semitoneSemitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
and also before intervals as large as a perfect fourth
Perfect fourth
In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
or larger.
In modern classical music
The neutral third has been used by a number of modern composers, including Charles IvesCharles Ives
Charles Edward Ives was an American modernist composer. He is one of the first American composers of international renown, though Ives' music was largely ignored during his life, and many of his works went unperformed for many years. Over time, Ives came to be regarded as an "American Original"...
, James Tenney
James Tenney
James Tenney was an American composer and influential music theorist.-Biography:Tenney was born in Silver City, New Mexico, and grew up in Arizona and Colorado. He attended the University of Denver, the Juilliard School of Music, Bennington College and the University of Illinois...
, and Gayle Young
Gayle Young
Gayle Young is a Canadian composer and author.Young is an adherent of microtonality who has invented a number of musical instruments and notational systems. She began writing for Musicworks magazine in 1978, becoming its managing editor in 1987. She has also written a biography of Hugh Le...
.
In traditional music
The equal-tempered neutral third may be found in the quarter tone scale and in some traditional Arab musicArab music
Arabic music or Arab music is the music of the Arab World, including several genres and styles of music ranging from Arabic classical to Arabic pop music and from secular to sacred music....
(see also Arab tone system
Arab tone system
The modern Arab tone system, or system of musical tuning, is based upon the theoretical division of the octave into twenty-four equal divisions or 24-tone equal temperament , the distance between each successive note being a quarter tone . Each tone has its own name not repeated in different...
). Undecimal neutral thirds appear in traditional Georgian music
Music of Georgia
Georgia has rich and still vibrant traditional music, which is primarily known as arguably the earliest polyphonic tradition of the Christian world. Situated on the border of Europe and Asia, Georgia is also a home of variety of urban singing styles with the mixture of native polyphony, Middle...
. Neutral thirds are also found in American folk music.
In contemporary popular music
Blue noteBlue note
In jazz and blues, a blue note is a note sung or played at a slightly lower pitch than that of the major scale for expressive purposes. Typically the alteration is a semitone or less, but this varies among performers and genres. Country blues, in particular, features wide variations from the...
s (a note found in country music
Country music
Country music is a popular American musical style that began in the rural Southern United States in the 1920s. It takes its roots from Western cowboy and folk music...
, blues
Blues
Blues is the name given to both a musical form and a music genre that originated in African-American communities of primarily the "Deep South" of the United States at the end of the 19th century from spirituals, work songs, field hollers, shouts and chants, and rhymed simple narrative ballads...
, and some rock music
Rock music
Rock music is a genre of popular music that developed during and after the 1960s, particularly in the United Kingdom and the United States. It has its roots in 1940s and 1950s rock and roll, itself heavily influenced by rhythm and blues and country music...
) on the third note of a scale can be seen as a variant of a neutral third with the tonic, as they fall in between a major third and a minor third. Similarly the blue note on the seventh note of the scale can be seen as a neutral third with the dominant. Unlike most classical music, blue notes do not have exact values.
In equal temperaments
Although there are no neutral thirds in any of the commonly used equally tempered tuning systems with less than 24 divisions of the octave, just neutral thirds are very closely approximated by all the commonly used equally-tempered tuning systems with larger numbers of division in the octave, including 24-ET, 31-ET31 equal temperament
In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO , , is the tempered scale derived by dividing the octave into 31 equal-sized steps...
, 34-ET
34 equal temperament
In musical theory, 34 equal temperament, also referred to as 34-tet, 34-edo or 34-et, is the tempered tuning derived by dividing the octave into 34 equal-sized steps...
, 41-ET
41 equal temperament
In music, 41 equal temperament, often abbreviated 41-tET, 41-EDO, or 41-ET, is the tempered scale derived by dividing the octave into 41 equally-sized steps . Each step represents a frequency ratio of 21/41, or 29.27 cents , an interval close in size to the septimal comma. 41-ET can be seen as a...
, 72-ET
72 equal temperament
In music, 72 equal temperament, called twelfth-tone, 72-tet, 72-edo, or 72-et, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps...
, and slightly less closely by 53-ET
53 equal temperament
In music, 53 equal temperament, called 53-TET, 53-EDO, or 53-ET, is the tempered scale derived by dividing the octave into 53 equal steps . Each step represents a frequency ratio of 21/53, or 22.6415 cents , an interval sometimes called the Holdrian comma.- History :Theoretical interest in this...
.
Close approximations to the tridecimal neutral third appear in 53-ET
53 equal temperament
In music, 53 equal temperament, called 53-TET, 53-EDO, or 53-ET, is the tempered scale derived by dividing the octave into 53 equal steps . Each step represents a frequency ratio of 21/53, or 22.6415 cents , an interval sometimes called the Holdrian comma.- History :Theoretical interest in this...
and 72-ET
72 equal temperament
In music, 72 equal temperament, called twelfth-tone, 72-tet, 72-edo, or 72-et, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps...
. Both of these temperaments distinguish between the tridecimal (16:13) and undecimal (11:9) neutral thirds. All the other tuning systems mentioned above fail to distinguish between these intervals; this can be interpreted as tempering out the comma 144:143.