Septimal whole tone
Encyclopedia
In music, the septimal whole tone, septimal major second, or supermajor second is the musical interval exactly or approximately equal to a 8/7 ratio of frequencies. It is about 231 cents
wide in just intonation
. Although 24 equal temperament does not match this interval particularly well, its nearest representation is at 250 cents, approximately 19 cents sharp. The septimal whole tone may be derived from the harmonic series
as the interval between the seventh and eighth harmonics and the term septimal refers to the fact that it utilizes the seventh harmonic
. It can also be thought of as the octave inversion of the 7/4 interval, the harmonic seventh
.
No close approximation to this interval exists in the standard 12 equal temperament used in most modern western music.
26 equal temperament matches this interval almost perfectly with an error of only 0.4 cents, but at the cost of the significant flatness of its major thirds and fifths.
Cent (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...
wide in just intonation
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
. Although 24 equal temperament does not match this interval particularly well, its nearest representation is at 250 cents, approximately 19 cents sharp. The septimal whole tone may be derived from the harmonic series
Harmonic series (music)
Pitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
as the interval between the seventh and eighth harmonics and the term septimal refers to the fact that it utilizes the seventh harmonic
Harmonic seventh
The harmonic seventh interval , also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio . This is somewhat narrower than and is "sweeter in quality" than an "ordinary" minor seventh, which has a just-intonation ratio of 9:5 , or an equal-temperament ratio of...
. It can also be thought of as the octave inversion of the 7/4 interval, the harmonic seventh
Harmonic seventh
The harmonic seventh interval , also known as the septimal minor seventh, or subminor seventh, is one with an exact 7:4 ratio . This is somewhat narrower than and is "sweeter in quality" than an "ordinary" minor seventh, which has a just-intonation ratio of 9:5 , or an equal-temperament ratio of...
.
No close approximation to this interval exists in the standard 12 equal temperament used in most modern western music.
26 equal temperament matches this interval almost perfectly with an error of only 0.4 cents, but at the cost of the significant flatness of its major thirds and fifths.