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In music, the septimal minor third , also called the subminor third (by eg Helmholtz) is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cent
Cent (music)

The cent is a logarithmic scale unit of measure used for musical interval . Typically cents are used to measure extremely small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive notes....
s, it is 267 cents, a quartertone of size 36/35
Septimal quarter tone

A septimal quarter-tone is an Interval with the ratio of 36:35 , which is the difference between Septimal minor third and Limit minor thirds ....
 flatter than a just minor third
Minor third

A minor third is a Interval of three semitones. It is the smaller of two commonly occurring musical intervals compounded of two steps of the diatonic scale....
 of 6/5.

The septimal minor third has a darker but generally pleasing character when compared to the 6/5 third. A triad formed by using it in place of the minor third is called a septimal minor or subminor triad ; however in fact that chord is a part of the overtone series, or in other words is an otonal chord, with ratios of 6:7:9, whereas the ordinary minor third is a utonal chord.






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In music, the septimal minor third , also called the subminor third (by eg Helmholtz) is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cent
Cent (music)

The cent is a logarithmic scale unit of measure used for musical interval . Typically cents are used to measure extremely small intervals, or to compare the sizes of comparable intervals in different tuning systems, and in fact the interval of one cent is much too small to be heard between successive notes....
s, it is 267 cents, a quartertone of size 36/35
Septimal quarter tone

A septimal quarter-tone is an Interval with the ratio of 36:35 , which is the difference between Septimal minor third and Limit minor thirds ....
 flatter than a just minor third
Minor third

A minor third is a Interval of three semitones. It is the smaller of two commonly occurring musical intervals compounded of two steps of the diatonic scale....
 of 6/5.

The septimal minor third has a darker but generally pleasing character when compared to the 6/5 third. A triad formed by using it in place of the minor third is called a septimal minor or subminor triad ; however in fact that chord is a part of the overtone series, or in other words is an otonal chord, with ratios of 6:7:9, whereas the ordinary minor third is a utonal chord. While the septimal minor third is classed as a 7-limit
Limit (music)

In music theory, limit can refer to a variety of methods used to characterize the harmonies found in a piece of music, genre of music, or by extension, the harmonies that can be made with a particular scale or class of scales....
 interval, and the septimal minor triad as a 9-limit chord, the fact that the chord is otonal makes it sound perhaps about as consonant as the just minor triad.

In the meantone
Meantone temperament

Meantone temperament is a musical temperament, which is a system of musical tuning. In general, a meantone is constructed the same way as Pythagorean tuning, as a chain of perfect fifths, but in a meantone, each fifth is narrowed by the same amount in order to make the other intervals, like the major third, closer to their ideal just intonat...
 era the interval made its appearance as the alternative minor third in remote keys, under the name augmented second
Augmented second

An augmented second is enharmonically equivalent to a minor third in equal temperament, but is not the same interval in other meantone tunings....
. Tunings of the meantone fifth in the neighborhood of 1/4 comma meantone will give three septimal minor thirds among the twelve minor thirds of the tuning; since the wolf fifth appears with an ordinary minor third, this entails there are three septimal minor triads, eight ordinary minor triads and one triad containing the wolf fifth arising from an ordinary minor third followed by a septimal major third
Septimal major third

In music, the septimal major third , also called the supermajor third and sometimes Bohlen-Pierce third is the musical interval exactly or approximately equal to a 9:7 ratio of frequencies....
.

In Equal-Temperament


The widely used 12-TET
Equal temperament

Equal temperament is a musical temperament, or a system of Musical tuning in which every pair of adjacent notes has an identical frequency ratios....
 does not provide a good match for this interval, and even quarter tones (24-TET) do not match it well. 19-TET
19 equal temperament

In music, 19 equal temperament, called 19-TET, 19-equal division of the octave, or 19-ET, is the Temperament scale derived by dividing the octave into 19 equally large steps....
, 22-TET
22 equal temperament

In music, 22 equal temperament, called 22-tet, equal division of the octave, or 22-et, is the Temperament scale derived by dividing the octave into 22 equally large steps....
, 31-TET
31 equal temperament

In music, 31 equal temperament , which can be abbreviated 31-TET, 31-equal division of the octave, 31-ET, is the Temperament scale derived by dividing the octave into 31 equal-sized steps....
, 41-TET
41 equal temperament

In music, 41 equal temperament, often abbreviated 41-tET, 41-EDO, or 41-ET, is the Musical temperament scale derived by dividing the octave into 41 equally-sized steps....
, and 72-TET
72 equal temperament

In music, 72 equal temperament, called twelfth-tone, 72-tet, equal division of the octave, or 72-et, is the Temperament scale derived by dividing the octave into twelfth-tones, or in other words 72 equally large steps....
 each offer successively better matches (measured in cents difference) to this interval. 34-TET
34 equal temperament

In musical theory, 34 equal temperament, also referred to as 34-tet, equal division of the octave or 34-et, is the Temperament tuning derived by dividing the octave into 34 equal-sized steps....
 has a poor match to this interval.

Listening


Because of its position in the harmonic series
Harmonic series (music)

Definite pitch 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....
, the sixth overtone being a perfect fifth
Perfect fifth

The perfect fifth is the musical interval between a note and the note seven semitones above it on the musical scale. For example, the note G lies a perfect fifth above C; D is a perfect fifth above G, C is a perfect fifth above F, and so on....
 above the root, the septimal minor third implies a root note a perfect fifth
Perfect fifth

The perfect fifth is the musical interval between a note and the note seven semitones above it on the musical scale. For example, the note G lies a perfect fifth above C; D is a perfect fifth above G, C is a perfect fifth above F, and so on....
 below the lower note in the interval. Depending on the timbre of the pitches, humans sometimes perceive this root pitch even if it is not played. The phenomenon of hearing this root pitch is evident in the following sound file, which uses a pure sine
Siné

Maurice Sinet, known as Sin? is a France cartoonist.As a young man he studied drawing and graphic arts, earning his life as a cabaret singer....
 wave. For comparison, the root pitch is played after the interval has been played.