Quartertone

A quartertone or quarter tone is an interval which is similar in size to a single step of 24edo, which is 50 cents. This makes "quartertone" an interval region, similar to "seventh" or "major third".

Properties

Quartertones have the highest harmonic entropy of any interval region. In harmony, they tend to be perceived as dissonant. In melody, they tend to produce a "bending" or "melting" effect. Due to this effect, they are often used as grace notes to smoothen and add color to the transition between more distant intervals.

In the classical and folk traditions of Arabia, North India, South India, Iran and Turkey, quartertones are not used as melodic intervals in their own right, but they are used as critical building blocks of larger melodic units. They are particularly used to build neutral intervals such as neutral seconds and neutral thirds (it should be noted that each of these traditions has multiple flavors of major, minor and neutral seconds, thirds, etc.)

In regular temperament theory and equal tuning theory, quartertones are sometimes used as melodic intervals in their own right, or sometimes not, depending which temperament is being used. In superpyth temperament for example, quartertones are usually treated as substantial melodic steps. By contrast, meantone usually treats them as only structural units for building larger neutral intervals. This difference may be due to how early or late quartertones appear on the generator chain (early in superpyth, late in meantone).

Upper and lower bounds

"Quartertone" is a slightly blurry region.

It is not clear exactly what a "tone" is (what this interval should be a quarter of). The most often used definition is a step of 6edo, which is 200 cents: the standard 12edo whole tone. However, the just whole tone, 9/8 (203.9 cents), could also be used, which would make the 'average' quarter tone 51 rather than 50 cents.

The lower bound of the "quartertone" region might be somewhere around 40 cents: below this, intervals become more like a "fifth tone" or "sixth tone". The upper bound might be somewhere around 60 cents: above this, intervals become more like a "third tone".

Though, it is also possible to call all of the above "quartertone" and make the bounds much wider: something in the ball park of 30 cents to 70 cents.

Examples

The EDOs: 21, 22, 23, 24, 25, 26, 27, 28 & 29 use a quartertone as their smallest step size. EDOs slightly larger or smaller are sometimes argued to do the same. This makes quartertones structurally important to those EDOs. They may sometimes also be used as melodic intervals depending on the approach taken.

24edo is sometimes called "the quartertone scale" or "the quarter tone scale".

A sampling of just intervals that sit towards the middle of the quartertone range: 36/35, 100/97, 33/32.

A sampling of just intervals that sit towards the outskirts of the quartertone range: 50/49, 49/48, 45/44, 128/125, 28/27, 27/26, 25/24, 23/22.