music Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...

, the schisma (also spelled ''skhisma'') is the interval between the syntonic comma (81:80) and the Pythagorean comma which is slightly larger. It equals or ≈ 1.00113, which corresponds to 1.9537 cents (). It may also be defined as: * the difference (in cents) between 8 justly tuned

perfect fifth In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so. In classical music from Western culture, a fifth is the interval f ...

s plus a justly tuned

major third In music theory, a third is a Interval (music), musical interval encompassing three staff positions (see Interval (music)#Number, Interval number for more details), and the major third () is a third spanning four Semitone, half steps or two ...

and 5 octaves; * the ratio of major limma to the Pythagorean limma; * the ratio of the syntonic comma and the

diaschisma The diaschisma (or diacisma) is a small interval (music), musical interval defined as the difference between three octaves and four perfect fifths plus two just major third, major thirds (in just intonation). It can be represented by the ratio 2 ...

. ''Schisma'' is a Greek word meaning a split or crack (see

schism A schism ( , , or, less commonly, ) is a division between people, usually belonging to an organization, movement, or religious denomination. The word is most frequently applied to a split in what had previously been a single religious body, suc ...

) whose musical sense was introduced by

Boethius Anicius Manlius Severinus Boethius, commonly known simply as Boethius (; Latin: ''Boetius''; 480–524 AD), was a Roman Roman Senate, senator, Roman consul, consul, ''magister officiorum'', polymath, historian, and philosopher of the Early Middl ...

at the beginning of the 6th century in the 3rd book of his ''De institutione musica''. Boethius was also the first to define the

. Andreas Werckmeister defined the ''grad'' as the twelfth root of the Pythagorean comma, or equivalently the difference between the justly tuned fifth (3:2) and the equally tempered fifth of 700 cents (2). This value, 1.955 cents, may be well approximated by converting the ratio 886:885 to cents. This interval is also sometimes called a ''schisma''. Curiously,

\ 2^\ 5^\

is very close to 4:3, the just

perfect fourth A fourth is a interval (music), musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth () is the fourth spanning five semitones (half steps, or half tones). For example, the ascending int ...

. This is because the difference between a grad and a schisma is so small. So, a rational intonation version of

equal temperament An equal temperament is a musical temperament or Musical tuning#Tuning systems, tuning system that approximates Just intonation, just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequency, frequencie ...

may be obtained by flattening the fifth by a ''schisma'' rather than a ''grad'', a fact first noted by Johann Kirnberger, a pupil of Bach. Twelve of these Kirnberger fifths of exceed seven octaves, and therefore fail to close, by the tiny interval of

\ \frac\ ,

called the ''atom of Kirnberger'' of 0.01536 cents. Tempering out the ''schisma'' leads to a schismatic temperament. Descartes used the word ''schisma'' to mean that which multiplied by a perfect fourth produces 27:20 (519.55 cents); his schisma divided into a perfect fifth produces 40:27 (680.45 cents), and a major sixth times a schisma is 27:16 (905.87 cents). However, by this definition a "schisma" would be what is better known as the syntonic comma (81:80).

References

External links

* * {{Intervals, state=expanded 5-limit tuning and intervals Commas (music)

See also

References

External links