Schisma
Encyclopedia
In music
, the schisma (also spelled skhisma) is the ratio between a Pythagorean comma
(531441:524288) and a syntonic comma
(81:80) and equals 32805:32768, which is 1.9537 cent
s . It may also be defined as:
Schisma is a Greek
word meaning a split (see schism). Its musical sense was introduced by Alexander J. Ellis, but earlier theorist Andreas Werckmeister
defined the grad as the twelfth root of the Pythagorean comma, or equivalently the difference between the justly tuned fifth and the equally tempered fifth of 700 cents, and this interval of 1.9550 cents is also sometimes called a schisma.
Curiously, 21/12 51/7 appears very close to 4:3, the just perfect fourth
. That's because the difference between a grad and a schisma is so small. So, a rational intonation version of equal temperament
may be realized 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 16384:10935 exceed seven octaves, and therefore fail to close, by the tiny interval of 2161 3−84 5−12, the atom of Kirnberger of 0.01536 cents.
Tempering out the schisma leads to schismatic temperament
.
As used by Descartes, a schisma added to a perfect fourth = 27:20 (519.55 cents), a schisma subtracted from a perfect fifth = 40:27 (680.45 cents), and a major sixth plus a schisma = 27:16 (= 81:48 = 905.87 cents). By this definition is a "schisma" is what is known as the syntonic comma
(81:80).
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
, the schisma (also spelled skhisma) is the ratio between a Pythagorean comma
Pythagorean comma
In musical tuning, the Pythagorean comma , named after the ancient mathematician and philosopher Pythagoras, is the small interval existing in Pythagorean tuning between two enharmonically equivalent notes such as C and B , or D and C...
(531441:524288) and a syntonic comma
Syntonic comma
In music theory, the syntonic comma, also known as the chromatic diesis, the comma of Didymus, the Ptolemaic comma, or the diatonic comma is a small comma type interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 cents...
(81:80) and equals 32805:32768, which is 1.9537 cent
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...
s . It may also be defined as:
- the difference between 8 justly tunedJust intonationIn 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...
perfect fifthPerfect fifthIn classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...
s plus a justly tuned major thirdMajor thirdIn 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...
and 5 octaves; - the difference between major limmaMajor limmaMajor limma is an interval with the ratio of 135:128, which is the difference between two major tones and a minor third. It is equal to about 92.18 cents....
and Pythagorean limma; - the difference between the syntonic comma and the diaschismaDiaschismaThe diaschisma is a small musical interval defined as the difference between three octaves and four perfect fifths plus two major thirds . It can be represented by the ratio 2048:2025 and is about 19.5 cents...
.
Schisma is a Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...
word meaning a split (see schism). Its musical sense was introduced by Alexander J. Ellis, but earlier theorist Andreas Werckmeister
Andreas Werckmeister
Andreas Werckmeister was an organist, music theorist, and composer of the Baroque era.-Life:Born in Benneckenstein, Germany, Werckmeister attended schools in Nordhausen and Quedlinburg. He received his musical training from his uncles Heinrich Christian Werckmeister and Heinrich Victor Werckmeister...
defined the grad as the twelfth root of the Pythagorean comma, or equivalently the difference between the justly tuned fifth and the equally tempered fifth of 700 cents, and this interval of 1.9550 cents is also sometimes called a schisma.
Curiously, 21/12 51/7 appears very close to 4:3, the just 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...
. That's because the difference between a grad and a schisma is so small. So, a rational intonation version of equal temperament
Equal temperament
An 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...
may be realized by flattening the fifth by a schisma rather than a grad, a fact first noted by Johann Kirnberger
Johann Kirnberger
Johann Philipp Kirnberger was a musician, composer , and music theorist. A pupil of Johann Sebastian Bach, he became a violinist at the court of Frederick II of Prussia in 1751. He was the music director to the Prussian Princess Anna Amalia from 1758 until his death. Kirnberger greatly admired J.S...
, a pupil of Bach
Bạch
Bạch is a Vietnamese surname. The name is transliterated as Bai in Chinese and Baek, in Korean.Bach is the anglicized variation of the surname Bạch.-Notable people with the surname Bạch:* Bạch Liêu...
. Twelve of these Kirnberger fifths of 16384:10935 exceed seven octaves, and therefore fail to close, by the tiny interval of 2161 3−84 5−12, the atom of Kirnberger of 0.01536 cents.
Tempering out the schisma leads to schismatic temperament
Schismatic temperament
The schismatic temperament is a musical tuning system that results from tempering the schisma of 32805:32768 to a unison. It is also called the schismic temperament or Helmholtz temperament.-Comparison with other tunings:...
.
As used by Descartes, a schisma added to a perfect fourth = 27:20 (519.55 cents), a schisma subtracted from a perfect fifth = 40:27 (680.45 cents), and a major sixth plus a schisma = 27:16 (= 81:48 = 905.87 cents). By this definition is a "schisma" is what is known as the syntonic comma
Syntonic comma
In music theory, the syntonic comma, also known as the chromatic diesis, the comma of Didymus, the Ptolemaic comma, or the diatonic comma is a small comma type interval between two musical notes, equal to the frequency ratio 81:80, or around 21.51 cents...
(81:80).
External links
- Septimal Comma, Encyclopedia of Microtonal Music Theory; Tonalsoft.
- List of Intervals