441/440: Difference between revisions
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'''441/440''', also known as '''Werckmeister's undecimal septenarian schisma''', or more simply, the '''werckisma''', is a [[small comma|small]] [[superparticular]] [[11-limit]] comma with a size of roughly 3.93 [[cent]]s. It is the difference between [[21/20]] and [[22/21]], and between [[80/63]] ( = ([[10/9]])([[8/7]])) and [[14/11]], as well as the amount by which a stack of two [[21/16]] septimal subfourths exceeds a single [[55/32]] supermajor sixth. Tempering it out splits [[11/10]] into two even halves, equates 21/16 with [[55/42]] to create some interesting-sounding triads, and | '''441/440''', also known as '''Werckmeister's undecimal septenarian schisma''', or more simply, the '''werckisma''', is a [[small comma|small]] [[superparticular]] [[11-limit]] comma with a size of roughly 3.93 [[cent]]s. It is the difference between [[21/20]] and [[22/21]], and between [[80/63]] ( = ([[10/9]])([[8/7]])) and [[14/11]], as well as the amount by which a stack of two [[21/16]] septimal subfourths exceeds a single [[55/32]] supermajor sixth. | ||
== Temperaments == | |||
Tempering it out splits [[11/10]] into two even halves, equates 21/16 with [[55/42]] to create some interesting-sounding triads, and makes [[werckismic chords]] possible. See [[Rank-4 temperament #Werckismic (441/440)]] for some technical data. | |||
== See also == | == See also == | ||
* [[Werckismic chords]] | * [[Werckismic chords]] | ||
* [[Rank-4 temperament]] | * [[Rank-4 temperament #Werckismic (441/440)]] | ||
* [[Werckismic temperaments]], a collection of rank-3 temperaments where it is tempered out | * [[Werckismic temperaments]], a collection of rank-3 temperaments where it is tempered out | ||
* [[Small comma]] | * [[Small comma]] | ||
Revision as of 14:06, 6 October 2021
| Interval information |
reduced
441/440, also known as Werckmeister's undecimal septenarian schisma, or more simply, the werckisma, is a small superparticular 11-limit comma with a size of roughly 3.93 cents. It is the difference between 21/20 and 22/21, and between 80/63 ( = (10/9)(8/7)) and 14/11, as well as the amount by which a stack of two 21/16 septimal subfourths exceeds a single 55/32 supermajor sixth.
Temperaments
Tempering it out splits 11/10 into two even halves, equates 21/16 with 55/42 to create some interesting-sounding triads, and makes werckismic chords possible. See Rank-4 temperament #Werckismic (441/440) for some technical data.
See also
- Werckismic chords
- Rank-4 temperament #Werckismic (441/440)
- Werckismic temperaments, a collection of rank-3 temperaments where it is tempered out
- Small comma
- List of superparticular intervals