441/440: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = werckisma | | Name = werckisma | ||
| Color name = Luzozogu | | Color name = 1uzzg2, luzozogu 2nd,<br>Luzozogu comma | ||
| | | Comma = yes | ||
}} | }} | ||
'''441/440''', also known as | '''441/440''', the '''werckisma''', also known as ''Werckmeister's undecimal septenarian schisma'', 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. It also arises as the following comma differences: ([[49/48]])/([[55/54]]), ([[56/55]])/([[64/63]]), ([[81/80]])/([[99/98]]), ([[126/125]])/([[176/175]]), and ([[243/242]])/([[540/539]]). | ||
== Temperaments == | |||
Tempering it out splits [[11/10]] into two even halves by equating 21/20 and 22/21, splits [[55/32]] into two even halves by equating 21/16 with [[55/42]], and makes [[werckismic chords]] possible. See [[Rank-4 temperament #Werckismic (441/440)]] for some technical data. See [[Werckismic temperaments]] for a collection of rank-3 temperaments where it is tempered out. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Werckismic]] | [[Category:Werckismic]] | ||
[[Category:Commas named after composers]] | |||
[[Category:Commas named after music theorists]] | |||
Latest revision as of 17:22, 14 December 2025
| Interval information |
Luzozogu comma
reduced
441/440, the werckisma, also known as Werckmeister's undecimal septenarian schisma, 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. It also arises as the following comma differences: (49/48)/(55/54), (56/55)/(64/63), (81/80)/(99/98), (126/125)/(176/175), and (243/242)/(540/539).
Temperaments
Tempering it out splits 11/10 into two even halves by equating 21/20 and 22/21, splits 55/32 into two even halves by equating 21/16 with 55/42, and makes werckismic chords possible. See Rank-4 temperament #Werckismic (441/440) for some technical data. See Werckismic temperaments for a collection of rank-3 temperaments where it is tempered out.