441/440: Difference between revisions

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re-added the approach mentioned in the original version of this article as an additional approach option and rewrote the last sentence
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mentioned additional effects caused by tempering out this comma
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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]], as well as the difference between a stack of two [[21/16]] septimal subfourths and a single [[55/32]] supermajor sixth.  Among other things, tempering it out splits [[11/10]] into two even halves and makes [[werckismic chords]] possible.
'''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]], 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, makes [[werckismic chords]] possible.


== See also ==
== See also ==

Revision as of 08:07, 24 December 2020

Interval information
Ratio 441/440
Factorization 2-3 × 32 × 5-1 × 72 × 11-1
Monzo [-3 2 -1 2 -1
Size in cents 3.930158¢
Name werckisma
Color name Luzozogu
FJS name [math]\displaystyle{ \text{m2}^{7,7}_{5,11} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 17.566
Weil height (log2 max(n, d)) 17.5693
Wilson height (sopfr(nd)) 42
Open this interval in xen-calc

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, 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, makes werckismic chords possible.

See also