Würschmidt comma: Difference between revisions
Jump to navigation
Jump to search
Jdfreivald (talk | contribs) m Related the comma to 3/2. |
m Cleanup |
||
| Line 1: | Line 1: | ||
The Würschmidt comma | The '''Würschmidt comma''', 393216/390625 = {{monzo|17 1 -8}}, is a [[5-limit]] [[comma]] of 11.445 cents. | ||
It is the amount by which eight major thirds | It is the amount by which eight major thirds fall short of a perfect fifth, octave-reduced: ((5/4)<sup>8</sup> × 393216/390625) / 4 = 3/2. | ||
Therefore, it is also the amount by which seven major thirds | Therefore, it is also the amount by which seven major thirds fall short of 24/5 (i.e. 6/5 plus two octaves). In other words, ((5/4)<sup>7</sup> × 393216/390625) / 4 = 6/5. | ||
Tempering it out leads to [[ | Tempering it out leads to [[Würschmidt family|würschmidt temperament]]. As in [[meantone]], it implies that 3/2 will be tempered flat and/or 5/4 will be tempered sharp, and therefore 6/5 will be tempered flat. | ||
== See also == | |||
* [[Würschmidt family]] | |||
* [[Small comma]] | |||
[[Category:5-limit]] | |||
[[Category:Small comma]] | |||
[[Category:Wuerschmidt]] | |||
Revision as of 06:58, 13 October 2020
The Würschmidt comma, 393216/390625 = [17 1 -8⟩, is a 5-limit comma of 11.445 cents.
It is the amount by which eight major thirds fall short of a perfect fifth, octave-reduced: ((5/4)8 × 393216/390625) / 4 = 3/2.
Therefore, it is also the amount by which seven major thirds fall short of 24/5 (i.e. 6/5 plus two octaves). In other words, ((5/4)7 × 393216/390625) / 4 = 6/5.
Tempering it out leads to würschmidt temperament. As in meantone, it implies that 3/2 will be tempered flat and/or 5/4 will be tempered sharp, and therefore 6/5 will be tempered flat.