Würschmidt comma: Difference between revisions
m +infobox |
bold redirect lemma |
||
| Line 10: | Line 10: | ||
}} | }} | ||
The '''Würschmidt comma''' | The '''Würschmidt comma''' ({{monzo| 17 1 -8 }} = '''393216/390625''') is a [[5-limit]] [[comma]] of 11.4 cents. | ||
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. | 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. | ||
| Line 16: | Line 16: | ||
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. | 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 the [[würschmidt family]] of temperaments. 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 == | == See also == | ||