Würschmidt comma: Difference between revisions
Jump to navigation
Jump to search
m Cleanup |
m +infobox |
||
| Line 1: | Line 1: | ||
The '''Würschmidt comma''', 393216/390625 = {{monzo|17 1 -8}}, is a [[5-limit]] [[comma]] of 11. | {{Infobox Interval | ||
| JI glyph = | |||
| Ratio = 393216/390625 | |||
| Monzo = 17 1 -8 | |||
| Cents = 11.445 | |||
| Name = Würschmidt comma | |||
| Color name = | |||
| FJS name = | |||
| Sound = | |||
}} | |||
The '''Würschmidt comma''', 393216/390625 = {{monzo|17 1 -8}}, 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. | ||
Revision as of 07:43, 13 October 2020
| Interval information |
The Würschmidt comma, 393216/390625 = [17 1 -8⟩, 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)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.