View source for Silver third

{{Mathematical interest}}
{{Infobox Interval
| Ratio = \sigma = \frac{ 1 + \sqrt{2} }{2}
| Cents = 325.8639637963343
| Name = silver third
}}

The '''silver third''' is the octave-reduced second [[Metallic_harmonic_series|metallic mean]], and is either a wide minor third or a narrow supraminor one. It differs from the first metallic mean ([[acoustic phi]]) by an interval that can act as a [[flattone]] fifth. This is not to be confused with [[argent tuning]], which uses the ''logarithmic'' silver ratio.

An interesting property of this interval is that a tetrad can be formed with the root, the silver third, the [[3/2|perfect fifth]], and a supermajor sixth 600{{C}} above the silver third (925.864{{C}}), such that the frequency difference between the sixth and the fifth is the same as that between the root. This means this tetrad has a [[DR]] signature of +1 +? +1, a property shared with tetrads like [[4:5:6:7]] (sometimes called the ''major tetrad'') and [[6:7:9:10]] (sometimes called the ''subminor tetrad''). This tetrad has this DR property, while also allowing tritone substitution due to the third and sixth being separated by 600{{C}}.

== Temperaments ==
It can be used as a generator for many temperaments using a sharpened [[6/5]], such as [[keemic]], [[orgone]] or [[doublewide]], and is closely approximated by [[11edo|3\11]].