Silver third

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

Interval information

Expression	[math]\displaystyle{ \sigma = \frac{ 1 + \sqrt{2} }{2} }[/math]
Size in cents	325.864¢
Name	silver third
Special properties	reduced

The silver third is the octave-reduced second 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 meantone fifth.

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

This is not to be confused with argent tuning, which uses the logarithmic silver ratio.