Metallic harmony is an approach of building harmony based on sevenths rather than thirds to produce consonant, resolved, sororities. Specifically, Metallic harmony treats 7/4 as the most consonant interval next to the octave. As a result, tunings that do not approximate 7/4 decently do not support metallic harmony. In addition, there must be an additional size of seventh/sixth that "clicks" with the 7/4. Intervals such as 13/7, 12/7 and 19/11 are notable possibilities. These sevenths chords have a characteristic metallic somewhat cold quality which earns them their name, metallic.
Basic Chord Types
There are symmetrical and asymmetrical chords in metallic harmony. Asymmetric chords have a more rooted sound while symmetrical chords sound more ambiguous.
However, because metallic chords use only foreign intervals, they tend to sound exotic, or like metal. The beauty however is that they are capable of expressive harmony if used correctly. The two types of asymmetric triads soft and hard. Soft triads place the 7/4 on top of the chord while hard triads place it on the bottom. The names come from that if when the 7/4 is placed on top, the chord sounds smoother and mellow, on the bottom the chord has a rougher, JI crunch to it. Both are very nice chords but soft chords are more dissonant than hard chords regardless of what the names might suggest.
EDOs that support metallic harmony
The most notable EDO to use metallic harmony is 10 EDO. It also contains a 7 note MOS that contains 3 hard and 3 soft metallic triads in addition to one symmetrical triad. In addition Metallic harmony can also be used to harmonize Mavila in 16 EDO. However Mavila 7 only contains two hard and soft triads on degrees 1 4 and 2 6. Mavila 9 adds two more soft triads but there are still only two hard triads. Therefore, metallic harmony in 16 EDO doesn't work nearly as well in it would in 10 or 20 EDO.