Metallic intonation

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Metallic intonation (MTI)^{[idiosyncratic term]} is a system which uses the irrational metallic harmonic series, based on metallic means, rather than the harmonic series as the basis for an exact or tempered tuning. It is related to and can sometimes overlap with merciful intonation. Except for the unison, it contains only irrational numbers and is inherently nonoctave. As the first metallic harmonic, acoustic phi is a possible candidate to serve as a period in the same way as octave.

The metallic means are taken as basis elements of subgroups rather than primes, but not all metallic means are included because some can be expressed in terms of other metallic means, similar to how some integers are composite. For example, the fourth metallic harmonic is a redundant generator because it is the golden ratio (the first metallic harmonic) cubed.