Metallic intonation

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 consists of only irrational intervals, and is inherently nonoctave. As the first metallic harmonic, acoustic phi is a possible candidate to serve as an equave 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.

Harmony

If reduced with acoustic phi as the period, the chord formed by the silver and bronze ratios above the root is, coincidentally, a fairly conventional major triad (0¢-402.2¢-692.7¢). This makes it so traditional chord types are easily accessible in MTI systems, but not octaves, similarly to the Carlos Alpha tuning. 6edφ offers a basic equal-tempered approximation of the metallic major triad by steps 0-3-5 (0¢-416.5¢-694.2¢), although the sharpness of the major third is more apparent and it may sound "more xenharmonic".

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