Metallic intonation: Difference between revisions
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'''Metallic intonation''' ('''MTI'''){{idiosyncratic}} is a system that is similar to [[just intonation]], but based on the irrational [[metallic harmonic series]] rather than the [[harmonic series]]. Intervals between these metallic harmonics are used as a basis for tuning. The metallic numbers are taken as [[basis element]]s of [[subgroup]]s rather than [[prime]]s, but not all metallic numbers are included since some are redundant. For example, the fourth metallic harmonic is a redundant generator because it is the golden ratio (the first metallic harmonic) cubed. It is related to and can sometimes overlap with [[merciful intonation]]. | '''Metallic intonation''' ('''MTI'''){{idiosyncratic}} is a system that is similar to [[just intonation]], but based on the irrational [[metallic harmonic series]] rather than the [[harmonic series]]. Intervals between these metallic harmonics are used as a basis for tuning. The metallic numbers are taken as [[basis element]]s of [[subgroup]]s rather than [[prime]]s, but not all metallic numbers are included (similar to how only some integers are prime) since some are redundant. For example, the fourth metallic harmonic is a redundant generator because it is the golden ratio (the first metallic harmonic) cubed. It is related to and can sometimes overlap with [[merciful intonation]]. | ||