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 because some can be expressed in terms of other metallic harmonics, 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~~. 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. It is related to and can sometimes overlap with [[merciful intonation]]. The metallic means are taken as [[basis element]]s of [[subgroup]]s rather than [[prime]]s, but not all metallic numbers are included because some can be expressed in terms of other metallic harmonics, 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.

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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 because some can be expressed in terms of other metallic harmonics, 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~~. 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. It is related to and can sometimes overlap with [[merciful intonation]]. The metallic means are taken as [[basis element]]s of [[subgroup]]s rather than [[prime]]s, but not all metallic numbers are included because some can be expressed in terms of other metallic harmonics, 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.