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. 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 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.

'''Metallic intonation''' ('''MTI'''){{idiosyncratic}} is a system which uses the irrational [[metallic harmonic series]], based on {{w|metallic mean}}s, 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 [[1/1|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 element]]s of [[subgroup]]s rather than [[prime]]s, 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.

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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. 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 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.
+'''Metallic intonation''' ('''MTI'''){{idiosyncratic}} is a system which uses the irrational [[metallic harmonic series]], based on {{w|metallic mean}}s, 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 [[1/1|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 element]]s of [[subgroup]]s rather than [[prime]]s, 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.