Metallic intonation: Difference between revisions

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'''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 was first described by [[User:CompactStar|CompactStar]] in 2024. Metallic intonation is related to and can sometimes overlap with [[merciful intonation]]. Except for the [[1/1|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. Metallic intonation is suitable for inharmonic [[timbre]]s based on metallic harmonics rather than harmonics.

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== 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 metallic intonation systems, but not [[~~2/1|~~octave]]s, similarly to the [[Carlos Alpha]] tuning.

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 metallic intonation systems, but not [[octave]]s, similarly to the [[Carlos Alpha]] tuning.

== Tempered systems ==

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[[Category:Math]]

[[Category:Xenharmonic series]]

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+{{Mathematical interest}}
 '''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 was first described by [[User:CompactStar|CompactStar]] in 2024. Metallic intonation is related to and can sometimes overlap with [[merciful intonation]]. Except for the [[1/1|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. Metallic intonation is suitable for inharmonic [[timbre]]s based on metallic harmonics rather than harmonics.
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 == 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 metallic intonation systems, but not [[2/1|octave]]s, similarly to the [[Carlos Alpha]] tuning.
+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 metallic intonation systems, but not [[octave]]s, similarly to the [[Carlos Alpha]] tuning.
 == Tempered systems ==
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-{{Stub}}
+{{todo|inline=1|expand}}
+[[Category:Math]]
+[[Category:Xenharmonic series]]