Metallic intonation: Difference between revisions

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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. [[6edφ]] offers a basic equal-tempered approximation of the metallic major triad by steps 0-3-5 (0¢-416.5¢-694.2¢), although with a noticeably sharp third. Systems containing "quasi-equalized" versions of 6edφ, such as [[17edφ]], [[23edφ]], and [[29edφ]] include more accurate approximations.

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.

== Tempered systems ==

[[6edφ]] offers a basic equal-tempered approximation of the metallic major triad by steps 0-3-5 (0¢-416.5¢-694.2¢), although with a noticeably sharp third. Systems containing "quasi-equalized" versions of 6edφ, such as [[17edφ]], [[23edφ]], and [[29edφ]] include more accurate approximations.

[[Category:Math]]

[[Category:Xenharmonic series]]

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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. [[6edφ]] offers a basic equal-tempered approximation of the metallic major triad by steps 0-3-5 (0¢-416.5¢-694.2¢), although with a noticeably sharp third. Systems containing "quasi-equalized" versions of 6edφ, such as [[17edφ]], [[23edφ]], and [[29edφ]]  include more accurate approximations.
+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.
+== Tempered systems ==
+[[6edφ]] offers a basic equal-tempered approximation of the metallic major triad by steps 0-3-5 (0¢-416.5¢-694.2¢), although with a noticeably sharp third. Systems containing "quasi-equalized" versions of 6edφ, such as [[17edφ]], [[23edφ]], and [[29edφ]]  include more accurate approximations.
-{{Stub}}
+{{todo|inline=1|expand}}
+[[Category:Math]]
+[[Category:Xenharmonic series]]