User:Unque/Buzzard: Difference between revisions

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While it makes little sense from the perspective of a target tuning, Meantone occurs quite often in low EDO tunings of 2.3.7 Buzzard, such as 38edo and 43edo, making it a reasonable extension to the Buzzard structure. This extension finds 5-limit consonances by equating them with 3-limit consonances, or equivalently by equating the aberrisma with [[36/35]] (thus tempering out [[81/80]]). 5/4, for instance, can be reached at one inflection below 9/7, and 5/3 at one inflection below 12/7.

Another possibility is to split the aberrisma into two "semi-aberrisma" intervals; this allows the 5-limit consonances to be reached as a midpoint between existing 3-limit and 7-limit consonances (thus tempering out [[~~413343~~/~~409600~~]]). 5/4, for instance, can be reached as the midpoint of 81/64 and 9/7; and 5/3 as the midpoint of 27/16 and 12/7. While this extension is of lower accuracy than Buteo or Canonical, it is supported by many low-EDO tunings of 2.3.7 Buzzard, such as 28edo and 33edo.

Another possibility is to split the aberrisma into two "semi-aberrisma" intervals; this allows the 5-limit consonances to be reached as a midpoint between existing 3-limit and 7-limit consonances (thus tempering out [[729/700]]). 5/4, for instance, can be reached as the midpoint of 81/64 and 9/7; and 5/3 as the midpoint of 27/16 and 12/7. While this extension is of lower accuracy than Buteo or Canonical, it is supported by many low-EDO tunings of 2.3.7 Buzzard, such as 28edo and 33edo.

== Interval Chain ==

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 While it makes little sense from the perspective of a target tuning, Meantone occurs quite often in low EDO tunings of 2.3.7 Buzzard, such as 38edo and 43edo, making it a reasonable extension to the Buzzard structure.  This extension finds 5-limit consonances by equating them with 3-limit consonances, or equivalently by equating the aberrisma with [[36/35]] (thus tempering out [[81/80]]).  5/4, for instance, can be reached at one inflection below 9/7, and 5/3 at one inflection below 12/7.
-Another possibility is to split the aberrisma into two "semi-aberrisma" intervals; this allows the 5-limit consonances to be reached as a midpoint between existing 3-limit and 7-limit consonances (thus tempering out [[413343/409600]]).  5/4, for instance, can be reached as the midpoint of 81/64 and 9/7; and 5/3 as the midpoint of 27/16 and 12/7.  While this extension is of lower accuracy than Buteo or Canonical, it is supported by many low-EDO tunings of 2.3.7 Buzzard, such as 28edo and 33edo.
+Another possibility is to split the aberrisma into two "semi-aberrisma" intervals; this allows the 5-limit consonances to be reached as a midpoint between existing 3-limit and 7-limit consonances (thus tempering out [[729/700]]).  5/4, for instance, can be reached as the midpoint of 81/64 and 9/7; and 5/3 as the midpoint of 27/16 and 12/7.  While this extension is of lower accuracy than Buteo or Canonical, it is supported by many low-EDO tunings of 2.3.7 Buzzard, such as 28edo and 33edo.
 == Interval Chain ==