Essential tempering comma: Difference between revisions

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The '''essential tempering commas''' are commas that induce [[Dyadic chord #Essentially tempered dyadic chords|essentially tempered chords]].
== Definition ==
Suppose S is a set of JI intervals ''i'' including 1 and 2 with 1 ≤ ''i'' ≤ 2 such that if ''i'' is in S, so is 2/''i''. S is intended to represent a set of pitch classes defining "consonance". A JI interval ''c'' is an essential tempering comma for S if:
Suppose S is a set of JI intervals ''i'' including 1 and 2 with 1 ≤ ''i'' ≤ 2 such that if ''i'' is in S, so is 2/''i''. S is intended to represent a set of pitch classes defining "consonance". A JI interval ''c'' is an essential tempering comma for S if:


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# There are three intervals ''i'', ''j'', and ''k'' in S such that ''c'' = ''ij''/''k''.  
# There are three intervals ''i'', ''j'', and ''k'' in S such that ''c'' = ''ij''/''k''.  


== Examples ==
For various odd limit diamonds, we get the following essential tempering commas:
For various odd limit diamonds, we get the following essential tempering commas:


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[[Category:Theory]]
[[Category:Theory]]
[[Category:Comma]]