Essential tempering comma: Difference between revisions
Cleanup |
+intro; +categories; sectioning |
||
| Line 1: | Line 1: | ||
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: | ||
| Line 4: | Line 7: | ||
# 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: | ||
| Line 31: | Line 35: | ||
[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Comma]] | |||