User:CompactStar/Ordinal interval notation: Difference between revisions

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== Explanation ==

Regular interval names corresponds to [[Pythagorean]] intervals, e.g. [[32/27]] is a minor third. To name non-Pythagorean intervals, they are given the name of a nearby Pythagorean interval (see [[#Mapping non-Pythagorean intervals]]), then prefixed with a sequence of lefts and rights (abbreviated as < and > respectively). Left and right have the following meaning (where X is any left/right sequence, and Y is a regular interval category like "major third"):

* Xleft Y = the ~~smallest~~ Y whose left/right sequence starts with X and is flatter than X Y

* Xleft Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is flatter than X Y

* Xright Y = the ~~smallest~~ Y whose left/right sequence starts with X and is sharper than X Y

* Xright Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is sharper than X Y

More simply, left means to find the simplest flatter interval, and right means to find the simplest sharper interval, with each new left/right having less and less of an impact. For example, [[5/4]] is a leftmajor third, since it is the simplest major third flatter than [[81/64]].

More simply, left means to find the simplest flatter interval, and right means to find the simplest sharper interval, with each new left/right having less and less of an impact. For example, [[5/4]] is the leftmajor third, since it is the simplest major third flatter than [[81/64]], and [[9/7]] is the rightmajor third,.

=== Mapping non-Pythagorean intervals ===

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 == Explanation ==
 Regular interval names corresponds to [[Pythagorean]] intervals, e.g. [[32/27]] is a minor third. To name non-Pythagorean intervals, they are given the name of a nearby Pythagorean interval (see [[#Mapping non-Pythagorean intervals]]), then prefixed with a sequence of lefts and rights (abbreviated as < and > respectively). Left and right have the following meaning (where X is any left/right sequence, and Y is a regular interval category like "major third"):
-* Xleft Y = the smallest Y whose left/right sequence starts with X and is flatter than X Y
+* Xleft Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is flatter than X Y
-* Xright Y = the smallest Y whose left/right sequence starts with X and is sharper than X Y
+* Xright Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is sharper than X Y
-More simply, left means to find the simplest flatter interval, and right means to find the simplest sharper interval, with each new left/right having less and less of an impact. For example, [[5/4]] is a leftmajor third, since it is the simplest major third flatter than [[81/64]].
+More simply, left means to find the simplest flatter interval, and right means to find the simplest sharper interval, with each new left/right having less and less of an impact. For example, [[5/4]] is the leftmajor third, since it is the simplest major third flatter than [[81/64]], and [[9/7]] is the rightmajor third,.
 === Mapping non-Pythagorean intervals ===