User:CompactStar/Ordinal interval notation: Difference between revisions

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* 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 the ~~leftmajor~~ third, since it is the simplest major third flatter than [[81/64]], and [[9/7]] is the ~~rightmajor~~ third, since it is the simplest major third sharper 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. Here are some examples with thirds:

* Leftmajor third = [[5/4]], since it is the simplest major third flatter than 81/64

* Rightmajor third = [[9/7]], since it is the simplest major third sharper than 81/64

* Leftleftmajor third = [[16/13]], since it is the simplest major third flatter than 5/4

* Leftrightmajor third = [[24/19]], since it is the simplest major third between 5/4 and 81/64

* Rightleftmajor third = [[14/11]], since it is the simplest major third between 81/64 and 9/7

* Rightrightmajor third = [[22/17]], since it is the simplest major third sharper than 9/7

=== Mapping non-Pythagorean intervals ===

@@ Line 5: / Line 5: @@
 * 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 the leftmajor third, since it is the simplest major third flatter than [[81/64]], and [[9/7]] is the rightmajor third, since it is the simplest major third sharper 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. Here are some examples with thirds:
+* Leftmajor third = [[5/4]], since it is the simplest major third flatter than 81/64
+* Rightmajor third = [[9/7]], since it is the simplest major third sharper than 81/64
+* Leftleftmajor third = [[16/13]], since it is the simplest major third flatter than 5/4
+* Leftrightmajor third = [[24/19]], since it is the simplest major third between 5/4 and 81/64
+* Rightleftmajor third = [[14/11]], since it is the simplest major third between 81/64 and 9/7
+* Rightrightmajor third = [[22/17]], since it is the simplest major third sharper than 9/7
 === Mapping non-Pythagorean intervals ===